What is the meaning and significance of extreme pathways

What is the meaning and significance of extreme pathways

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Can someone please explain me what extreme pathways are? I found this definition in this article:

Extreme pathways are a unique and minimal set of vectors that completely characterize the steady-state capabilities of genome-scale metabolic networks.

Now, frankly speaking, I did not understand the head or tail of this definition? What is steady state? What does it mean by steady state capabilities? Can someone please explain me in a simpler way? PS: I am a computer Science student

For any dynamic system defined by different components, the steady state is the state of the system in which the components remain constant over time. If you consider the example of growth (by cell division) the point at which the total number of cells remain constant would be the steady state. This is a point at which birth rate = death rate. Similarly for a multi-component system such as a gene and its activator, the steady state would be the point where the mRNAs and the proteins of the gene and its activator are constant. If only few components are constant then the system is said to be in a quasi-steady state.

A point to be noted that in chemical (or biochemical) systems steady state, as a term, is different from equilibrium (in physics these terms are used interchangeably). Equilibrium is a condition when, for a single reversible reaction, the forward rate = backward rate.

In mathematical terms steady state is a point where the rate of change of components = 0. In an ordinary differential equations based model:

$$frac{dar{X}}{dt}=0 $$ where $ar{X}$ is a vector in which each element is a component of the system. In case of the transcription example, $X(1),X(2)… $ would be mRNA, protein, activator mRNA and so on. In other words $dfrac{dX(i)}{dt}=0$ for all $i$.

Steady state capabilities should mean the properties of the system at its steady state.

The kind of study described in the question is called metabolic flux balance analysis in which different metabolic reactions are described in the form of linear equations represented by $Sv=0$ where $v$ is the vector of all fluxes (metabolic reaction rates) $S$ is the stoichiometry matrix (which has the stoichiometry of all components in different metabolic reactions). The RHS is zero because we are evaluating the system at its steady state i.e. we are interested in finding out the condition in which the net metabolic reaction flux is 0. In other words all metabolic reactions, balance each other.

You need to read more about this. There are a lot of books on this topic. You can start with this review.

In flux balance analysis, the linear equations are overdetermined i.e. there are many solutions. People generally use linear programming (simplex algorithm) to find optimal solutions. In the space of the optimal solutions, the vertices represent extreme reactions. The entire optimal solution space can be described as a linear combination of these extreme reactions.

Schematic representation of a convex cone characterized by five extreme pathways. Extreme Pathways 1-5 (EP1, EP2, EP3, EP4, and EP5) circumscribe the solution space for the three fluxes indicated (vA, vB, vC). EP4 lies in the plane formed by fluxes vA and vB. Consequently, flux vC does not participate in that extreme pathway. EP3, EP4, and EP5 are all close and represent different uses of a network to achieve a similar overall result. All points within the convex cone can be described as a non-negative linear combination of the extreme pathways [1].

Extreme pathway analysis reveals the organizing rules of metabolic regulation

Affiliations Shanghai Key Lab of Intelligent Information Processing, Fudan University, Shanghai, China, School of Computer Science and Technology, Fudan University, Shanghai, China, Shanghai Ji Ai Genetics & IVF Institute, Obstetrics and Gynecology Hospital of Fudan University, Shanghai, China

Roles Conceptualization, Supervision, Validation, Writing – review & editing

Affiliations Shanghai Key Lab of Intelligent Information Processing, Fudan University, Shanghai, China, School of Computer Science and Technology, Fudan University, Shanghai, China


Genome-scale metabolic networks can be characterized by a set of systemically independent and unique extreme pathways. These extreme pathways span a convex, high-dimensional space that circumscribes all potential steady-state flux distributions achievable by the defined metabolic network. Genome-scale extreme pathways associated with the production of non-essential amino acids in Haemophilus influenzae were computed. They offer valuable insight into the functioning of its metabolic network. Three key results were obtained. First, there were multiple internal flux maps corresponding to externally indistinguishable states. It was shown that there was an average of 37 internal states per unique exchange flux vector in H. influenzae when the network was used to produce a single amino acid while allowing carbon dioxide and acetate as carbon sinks. With the inclusion of succinate as an additional output, this ratio increased to 52, a 40% increase. Second, an analysis of the carbon fates illustrated that the extreme pathways were non-uniformly distributed across the carbon fate spectrum. In the detailed case study, 45% of the distinct carbon fate values associated with lysine production represented 85% of the extreme pathways. Third, this distribution fell between distinct systemic constraints. For lysine production, the carbon fate values that represented 85% of the pathways described above corresponded to only 2 distinct ratios of 1:1 and 4:1 between carbon dioxide and acetate. The present study analysed single outputs from one organism, and provides a start to genome-scale extreme pathways studies. These emergent system-level characterizations show the significance of metabolic extreme pathway analysis at the genome-scale.

These authors contributed equally to this work.

Author to whom correspondence should be addressed. E-mail: [email protected]

Absolute vs Relative Refractory Period

With the above information, it is now possible to understand the difference between the absolute refractory period and relative refractory period. In terms of an action potential, refractory periods prevent the overlapping of stimuli.

In theory, each action potential requires around one millisecond to be transmitted. This means we could expect a single axon to forward at least one thousand action potentials every second in reality, this number is much lower. The absolute refractory period lasts for approximately one millisecond the relative refractory period takes approximately two milliseconds.

Multiple action potentials do not occur in the same neuron at exactly the same time. This is because a neuron experiences two different situations in which it is either impossible or difficult to initiate a second action potential. These two situations describe the two types of refractory periods.

During the depolarization phase when Na + ion channels are open, no subsequent stimulus can create a further effect. An ion channel does not open by degrees – it is either open or closed. This is the absolute refractory period (ARP) of an action potential. A second action potential ‘absolutely’ cannot occur at this time. Only after the Na + ion channels in this part of the membrane have closed can they react to a second stimulus.

The relative refractory period (RRP) occurs during the hyperpolarization phase. The neuron membrane is more negatively-charged than when at resting state K + ion channels are only just starting to close. However, all sodium ion channels are closed so it is – in principle – possible to initiate a second action potential. This requires a stronger stimulus as the intracellular space is more negatively charged. To excite a neuron by reaching the threshold level of – 55 mV, a greater stimulus is required. It is, therefore, ‘relatively’ difficult but not impossible to start up a second action potential during the relative refractory period.

The relative refractory period is extremely important in terms of stimulus strength. The rate at which a neuron transmits action potentials decides how important that stimulus is. There is no such thing as a weak or strong action potential as all require the same level of electrical or chemical stimulus to occur. Either threshold level is achieved and the neuron fires, or it does not.

It is the firing rate not the firing strength that causes different effects. For example, in low light levels, cells in the retina of the eye transmit fewer action potentials than in the presence of bright light. We see much better when light levels are high because more information is passed from the retina to the brain in a short time.

IV. Controlling the Family-Wise Error Rate (FWER)

Definition The family-wise error rate (FWER) is the probability of at least one (1 or more) type I error

The Bonferroni Correction

The most intuitive way to control for the FWER is to make the significance level lower as the number of tests increase. Ensuring that the FWER is maintained at across independent tests

is achieved by setting the significance level to .

Fix the significance level at . Suppose that each independent test generates a p-value and define

Caveats, concerns, and objections

The Bonferroni correction is a very strict form of type I error control in the sense that it controls for the probability of even a single erroneous rejection of the null hypothesis (i.e. ). One practical argument against this form of correction is that it is overly conservative and impinges upon statistical power (Whitley 2002b).

Definition The statistical power of a test is the probability of rejecting a null hypothesis when the alternative is true

Indeed our discussion above would indicate that large-scale experiments are exploratory in nature and that we should be assured that testing errors are of minor consequence. We could accept more potential errors as a reasonable trade-off for identifying more significant genes. There are many other arguments made over the past few decades against using such control procedures, some of which border on the philosophical (Goodman 1998, Savitz 1995). Some even have gone as far as to call for the abandonment of correction procedures altogether (Rothman 1990). At least two arguments are relevant to the context of multiple testing involving large-scale experimental data.

1. The composite “universal” null hypothesis is irrelevant

The origin of the Bonferroni correction is predicated on the universal hypothesis that only purely random processes govern all the variability of all the observations in hand. The omnibus alternative hypothesis is that some associations are present in the data. Rejection of the null hypothesis amounts to a statement merely that at least one of the assumptions underlying the null hypothesis is invalid, however, it does not specify exactly what aspect.

Concretely, testing a multitude of genes for differential expression in treatment and control cells on a microarray could be grounds for Bonferroni correction. However, rejecting the composite null hypothesis that purely random processes governs expression of all genes represented on the array is not very interesting. Rather, researchers are more interested in which genes or subsets demonstrate these non-random expression patterns following treatment.

2. Penalty for peeking and ‘p hacking’

This argument boils down to the argument: Why should one independent test result impact the outcome of another?

Imagine a situation in which 20 tests are performed using the Bonferroni correction with and each one is deemed ‘significant’ with each having . For fun, we perform 80 more tests with the same p-value, but now none are significant since now our . This disturbing result is referred to as the ‘penalty for peeking’.

Alternatively, ‘p-hacking’ is the process of creatively organizing data sets in such a fashion such that the p-values remain below the significance threshold. For example, imagine we perform 100 tests and each results in a . A Bonferroni-adjusted significance level is meaning none of the latter results are deemed significant. Suppose that we break these 100 tests into 5 groups of 20 and publish each group separately. In this case the significance level is and in all cases the tests are significant.

What Is the Importance of Biology?

Biology is important because it allows people to understand the diversity of life forms and their conservation and exploitation. Through various biological disciplines, people obtain knowledge about life and living organisms, including the origin, growth, evolution, structure, distribution and function of these organisms.

Biology implies an essential responsibility for the welfare and protection of all living species. It studies all living beings and how organisms interact in the biosphere. This is essential because it enables people to know the behavior and functions of each population that interacts with individuals from other populations or communities. Biologists discover how the specific aspects of the biosphere affect and benefit from the behaviors of a particular population.

Biology also studies the origin of diseases and plagues, such as infections, pathologies of animals and damage to plants and trees. Biology encompasses the study of the functions of living beings, enhancement of useful species, factors that cause illnesses, discovery and production of medicines and sustainable use of natural resources. Through biotechnology, biologists find efficient ways to produce food and other supplies for people. They investigate the processes involved in producing various nutritional substances.

Furthermore, biologists investigate environmental factors surrounding living beings and seek effective methods to grasp the variations of the environment that threaten the existence of living organisms on Earth.

The Difference Between Apoplast and Symplast

Apoplast refers to the non protoplasmic components of a plant, including the cell wall and the intracellular spaces.

Symplast refers to the continuous arrangement of protoplasts of a plant, which are interconnected by plasmodesmata.

Apoplast consists of non protoplasmic parts such as cell wall and intracellular space.

Symplast Consists of protoplast

Apoplast composed of nonliving parts of a plant.

Symplast composed of living parts of a plant.

In apoplast, the water movement occurs by passive diffusion.

In symplast, the water movement occurs by osmosis.

In apoplast, the water movement is rapid.

In the symplast, the water movement is slower.

The metabolic rate of the cells in the root cortex does not affect the water movement.

The metabolic rate of the cells in the root cortex highly affects the water movement.

It shows less resistance to the water movement.

It shows some resistance to the water movement.

With the secondary growth of the root, most of the water moves by the apoplast route.

Beyond the cortex, water moves through the symplast route.

Similarities Between Apoplast and Symplast:

Apoplast and symplast are two ways in which the water moves from root hair cells to the xylem.

Both the apoplast and symplast occur in the root cortex.

Both the apoplast and symplast carry water and nutrients towards the xylem.

Pathways For Root Absorption Through Apoplast:

The apoplastic pathway provides a way towards the vascular cell through free spaces and cell walls of the epidermis and cortex. An additional apoplastic route that allows the direct access to the xylem and phloem is along the margins of the secondary roots. The secondary root is developed from the pericycle, a cell layer just inside the endodermis. The endodermis is characterized by the Casparian strip. Apoplast was previously defined as the whole thing but the symplast, consisting of cell walls and spaces between cells in which water and solutes can move freely.


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What is the meaning and significance of extreme pathways - Biology

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Materials and methods

DNA microarray data

The nine data sets used to compare the gene-set activation metrics were selected from eight studies in the GEO database. Each data set contained two relatively homogeneous subsets of samples. One study (GDS1329) provided two data sets. These subsets consisted of a baseline type and pathological samples or, in some cases, two different but related disease types. (Samples not in either subset were omitted from the comparisons.) We treated these single-channel data sets as ratio data sets by computing the median for each gene over all the baseline samples and dividing all expression values by the corresponding median and taking the base-10 logarithm. For each data set, Table 1 contains the GEO identifier and nature and sizes (in parentheses) of the two sample subgroups. In each data set the samples in Subgroup 1 constitute the baseline set.

To create the human body atlas, oligonucleotide probes were placed at each exon-exon junction of 11,138 RefSeq transcripts [35]. Purchased mRNA from 44 tissues in normal physiological state, pooled from multiple individuals, and 8 cell lines were amplified and labeled using a full-length amplification protocol and hybridized in duplicate in a two-color dye swap experiment[54]. In Johnson et al. [35], six of 52 tissues contained data for only 80% of the genes. For five of these tissues (pancreas, kidney, Burkitt's lymphoma (Raji), lung carcinoma (A549), and melanoma (G361)), new hybridizations were performed here to fill in the missing data. After background normalization, the intensity value of each probe in each tissue was divided by the average intensity across all 52 tissues to determine a ratio, and then the log10 of that ratio used for further analysis. Standard deviations (SDs) for each intensity measurement were calculated using the equation:

SD = a + b ∗ i n t e n s i t y [email protected]@[email protected]@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8tuQ8FMI8Gi=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciGacaGaaeqabaqadeqadaaakeaacaqGtbGaaeiraiabg2da9maakaaabaGaamyyaiabgUcaRiaadkgacqGHxiIkieGacaWFPbG[email protected][email protected]

where a = 100 and b = 0.2 were empirically derived from individual same-versus-same and same-versus-different hybridization experiments and represent single-hybridization, single-probe estimates of background (a) and fractional error (b). As we used multiple probes per gene and two hybridizations per sample pair (a dye-swap), final error estimates for gene expression are a combination of both propagation of this model measurement error and variance over the repeat measurements. These error estimates were then propagated to ratio and log10 ratio error estimates (Supplemental Tables T10 and T11 in Additional data file 2). Since the initial array design, NCBI has removed over 300 of the RefSeq transcripts from their databases. After removing these transcripts and any other transcripts currently unmapped to Entrez gene identifiers from our data set, the remaining 10,815 RefSeq transcripts map to 9,982 genes. Finally, using all gene-associated probes, we calculated an error-weighted average of log10 ratios for each gene in each tissue. Probe-level expression data have been deposited in the GEO database [35] (GSE740), and all gene and pathway expression data are available online [21].

Gene sets and coherence filtering

We compiled 1,281 gene sets from the 1 November 2004 Release of GO (241 from cellular component and 1,040 from biological process), and 117 gene sets from KEGG Release 33, downloaded 11 January 2005. The mean number of genes in each set was 23.8 ± 28.5 (mean ± SD minimum 1, maximum 159). To build the human pathway expression map we reduced these to 290 gene sets (23 from KEGG, 89 from the GO Cellular Component hierarchy, and 178 from the GO Biological Process hierarchy) by applying two filters. First, we required that each gene set retained contain at least five genes and no more than 200 genes. Second, we filtered gene sets based on their coherence, the percentage of total variance of the expression values within a gene set captured by the first principal component across all tissues. This idea has been discussed previously [20], although we used a different test for coherence here. To determine the appropriate cutoff for a gene set of size |S|, we generated 1,000 random gene sets of size |S|, and calculated the distribution of coherence values. The random-set coherence distribution was approximately normal, although its mean and standard deviation were size-dependent. Of the initial 1,401 gene sets, 290 had a coherence over the human body atlas data set that was more than 2.6 standard deviations greater than the mean of the random-set distribution for that size (corresponding to a one-sided p value of 0.005), and these 290 sets were retained for further analysis. The mean number of genes in these 290 coherent gene sets was 33.8 ± 32.9 (mean ± SD minimum 5, maximum 159).

Some of the 290 gene sets overlap in component genes, and some gene sets are subsets of others. This is due to the hierarchical nature of GO and functional overlap with gene sets in KEGG. Rather than merge these sets we kept them all in order to maximize the functional annotation conveyed by the gene set names. To measure the overlap between two gene sets we used the average of the two ratios of the number of genes in the intersection of the two gene sets to the total number of genes in each gene set. The overlap is most significant between gene sets in the same block ranging from a low of 7% in the Cell-selective block to a high of 85% in the Hemoglobin block with a mean within-block overlap over all 14 blocks of 31%.

Measuring gene set expression

We compared five gene-set activation metrics. Given a gene g, let X tgbe the expression value (log10 fold change, relative to background) for gene g in tissue t. Let S be the set of genes in a pathway. For tissue t, if <X tS> and <X t> are the mean of X tgover the genes in S and all the genes on the microarray, respectively, and σ tis the standard deviation of X tgover all the genes on the microarray, then the Z-score activation metric used to measure the relative expression level of pathway S in tissue t is:

Z t S = < X t S > − < X t > σ t | S | [email protected]@[email protected]@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8tuQ8FMI8Gi=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciGacaGaaeqabaqadeqadaaakeaacaWGAbWaaSbaaSqaaiaadshacaWGtbaabeaakiabg2da9maalaaabaGaeyipaWJaamiwamaaBaaaleaacaWG0bGaam4uaaqabaGccqGH+aGpcqGHsislcqGH8aapcaWGybWaaSbaaSqaaiaadshaaeqaaOGaeyOpa4dabaGaeq4Wdm3aaSbaaSqaaiaad[email protected][email protected]

where |S| is the number of genes in S. The value of Z is expressed in units of standard deviation and is a measure of violation of the null hypothesis that the genes in S are independently sampled from a distribution similar to that of all the genes on the microarray. If the null hypothesis is valid, then Z will have approximately a standard normal distribution, and so a large positive value of Z tsuggests collective upregulation of the genes in S (which we consider to represent 'activation' of S) in tissue t a large negative value suggests collective downregulation. The normalization by | S | [email protected]@[email protected]@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8tuQ8FMI8Gi=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciGacaGaaeqabaqa[email protected][email protected] makes comparison of different-sized gene sets possible and reflects the fact that, for larger gene sets, even a slight collective shift in fold change can be significant.

Because the Z-statistic essentially measures a shift in location (mean expression) for the genes in S, we compared its sensitivity to several other possible signed measures of location shift, which were created by modifying, where necessary, standard statistics with a sign to indicate the direction of expression change. The Wilcoxon Z statistic is a well-known statistic that is calculated according to a similar formula, but using the ranks of the X tgamong all genes in tissue t, rather than the actual fold changes. To calculate a signed KS statistic, we computed each of the two one-sided KS statistics, comparing the distribution of the expression values in S with the distribution of the genes on the microarray as a whole, and took the larger of the two statistics, with the appropriate sign. To calculate a hypergeometric p value, we used a threshold of two-fold differential expression (other threshold values showed qualitatively similar results, data not shown) to define an induced or repressed gene, and then calculated the probability that the relative enrichment of differentially expressed genes observed in a gene set in a particular tissue could have been observed by chance, using the hypergeometric distribution. To provide a sign for the hypergeometric p value, the calculation was done separately for the induced and repressed genes in each set, and the smaller of the two p value was used, as well as its 'sign' (negative if repressed genes were more enriched in the gene set than induced genes, positive otherwise). The relative insensitivity of the HG metric was little changed by varying the differential expression threshold. Finally, for the PCA statistic, we calculated PC1, the first principal component of the expression values of the genes in S across all tissues, and used the projection (scalar product) of the expression values in a tissue with PC1 as a measure of activation of the gene set in that tissue.

ROC comparison of activation metrics

We compared the five activation metrics for measuring gene set expression, and the individual genes in the expression data set, for their detection sensitivity. We applied each metric to measure the activation of the gene sets that met a coherence threshold (p ≤ 0.01, 0.05, 0.10, and 1.0) in each of the nine GEO data sets. For each data set we compared two classes that were known to be different (typically one class was normal and the other pathological). Each gene set was measured in each sample in each of the two classes by each metric. We used a two-sided Wilcoxon rank sum test for equal medians to test the null hypothesis that the activation metric values for each gene set in the two classes come from distributions with equal medians. The result of this test is quantified by the returned p value. The smaller the p value, the more unlikely is the null hypothesis that the gene set median values are equal. We performed this test between the two classes for all gene sets. In a similar manner, we used the same test to compare individual gene expression values between the two classes. We used the p value from the two-sided Wilcoxon rank sum statistic to compute a false detection rate for each p value threshold using the adaptive method of Benjamini and Hochberg [55] and displayed the results using ROC curves [56]. The x-axis is the proportion of false positives the percent of gene sets that did not distinguish the two classes at the specified p value threshold. The y-axis is the true positive rate the percent of gene sets that did distinguish the two classes at the specified threshold. The interval of [0, 0.3] was chosen to correspond to what might be an acceptable FDR. The percent of true positives varies between data sets and is presumably indicative of the type(s) of biological differences between the two classes in each data set.

Watch the video: PathWhiz Tutorial: An Introduction to Pathways (September 2022).