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Problem in understanding Operon

Problem in understanding Operon


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Is there a good book that explains operons: lac operon and trp operon in details.

I was reading the functioning of the trp repressor protein from 'Principles of genetics-by Snustard and Simmons',they have mentioned that the binding of the repressor-corepressor complex to O$_t$$_r$$_p$ prevents the transcription of the structural genes. But they don't explain how.

Khan academy says that the repressor-corepressor complex physically comes in the way of the RNA polymerase. They have used this diagram below which shows that the large RNA polymerase cannot bind to the promoter site due to steric hindrance.

I'm looking for a more authentic source to study exactly how this RNA polymerase is being prevented from transcribing the DNA in both the operons.


Chapter 31 in the Voet and Voet biochemistry book (I have the 4th edition) link has a rather extensive explanation on this subject. It is rather pricey but you can find a copy of this one in nearly every university library. It generally is a good resource if you want to know more about the DNA or Protein structure of a basic process


10.3: Prokaryotic Gene Regulation

The DNA of prokaryotes is organized into a circular chromosome supercoiled in the nucleoid region of the cell cytoplasm. Proteins that are needed for a specific function are encoded together in blocks called operons. For example, all of the genes needed to use lactose as an energy source are coded next to each other in the lactose (or lac) operon.

In prokaryotic cells, there are three types of regulatory molecules that can affect the expression of operons: repressors, activators, and inducers. Repressors are proteins that suppress transcription of a gene in response to an external stimulus, whereas activators are proteins that increase the transcription of a gene in response to an external stimulus. Finally, inducers are small molecules that either activate or repress transcription depending on the needs of the cell and the availability of substrate.

Understand the basic steps in gene regulation in prokaryotic cells

In bacteria and archaea, structural proteins with related functions&mdashsuch as the genes that encode the enzymes that catalyze the many steps in a single biochemical pathway&mdashare usually encoded together within the genome in a block called an operon and are transcribed together under the control of a single promoter. This forms a polycistronic transcript (Figure 1). The promoter then has simultaneous control over the regulation of the transcription of these structural genes because they will either all be needed at the same time, or none will be needed.

Figure 1. In prokaryotes, structural genes of related function are often organized together on the genome and transcribed together under the control of a single promoter. The operon&rsquos regulatory region includes both the promoter and the operator. If a repressor binds to the operator, then the structural genes will not be transcribed. Alternatively, activators may bind to the regulatory region, enhancing transcription.

French scientists François Jacob (1920&ndash2013) and Jacques Monod at the Pasteur Institute were the first to show the organization of bacterial genes into operons, through their studies on the lac operon of E. coli. They found that in E. coli, all of the structural genes that encode enzymes needed to use lactose as an energy source lie next to each other in the lactose (or lac) operon under the control of a single promoter, the lac promoter. For this work, they won the Nobel Prize in Physiology or Medicine in 1965.

Each operon includes DNA sequences that influence its own transcription these are located in a region called the regulatory region. The regulatory region includes the promoter and the region surrounding the promoter, to which transcription factors, proteins encoded by regulatory genes, can bind. Transcription factors influence the binding of RNA polymerase to the promoter and allow its progression to transcribe structural genes. A repressor is a transcription factor that suppresses transcription of a gene in response to an external stimulus by binding to a DNA sequence within the regulatory region called the operator, which is located between the RNA polymerase binding site of the promoter and the transcriptional start site of the first structural gene. Repressor binding physically blocks RNA polymerase from transcribing structural genes. Conversely, an activator is a transcription factor that increases the transcription of a gene in response to an external stimulus by facilitating RNA polymerase binding to the promoter. An inducer, a third type of regulatory molecule, is a small molecule that either activates or represses transcription by interacting with a repressor or an activator.

Other genes in prokaryotic cells are needed all the time. These gene products will be constitutively expressed, or turned on continually. Most consitutively expressed genes are &ldquohousekeeping&rdquo genes responsible for overall maintenance of a cell.

What are the parts in the DNA sequence of an operon?

[practice-area rows=&rdquo2&Prime][/practice-area]
[reveal-answer q=&rdquo665976&Prime]Show Answer[/reveal-answer]
[hidden-answer a=&rdquo665976&Prime]An operon is composed of a promoter, an operator, and the structural genes. They must occur in that order.

What types of regulatory molecules are there?

[practice-area rows=&rdquo2&Prime][/practice-area]
[reveal-answer q=&rdquo665979&Prime]Show Answer[/reveal-answer]
[hidden-answer a=&rdquo665979&Prime]There are three types of regulatory molecules: repressors, activators, and inducers.[/hidden-answer]


[The establishment process of lac operon model and the analysis of several teaching problems]

Gene structure and expression regulation mechanism are the research hotspots and focus of modern life sciences. The lac operon is a cluster of genes through which Escherichia coli catabolizes lactose. It was first proposed by F. Jacob and J. Monod, who were also awarded the Nobel Prize in Physiology or Medicine in 1965 for their contributions. Thereafter, the lac operon has become the classic teaching case of the gene regulation mechanism in microbiology, genetics and molecular biology, and been highly valued by teachers and students alike. Although the conclusion is easy to follow and memorize, its rich connotation and esoteric reasoning has rendered it difficult to understand, neither is it easy for teachers to fully exploit the advantages of this teaching case. Therefore it is necessary to have an in-depth understanding of the genetic structure and working principle of the lac operon, especially the scientific background and thinking process through which scientists revealed these mysteries. In this paper, the historical discovery and analysis process of the E. coli lac operon was reviewed by following their footprints, listening to their analysis of experimental results. Based on the DNA sequences, the reasons for several unusual phenomena of lac operon expression were also discussed to exemplify the teaching value of the classic cases in genetics and molecular biology.


Regulation of Gene Expression in Prokaryotes (With Diagram)

All the activities of an organism are controlled by genes. Most of the genes of an organism express themselves by producing proteins. The genes which produce proteins are called structural genes or cistrons. Every cell of an organism posses all the genes. But all of them are not functional all the time. If all the genes function all the time, enzymatic chaos will prevail and there will not be much cell differentiation.

The products of many genes are needed only occasionally by the cell. Therefore, those proteins are synthesized only when the substrate on which they act is present or when they are needed by the cell. In highly differentiated cells of eukaryotes only a few genes are functional and all other genes are permanently shut off. Even a lowly E. coli bacterium expresses only some of its genes at any given time out of the total of about three thousand genes.

Various mechanisms exist in the cell, which control and regulate the expression of genes. The regulatory system turns the genes “on” when needed and turns “off’ when not needed. This proves that gene activity can be regulated.

There are various stages at which the expression of a gene can be regulated but most common is the initiation of transcription. It is here that bulk of the gene regulation takes place. Other levels of gene regulation are transcriptional elongation, mRNA processing during translation and post translation stage.

Gene Regulation in Prokaryotes:

In bacteria the expression of genes is controlled by extracellular signals often present in the medium in which bacteria are grown. These signals are carried to the genes by regulatory proteins. Regulatory proteins are of two types. They are positive regulators called activators and negative regulators called repressors. These activators and repressors are DNA binding proteins.

Negative Regulators or Repressors:

The repressor or inhibitor protein binds to the target site (operator) on DNA. These block the RNA polymerase enzyme from binding to the promoter, thus preventing the transcription. The repressor binds to the site where it overlaps the polymerase enzyme. Thus, activity of the genes is turned off. It is called negative control mechanism.

An anti-repressor or anti-inhibitor called inducer is needed to inactivate the repressor and thereby activating the genes. Thus, the genes are switched on. This is demonstrated by lactose operon.

Positive Regulators or Activators:

To activate the transcription by the promoter, the activator helps polymerase enzyme to bind to the promoter.

Genes under positive control mechanism are expressed only when an activator or stimulator or active regulator is present.

Operon:

In bacteria cistrons or structural genes, producing enzymes of a metabolic pathway are organised in a cluster whose functions are related. Polycistronic genes of prokaryotes along with their regulatory genes constitute a system called operon. Operon is a unit of expression and regulation.

1. Lactose Operon or Lac Operon:

This is a negative control mechanism. In 1961 Francois Jacob and Jacques Monod proposed operon model for the regulation of gene expression in E. coli. The synthesis of enzyme (3-galactosidase has been studied in detail. This enzyme causes the breakdown of lactose into glucose and galactose.

In the absence of lactose, β-galactosidase is present in negligible amounts. As soon as lactose is added from outside, the production of β- galactosidase increases thousand times. As soon as the lactose in consumed, the production of the enzyme again drops. The enzymes whose production can be increased by the presence of the substrate on which it acts are called inducible enzymes.

Addition of lactose to the culture medium of E. coli induces the formation of three enzymes (5-galactosidase, permease and transacetylase, which degrade lactose into glucose and galactose. The genes, which code for these enzymes lie in a cluster and are called cistrons or structural genes. They are transcribed simultaneously into a single mRNA chain, which has codons for all the three enzymes. The mRNA transcribed from many genes is called polycistronic. The functioning of structural genes to produce mRNA is controlled by regulatory genes.

There are three structural genes Z, Y and A, which code for enzymes p-galactosidase, lac permease and transacetylase respectively. Regulatory genes consist of Regulator I, Promoter P and a control gene called operator gene O. Regulator I gene produces a protein called repressor or inhibitor. The repressor is active and binds to the operator gene O and switches it “off” and the transcription is stopped.

This happens because RNA polymerase enzyme which binds to the promoter is unable to do so because binding site of RNA polymerase and the binding site of repressor on operator overlap each other. Hence in negative control mechanism, the active genes are turned “off” by the repressor protein.

When the inducer (lactose) in supplied from outside, the inducers binds to the repressor. The lactose on entering the bacteria changes into allolactase. Allolactose changes the shape of the repressor (conformational changes) which renders it inactive and unable to bind to the operator. The operator becomes free and is “turned on” and thus transcription starts.

In this way, the presence of the inducer permits the transcription of Lac operon, which is no longer blocked by the repressor protein. The synthesis of enzymes in response to the presence of specific substrate (lactose) is called induction. It is also called de-repression.

The inducible system operates in a catabolic pathway. In the absence of lactose, E. coli cells have an average of only three molecules of P-galactosidase enzyme per cell. Within 2-3 minutes of induction of lactose, 3000 molecules of P-galactosidase are produced in each cell.

It is also a negative control system but forms a biosynthetic pathway. It is known as repressible system. It works on the principle that when the amino acid tryptophan is present, there is no need to activate the tryptophan operon.

Repressor protein is activated by the co-repressor (tryptophan-the end product) and it binds the operator to switch it “off’. Tryptophan is synthesized in five steps, each step requiring a particular enzyme. The genes for encoding these enzymes lie adjacent to one another, called trp E, trp D, trp C, trp B and trp A.

Tryptophan operon codes for five enzymes that are required for the synthesis of amino acid tryptophan. In repressible system, the regulatory gene produces a repressor protein, which is normally inactive and unable to bind to operator on DNA. The repressor upon joining the co-repressor (which is the end product tryptophan in this case) undergoes conformational changes that activate it and enable it to bind to the operator. This prevents the binding of RNA polymerase enzyme to the promoter. This is opposite to the situation of lac operon in which the repressor is active on its own and loses the affinity for the operator when bound to the inducer.

Here the availability of tryptophan which is the end product regulates the expression of this operon and represses the synthesis of tryptophan. In this way the synthesis of enzymes of a metabolic pathway is stopped by the end product of the metabolic chain. This mechanism enables the bacteria to synthesize enzymes only when they are required. This is known as feed back repression.

In feed back inhibition the end product of a metabolic pathway acts as an allosteric inhibitor of the first enzyme of the metabolic chain.

Induction and repression save valuable energy by preventing the synthesis of unnecessary enzymes.

Positive Control of Transcription:

The system of regulation in lactose and tryptophan operon is essentially a negative control in the sense that the operon is normally “on” but is kept “off’ by the regulator protein. In other words the structural genes are not allowed to express unless required.

Catabolic Repression:

Lac operon also shows positive control by catabolic repression. This is an additional control system, which binds the repressor-operator. In E. coli, in the presence of both glucose and lactose, the glucose in first fully utilized and then lactose is taken up for production of energy.

Glucose is richest and more efficient source of energy. Glucose has an inhibitory effect on the expression of lac operon. The mechanism of positive control enables E. coli to adapt more efficiently to the changing environment of its natural habitat, which is the human intestine.

In the presence of glucose, synthesis of β-galactosidase enzyme becomes suppressed. The inhibitory effect of glucose is due to the marked drop in the level of a nucleotide called cyclic AMP (c-AMP), which inhibits the transcription of mRNA.

Lactose operon transcription requires not only cyclic AMP but also another protein called catabolic activator protein (CAP). The cAMP and CAP form a complex called cAMP-CRP complex, which is necessary for the functioning of lactose operon.

A catabolic breakdown product of glucose, called glucose catabolite, prevents the activation of lac operon by lactose. This effect is called catabolic repression. When glucose concentration increases, the cAMP concentration decreases and vice versa. High concentration of cAMP is necessary for the activation of lac operon.

Normally in the presence of glucose, the lactose operon remains inactive.

Glucose catabolite prevents the formation cAMP-CRP complex.

In this way cAMP-CRP system is positive control because expression of lac operon requires the presence of an activating signal which is this case in cAMP-CRP complex.

There are some promoters on DNA at which RNA polymerase cannot initiate transcription without the presence of some additional protein factors such as cAMP-CRP complex. These factors are positive regulators because their presence is necessary to switch on the cistrons. These are called activators or stimulators.


A. Mechanisms of Control of the Lac Operon

In the animal digestive tract (including ours), genes of the E. coli lac operon regulate the use of lactose as an alternative nutrient to glucose. Think cheese instead of chocolate! The operon consists of lacZ, lacY, and lacA genes that were called structural genes. By definition, structural genes encode proteins that participate in cell structure and metabolic function. As already noted, the lac operon is transcribed into an mRNA encoding the Z, Y and A proteins.

Let&rsquos take a closer look at the structure of the lac operon and the function of the Y, Z and A proteins (below).

The lacZ gene encodes &beta-galactosidase, the enzyme that breaks lactose (a disaccharide) into galactose and glucose. The lacY gene encodes lactose permease, a membrane protein that facilitates lactose entry into the cells. The role of the lacA gene (a transacetylase) in lactose energy metabolism is not well understood. The I gene to the left of the lac Z gene is a regulatory gene (to distinguish it from structural genes). Regulatory genes encode proteins that interact with regulatory DNA sequences associated with a gene to control transcription. The operator sequence separating the I and Z genes is a transcription regulatory DNA sequence.

The E. coli lac operon is usually silent (repressed) because these cells prefer glucose as an energy and carbon source. In the presence of sufficient glucose, a repressor protein (the I gene product) is bound to the operator, blocking transcription of the lac operon. Even if lactose is available, cells will not be use it as an alternative energy and carbon source when glucose levels adequate. However, when glucose levels drop, the lac operon is active and the three enzyme products are translated. We will see how limiting glucose levels induce maximal lac operon transcription by both derepression and direct induction, leading to maximal transcription of the lac genes only when necessary (i.e., in the presence of lactose and absence of glucose). Let&rsquos look at some of the classic experiments that led to our understanding of E. coli gene regulation in general, and of the lac operon in particular.

In the late 1950s and early 1960s, Francois Jacob and Jacques Monod were studying the use of different sugars as carbon sources by E. coli. They knew that wild type E. coli would not make the (eta )-galactosidase, (eta )-galactoside permease or (eta )-galactoside transacetylase proteins when grown on glucose. Of course, they also knew that the cells would switch to lactose for growth and reproduction if they were deprived of glucose! They then searched for and isolated different E. coli mutants that could not grow on lactose, even when there was no glucose in the growth medium. Here are some of the mutants they studied:

  1. One mutant failed to make active (eta )-galactosidase enzyme but made permease.
  2. One mutant failed to make active permease but made normal amounts of (eta )-galactosidase.
  3. Another mutant failed to make transacetylase. but could still metabolize lactose in the absence of glucose. Hence the uncertainty of its role in lactose metabolism.
  4. Curiosly, one mutant strain failed to make any of the three enzymes!

Since double mutants are very rare and triple mutants even rarer, Jacob and Monod inferred that the activation of all three genes in the presence of lactose were controlled together in some way. In fact, it was this discovery that defined the operon as a set of genes transcribed as a single mRNA, whose expression could therefore be effectively coordinated. They later characterized the repressor protein produced by the lacI gene. Jacob, Monod and Andre Lwoff shared the Nobel Prize in Medicine in 1965 for their work on bacterial gene regulation. We now know that negative and positive regulation of the lac operon (described below) depend on two regulatory proteins that together, control the rate of lactose metabolism.

1. Negative Regulation of the Lac Operon by Lactose

Refer to the illustration below to identify the players in lac operon derepression.

The repressor protein product of the I gene is always made and present in E. coli cells. I gene expression is not regulated! In the absence of lactose in the growth medium, the repressor protein binds tightly to the operator DNA. While RNA polymerase is bound to the promoter and ready to transcribe the operon, the presence of the repressor bound to the operator sequence close to the Z gene physically blocks its forward movement. Under these conditions, little or no transcript is made. If cells are grown in the presence of lactose, the lactose entering the cells is converted to allolactose. Allolactose binds to the repressor sitting on the operator DNA to form a 2-part complex, as shown below.

The allosterically altered repressor dissociates from the operator and RNA polymerase can transcribe the lac operon genes as illustrated below

2. Positive Regulation of the Lac Operon Induction by Catabolite Activation

The second control mechanism regulating lac operon expression is mediated by CAP (cAMP-bound catabolite activator protein or cAMP receptor protein). When glucose is available, cellular levels of cAMP are low in the cells and CAP is in an inactive conformation. On the other hand, if glucose levels are low, cAMP levels rise and bind to the CAP, activating it. If lactose levels are also low, the cAMP-bound CAP will have no effect. If lactose is present and glucose levels are low, then allolactose binds the lac repressor causing it to dissociate from the operator region. Under these conditions, the cAMP-bound CAP can bind to the operator in lieu of the repressor protein. In this case, rather than blocking the RNA polymerase, the activated Camp-bound CAP induces even more efficient lac operon transcription. The result is synthesis of higher levels of lac enzymes that facilitate efficient cellular use of lactose as an alternative to glucose as an energy source. Maximal activation of the lac operon in high lactose and low glucose is shown below.

cAMP-bound CAP is an inducer of transcription. It does this by forcing the DNA in the promoter-operator region to bend. And since bending the double helix loosens H-bonds, it becomes easier for RNA polymerase to find and bind the promoter on the DNA strand to be transcribed&hellip, and for transcription to begin. cAMP-CAPinduced bending of DNA is illustrated below.

3. Lac Operon Regulation by Inducer Exclusion and Multiple Operators

In recent years, additional layers of lac operon regulation have been uncovered. In one case, the ability of lac permease to transport lactose across the cell membrane is regulated. In another, additional operator sequences have been discovered to interact with a multimeric repressor to control lac gene expression.

A) Regulation of Lactose use by Inducer Exclusion

When glucose levels are high (even in the presence of lactose), phosphate is consumed to phosphorylate glycolytic intermediates, keeping cytoplasmic phosphate levels low. Under these conditions, unphosphorylated EIIAGlc binds to the lactose permease enzyme in the cell membrane, preventing it from bringing lactose into the cell.

The role of phosphorylated and unphosphorylated EIIA Glc in regulating the lac operon are shown below.

High glucose levels block lactose entry into the cells, effectively preventing allolactose formation and the derepression of the lac operon. Inducer exclusion is thus a logical way for the cells to handle an abundance of glucose, whether or not lactose is present. On the other hand, if glucose levels are low in the growth medium, phosphate concentrations in the cells rise sufficiently for a specific kinase to phosphorylate the EIIAGlc. Phosphorylated EIIAGlc then undergoes an allosteric change and dissociates from the lactose permease, making it active so that more lactose can enter the cell. In other words, the inducer is not &ldquoexcluded&rdquo under these conditions!

The kinase that phosphorylates EIIA Glc is part of a phosphoenolpyruvate (PEP)- dependent phosphotransferase system (PTS) cascade. When extracellular glucose levels are low, the cell activates the PTS system in an effort to bring whatever glucose is around into the cell. But the last enzyme in the PTS phosphorylation cascade is the kinase that phosphorylates EIIA Glc . Phosphorylated EIIA Glc dissociates from the lactose permease, re-activating it, bringing available lactose into the cell from the medium.

B) Repressor Protein Structure and Additional Operator Sequences

The lac repressor is a tetramer of identical subunits (below).

Each subunit contains a helix-turn-helix motif capable of binding to DNA. However, the operator DNA sequence downstream of the promoter in the operon consists of a pair of inverted repeats spaced apart in such a way that they can only interact two of the repressor subunits, leaving the function of the other two subunits unknown&hellip that is, until recently!

Two more operator regions were recently characterized in the lac operon. One, called O2, is within the lac z gene itself and the other, called O3, lies near the end of, but within the lac I gene. Apart from their unusual location within actual genes, these operators, which interact with the remaining two repressor subunits, went undetected at first because mutations in the O2 or the O3 region individually do not contribute substantially to the effect of lactose in derepressing the lac operon. Only mutating both regions at the same time results in a substantial reduction in binding of the repressor to the operon.

B. Mechanism of Control of the Tryptophan Operon

If ample tryptophan (trp) is available, the tryptophan synthesis pathway can be inhibited in two ways. First, recall how feedback inhibition by excess trp can allosterically inhibit the trp synthesis pathway. A rapid response occurs when tryptophan is present in excess, resulting in rapid feedback inhibition by blocking the first of five enzymes in the trp synthesis pathway. The trp operon encodes polypeptides that make up two of these enzymes.

Enzyme 1 is a multimeric protein, made from polypeptides encoded by the trp5 and trp4 genes. The trp1 and trp2 gene products make up Enzyme 3. If cellular tryptophan levels drop because the amino acid is rapidly consumed (e.g., due to demands for proteins during rapid growth), E. coli cells will continue to synthesize the amino acid, as illustrated below.

On the other hand, if tryptophan consumption slows down, tryptophan accumulates in the cytoplasm. Excess tryptophan will bind to the trp repressor. The trp-bound repressor then binds to the trp operator, blocking RNA polymerase from transcribing the operon. The repression of the trp operon by trp is shown below.

In this scenario, tryptophan is a co-repressor. The function of a co-repressor is to bind to a repressor protein and change its conformation so that it can bind to the operator.


Jacob, Monod, the Lac Operon, and the PaJaMa Experiment—Gene Expression Circuitry Changing the Face of Cancer Research

Visit the Cancer Research 75 th Anniversary timeline.

See related article by Pitot and Heidelberger, Cancer Res 196323:1694–700.

It is a virtually universal rule in science that if we step back to reflect upon a field currently viewed as extremely dynamic and novel, we find ourselves standing on the shoulders of those whose seminal observations gave birth to it far earlier. For those of us working in the fields of signal transduction and epigenetics within the cancer research arena, this is absolutely the case when we consider the brilliant realizations of Jacob and Monod that regulatory networks control gene expression in bacteria (1–5). Their recognition that expression of a single gene can be repressed by another gene for response to regulatory cues from the environment ranks as one of the top, and now most heavily explored, areas of biology in general and cancer biology. A review in Cancer Research in 1961 by Pitot and Heidelberger not only pays tribute to this pivotal work of Jacob and Monod but with the prescient intent of predicting how the concepts might be woven into our understanding of carcinogenesis (6). To say their predictions were accurate would be an understatement, as is readily apparent from today's marriage between the exploration of regulation of gene expression and our current efforts to dissect basic mechanisms underlying the origins, initiation, and progression of cancer. It becomes evident as well that the studies of Jacob and Monod, and their implications as visualized by Pitot and Heidelberger, helped usher in a biology that underpins our current quest to evolve new strategies for improving the management of cancer. Hence the selection of the review by Pitot and Heidelberger for inclusion in the current celebration of 75 years of publishing in Cancer Research.

The revelations provided by Jacob and Monod started, as do many great stories in science, with a series of epiphanies by the younger investigator, Jacob, which he brought to conversations with the more established scientist, Monod. They followed their eventual joint excitement over the possibilities raised with a series of experiments, conducted during 1958 through 1961 at the Pasteur Institute in Paris. These resulted in their outlining a model for gene regulation, which survives as a core paradigm today. Their observations established the principle that to properly regulate response of an organism to changing environmental conditions, in specific bacteria for their experiments, a gene circuitry exists wherein one gene product regulates control of another gene. The result is a change in cellular phenotype for cellular metabolism (2–5). Building on experiments for demonstrating that lambda phage genes can be both induced and repressed in bacteria, the investigators established that changes in need for lactose utilization lead to negative regulation of β-galactosidase (2–5). The circuitry for this switch formed what is now famously known as the lac operon (1–5). The studies took advantage of the mating system employed in bacteria, in which the chromosomal material of the male is progressively injected over time into the female, thus progressively carrying genetic material with it. This allowed investigators to map male genes by chromosome position as their entry facilitated gene expression events in the female. Toning down the sexual connotations for the literature, the seminal study of Jacob and Monod, with participation of Arthur Pardee, was first published as a preliminary report in 1958 where it was dubbed the “PaJaMa” experiment (1, 3, 5). In this study, the investigators were able to show that a gene lacl encoded a trans-acting repressor for the lac gene. In this concept, the activity of the regulator gene is induced when the repressor protein in the cytoplasm is induced by a small molecular weight product generated by the target enzyme. This circuitry paradigm contributes robustly to mechanisms for pathway feedback inhibition.

The nature of the trans-acting molecules through which the repressive process is mediated remained to be determined with many discussions of whether direct DNA–DNA interactions, RNA, proteins, etc., would play this role. These subsequent discussions, held at the headiest of meetings attended by many luminaries in the embryonic field of molecular biology, are credited with leading to the discovery of mRNA as put forth in a review by Alexander Gann (3). Herein is described a lunch in Sydney Brenner's rooms in King's College on Good Friday, now some 55 years ago, attended by Jacob, Brenner, Francis Crick, Alan Garen, and others where “suddenly that afternoon it became obvious—first to Brenner and Crick, and then to the others present—that the PaJaMa experiment predicted an unstable intermediate in gene expression,” which was concluded to be RNA. This suggested to the attendees that the mediator for the repressor action potentially “really did act at the genetic level controlling production of the unstable mRNA. This discussion, continued that evening at a party at Crick's house, led directly to the experiment by Brenner and Jacob, who, together with Matt Meselson at Caltech that summer, demonstrated the existence of mRNA. Separately, Jim Watson, Wally Gilbert, and Francois Gros arrived at a similar result through different means at Harvard” (3). The years to come in our current age of biology have revealed that all of the hypotheses derived from the first findings of Jacob and Monod were relevant and presaged the findings of how many different ways such transacting events can be molecularly mediated.

In decades following the above observations, the paradigm of the lac operon and its constituent repressor binding to an operator and inducer ushered in an era, ever growing today, for our understanding of cellular control through signal transduction circuitry and the concepts embodied for heritability of resultant gene expression changes established by epigenetic mechanisms (2–4, 7). It has been justifiably stated that “few proteins have had such a strong impact on a field as the lac repressor has had in Molecular Biology” (2). It is hard to imagine, looking back, the degree to which the work of Jacob and Monod would become a knowledge base to build upon in elucidating the vast series of mechanisms used by cells to interpret environmental cues in processes ranging from development to those of adult cell renewing systems challenged by a myriad of normal and abnormal stimuli. A staggering portfolio of cellular machinery to implement these processes continues to unravel in what we now investigate every day as activation of, and heritably transmitting of, information from cell signaling pathways. These include switches in patterns of gene expression and the cell nuclear events that fix these gene events, including looping between DNA regions for control by gene enhancers of promoters, the roles of noncoding RNAs such as long-noncoding and miRNAs, and the roles of DNA methylation, chromatin, and nucleosome positioning in heritably locking in gene expression changes, which can all contribute to creating new cellular phenotypes (8). Indeed, one may view this as the expansion of, and definition of mechanisms for, the types of gene circuitry proposed and documented by Jacob and Monod.

With the above background in mind, it is remarkable how quickly, and with such prescience, Pitot and Heidelberger brought forth the concepts outlined in their 1961 Cancer Research review (6). They hypothesized components of the systems outlined by Jacob and Monod could be transposed to a concept of induced phenotypes that are heritably perpetuated and maintained for cellular responses to short, transient exposure to carcinogens (6). They theorized that ongoing experiments in the carcinogenesis field suggested these above interactions might possibly allow engendering of a malignant cell without necessitating participation of genetic (DNA) changes such as gene mutations. Critical to this proposal, they envisioned a potential state of “reversion” which might allow for changing the malignant phenotype back to the nonmalignant state (6). These concepts are dear to the heart of researchers on the continuing quest to outline the precise roles for epigenetic alterations in the initiation and progression of cancer and the possibility that targeting such changes, and/or what controls them, could provide for potent cancer management strategies (9, 10). They perceptively weave the concepts of Jacob and Monod into a possible alternative to the then prevailing doctrine that “cancer may result from a direct interaction of carcinogen with genetic material”—a theory they reasoned had developed by “acceptance by many as the mechanism of carcinogenesis on the basis of theoretical simplicity rather than of scientific data.” As an alternative, Pitot and Heidelberger considered, and deeply modeled, how the findings of Jacob and Monod might lead to the possibility that “a cytoplasmic interaction of a carcinogen and a target protein could lead to a permanently altered and stable metabolic situation without the necessity of any direct interaction of the carcinogen and genetic material” (6). A critical feature of their hypothesis was that “under the proper circumstances and before chromosomal alterations occurred, the process might be reversed and lead to the production of a normal from a tumor cell.”

In their proposal, via a series of presented complex models, they proposed multiple scenarios and different variations of biochemical and genetic themes that could mediate their proposed interactions, arriving at the following bottom line prediction—that a carcinogen can bind to and interfere with the repressor of a growth process, thus effectively negating function of the repressor through a process of “cytoplasmic inheritance.” Thus, this interference is not dependent on continued presence of the carcinogen in daughter cells as they divide (6). Clearly, in modern parlance, we visualize these dynamics as proceeding through the cytoplasm to the nucleus via a series of signal transduction events that subsequently get abnormally fixed by epigenetic processes involving DNA methylation, chromatin, and changes in nucleosome position (8–10). Clearly, this suggests a profound role of epigenetic abnormalities early during cancer initiation and this possibility is the subject of many investigations today (9, 10). In this regard, Pitot and Heidelberger wisely articulate several key rules, and cautions, inherent to their proposed mechanisms and this wisdom enriches their predictions as they are playing out today. First, they stress that “it must be apparent to the reader that we are here dealing only with the earliest changes in carcinogenesis. Once the altered regulation is established (possibly within minutes or hours), other effects appear, such as aneuploidy, increased glycolysis, apparent multiple enzyme deletions, etc., which are probably secondary to the primary changes” (6). Second, “it is not our intention to rule out or deny the possibility that chemical carcinogenesis is a consequence of the direct interaction of the compound with genetic material. Rather, it is our purpose to call attention to alternative explanations, based upon current concepts of metabolic regulation and control, that permit the perpetuation of metabolic changes brought about by the temporary interaction of the carcinogen and a cytoplasmic protein” (6). Finally, they conclude that “by the application of these or similar theoretical models, it is possible to reconcile the large body of sound experimental data on chemical carcinogenesis with current concepts of metabolic regulation, and early cancer could be considered as a phenotypic rather than a genotypic disease” (6).

In reviewing the work of Jacob and Monod, John Beckwith (5) provides a wonderful sentiment that might serve also as a coda to the ingenious joining by Pitot and Heidelberger of the lac operon story with the field of human carcinogenesis—“new theories that become successful paradigms for their field, in their initial form at least, do not provide a correct explanation for all of the phenomena that are considered important to that field.” And, yet as implied here, any initial flaws in such theories do not prevent their never being separated from the body of invaluable work they help to spawn. Our understanding today of gene transcription is driving virtually every aspect of basic and translational tumor biology, again reminding us of our ride on the shoulders of those coming before. The publication by Pitot and Heidelberger is, then, emblematic of why we are celebrating 75 years of publishing in Cancer Research.


Discussion

In this study we found that gene expression increases linearly with the distance from the start of a gene to the end of the operon (transcription distance). This relationship was observed in multiple sets of operons of different lengths, at different gene positions in multiple operons, with multiple coding sequences, and with different 5′-UTR sequences. Furthermore, the relative increase in translation per nucleotide of transcription distance (i.e., the translation coefficient) was similar across the different experiments and operons. Together these findings provide compelling support for a relationship between gene expression and the transcription distance and they indicate a common mechanism.

We proposed a general model that shows that genes with longer transcription distances have increased expression because they have a longer period for translation during transcription. There are three points in support of the model. First, it correctly predicts from first principles that the relationship between gene expression and the transcription distance is linear. Second, increasing the transcription distance was found to increase translation as predicted. Third, it provides a single explanation for why varying operon length and varying gene position have the same effect on gene expression (i.e., the same translation coefficient).

The most intriguing prediction of the model is that the production rate of proteins during transcription (β1) is sixfold greater than after mRNA release (β2). This result means that increasing the transcription time by 24 s (resulting from a 1-kb increase in transcription distance) has an equivalent effect on expression to increasing the mRNA lifetime by 144 s. The difference in transcriptional and posttranscriptional protein production rates could be due to local differences in ribosome concentrations and/or due to a different mRNA structure during transcription (15). In support of the former, ribosomes have been shown to be preferentially located at sites of active transcription in Bacillus subtilus (16) and there is mounting evidence that spatial localization is important for bacterial translation (17, 18). Both mechanisms would increase translation initiation.

The transcription distance had a measurable impact on expression in a wide variety of operons and there is evidence to suggest an association between gene expression and transcription distance in some native operons (19, 20). Therefore, although the transcription distance has only a moderate effect on gene expression, its role should not be ignored. In addition, altering gene expression by varying the transcription distance is fundamentally different from changing the RBS (21) or the transcription rate (22, 23) consequently it may have unique effects on gene noise and for coordinating expression from multiple genes. Furthermore, varying the transcription distance has a predictable effect on gene expression and this could be exploited to tune patterns and levels of gene expression in synthetic and native operons (24). In particular, it could be used to optimize gene order in operons to increase the output of a pathway (25) and to generate specific stoichiometries for protein complexes.

In conclusion, we show that operon organization can modulate levels and patterns of gene expression. It was known that the proximal genes in an operon can influence the expression of distal genes (e.g., polar mutations). Here we demonstrated that the converse also occurs distal genes can regulate proximal genes in an operon via their effect on the transcription distance. These findings also provide an example of how synthetic biology can help deconstruct complex biological processes. In this case, synthetic operons enabled the effect of operon organization on gene expression to be decoupled from the regulatory mechanisms that exist in native operons, thereby making it easier to identify. The next and more difficult task will be to investigate the role of the transcription distance in modulating the expression of nonfluorescent genes in native operons.


Quantitative approaches to the study of bistability in the lac operon of Escherichia coli

In this paper, the history and importance of the lac operon in the development of molecular and systems biology are briefly reviewed. We start by presenting a description of the regulatory mechanisms in this operon, taking into account the most recent discoveries. Then we offer a survey of the history of the lac operon, including the discovery of its main elements and the subsequent influence on the development of molecular and systems biology. Next the bistable behaviour of the operon is discussed, both with respect to its discovery and its molecular origin. A review of the literature in which this bistable phenomenon has been studied from a mathematical modelling viewpoint is then given. We conclude with some brief remarks.

1. Introduction

Glucose is the favourite carbon and energy source for Escherichia coli, as well as for many other organisms. Although this bacterium can also feed on other sugars, it only does so when glucose is absent. Thus, if a bacterial culture grows in a medium containing a mixture of glucose and another sugar (such as lactose), it will exclusively feed on the former until it is exhausted, before switching on to the second one. A consequence of this behaviour is that the bacterial growth curve shows two distinctive phases, as can be seen in figure 1. This phenomenon was originally studied by Monod (1941), who described it as diauxic growth. It is worth mentioning at this point that diauxic growth only occurs in batch cultures, and simultaneous usage of sugars is often observed in continuous cultures (Lendenmann et al. 1996).

Figure 1 Typical diauxic growth curve. Note the existence of two different exponential growth phases, separated by a short interval in which the culture does not grow. The first (second) phase corresponds to the bacterial culture feeding on glucose (lactose), while the interval with no growth corresponds to the time the bacteria need to turn on the genes needed to metabolize lactose after glucose exhaustion.

Molecular level understanding of how an organism sequentially uses different metabolites has been attracting tremendous interest for the past fifty years. Jacob & Monod (1961a,b) tackled this problem and conceptually outlined how bacterial cultures could switch from one mode of growth to another so rapidly and completely. In the process of doing so, they introduced the operon concept (Jacob et al. 1960), which has become a paradigmatic example of gene regulation.

According to the construction of Jacob & Monod, an operon consists of a set of structural genes that are regulated together, depending on the cell metabolic requirements. These structural genes code for a group of enzymes or proteins that are responsible for a specific task or metabolic process, and their regulation is achieved via one or more common regulatory mechanisms. Repression was the first regulatory mechanism to be discovered by them. In it, a repressor molecule binds a specific DNA site (which they termed the operator) located upstream from the structural genes, and inhibits their transcription. The regulation of the structural genes' expression is achieved by varying the number of active repressor molecules. Although Jacob and Monod originally thought of the repressors as RNA molecules, they are now known to be proteins.

The lactose (or simply lac) operon is composed of three structural genes: lacZ, lacY and lacA. These genes, respectively, code for β-galactosidase, lac permease and a transacetylase. β-Galactosidase acts to cleave lactose into galactose and glucose, which is the first step in lactose metabolism lac permease is a transmembrane protein, which is necessary for lactose uptake transacetylase transfers an acetyl group from coenzyme A (CoA) to the hydroxyl group of the galactosides. Of these proteins, only β-galactosidase and lac permease play an active role in the regulation of the lac operon. The regulatory gene lacI (in a different operon) codes for the lac repressor which, when active, is capable of inhibiting the transcription of the structural genes by binding an operator. The lac repressor is inactivated when it is bound by allolactose, a by-product of lactose metabolism. Finally, the lac operon genes are also upregulated by an activator that increases the affinity of the mRNA polymerase for the lac promoter, and whose production is controlled by the concentration of extracellular glucose.

The lac operon has been pivotal in the development of molecular biology and is currently having an important impact on the development of systems biology. In §2 we present a more detailed description of the lac operon regulatory mechanisms, in §3 we review the most significant aspects of the development of molecular biology influenced by the lac operon and in §4 we give a comprehensive review of the quantitative studies of the lac operon bistable behaviour.

2. The lac operon regulatory mechanisms in detail

In §1, the lac operon control system was briefly reviewed. Although that brief review gives a good idea of how this system functions, in reality it is far more complex. In the following paragraphs, a more detailed description of all the regulatory mechanisms in the lac operon, including the most recent discoveries, will be given.

The lac operon regulatory elements (pictured in figure 2a) are distributed along the DNA chain as follows (Reznikoff 1992 Müller-Hill 1998): the lac promoter is located between bp −36 (bp stands for base pair, and positions are referred relative to the starting point of gene lacZ, bp +1) and bp −7. Operator O1 is 21 bp long and is centred around bp +11. There are two additional operators, denoted O2 and O3, which are, respectively, located at 401 bp downstream and 92 bp upstream from O1. Finally, the activator (CAP)-binding site spans from bp −72 to bp −50.

Figure 2 (a) Schematic of the regulatory elements located in lac operon DNA. P denotes the promoter, O1, O2 and O3 correspond to the three operators (repressor-binding sites), and C is the binding site for the cAMP–CRP complex. The different ways in which a repressor molecule can interact with the operator sites are represented in b, c, d and e. Namely, a free repressor molecule (b), one with a single subunit bound by allolactose (d) or one with the two subunits in the same side bound by allolactose (e) can bind a single operator. Moreover, a free repressor molecule can bind two different operators simultaneously (c). Figure adapted from Santillán (2008).

The lac repressor is a homotetramer (consisting of two functional homodimers) of lacI polypeptides (Lewis 2005 Wilson et al. 2007). Each functional dimer can bind operators O1, O2 and O3. Furthermore, DNA can also fold in such a way that a single repressor binds two operators simultaneously, one per dimer. Each monomer in the lac repressor can be bound by an allolactose molecule, inhibiting the capability of the corresponding dimer to bind an operator. This means that free repressors can bind one operator (figure 2b) or two of them simultaneously (figure 2c), repressors with three free monomers can bind one but not two operators (figure 2d), repressors with two free monomers can bind one operator, if the bound monomers belong to the same dimer (figure 2e), or none at all, and that repressors with only one free monomer are unable to bind any operator, as are repressors with all four monomers bound by allolactose (Narang 2007).

Deletion experiments have shown that a repressor bound to O1 inhibits transcription initiation, while a repressor bound to either O2 or O3 has almost no effect on the expression of the lac operon structural genes. Nevertheless, O2 and O3 do have an indirect effect because the complex formed by a single repressor simultaneously bound to O1 and either O2 or O3 is far more stable than that of a repressor bound only to O1. The consequence of this is that by interacting with the lac repressor operator O1 is only capable of decreasing the expression of the operon genes 18 times when it cooperates with O2, the repression level can be as high as 700-fold when O1 and O3 act together, they can reduce the operon activity up to 440 times when all three operators are present, the repression intensity can be as high as 1300-fold (Oehler et al. 1990).

The intracellular production of cyclic AMP (cAMP) decreases as the concentration of extracellular glucose increases. cAMP further binds a specific receptor molecule (CRP) to form the so-called CAP complex. Finally, CAP binds a specific DNA site (denoted here as C) upstream from the lac promoter, and by doing so it increases the affinity of the mRNA polymerase for this promoter (Reznikoff 1992). This regulatory mechanism is known as catabolite repression.

A novel source of cooperativity has been recently discovered in the lac operon: when a CAP complex is bound to site C, it bends DNA locally and increases the probability of the complex in which a repressor simultaneously binds operators O1 and O3 (Kuhlman et al. 2007).

The last regulatory mechanism in the lac operon is the so-called inducer exclusion. In it, external glucose decreases the efficiency of lac permease to transport lactose (Reznikoff 1992), and by doing so negatively affects the induction of the operon genes.

These regulatory mechanisms reviewed above are summarized in figure 3. As we have seen, the activity of the lac operon is regulated by extracellular glucose and lactose. While extracellular glucose decreases the operon activity via catabolite repression and inducer exclusion, extracellular lactose increases the operon expression level by deactivating the repressor. Another fact worth noticing is the existence of a positive feedback loop: as more molecules of lac permease and β-galactosidase are produced, there is an elevated lactose uptake flux and an increased lactose metabolism rate this further increases the production of allolactose and, as a consequence, diminishes the amount of active repressor. This, in turn, increases the operon activity, and thus more lac permease and β-galactosidase molecules are produced.

Figure 3 Schematic of the lac operon regulatory mechanisms. This operon consists of genes lacZ, lacY and lacA. Protein LacY is a permease that transports external lactose into the cell. Protein LacZ polymerizes into a homotetramer named β-galactosidase. This enzyme transforms internal lactose (Lac) to allolactose (Allo) or to glucose and galactose (Gal). It also converts allolactose to glucose and galactose. Allolactose can bind to the repressor (R) inhibiting it. When not bound by allolactose, R can bind to a specific site upstream of the operon structural genes and thus avoid transcription initiation. External glucose inhibits the production of cAMP that, when bound to protein CRP to form complex CAP, acts as an activator of the lac operon. External glucose also inhibits lactose uptake by permease proteins. Figure adapted from Santillán et al. (2007).

The reader interested in the details of the lac operon regulatory mechanisms is referred to the excellent review by Beckwith (1987) and the references there. A good description of the operon regulatory elements and their location on the DNA chain can be found in Reznikoff (1992). The most recent discoveries regarding the cooperativity between CAP-binding site and operator O3 are reported in Kuhlman et al. (2007).

3. Importance of the lac operon

The operon model, developed by Jacob and Monod in their attempt to explain diauxic growth, depicted how genetic mechanisms can control metabolic events in response to environmental stimuli via the coordinated transcription of a set of genes with related function. It literally became a paradigm for gene regulation in prokaryotes, where many more operons have been discovered, and has also influenced the understanding of gene regulation in eukaryotes. Furthermore, not only the lac operon as a whole, but also its individual components, such as the lac repressor, the three known lac operators, the enzyme β-galactosidase and the protein lac permease, have influenced the development of molecular biology themselves.

3.1 The lac repressor

A year after Jacob and Monod received the Nobel Prize for their contributions to gene regulation, Müller-Hill and Gilbert isolated the lac repressor. This is a protein of 360 amino acids which associates with a homotetramer with 154 520 Da molecular mass (Lewis 2005).

The molecular mechanism of repressing the lac operon requires the repressor to be capable of binding both operator DNA and allolactose (or similar inducers). The possibility of competitive binding by these ligands was eliminated by the demonstration that protease digestion selectively cleaves the repressor into two fragments: a tetrameric ‘core’ (residues 60–360 of the monomer) that retains inducer-binding properties, and a monomeric N-terminal headpiece (amino acids 1–59) capable of binding DNA. To explain the repressor inactivation by allolactose, Monod, Changeux and Jacob proposed that the repressor undergoes a conformational transition in response to bound ligands, and that this alters its ability to bind DNA. They named this phenomenon allostery (Monod et al. 1963).

In the early 1970s, several hundred milligrams of the repressor were purified and used for crystallization. Yet, its three-dimensional architecture remained elusive until the early 1990s (Lewis 2005). The three-dimensional structure of the lac repressor provided insight into how the repressor may function, as well as the three-dimensional framework for interpreting a huge amount of biochemical and genetic information. Most importantly, when the biochemical and genetic data were viewed in the context of the structure, a detailed molecular model could be constructed to provide a physical basis for the allosteric response, as well as a more detailed understanding of the genetic switch in the lac operon.

The allosteric response discovered in the lactose repressor opened a whole new area of research. Allostery has been found in many other proteins and has also been extended to a variety of cellular signalling pathways in all organisms. Notwithstanding, the transcendence of the lactose repressor does not end there. For instance, its monomer has recently been used as a model system for experimental and theoretical explorations of protein-folding mechanisms (Wilson et al. 2005).

Those interested in knowing more about the lactose repressor can refer to the review papers by Lewis (2005) and Wilson et al. (2007).

3.2 The three lac operators

The primary operator site (O1) for the lac operon was sequenced by Gilbert & Maxam (1973) nearly a decade after Jacob and Monod had published their model. In addition to O1, two auxiliary operators (O2 and O3) were identified with sequences similar to those of the primary operator (Reznikoff et al. 1974). We now know that tetrameric lac repressor is ideally suited to bind two operators simultaneously, creating the so-called ‘repression loops’ (Reznikoff 1992). DNA looping enhances the repressor affinity for multi-operator sequences, and supercoiling these DNAs yields complexes with remarkable stability. A number of synthetic operator variants have also been constructed and have proved very useful for understanding the molecular mechanisms of repression (Wilson et al. 2007).

It was thought for decades that all the signals that control the initiation of bacterial gene transcription are clustered at the 5′ ends of operons, as proposed originally in the models of Jacob, Monod and co-workers. This aspect of their pioneering work is now known to be an oversimplification, as initiation control signals have since been found within, downstream and upstream of the genes regulated by them. Although the phenomenon is not as widespread as in higher cells, its study in bacteria can be, in particular, illuminating. Together with phage lambda switch, the three-operator system of the lac operon has been extremely useful (Gralla 1989) in this respect. Moreover, not only have the lac operators been helpful to understand the molecular mechanisms of gene regulation, but they have also been employed for other practical purposes. For instance, a technique for in vivo visualizing chromosome dynamics using lac operator–repressor binding has been proposed (Belmont & Straight 1998).

3.3 The β-galactosidase enzyme

Few genes have a history of study as long and distinguished as lacZ. The lacZ gene encodes an open reading frame of 1024 amino acids and is one of the first large genes to be completely sequenced. In E. coli, the biologically active β-galactosidase protein exists as a tetramer of four identical subunits and has a molecular weight of approximately 480–500 kDa. The primary enzymatic function of β-galactosidase relevant to its role as a biotechnological tool is to cleave the chemical bond between the anomeric carbon and glycosyl oxygen of appropriate substrates (Serebriiskii & Golemis 2000).

Induction of β-galactosidase synthesis occurs over a large dynamic range (up to 10 000-fold over baseline levels with some inducers). This large range is achievable, in part, because the β-galactosidase protein can be tolerated at extremely high levels in E. coli, as well as in many other organisms such as yeasts, Caenorhabditis elegans, Drosophila melanogaster and mammals. Further, the β-galactosidase protein is readily purified by a number of relatively simple techniques, facilitating in vitro analysis of its activity.

A number of substrates (inducers) for β-galactosidase are either naturally available or very easily chemically synthesized. These enhance the development of models for β-galactosidase enzymatic activity and also provide a practical tool to finely modulate the expression or dissect catalytic activity of the β-galactosidase protein product.

β-Galactosidase activity is easily assayed, both in vivo and in vitro. Assays that have achieved prominence involve the use of colorimetric substrates in which the cleavage of specific β- d -galactopyranoside-coupled aglycone moieties releases coloured dyes. More recently, the panel of available colorimetric substrates has been augmented with fluorescent or chemiluminescent alternative substrates, which further expand sensitivity and applications.

The β-galactosidase protein is structurally malleable. It consists of three separable functional domains: alpha (α, amino-terminal), beta (β, central) and omega (ω, carboxy-terminal). Independent coexpression of the separated domains of the β-galactosidase protein successfully reconstitutes the activity of the full enzyme. This ability, as well as the additional capacity of β-galactosidase to function enzymatically when expressed as a translational fusion to a varied group of protein or peptide moieties, enables further applications.

These characteristics have allowed the usage of lacZ and its product (β-galactosidase) in many scientific and technological applications. Reviewing them all is quite beyond the scope of this paper, but the excellent review by Silhavy & Beckwith (1985) can be consulted. Further, those interested in learning more about the applications of the gene lacZ and the protein β-galactosidase can consult Silhavy & Beckwith (1985), Josephy (1996), Serebriiskii & Golemis (2000) and Shuman & Silhavy (2003).

3.4 The lac permease protein

Active transporters (pumps) require a cellular energy source (i.e. ATP hydrolysis) to catalyse the transport of charged components against an electrochemical gradient. Depending on their energy source, active transporters are classified as primary or secondary. Secondary transporters, in particular, use the free energy stored in a given electrochemical ion gradient (Abramson et al. 2004). LacY is a secondary transporter that couples free energy released from downhill translocation of protons to drive the uphill translocation of galactosides against a concentration gradient.

Lactose permease of E. coli (LacY) is composed of 417 amino acid residues and has 12 helices that transverse the membrane in zigzag fashion, connected by relatively hydrophilic loops with both N and C termini on the cytoplasm side. This protein is encoded by lacY, the second structural gene in the lac operon. lacY was the first gene encoding a membrane transport protein to be cloned into a recombinant plasmid, overexpressed and sequenced (see Kaback 2005 and references therein). This success in the early days of molecular biology opened the study of secondary active transport at the molecular level. Thus, LacY was the first protein of its class to be solubilized and purified in a completely functional state, thereby demonstrating that this single gene product is solely responsible for all the translocation reactions catalysed by the galactoside transport system in E. coli. It has also been shown that LacY is both structurally and functionally a monomer in the membrane (Kaback 2005).

Since the discovery of lactose permease, a number of molecular biological, biochemical and biophysical approaches have been used to study this protein. Analysis of this extensive data, and in particular of recent discoveries regarding the LacY structure and the properties of mutants in the irreplaceable residues (Kaback 2005), has led to the formulation of a model for this protein transport mechanism (Abramson et al. 2004). Furthermore, comparison of the structures of LacY and other MFS transporters (such as the Pi/glycerol-3-phosphate antiporter (GlpT)) has yielded valuable information on the functioning of secondary active transporters in general.

Abramson et al. (2004) and Kaback (2005) review the state of knowledge on secondary active transporters, of which the lactose permease is a paradigm.

In summary, we can see from the above considerations that the lac system has been extremely important and continues to advance our molecular understanding of genetic control and the relationship between sequence, structure and function.

4. Quantitative experimental and theoretical approaches

Two different interpretations of the lac operon dynamic performance existed in the beginning. Monod argued that the inducer concentration in the growing environment completely determines the operon induction level. On the other hand, Cohn & Horibata (1959) proposed a more subtle interpretation of their experiments. They suggested that the lac system provides an ‘experimental example of the Delbrück model’ (Delbrück 1949). According to Delbrück, biological systems with identical genotypes may display different behaviours under particular external conditions, due to ‘epigenetic’ differences that can be transmitted in the cell lineage in the absence of genetic modification. This hypothesis corresponds to a very early formulation of the general principle of phenotypic inheritance.

Novick & Weiner (1957) and Cohn & Horibata (1959) discovered the so-called ‘maintenance effect’, according to which a single cell may have two alternative states: induced, in which it can metabolize lactose, or uninduced, in which the corresponding genes are switched off and lactose metabolism does not occur. Their experimental protocol was as follows. First, a large amount of inducer was added to the extracellular medium of a culture of uninduced E. coli cells then, the culture was split into two parts: U and I. Part U was immediately diluted, and so the cells remained uninduced part I was diluted after several minutes, allowing the cells in this subculture to become induced. They further observed that, when induced cells were transferred to a medium with an intermediate ‘maintenance concentration’ of inducer, they and their progeny remained induced. Similarly, when uninduced cells were transferred to a medium with a ‘maintenance’ concentration, they and their progeny remained uninduced.

The ‘maintenance effect’ was interpreted as the consequence of a high permease concentration in induced cells, which would also have high inducer pumping efficiency. This would enable these cells to maintain the induced state and to transmit it to their progeny, even if placed in a medium with a low concentration of inducer. This interpretation accounts for the existence of two distinct phenotypes and provides an explanation of why induced cells placed in media with low inducer concentrations remain indefinitely induced, whereas cells that have never been induced stay uninduced. However, it does not explain what makes the cells switch between alternative states. This switching remained a mystery for a long time and it had to wait for the introduction of the concept of multistability to be fully explained.

Griffith (1968) developed a mathematical model (using ordinary differential equations, ODEs) for a single gene controlled by a positive feedback loop. He found that, under certain conditions, two stable states may be accessible for the system simultaneously. However, Griffith did not use his model to explain the maintenance effect of the lac operon. The first models that took into account all the relevant processes to unravel the dynamics of the lac operon were by Babloyantz & Sanglier (1972) and Nicolis & Prigogine (1977). Using a mathematical modelling approach, they interpreted the maintenance effect as the biological facet of the physical process of multistability. This model, involving a nonlinear feedback loop, accounted for the main behavioural features of the lactose–operon bistable transition. However, even though the mathematical description of the model required five differential equations (plus one conservation equation), the model did not take into account the detailed information available concerning molecular interactions between the operon components.

4.1 The Ozbudak et al. experiments

In the last few years, the interest in the bistable behaviour of the lactose operon has been renewed, and this is in part due to a paper recently published by Ozbudak et al. (2004). In it, the authors report the results of a series of ingenious experiments designed to study the bistable lac operon response when induced with lactose and the artificial non-metabolizable inducer thiomethylgalactoside (TMG). Ozbudak et al. incorporated a single copy of the green fluorescent protein gene (gfp) under the control of the lac promoter into the chromosome of E. coli. The cells also contained a plasmid encoding a red fluorescent reporter (HcRed) under the control of the galactitol (gat) promoter. This promoter includes a CRP-binding site, as well as a binding site for the galactitol repressor GatR. However, GatR is absent in E. coli. Therefore, transcription at the gat promoter, measured by red fluorescence, is a direct measure of CRP-cAMP levels. They further measured the response of single cells, initially in a given state of lac expression, to exposure to various combinations of glucose and TMG levels.

Ozbudak et al. report that, for a given concentration of extracellular glucose, the lac operon is uninduced at low TMG concentrations and fully induced at high TMG concentrations regardless of the cell's history. Between these switching thresholds, however, the system response is hysteretic (history dependent). By measuring the fluorescence of single cells, Ozbudak et al. obtained bimodal distributions between the switching thresholds, confirming the existence of bistability. When the experiments were repeated with lactose, instead of TMG, no evidence of bistability was found. The results in this paper not only confirmed bistability in the lac operon when induced with TMG, but also provided new and novel quantitative data that raise questions that may be answered via a modelling approach.

4.2 A minimal model

A number of mathematical models have been developed to investigate the dynamic behaviour of the lac operon. In §4.3, the characteristics of some of these models will be analysed by contrasting them with the minimal model introduced below.

Let M, E and L, respectively, denote the intracellular concentrations of mRNA, LacZ polypeptide and lactose. The differential equations governing the dynamics of these variables are

The processes governing the dynamics of all the chemical species other than M, E and L are assumed to be fast enough to make quasi-steady state approximations to the corresponding dynamic equations.

Since half of the lactose taken up is directly metabolized into glucose and galactose by β-galactosidase, while the rest is turned into allolactose (which is also later metabolized into glucose and galactose), it can be assumed that the intracellular concentrations of lactose and allolactose are very similar (see Santillán et al. 2007 for more details).

The translation and degradation rates of genes lacZ and lacY are assumed to be identical. Thus since β-galactosidase (lac permease) is a tetramer (monomer), its concentration is assumed to be one-quarter of (equal to) E.

It is important to note that the published lac operon models differ in the way the function R(L,Ge) is formulated. In some cases, heuristic reasoning is used to propose Hill-type equations for R(L,Ge). Some other models take into account, with different levels of detail, the interactions between the mRNA polymerase and the repressor molecules with the DNA chain to model this function. We discuss these differences in our review of various models in §4.3.

4.3 Recent modelling approaches

Wong et al. (1997) developed a 13-dimensional model for the lac operon. Besides the structural genes' mRNA and the intracellular lactose concentrations, the variables they consider are repressor mRNA and protein concentrations β-galactosidase and permease concentrations (each governed by a different differential equation) the internal concentrations of allolactose, cAMP, glucose and phosphorylated glucose and the external concentrations of glucose and lactose. Their model includes catabolite repression, inducer exclusion, lactose hydrolysis to glucose and galactose, synthesis and degradation of allolactose, and a variable growth rate. Wong et al. employed their model to study the diauxic growth of E. coli on glucose and lactose. For this, they tested different models for catabolite repression and the phosphorylation of the glucose produced from lactose hydrolysis, and analysed the influence of the model parameters on the two diauxic phases. Besides being quite detailed, this model has the virtue that most of the parameters in it were estimated from experimental data. However, even though Wong et al. considered the existence of the three known operator sites, they ignored their cooperative behaviour and incorrectly assumed that a repressor bound to any operator inhibits transcription initiation. Furthermore, Wong et al. also took into account the effect of the CAP activator by assuming that it must be bound to its specific site in the DNA regulatory region in order for the polymerase to bind the promoter.

Vilar et al. (2003) introduced a simple model of the lac operon to illustrate the applicability and limitations of mathematical modelling of the dynamics of cellular networks. In particular, they study the lac operon induction dynamics and its relation to bistability. Vilar et al. aimed at integrating three different levels of description (molecular, cellular and that of cell population) into a single model, and used it to investigate the system dynamics when an artificial (non-metabolizable) inducer is employed to activate it. In contrast to the minimal model, that of Vilar et al. lumps (through a quasi-steady state assumption) the mRNA dynamics into the equations governing the corresponding protein concentrations. It further accounts for the LacZ and LacY dynamics by means of two differential equations, assumes that LacY can be in either a non-functional or a functional state and includes one more equation for this last chemical species. Finally, this model takes into account neither catabolite repression nor inducer exclusion and accounts for the repression mechanism by means of a Hill-type equation.

Yildirim & Mackey (2003) investigated the bistable behaviour of the lac operon. For this, they introduced a five-dimensional mathematical model. The model of Yildirim and Mackey accounts for the dynamics of β-galactosidase and lac permease by means of two different differential equations, as well as for the dynamics of intracellular lactose and allolactose. This model also takes into account the delays due to transcription and translation processes. The authors paid particular attention to the estimation of the parameters in the model. They further tested their model against two sets of β-galactosidase activity versus time data, and against a set of data on β-galactosidase activity during periodic phosphate feeding. Their analytical and numerical studies indicate that for physiologically realistic values of external lactose and the bacterial growth rate, a regime exists where there may be bistability, and that this corresponds to a cusp bifurcation in the model dynamics. Deficiencies of Yildirim & Mackey's model are that it does not take into account catabolite repression or the inducer exclusion regulatory mechanisms. Furthermore, though they built the repression regulatory function by taking into account the repressor–operator and the polymerase–promoter interactions, they ignored the existence of three operators and considered operator O1 only.

In a later paper, Yildirim et al. (2004) attempted to identify as the origin of bistability one of the mechanisms involved in the regulation of the lac operon. To do this, they simplified the model presented in Yildirim & Mackey (2003) by ignoring permease dynamics and assuming a constant permease concentration. They numerically and analytically analysed the steady states of the reduced model and showed that it may indeed display bistability, depending on the extracellular lactose concentration and growth rate.

Santillán & Mackey (2004) developed a mathematical model of the lac operon, which accounts for all of the known regulatory mechanisms, including catabolite repression and inducer exclusion (both of which depend on external glucose concentrations), as well as the time delays inherent to transcription and translation. With this model, they investigated the influence of catabolite repression and inducer exclusion on the bistable behaviour of the lac operon. The model of Santillán & Mackey is six dimensional and the free variables are the lacZ and lacY mRNA concentrations, the β-galactosidase and lac permease concentrations, and the allolactose and cAMP concentrations. It is important to note that Santillán & Mackey's model considers all three known operators and the cooperativity among them, and that all the parameters in it were estimated from experimental data. In particular, they used a thermodynamic approach to model the interactions between the CAP activator, the repressor and the polymerase with their respective binding sites along the DNA chain, as well as the cooperative behaviour of the three known operators.

Van Hoek & Hogeweg (2006) carried out in silico simulation of the lac operon evolution in bacterial populations. From their results, the parameters that control the expression of the lac operon genes evolve in such a way that the system avoids bistability with respect to lactose, but does exhibit bistability with respect to artificial inducers. Thus, they argue from their computational experiments that the wild-type lac operon, which regulates lactose metabolism, is not a bistable switch under natural conditions. The model used by van Hoek & Hogeweg contains 10 independent differential equations and is based on the model of Wong et al. (1997). This model takes into account all known regulatory mechanisms. However, rather than considering the chemical details, van Hoek & Hogeweg modelled the repressor–DNA and the CAP activator–DNA interactions by means of Hill-type equations.

In a later paper, van Hoek & Hogeweg (2007) modified the lac operon model in Van Hoek & Hogeweg (2006) to incorporate stochasticity and study its effects from an evolutionary point of view. Through a mutation-selection process, they evolved the shape of the promoter function, and thus the effective amount of stochasticity. Van Hoek and Hogeweg concluded from their results that noise values for lactose, the natural inducer, are much lower than those for artificial, non-metabolizable inducers, because these artificial inducers experience a stronger positive feedback. They further showed that a high repression rate and hence high stochasticity increase the delay in lactose uptake in a variable environment. From this, the authors concluded that the lac operon has evolved such that the impact of stochastic gene expression is minor in its natural environment, but happens to respond with much stronger stochasticity when confronted with artificial inducers.

Santillán et al. (2007) investigated the origin of bistability in the lac operon. For this, they developed a mathematical model for the regulatory pathway in this system and compared the model predictions with the experimental results of Ozbudak et al. (2004). Santillán et al. examined the effect of lactose metabolism using this model, and showed that it greatly modifies the bistable region in the external lactose versus external glucose parameter space. The model also predicts that lactose metabolism can cause bistability to disappear for very low external glucose concentrations. The authors further carried out stochastic numerical simulations for several levels of external glucose and lactose and concluded from their results that bistability can help guarantee that E. coli consumes glucose and lactose in the most efficient possible way. Namely, the lac operon is induced only when there is almost no glucose in the growing medium, but if the external lactose is high, the operon induction level increases abruptly when the levels of glucose in the environment decrease to very low values. Finally, they demonstrated that this behaviour could not be obtained without bistability if the stability of the induced and uninduced states is to be preserved.

In a continuation of the work in Santillán et al. (2007), Santillán (2008) improved the mathematical model to account, in a more detailed way, for the interaction of the repressor molecules with the three lac operators. Besides, Santillán includes in the model a recently discovered cooperative interaction between the CAP molecule (an activator of the lactose operon) and operator 3, which influences DNA folding. Finally, this new model also includes the growth rate dependence on bacterial energy input rate in the form of transported glucose molecules and of metabolized lactose molecules. A large number of numerical experiments were carried out with the improved model, and the results are discussed along the same lines as in Santillán et al. (2007), including a detailed examination of the effect of a variable growth rate on the system dynamics. The models in both Santillán et al. (2007) and Santillán (2008) have the same structure as the minimal model above. Furthermore, both models take into account the chemical details of the repressor–DNA and CAP activator–DNA interactions, as well as the cooperativity observed between repressor molecules bound to different operators.

The models here reviewed are summarized in table 1. All of them deal with the bistable behaviour of the lac operon. However, most of the ones published prior to Ozbudak et al. (2004) only consider the use of lactose as inducer, and they predict that the lac operon shows bistability for physiological lactose concentrations. In this sense, the experimental work of Ozbudak et al. provided new data and opened new questions suitable for a mathematical modelling approach. One of these questions is why bistability cannot be observed when the lac operon natural inducer is employed. The most recent quantitative approaches have made use of Ozbudak et al.'s results to develop more accurate models, and two different answers to the above question have been proposed. Van Hoek & Hogeweg (2006, 2007) argue that bistability disappears altogether due to bacteria evolutionary adaptation to a fluctuating environment of glucose and lactose, while Santillán et al. (2007) and Santillán (2008) assert that bistability does not disappear but becomes extremely hard to identify with the experimental setup of Ozbudak et al. They, furthermore, discuss its significance from an evolutionary perspective. New experiments are needed to resolve this discrepancy.

Table 1 Summary of the mathematical models of the lac operon that we have reviewed here. (The dimension number refers to the number of dependent variables. A model type can be either deterministic (D) or stochastic (S). Finally, the inducer column states whether model induction with lactose (L) or an artificial inducer (A) is taken into account).

Most of the models reviewed in this subsection involve ODEs. Given that chemical kinetics is the formalism behind ODE models, they are valid only when the molecule count (N) is such that is small enough. However, in the lac operon, the lacZ mRNA degradation rate is so high that the average number of mRNA molecules per bacterium is approximately 0.75, when the operon is fully induced (Santillán 2008). Furthermore, the lac repressor LacI is present in only approximately 10 tetramers per cell (Müller-Hill 1998). It follows from this that an essential aspect of modelling the lac operon is its stochastic nature. As seen in table 1, only the most recent models (Santillán et al. 2007 van Hoek & Hogeweg 2007 Santillán 2008) account for this inherent system stochasticity. Van Hoek & Hogeweg claim that noise has a large effect on the evolution of the lac operon: cells evolve such that noise has little effect on the system dynamical behaviour. By contrast, Santillán et al. do claim that noise has a large effect on the system dynamical behaviour. It is our belief that a huge amount of work remains to be done on this issue.

5. Conclusions

In this paper, we have presented a description of the regulatory mechanisms in the lac operon, taking into consideration the most recent discoveries. The system history has been surveyed as well, emphasizing the discovery of its main elements and the influence they have had on the development of molecular and systems biology. The operon bistable behaviour has also been analysed, including the discovery and origin of this complex phenomenon.

Multistability (of which bistability is the simplest example) corresponds to a true switch between alternate and coexisting steady states, and so allows a graded signal to be turned into a discontinuous evolution of the system along several different possible pathways. Multistability has certain unique properties not shared by other mechanisms of integrative control. These properties may play an essential role in the dynamics of living cells and organisms. Moreover, multistability has been invoked to explain catastrophic events in ecology (Rietkerk et al. 2004), mitogen-activated protein kinase (MAPK) cascades in animal cells (Ferrell & Machleder 1998 Bagowski & Ferrell 2001 Bhalla et al. 2002), cell cycle regulatory circuits in Xenopus and Saccharomyces cerevisiae (Cross et al. 2002 Pomerening et al. 2003), the generation of switch-like biochemical responses (Ferrell & Machleder 1998 Bagowski & Ferrell 2001 Bagowski et al. 2003), and the establishment of cell cycle oscillations and mutually exclusive cell cycle phases (Pomerening et al. 2003 Sha et al. 2003), among other biological phenomena.

Not only was the lac operon the first system in which bistability was discovered but, as the literature reviewed in this paper demonstrates, it has been and is still one of the ideal model systems to analyse this complex behaviour. According to the quantitative studies we have reviewed, the lac operon has helped to understand the origin, biological implications and subtleness of bistability it may also help to tackle similar questions in other systems and organisms. For this and other reasons not addressed in this paper, it is our opinion that the lactose operon may be as influential in the development of the nascent field of systems biology as it was in the development of molecular biology.

The different mathematical models of the lac operon here reviewed present a good example of what the philosophy of model making is and how mathematical models can influence the development of a given scientific discipline. To discuss this issue we make extensive use of the excellent essay by Rosenblueth & Wiener (1945), which we shall quote a number of times in the forthcoming paragraphs.

According to Rosenblueth and Wiener, models are a central necessity of scientific procedure because no substantial part of the universe is so simple that it can be grasped and controlled without abstraction, abstraction being replacing the part of the universe under consideration by a model of similar but simpler structure. Rosenblueth and Wiener further classify scientific models as either material or formal. In their view, a material model is the representation of a complex system by a system that is assumed simpler and is also assumed to have some properties similar to those selected for study in the original complex system. By contrast, a formal model is a symbolic assertion in logical terms of an idealized relatively simple situation sharing the structural properties of the original factual system. Here we are concerned with formal models of which the mathematical ones are a subset.

Closed boxes (in which a finite number of output variables are causally related to a finite number of input variables, without the knowledge of the detailed mechanisms inside the box) are often employed in formal models. Indeed, according to Rosenblueth and Wiener, all scientific problems begin as closed-box problems (i.e. only a few of the significant variables are recognized), and scientific progress consists of a progressive opening of those boxes. The successive addition of variables gradually leads to more elaborate theoretical models, hence to a hierarchy in these models, from relatively simple, highly abstract ones to more complex, more concrete theoretical structures. The setting up of a simple model for a closed box is based on the assumption that a number of variables are only loosely coupled with the rest of those belonging to the system. As the successive models become progressively more sophisticated, the number of closed regions usually increases, because the process may be compared to the subdivision of an original single box into several smaller shut compartments. Many of these small compartments may be deliberately left closed, because they are considered only functionally, but not structurally, important.

Early closed-box models, such as that of Griffith (1968), acknowledged that a gene subjected to positive feedback regulation can show bistability. However, since having positive feedback does not guarantee bistability, these models could not predict whether the lac operon would show this behaviour and, if so, what the responsible mechanisms are. More detailed models were needed to address these questions, and they have been developed as the necessary experimental information is available now. As foreseen by Rosenblueth and Wiener more than 60 years ago, these more detailed models are heterogeneous assemblies of elements, some treated in detail (that is, specifically or structurally) and some treated merely with respect to their overall performance (that is, generically or functionally). The models by Santillán et al. and van Hoek and Hogeweg are good examples. For instance, while the Santillán et al. models take into consideration the details of the polymerase–DNA, the repressor–DNA and the activator–DNA interactions, the models of van Hoek and Hogeweg lump them together into a closed box. On the other hand, van Hoek and Hogeweg model with more detail the dynamics of the lactose, allolactose, glucose, cAMP, and ATP intracellular concentrations, and this is reflected in the number of independent equations that the van Hoek and Hogeweg and the Santillán et al. models have. Finally, while van Hoek and Hogeweg use an evolutionary modelling approach to study bistability in the lac operon, Santillán et al. use a more static approach, trying to model the lac operon in full detail. To develop more elaborate models, more accurate quantitative data on the system components and their interactions are required. Ideally, a cycle of modelling and experimental efforts shall continue, with one of the outcomes being models progressively more sophisticated and capable of addressing more specific questions. However, there is no point in carrying this process out until its obvious limit. To explain this, we refer once more to Rosenblueth & Wiener (1945), who asserted that as a model becomes more detailed and accurate, it will tend to become identical with the original system. As a limit, it will become the system itself. The ideal model would then be one which agrees with the system in its full complexity and which leaves no closed boxes. However, any one capable of elaborating and comprehending such a model in its entirety would find it unnecessary, because he/she could then grasp the complete system directly as a whole.

We hope that readers of this paper will appreciate that mathematical modelling is a process that constantly evolves as the predictions of the models are iterated against laboratory data. The results of the past three decades in modelling the dynamics of the lac operon exemplify this. The reader will, no doubt, also realize that each model has its positive and negative aspects. The level of detail of the model depends on the availability and quality of the data and also on the questions we want to address. The more the detail, the more complicated the model will be. A mathematical analysis might then be hard to undertake and the conclusions may only be based on numerical experiments that many, including us, find less than satisfactory. On the other hand, a simple model may be easier to analyse and a mathematical analysis can give more insights into the dynamical properties or the underlying system but it may oversimplify and fail to capture some important features of the reality.

The issue of model complexity is intimately tied to the issue of the dimensionality of the parameter space, and this is tied directly to one of the quandaries that face every modeller. The more complex the model, the more parameters must be estimated. It is a virtual truism in mathematical biology that one is almost never able to obtain all of the parameters in a model from the same laboratory setting using the same procedures and techniques and subjects. So, as mathematical model construction is something of an art in itself, the same can be said for parameter estimation. The senior author (M.C.M.) with over 45 years of experience in mathematical biology suggests that the hardest part of the modelling exercise is obtaining decent parameter estimations.


Problem in understanding Operon - Biology

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Teaching the Big Ideas of Biology with Operon Models

1 Robert A. Cooper is a biology teacher at Pennsbury High School, Fairless Hills, PA 19030 e-mail: . [email protected]

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This paper presents an activity that engages students in model-based reasoning, requiring them to predict the behavior of the trp and lac operons under different environmental conditions. Students are presented six scenarios for the trp operon and five for the lac operon. In most of the scenarios, specific mutations have occurred in genetic elements of the system that alter the behavior from the norm. Students are also challenged to relate their understanding of operon behavior to the “Big Ideas” of homeostasis, evolution, information, interactions, and emergent properties. By using operons to teach students to reason with models of complex systems and understand broad themes, we equip them with powerful skills and ideas that form a solid foundation for their future learning in biology.


Computer Methods, Part C

Necmettin Yildirim , Caner Kazanci , in Methods in Enzymology , 2011

4 An Example: Lactose Operon in E. coli

We use the lactose operon (the lac operon) of E. coli and a modified version of the Yildirim–Mackey model ( Mackey et al., 2004 Yildirim and Mackey, 2003 Yildirim et al., 2004 ) developed for this bacterial regulatory circuit to demonstrate the methods and analysis described in previous sections. The lac operon is the classical example of an inducible circuit which encodes the genes for the transport of external lactose into the cell and its conversion to glucose and galactose. A cartoon that depicts the major components of this circuit is shown in Fig. 12.9 . The molecular mechanism of the lac operon works as follows: The lac operon has a small promoter/operator region (P and O) and three larger structural genes lacZ, lacY, and lacA. There is a regulatory gene lacI preceding the lac operon. lacI is responsible for producing a repressor (R ) protein. In the presence of allolactose , a binary complex is formed between allolactose and the repressor that makes binding of the repressor to the operator region impossible. In that case, the RNA polymerase bound to the promoter is able to initiate transcription of the structural genes to produce mRNA( M). However, in the absence of allolactose (A) the repressor protein R binds to the operator region O and prevents the RNA polymerase from transcribing the structural genes. Once the mRNA has been produced, the process of translation starts. The lacZ gene encodes the portion of the mRNA that is responsible for the production of β-galactosidase (B) and translation of the lacY gene produces the section of mRNA that is ultimately responsible for the production of an enzyme permease (P). The final portion of mRNA produced by transcription of the lacA gene encodes for the production of thiogalactoside transacetylase which is thought not to play a role in the regulation of the lac operon ( Beckwith, 1987 ). This positive control system works as follows: When there is no glucose available for cellular metabolism but if lactose (L) is available in a media, the lactose is transported into the cell by the permease. This intracellular lactose is then broken down into glucose, galactose, and allolactose by β-galactosidase. The allolactose is also converted to glucose and galactose by the same enzyme β-galactosidase. The allolactose feeds back to bind with the lactose repressor and enable the transcription process which completes the positive feedback loop.

Figure 12.9 . Schematic representation of the lactose operon regulatory system. See the text for details.

Yildirim et. al. ( Mackey et al., 2004 Yildirim and Mackey, 2003 ) devised a mathematical model which takes into account the dynamics of the permease, internal lactose, β-galactosidase, the allolactose interactions with the lac repressor, and mRNA. The final model consists of five nonlinear differential delay equations with delays due to the transcription and translation process. We modified this model in this study and eliminated the delay terms. This change reduced the original model to a five-dimensional system of ODEs. The equation of this model are given in Eqs. (12.25)–(12.29) . The estimated values for the model parameters from the published data are listed in Table 12.1 . The details on the development of this model and estimation of the parameters can be found in Mackey et al. (2004), Yildirim and Mackey (2003), Yildirim et al. (2004) ( Table 12.2 ).

Table 12.1 . The model parameters estimated from experimental data (from Yildirim and Mackey, 2003 )

n2μmax3.47 × 10 − 2 min − 1
γM0.411 min − 1 γB8.33 × 10 − 4 min − 1
γA0.52 min − 1 Γ07.25 × 10 − 7 mM/min
K7200αM9.97 × 10 − 4 mM/min
KL11.81 mMαA1.76 × 10 4 min − 1
KA1.95 mMαB1.66 × 10 − 2 min − 1
γL0.0 min − 1 βA2.15 × 10 4 min − 1
αL2880 min − 1 KL9.7 × 10 − 4 M
KLe0.26 mMγP0.65 min − 1
βL21.76 × 10 4 min − 1 αP10.0 min − 1
K12.52 × 10 − 2 (μM) − 2 βL12.65 × 10 3 min − 1
KL29.7 × 10 − 4 M

Table 12.2 . The equations describing the evolution of the variables M, B, L, A, and P in the Yildirim–Mackey model for the lac operon


Watch the video: Gene Regulation and the Order of the Operon (July 2022).


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