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Introduction to Complexity: Models of Biological Self-Organization

The goal of our work is to facilitate the identification of the basins of attraction in the context of logical, asynchronous models. To do so, we propose to explore in the reverse dynamics, the reachable state space from each model attractor. We thus start by formally define the reverse of a logical model as the model producing the reverse asynchronous dynamics. We establish remarkable properties of reverse models and contrast the Boolean and multi-valued cases. We demonstrate the use of model reversal to identify basins of attraction and their boundaries on a Boolean model of cell-fate decision upon death receptor activation Calzone et al PLOS Computational Biology, Model reversal was implemented in the modelling software GINsim, and we relied on boolSim for an efficient reachability analysis.

We further provide a set of scripts for reproducing the analyses presented for the aforementioned case studies. MYC is a proto-oncogenic transcription factor with an enhanced expression in the majority of tumours. As an explanation two seemingly conflicting hypotheses have been proposed: one hypothesis proposes that MYC enhances expression of all genes, while the other suggests gene-specific regulation. We have explored the hypothesis that specific gene expression profiles arise since target gene promoters differ in their affinity for MYC. Our mathematical modelling approach demonstrated that binding affinities for interactions of MYC with DNA and with core promoter-bound factors are sufficient to explain promoter occupancies observed in vivo.

Our work can explain why tumour-specific expression levels of MYC induce specific gene expression programs that alter cellular behaviour. The comprehensive analysis of our mathematical model indicates that our mechanistic insights are valid for many human cell types. Benary U. Motivation: Signaling systems like the TNFR1 tumor necrosis factor receptor 1 pathway process environmental stimuli to mediate the adequate immune response ranging from cell death induction to activation of gene expression.

The signaling system is highly intertwined and forms a complex regulatory network. Generally, the underlying biological data are incomplete, and the kinetic parameters are often unknown or hardly accessible. Mathematical network analysis allows for decomposition into smaller, biologically meaningful modules and supports to unravel system—wide processes. Automatic detection of complete pathways from the receptor to the cell response remains an issue for the analysis of signaling networks.

Due to regulatory characteristics of signaling systems, like feedback loops, cross-talks or signal amplification, straightforward detection of all possible signal flows is often impaired. Methods: We present an approach for the automatic enumeration of all signal transduction pathways from the receptor to the cellular response. The approach is based on elementary mode analysis expressed as transition invariants in the Petri net formalism [1, 2].

We introduce the concept of Manatee invariants to detect all complete signal flows from signal reception to cellular response. The concept of Manatee invariants is based on feasible transition invariants [3], which combine interrelated transition invariants in a specific way. We demonstrate that Manatee invariants cover the whole signaling pathway without interruptions. Results: The computation of Manatee invariants yielded the combinatorial diversity of possible signal flows. In silico knockout experiments based on Manatee invariants revealed biologically relevant results, since pathway dependencies were properly captured.

We demonstrate that Manatee invariants determine all complete signal flows from the receptor to the cellular response, thus, revealing essential pathway dependencies, which could be used, for example, for in silico knockout analyses [6]. This inter-patient variability poses a challenge for clinicians. A priori it is not clear which drug or drug combination will be most beneficial for an individual. Methods: We approach the problem of drug response prediction using a systems biological approach. We developed a generic large-scale mechanistic dynamic model covering multiple cancer associate signaling pathways.

This ordinary differential equation model can be individualized using exome and transcriptome sequencing data — carrying information about mutation status and expression levels. For statistical inference of the model parameters we implemented adjoint sensitivity analysis methods. These methods facilitate the study of large-scale models with thousands of parameters and state variables. Results: To evaluate the proposed model-based approach, we studied data response from the Cancer Cell Line Encyclopaedia CCLE for 7 drugs and cell lines originating from five different tissues.

These results demonstrate the potential of large-scale mechanistic modeling for drug selection in personalized therapy. Prostate cancer is a leading cause of cancer death amongst men, but also prone to over-treatment. Based on public data TCGA , we build a mathematical model of pathways frequently altered in prostate cancer tumors and simulate patient-specific outcomes.

This model allows to improve our understanding of the mechanisms underlying this complex disease, and to suggest optimized and personalized strategies for therapeutic interventions. We first propose a methodology for building a curated network from both prior knowledge and experimental data. The resulting signaling network is based on the most frequently altered genes and pathways in prostate cancer.

Enrichment analyses of publicly available experimental data guide the inclusion of new molecular processes to complement the network. In particular, we use a gene set quantification tool ROMA: Representation of Module Activity to select pathways whose activity is significantly dispersed in prostate cancer samples. Detailed protein interactions relevant in these pathways are retrieved from the literature.

Investigating Biological Systems Using Modeling : Strategies and Software

This search is facilitated by pypath, a Python module that gives access to different signaling databases gathered in Omnipath. A Boolean model is then derived from the network, with outputs characterizing several cancer-related phenotypes. Using MaBoSS, a probabilistic framework based on continuous time Markov chains, we estimate time evolution of phenotypic probabilities in specific contexts.

This model provides a support to incorporate multi-omics patient-specific molecular data. Mutations and copy number variations of individual patients are encoded as perturbations of the model, while transcriptomics and proteomics data are discretized and compared with simulated probabilities. For that purpose, different methods of discretization of quantitative data have been explored.

This leads to the definition of a set of model variants specific to tumor samples. The model is then validated by correlating the simulated phenotypical outputs for individual patients to clinical data, and is used to stratify patients. The effect of different drugs on the model can be simulated and compared to experimental observations. One of the biggest advantages of the predictions made under this framework is that they are intrinsically accompanied by a mechanistic explanation.

Ultimately, the objective is to identify disease mechanisms and novel therapeutic targets, as well as produce treatment recommendations for individual patients based on a therapeutic biomarker panel. Motivation: Intratumour heterogeneity poses many challenges to the treatment of cancer. Unfortunately, the transcriptional and metabolic information retrieved by currently available computational and experimental techniques portrays the average behaviour of intermixed and heterogeneous cell subpopulations within a given tumour. Emerging single-cell genomic analyses are nonetheless unable to characterise the interactions among cancer subpopulations.

In this work, we propose popFBA, an extension to classic Flux Balance Analysis FBA , to explore how metabolic heterogeneity and cooperation phenomena affect the overall growth of cancer cell populations. Results: We show how clones of a metabolic network of human central carbon metabolism, sharing the same stoichiometry and capacity constraints, may follow several different metabolic paths and cooperate to maximise the growth of the total population.

We also introduce a method to explore the space of possible interactions, given some constraints on plasma supply of nutrients. We finally provide a technique to identify the most proliferative cells within the heterogeneous population. Cell cycle and metabolism are coupled networks. Cell growth and division require synthesis of macromolecules which is dependent on metabolic cues. Conversely, metabolites involved in nucleotide and protein synthesis are fluctuating periodically as a function of cell cycle progression.


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To date, no effort has been made to integrate, and to investigate the mutual regulation of, these two systems in any organism. Connections among cell cycle and metabolism have been recently elucidated in budding yeast. However, high-throughput and manually curated studies point at many more physical interactions between these two networks.

Here we aim to investigate cell cycle robustness by generating the first multi-scale model that integrates cell cycle with metabolism, and investigating their bidirectional regulation. Here a framework is presented integrating a Boolean cell cycle model with a constraint-based model of metabolism, incorporating mechanistic and high-throughput interactions on the bidirectional regulation. For the mechanistic interactions, directionality and effect are known.

As this information is unknown for the high-throughput interactions, an informed optimization algorithm has been developed to generate models that can incorporate it iteratively. Through Boolean logic, activity of cell cycle nodes can activate or inhibit metabolic reactions. Conversely, presence or absence of a metabolic flux can promote or prevent the activity of cell cycle nodes, respectively.

The results of the informed optimization algorithm agnostic to the information regarding directionality and effect of interactions are verified against metabolomic data. Specifically, changes in flux through 15 metabolic pathways are compared to metabolic pathway enrichment time-series. The multi-scale model predicts expected changes in the majority of the pathways, spread over amino-acid, pentose phosphate, and lipid metabolism. Furthermore, many models that differ in number and directionality of interactions robustly predict a definite set of interactions underlying the bidirectional regulation between cell cycle and metabolism.

Furthermore, the integrative model shows a temporal export of acetate, pyruvate and alanine, qualitatively reminiscent of yeast metabolic oscillations. Altogether, our multi-scale framework is able to integrate computer models of biological networks with high-throughput data, to capture the functional connectivity among their elements that ultimately results in systems robustness.

The capacity of modern experimental methods to generate data about biological processes has surpassed the ability of existing informatics approaches to generate meaningful mechanistic explanations. Mechanistic systems biology models could potentially address this gap, but model construction remains a labor-intensive process requiring both biological knowledge and modeling expertise. As a result, modeling studies remain fairly small in scope and are disconnected from genome-scale research. To address this problem we have developed the Integrated Network and Dynamical Reasoning Assembler INDRA , a system that automatically assembles mechanistic models from pathway databases, literature, and expert knowledge expressed in natural language.

INDRA draws on three existing natural language processing systems and uses a modular architecture to build different types of models from a variety of sources. Mechanisms are extracted from each source format and converted into Statements, a normalized representation of biological mechanisms. To identify redundancies and overlaps, Statements are sorted into a hierarchy graph that identifies which are generic e. The reliability of each mechanism is scored probabilistically based on the sources and frequency of extractions.

Manual evaluation of the system on a corpus of papers indicated that this assembly process can reliably extract previously uncurated protein-protein interactions and post-translational modifications, and eliminates many of the errors that arise in automated model construction. A key feature of this approach is that the assembled models are not only broad in scope but also mechanistic, capturing information about sites of post-translational modification and necessary molecular context.

To evaluate the ability of INDRA to systematically generate explanations of high-throughput data, we assembled a rule-based executable model to explain a previously published dataset of the phospho-proteomic response of a melanoma cell line to 12 different drugs. Static analysis of the rule influence map provided by Kappa allowed us to identify possible mechanistic paths linking drug targets to experimentally observed effects on phospho-protein abundances.

Notably, manual inspection revealed that several of the unexplained effects were due to a feedback mechanism from MTOR to AKT that was evidently missing from the model. Taken together, this study shows the potential of automatically assembled models to systematically explain high-throughput data, generating mechanistic hypotheses and identifying genuinely novel phenomena. A single mammalian cell includes an order of mRNA molecules and as many as ribosomes. Developing a better understanding of the intricate correlations between these simultaneous processes, rather than focusing on the translation of a single isolated transcript, should help in gaining a better understanding of mRNA translation regulation, and the way elongation rates affect organismal fitness and the nucleotide composition of transcripts.

In this study, we report for the first time whole cell translation simulations of several organisms e. The models consider all the biophysical aspects of translation e. We developed tools for comparing such a set of whole cell translation models, and for understanding the evolution of transcriptomes via directly connecting the genotype to the phenotypes i. Specifically, among others we show that in S. The algorithm introduces silent mutations that improve the allocation of resources e. As a result, more resources are available for the cell promoting improved fitness and growth-rate.

Ordinary differential equations ODEs are a popular approach to quantitatively model molecular networks based on biological knowledge. However, such knowledge is typically restricted. Wrongly modeled biological mechanisms as well as relevant external influence factors that are not included into the model likely manifest in major discrepancies beween model predictions and experimental data. Finding the exact reasons for such observed discrepancies can be quite challenging in practice. In order to address this issue we suggest a Bayesian approach to estimate hidden influences in ODE based models.

The method can distinguish between exogenous and endogenous hidden influences. Thus, we can detect wrongly specied as well as missed molecular interactions in the model. We demonstrate the performance of our Bayesian Dynamic Elastic-Net with several ordinary differential equation models from the literature, such as human JAK-STAT signaling, information processing at the erythropoietin receptor, isomerization of liquid a-Pinene, G-protein cycling in yeast and UV-B triggered signaling in plants. Moreover, we investigate a set of commonly known network motifs and a gene-regulatory network.

Altogether our method supports the modeler in an algorithmic manner to identify possible sources of errors in ODE based models on the basis of experimental data. Biomarker discovery is extraordinarily important in gene expression analysis in context of toxicant exposure. Among gene selection methods, differential expression analysis is often applied because of its simplicity and interpretability.

Investigating Biological Systems Using Modeling - 1st Edition

But it treats genes individually, disregarding the correlation between them. So some multivariate feature selection methods are proposed for biomarker discovery. We compared three methods that stem from different theories, namely Significance Analysis of Microarrays SAM which finds out the differentially expressed genes, minimum Redundancy Maximum Relevance mRMR based on information theory, and Characteristic Direction GeoDE from a geometrical aspect, according to the stability and classification accuracy. The stability of feature selection methods is measured based on the overlap of selected features from different sampling steps.

Based on these two aspects, we studied the performance of 3 feature selection methods. Tested on the gene expression data from two toxicant exposure experiments on Atlantic Cod liver, we found that GeoDE is more stable, and can give higher prediction accuracy in low-dose condition. Identifying and characterizing patterns of association between variables is a common aim in biology today. Studying these associations has played a crucial role in understanding a wide variety of biological phenomena, such as the dynamics of human disease, transcriptional changes associated with aging, or condition-specific alterations to metabolic pathways.

In a statistical framework, these associations between variables are commonly described in terms of precision matrices which encode conditional associations or covariance matrices which capture marginal associations. In the latter case, most attention in the statistical literature has been placed on testing and estimation of only two covariance matrices, or two correlation matrices. We present a factor analysis based method to model the structure of related covariance matrices. Our method captures both common structural elements across all conditions and condition specific differences in associations between variables.

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The approach is extendable to a wide range of datasets, including those that have more than two conditions, or have more complicated experimental design such as having two experimental design factors, each with multiple levels. Additionally, our method allows us to use all available data to estimate the common structure and thereby gain the advantage of a larger sample size. We will detail the theoretical framework for this model, briefly discuss simulation results and present an in depth example on a metabolomics dataset from breast cancer patients treated with aromatase inhibitors AIs.

Half of the patients in our dataset are unable to continue treatment with AIs for more than 6 months, due to side effects. These patients exhibit no mean differences in their metabolomic profiles from those who can continue treatment; however, subtle changes in the patterns of association between metabolites do exist between patient groups. Our method captures the similarities and differences in the patterns of association between metabolites across these patient groups, and provides a data driven way to group the metabolites into sets, thus allowing us to characterize the differences between conditions in a biologically meaningful way.

Eubacterium limosum is an acetogenic bacterium with growing importance both in medical sciences and biofuel research. From the bioengineering perspective, E. Characterization and optimization of its growth under variety of growth conditions is of interest both for better understanding of gut microbiota and for bioengineering applications.

Genome-scale metabolic reconstructions GENREs of organisms are often used for systematic analysis of their metabolic activities. However, manual generation of such models is time consuming, therefore algorithms have been developed to automise the generation procedure. One such reconstruction of E.

Systems biology

However, the model lacks the reactions that describe utilization of CO, a major carbon source of E. Therefore, the existing model fails to represent the metabolism under some of the growth conditions of interest. To address the limited capabilities of the semi-generated metabolic network of E.

Using the workflow in Figure 1, the network was corrected, refined and validated based on the genome databases and growth characteristics of E. One approach is using survival time—based dynamic datasets, and the other is using grade- and stage-based dynamic datasets. Based on cancer grades and stages, we generated 6 dynamic levels and obtained two pairs of significant pathways out of 12 enriched pathways via GSEA. Ambiguity in genetic codes exists in cases where certain stop codons are alternatively used to encode non-canonical amino acids.

In selenoprotein transcripts, the UGA codon may represent either a translation termination signal or a selenocysteine Sec codon, and results in the expression of full-length PL and truncated PS selenoproteins respectively. In contrast, translation termination takes place when UGA is bound by a release factor and triggers the release of the translated protein from the ribosome. How these factors quantitatively affect alternative assignments of UGA has not been fully investigated. We developed a model simulating the UGA decoding process.

We demonstrated that this model captured two prominent characteristics observed from experimental data. First, UGA to Sec decoding increases with elevated selenium availability, but saturates under high selenium supply. Second, the efficiency of Sec incorporation is reduced with increasing selenoprotein synthesis, and increases with elevated selenium concentration but saturates under high selenium supply. Figure 1 displays predicted Sec incorporation efficiencies under four different constraints with various mRNA quantities and selenium concentrations.

Models with the mRNA constraint assumption 4 exhibits saturated protein abundance with increased selenium supply. Models with the tRNA constraint assumption 5 shows increased Sec incorporation efficiency with reduced selenoprotein synthesis and saturates with abundant selenium supply. Thus both constraints are required to capture the observed characteristics. We further developed an algorithm to estimate model parameters to fit the experimental data of selenoprotein synthesis and abundance.

It is well known that hierarchical selenoprotein expression depends on the SECIS-SBP2 interaction, but whether this interaction is the sole determinant for selenoprotein hierarchy remains unclear. We measured the expressions of four selenoprotein constructs and estimated their model parameters. Their inferred Sec incorporation efficiencies did not correlate well with their SECIS-SBP2 binding affinities, suggesting the existence of additional factors determining the hierarchy of selenoprotein synthesis under selenium deficiency. This model provides a framework to systematically study the interplay of factors affecting the dual definitions of a genetic codon.

Intestinal organoid cultures recently emerged as an ideal in vitro model system to study adult stem cell maintenance and differentiation in a controlled manner. We are investigating the molecular mechanisms that drive cell fate changes in mouse intestinal organoids by generating stem cell enriched and stem cell depleted organoid cultures using small-molecule driven perturbations.

Analyses of the transcriptome and the proteome of these organoids revealed that, besides the expected dynamics of intestinal stem cell and differentiation markers, hundreds of additional genes are differentially expressed during adult intestinal stem cell differentiation. Strikingly, we observed post-transcriptionally regulated transcription factor module switching in stem cell enriched versus stem cell depleted organoid cultures. Furthermore, probing the epigenetic landscapes of intestinal stem cells using ChIP-sequencing and ATAC-sequencing revealed a large number of cell-type specific regulatory elements.

Finally, by using an integrative systems biology approach, we aim to uncover all layers of gene expression regulation in perturbed organoid cultures. These layers range from transcription factor binding to feedback from the metabolome and uncover the regulatory networks that define the remarkable cellular plasticity of the mouse intestinal epithelium.

The construction of kinetic models of metabolic pathways has always been hindered by the limited availability of kinetic parameters, in addition to incomplete knowledge for many of the reaction mechanisms. Strategies have been developed to allow the generation of kinetic models with limited information. Despite this, not many large-scale dynamic and integrative models have been generated.

The aim of this research is to streamline the process of generating large-scale metabolic models, while using metabolomic, proteomic and fluxomics to inform parameter values. Previously, we developed the GRaPe tool in order to streamline the construction of metabolic models through automated generation of kinetic equations.

However a number of limitations affected the performance of the tool, which are now being addressed in this project. Firstly, convenience kinetics developed by Liebermeister and Klipp has been introduced to replace the previously used reversible Michaelis-Menten rate equations. Convenience kinetics requires fewer parameters, which reduces the burden on parameter estimation for the models. Additionally, it allows for inclusion of enzymatic modifiers into model building.

Secondly, parameter estimation was performed locally on each reaction, which has now been replaced by global parameter estimation for the system as a whole. Thirdly, the parameter estimation was skewed to favour flux values at steady state, which resulted in limited applicability of the models generated. The fitness measurement in the genetic algorithm used for parameter estimation has been updated to account for metabolite values as well flux and protein values, improving the model fitting to dynamic series of experimental data. As a proof of concept, a model of yeast glycolysis is being built using flux values, and protein amounts obtained in a heat stress experiment.

We show that our method is capable of generating a dynamic model, which accounts for both types of data. This work will be extended towards providing a general platform for the integration of multiple omics data sets and expedited construction of large-scale kinetic models. Eukaryotic metabolic networks exhibit a high degree of redundancy at the level of individual enzymes and entire pathways. This redundancy increases the regulatory potential and it confers robustness to external and internal perturbations.

Enzyme-level redundancy is at least in part mediated through enzyme promiscuity, i. Although these phenomena are well described for specific examples, we lack systematic understanding of metabolic plasticity and of its adaptation to genetic and environmental perturbations. We developed new computational approaches to investigate the impact of natural genetic variation on single-enzyme and network-level redundancy. This new framework uses reaction molecular signatures RMS- Carbonell et al. RMS were used to group reactions and enzymes based on the chemical modifications that they execute on their substrates.

This approach is particularly powerful for detecting and formally describing enzyme promiscuity and partial redundancy of metabolic pathways. In order to understand how metabolic redundancy mediates resistance to inter-individual genetic variability we used quantitative trait locus QTL analysis.

This method was applied to multi-layer omics data transcriptome and proteome from fission yeast Schizosaccharomyces pombe. By linking the RMS-based framework with QTL analysis we identified genetic variants segregating in this fission yeast cross that trigger specific adaptive changes in the metabolic networks. Alleles at the QTL locus associated with these enzymes affected whether or not the backup functionality was properly utilized under oxidative stress.

Reduced capacity for backup was in turn correlated with reduced cellular fitness, measured with yeast cell growth in liquid medium. Thus, these results suggest that metabolic redundancy is important for response to stress and that this redundancy might be specifically affected by genomic variability. This work sets the foundation for better understanding the requirements and limitations of metabolic networks to cope with natural genetic variability. Tools and models we created will be further used to better understand inter-individual variability in disease susceptibility and drug response.

Introduction: High-throughput techniques allow for massive screening of drug combinations. To find compound combinations that exhibit an interaction effect, one filters for the most promising compound combinations by comparing to an expected response without interaction.

The larger the deviance to such a null reference model, the larger the interaction effect. Over the past century, many null reference models have been introduced, compared, and often found to be insufficient [1, 2]. The Loewe Additivity model [3] is one of the few that survived the critiques.

Loewe Additivity: Loewe Additivity is based on the assumption that no compound should interact with itself. It is originally defined in form of the General Isobole GI equation, which is an implicit formulation of the response surface. For the model to be consistent, the individual compound responses have to be restricted.

This condition requires that the doses yielding the same effect have to be linearly related or, equivalently, that they are related by a shift on the log scale. Despite the potential inconsistencies, the model is very simple in its idea of yielding a fixed effect for a linear combination of both compounds, the so-called isoboles. Contributions: We formally derive explicit and implicit formulations of the Loewe Additivity model. Moreover, we show that these formulations are equivalent given that the LACC holds, and are negligibly different otherwise.

Both, the explicit formulation and LACC have not yet been studied in their own right. The LACC is violated in a significant number of cases. The choice of the GI model becomes therefore arbitrary. We show this by analyzing two datasets of drug screening that are supplied with a categorization into the three synergy cases: synergistic, non-interactive and antagonistic [4, 5].

On the non-interactive cases of both datasets, we conduct a mean-squared error analysis to the theoretical null reference models. We demonstrate that the explicit formulation of the null reference model leads to smaller errors than the implicit one. Further, we show that its computation time is significantly faster by a factor of We show, based on the two data sets at hand, that this LACC is statistically significantly violated in practice.

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References W. Greco, et al. Understanding Synergy. Die quantitativen Probleme der Pharmakologie. Ergebnisse der Physiol. Yadav, et al.

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Cokol, et al. Systematic exploration of synergistic drug pairs. Human vocal folds VFs are pliable soft tissue enriched with hyaluronan HA. HA acts as a shock absorber in high-frequency phonation to prevent tissue fatigue and provide a shelter for resident cells. In addition, HA modulates a wide range of cellular activity such as proliferation and collagen production for tissue homeostasis and repair.

Cellular activities modulated by HA are dependent on the origin of HA native versus exogenous , molecular weight of HA, stiffness of the surrounding extracellular matrix ECM , as well as the time exposured to HA. The primary goal of this study is to develop a computational agent-based model ABM to simulate the dynamics of HA and cells in vocal fold wound repair.

Rejecting Hypotheses and Accepting a Model. Model Summarization. Multiple Studies Analysis. Information in the Model. Errors in Compartmental Modeling. Testing Robustness: Sensitivity, Identifiability, and Stability. Reviewing and Summarizing Published Models. The Model Translation Process. Verification and Validation.

Using the Model. A Library of Models. Subject Index. She received her Ph. She is the author of 30 articles and has presented over 40 invited lectures and workshops on modeling biological systems. We are always looking for ways to improve customer experience on Elsevier. We would like to ask you for a moment of your time to fill in a short questionnaire, at the end of your visit.

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