A stochastic analysis of first-order reaction networks

A stochastic model for a general system of first-order reactions in which each reaction may be either a conversion reaction or a catalytic reaction is derived. The governing master equation is formulated in a manner that explicitly separates the effects of network topology from other aspects, and the evolution equations for the first two moments are derived. We find the surprising, and apparently unknown, result that the time evolution of the second moments can be represented explicitly in terms of the eigenvalues and projections of the matrix that governs the evolution of the means. The model is used to analyze the effects of network topology and the reaction type on the moments of the probability distribution. In particular, it is shown that for an open system of first-order conversion reactions, the distribution of all the system components is a Poisson distribution at steady state. Two different measures of the noise have been used previously, and it is shown that different qualitative and quantitative conclusions can result, depending on which measure is used. The effect of catalytic reactions on the variance of the system components is also analyzed, and the master equation for a coupled system of first-order reactions and diffusion is derived.

Short- and long-range effects of Sonic hedgehog in limb development

The secreted protein Sonic hedgehog (Shh) and its transmembrane receptor Patched (Ptc) control a major signal transduction pathway in early vertebrate limb development. Ligand-free Ptc interacts with the transmembrane protein Smoothened (Smo) and blocks expression of Smo-controlled genes including ptc. Ligand-bound Ptc removes the block and leads to further expression of ptc, which in turn restricts the range of Shh transport. Currently it is not certain that Shh functions as a morphogen on the 300-microm scale of early chick limb development, because it has been difficult to determine how far different forms of Shh are transported. We develop a model to study the effects of two forms of Shh used experimentally and propose a mechanism for Shh signal transduction based on a two-state model for the Ptc-Smo interaction. Recent bead- and tissue-implant experiments can be explained by using this model without postulating different diffusivities for the two forms of Shh; a difference in other parameters such as the rate of release of Shh from the bead or transplant can explain the results equally well. The model also predicts that lower concentrations of Shh in a bead will produce a response similar to that after a tissue transplant. Our results provide an explanation for the counterintuitive experimental results and show that the same signal transduction mechanism can explain both short- and long-range Shh signaling. We conclude that Shh can function as a long-range morphogen.

A diffusion–reaction model for DNA microarray assays

DNA microarrays are extensively used for the quantification of the degree of differential mRNA expression. The assay involves hybridization of mobile DNA strands with immobilized complementary DNA strands to form duplexes. The overall duplex formation rate depends on the rate of transport of strands in solution to the corresponding spot on the surface, and the rate of the hybridization reaction. We present a theoretical model that incorporates both kinetics of the reversible hybridization reaction and diffusional transport of the labeled strands, and analyze DNA microarray hybridization using this model. Simulations are carried out in a geometrically realistic domain for labeled DNA concentrations corresponding to rare and abundant transcripts for typical assay conditions. The rate of strand diffusion in solution is shown to strongly affect the overall hybridization rate. We compute the minimum inter-spot spacing for replicate spots to enhance sensitivity. We also determine the hybridization time for which reliable estimates of the relative mRNA abundance of two species can be obtained using total fluorescence intensities. An analytical solution for the concentration distribution of mobile strands at intermediate hybridization times provides a convenient tool to calculate the mobile strand concentration profiles. This model provides a framework for the process analysis of all microarray assays currently used for genomic transcriptional analysis.

Web-gLV: A Web Based Platform for Lotka-Volterra Based Modeling and Simulation of Microbial Populations

The affordability of high throughput DNA sequencing has allowed us to explore the dynamics of microbial populations in various ecosystems. Mathematical modeling and simulation of such microbiome time series data can help in getting better understanding of bacterial communities. In this paper, we present Web-gLV-a GUI based interactive platform for generalized Lotka-Volterra (gLV) based modeling and simulation of microbial populations. The tool can be used to generate the mathematical models with automatic estimation of parameters and use them to predict future trajectories using numerical simulations. We also demonstrate the utility of our tool on few publicly available datasets. The case studies demonstrate the ease with which the current tool can be used by biologists to model bacterial populations and simulate their dynamics to get biological insights. We expect Web-gLV to be a valuable contribution in the field of ecological modeling and metagenomic systems biology.

An analysis of the use of genomic DNA as a universal reference in two channel DNA microarrays

Background

DNA microarray is an invaluable tool for gene expression explorations. In the two-dye microarray, fluorescence intensities of two samples, each labeled with a different dye, are compared after hybridization. To compare a large number of samples, the 'reference design' is widely used, in which all RNA samples are hybridized to a common reference. Genomic DNA is an attractive candidate for use as a universal reference, especially for bacterial systems with a low percentage of non-coding sequences. However, genomic DNA, comprising of both the sense and anti-sense strands, is unlike the single stranded cDNA usually used in microarray hybridizations. The presence of the antisense strand in the 'reference' leads to reactions between complementary labeled strands in solution and may cause the assay result to deviate from true values.

Results

We have developed a mathematical model to predict the validity of using genomic DNA as a reference in the microarray assay. The model predicts that the assay can accurately estimate relative concentrations for a wide range of initial cDNA concentrations. Experimental results of DNA microarray assay using genomic DNA as a reference correlated well to those obtained by a direct hybridization between two cDNA samples. The model predicts that the initial concentrations of labeled genomic DNA strands and immobilized strands, and the hybridization time do not significantly affect the assay performance. At low values of the rate constant for hybridization between immobilized and mobile strands, the assay performance varies with the hybridization time and initial cDNA concentrations. For the case where a microarray with immobilized single strands is used, results from hybridizations using genomic DNA as a reference will correspond to true ratios under all conditions.

Conclusion

Simulation using the mathematical model, and the experimental study presented here show the potential utility of microarray assays using genomic DNA as a reference. We conclude that the use of genomic DNA as reference DNA should greatly facilitate comparative transcriptome analysis.

Clathrin-Mediated Endocytosis Regulates a Balance between Opposing Signals to Maintain the Pluripotent State of Embryonic Stem Cells

Endocytosis is implicated in the maintenance of embryonic stem cell (ESC) pluripotency, although its exact role and the identity of molecular players remain poorly understood. Here, we show that the clathrin heavy chain (CLTC), involved in clathrin-mediated endocytosis (CME), is vital for maintaining mouse ESC (mESC) pluripotency. Knockdown of Cltc resulted in a loss of pluripotency accompanied by reduced E-cadherin (E-CAD) levels and increased levels of transforming growth factor β (TGF-β) and extracellular signal-regulated kinase (ERK) signaling. We demonstrate that both E-CAD and TGF-β receptor type 1 (TGF-βR1) are internalized through CME in mESCs. While E-CAD is recycled, TGF-βR1 is targeted for lysosomal degradation thus maintaining inverse levels of these molecules. Finally, we show that E-CAD interacts with ERK, and that the decreased pluripotency upon CME loss can be rescued by inhibiting TGF-βR, MEK, and GSK3β, or overexpressing E-CAD. Our results demonstrate that CME is critical for balancing signaling outputs to regulate ESC pluripotency, and possibly cell fate choices in early development.

•

Knockdown of Cltc results in loss of mESC pluripotency

•

CME regulates E-CAD and TGF-βR1 trafficking in mESCs

•

ESCs lacking CME can be rescued by TGF-βR1/MEK inhibition or E-CAD overexpression

•

CME balances opposing signaling outputs to maintain ESC pluripotency

A systems view of the protein expression process

Many biological processes are regulated by changing the concentration and activity of proteins. The presence of a protein at a given subcellular location at a given time with a certain conformation is the result of an apparently sequential process. The rate of protein formation is influenced by chromatin state, and the rates of transcription, translation, and degradation. There is an exquisite control system where each stage of the process is controlled both by seemingly unregulated proteins as well as through feedbacks mediated by RNA and protein products. Here we review the biological facts and mathematical models for each stage of the protein production process. We conclude that advances in experimental techniques leading to a detailed description of the process have not been matched by mathematical models that represent the details of the process and facilitate analysis. Such an exercise is the first step towards development of a framework for a systems biology analysis of the protein production process.

ELECTRONIC SUPPLEMENTARY MATERIAL

The online version of this article (doi:10.1007/s11693-011-9088-1) contains supplementary material, which is available to authorized users.

Temporal analysis of melanogenesis identifies fatty acid metabolism as key skin pigment regulator

Therapeutic methods to modulate skin pigmentation has important implications for skin cancer prevention and for treating cutaneous hyperpigmentary conditions. Towards defining new potential targets, we followed temporal dynamics of melanogenesis using a cell-autonomous pigmentation model. Our study elucidates 3 dominant phases of synchronized metabolic and transcriptional reprogramming. The melanogenic trigger is associated with high MITF levels along with rapid uptake of glucose. The transition to pigmented state is accompanied by increased glucose channelisation to anabolic pathways that support melanosome biogenesis. SREBF1-mediated up-regulation of fatty acid synthesis results in a transient accumulation of lipid droplets and enhancement of fatty acids oxidation through mitochondrial respiration. While this heightened bioenergetic activity is important to sustain melanogenesis, it impairs mitochondria lately, shifting the metabolism towards glycolysis. This recovery phase is accompanied by activation of the NRF2 detoxication pathway. Finally, we show that inhibitors of lipid metabolism can resolve hyperpigmentary conditions in a guinea pig UV-tanning model. Our study reveals rewiring of the metabolic circuit during melanogenesis, and fatty acid metabolism as a potential therapeutic target in a variety of cutaneous diseases manifesting hyperpigmentary phenotype.

Temporal analysis of melanogenesis, based on transcriptomic and metabolomic signatures, reveals fatty acid metabolism as a crucial mediator of the transition between pigmentation phases. Inhibitors of the fatty acid pathway could represent a new target for modulating pigmentation.

A mathematical model for suppression subtractive hybridization

Suppression subtractive hybridization (SSH) is frequently used to unearth differentially expressed genes on a whole-genome scale. Its versatility is based on combining cDNA library subtraction and normalization, which allows the isolation of sequences of varying degrees of abundance and differential expression. SSH is a complex process with many adjustable parameters that affect the outcome of gene isolation.We present a mathematical model of SSH based on DNA hybridization kinetics for assessing the effect of various parameters to facilitate its optimization. We derive an equation for the probability that a particular differentially expressed species is successfully isolated and use this to quantify the effect of the following parameters related to the cDNA sample: (a) mRNA abundance; (b) partial sequence complementarity to other species; and (3) degree of differential expression. We also evaluate the effect of parameters related to the process, including: (a) reaction times; and (b) extent of driver excess used in the two hybridization reactions. The optimum set of process parameters for successful isolation of differentially expressed species depends on transcript abundance. We show that the reaction conditions have a significant effect on the occurrence of false-positives and formulate strategies to isolate specific subsets of differentially expressed genes. We also quantify the effect of non-specific hybridization on the false-positive results and present strategies for spiking cDNA sequences to address this problem.

Robustness of the Drosophila segment polarity network to transient perturbations

Continuous and Boolean models for the Drosophila segment polarity network have shown that the system is able to maintain the wild-type pattern when subjected to sustained changes in the interaction parameters and initial conditions. Embryo development is likely to occur under fluctuating environmental conditions. Here, a well-established Boolean model is used to explore the ability of the segment polarity network to resist transient changes. Paths along which alternate unviable states are reached, and hence critical nodes whose state changes lead the system away from the wild-type state, are identified. It is found that the system appears to be more sensitive to changes that involve activation of normally inactive nodes. Through a simulation of the heat shock response, it is shown how a localised perturbation in one parasegment is more deleterious than a global perturbation affecting all parasegments. The sequence of events involved in the recovery of the system from a global transient heat shock condition is identified. Finally, these results are discussed in terms of the robustness of the system response.

A simple method for incorporating dynamic effects of intronic miRNA mediated regulation

The importance of microRNA (miRNA) in modulating gene expression at the post-transcriptional level is well known. Such regulation has been shown to influence the dynamics of several regulatory networks including the cell cycle. In this study we incorporated regulatory effects of intronic miRNA into an existing mathematical model of the cell cycle through the use of an existing 'proxy' protein--the host protein. It was observed that the incorporation of intronic miRNA mediated regulation improved the performance of the model resulting in a closer match to experimental results. To test the universality of this approach we compared the effects of intronic miRNA mediated regulation and host protein mediated regulation. Further, we compared miRNA mediated and protein mediated positive and negative feedback regulations of the target protein. We found that the target protein profiles were predominantly similar. These observations show the applicability of our method for incorporating intronic miRNA mediated dynamic effects in models for regulation of gene expression.

CHO Cells adapted to inorganic phosphate limitation show higher growth and higher pyruvate carboxylase flux in phosphate replete conditions

Inorganic phosphate (P_i ) is an essential ion involved in diverse cellular processes including metabolism. Changes in cellular metabolism upon long term adaptation to P_i limitation have been reported in E. coli. Given the essential role of P_i , adaptation to P_i limitation may also result in metabolic changes in animal cells. In this study, we have adapted CHO cells producing recombinant IgG to limiting P_i conditions for 75 days. Not surprisingly, adapted cells showed better survival under P_i limitation. Here, we report the finding that such cells also showed better growth characteristics compared to control in batch culture replete with P_i (higher peak density and integral viable cell density), accompanied by a lower specific oxygen uptake rate and cytochrome oxidase activity towards the end of exponential phase. Surprisingly, the adapted cells grew to a lower peak density under glucose limitation. This suggests long term P_i limitation may lead to selection for an altered metabolism with higher dependence on glucose availability for biomass assimilation compared to control. Steady state U-¹³ C glucose labeling experiments suggest that adapted cells have a higher pyruvate carboxylase flux. Consistent with this observation, supplementation with aspartate abolished the peak density difference whereas supplementation with serine did not abolish the difference. This supports the hypothesis that cell growth in the adapted culture might be higher due to a higher pyruvate carboxylase flux. Decreased fitness under carbon limitation and mutations in the sucABCD operon has been previously reported in E. coli upon long term adaptation to P_i limitation, suggestive of a similarity in cellular response among such diverse species. © 2017 American Institute of Chemical Engineers Biotechnol. Prog., 33:749-758, 2017.

Comparison of methods for identifying periodically varying genes

Several methods have been reported for identifying periodically varying genes from gene expression datasets. We compare the performance of five existing methods and a combination of G-statistic and autocovariance (called GVAR) using simulated sine-function-based and cell-cycle-based datasets. Based on this analysis we recommend appropriate methods for different experimental situations (length of the time series, sampling interval and noise level). No single method performs the best under all tested conditions. None of the evaluated methods perform well at high noise levels for short time series data. At lower noise levels, GVAR performed the best.

Boolean model for melanogenesis

Melanogenesis is a highly regulated process through which the pigment melanin is produced in skin cells. Irregularities in the molecular events that govern the process of skin pigmentation can cause disorders like vitiligo. In order to understand the biology of disease progression, it is important to have an in depth understanding of intracellular events. Mathematical models provide an integrated view of intracellular signalling. There are very few models to date that incorporate intracellular processes relevant to melanogenesis and only one to our knowledge that simulates the dynamics of response to varying levels of input. Here, we report the formulation of the largest Boolean model (265 nodes) for melanogenesis to date. The model was built on the basis of a detailed interaction network graph published by Raghunath et al. Through additional manual curation of the reported interactions, we converted the graph into a set of Boolean rules, following the procedure of the first Boolean model (62 nodes) for melanogenesis published by Lee et al. Simulations show that the predicted response to varying UV levels for most of the nodes is similar to the predictions of the existing model. The greater complexity allows investigation of the sensitivity of melanin to additional nodes. We carried out perturbation analysis of the network through node deletion and constitutive activation to identify sensitivity of outcomes, and compared the nodes identified as sensitive to previous reports.

Corrigendum: Web-gLV: A Web Based Platform for Lotka-Volterra Based Modeling and Simulation of Microbial Populations

[This corrects the article DOI: 10.3389/fmicb.2019.00288.].

Feedback driven autonomous cycles of assembly and disassembly from minimal building blocks

The construction of complex systems by simple chemicals that can display emergent network dynamics might contribute to our understanding of complex behavior from simple organic reactions. Here we design single amino acid/dipeptide-based systems that exhibit multiple periodic changes of (dis)assembly under non-equilibrium conditions in closed system, importantly in the absence of evolved biocatalysts. The two-component based building block exploits pH driven non-covalent assembly and time-delayed accelerated catalysis from self-assembled state to install orthogonal feedback loops with a single batch of reactants. Mathematical modelling of the reaction network establishes that the oscillations are transient for this network structure and helps to predict the relative contribution of the feedback loop to the ability of the system to exhibit such transient oscillation. Such autonomous systems with purely synthetic molecules are the starting point that can enable the design of active materials with emergent properties.

Leveraging machine learning to dissect role of combinations of amino acids in modulating the effect of zinc on mammalian cell growth

Although the contributions of individual components of cell culture media are largely known, their combinatorial effects are far less understood. Experiments varying one component at a time cannot identify combinatorial effects, and analysis of the large number of experiments required to decipher such effects is challenging. Machine learning algorithms can help in the analysis of such datasets to identify multi-component interactions. Zinc toxicity in vitro is known to change depending on amino acid concentration in the extracellular medium. Multiple amino acids are known to be involved in this protection. Thirty-two amino acid compositions were formulated to evaluate their effect on the growth of CHO cells under high zinc conditions. A sequential machine learning analysis methodology was used, which led to the identification of a set of amino acids (threonine, proline, glutamate, aspartate, asparagine, and tryptophan) contributing to protection from zinc. Our results suggest that a decrease in availability of these set of amino acids due to consumption may affect cell growth in media formulated with high zinc concentrations, and in contrast, normal levels of these amino acids are associated with better tolerance to high zinc concentration. Our sequential analysis method may be similarly employed for high throughput medium design and optimization experiments to identify interactions among a large number of cell culture medium components.

Ranking of Reactions Based on Sensitivity of Protein Noise Depends on the Choice of Noise Measure

Gene expression is a stochastic process. Identification of the step maximally affecting noise in the protein level is an important aspect of investigation of gene product distribution. There are numerous experimental and theoretical studies that seek to identify this important step. However, these studies have used two different measures of noise, viz. coefficient of variation and Fano factor, and have compared different processes leading to contradictory observations regarding the important step. In this study, we performed systematic global and local sensitivity analysis on two models of gene expression to investigate relative contribution of reaction rate parameters to steady state noise in the protein level using both the measures of noise. We analytically and computationally showed that the ranking of parameters based on the sensitivity of the noise to variation in a given parameter is a strong function of the choice of the noise measure. If the Fano factor is used as the noise measure, translation is the important step whereas for coefficient of variation, transcription is the important step. We derived an analytical expression for local sensitivity and used it to explain the distinct contributions of each reaction parameter to the two measures of noise. We extended the analysis to a generic linear catalysis reaction system and observed that the reaction network topology was an important factor influencing the local sensitivity of the two measures of noise. Our study suggested that, for the analysis of contributions of reactions to the noise, consideration of both the measures of noise is important.