Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri nets

HM, Marshall JM. MGDrivE 3: A decoupled vector-human framework for epidemiological simulation of mosquito genetic control tools and their surveillance

Novel mosquito genetic control tools, such as CRISPR-based gene drives, hold great promise in reducing the global burden of vector-borne diseases. As these technologies advance through the research and development pipeline, there is a growing need for modeling frameworks incorporating increasing levels of entomological and epidemiological detail in order to address questions regarding logistics and biosafety. Epidemiological predictions are becoming increasingly relevant to the development of target product profiles and the design of field trials and interventions, while entomological surveillance is becoming increasingly important to regulation and biosafety. We present MGDrivE 3 (Mosquito Gene Drive Explorer 3), a new version of a previously-developed framework, MGDrivE 2, that investigates the spatial population dynamics of mosquito genetic control systems and their epidemiological implications. The new framework incorporates three major developments: i) a decoupled sampling algorithm allowing the vector portion of the MGDrivE framework to be paired with a more detailed epidemiological framework, ii) a version of the Imperial College London malaria transmission model, which incorporates age structure, various forms of immunity, and human and vector interventions, and iii) a surveillance module that tracks mosquitoes captured by traps throughout the simulation. Example MGDrivE 3 simulations are presented demonstrating the application of the framework to a CRISPR-based homing gene drive linked to dual disease-refractory genes and their potential to interrupt local malaria transmission. Simulations are also presented demonstrating surveillance of such a system by a network of mosquito traps. MGDrivE 3 is freely available as an open-source R package on CRAN (https://cran.r-project.org/package=MGDrivE2) (version 2.1.0), and extensive examples and vignettes are provided. We intend the software to aid in understanding of human health impacts and biosafety of mosquito genetic control tools, and continue to iterate per feedback from the genetic control community.

Perspective on Integrative Simulations of Bioenergetic Domains

Bioenergetic processes in cells, such as photosynthesis or respiration, integrate many time and length scales, which makes the simulation of energy conversion with a mere single level of theory impossible. Just like the myriad of experimental techniques required to examine each level of organization, an array of overlapping computational techniques is necessary to model energy conversion. Here, a perspective is presented on recent efforts for modeling bioenergetic phenomena with a focus on molecular dynamics simulations and its variants as a primary method. An overview of the various classical, quantum mechanical, enhanced sampling, coarse-grained, Brownian dynamics, and Monte Carlo methods is presented. Example applications discussed include multiscale simulations of membrane-wide electron transport, rate kinetics of ATP turnover from electrochemical gradients, and finally, integrative modeling of the chromatophore, a photosynthetic pseudo-organelle.

Stochastic model of vesicular stomatitis virus replication reveals mutational effects on virion production

We present the first complete stochastic model of vesicular stomatitis virus (VSV) intracellular replication. Previous models developed to capture VSV's intracellular replication have either been ODE-based or have not represented the complete replicative cycle, limiting our ability to understand the impact of the stochastic nature of early cellular infections on virion production between cells and how these dynamics change in response to mutations. Our model accurately predicts changes in mean virion production in gene-shuffled VSV variants and can capture the distribution of the number of viruses produced. This model has allowed us to enhance our understanding of intercellular variability in virion production, which appears to be influenced by the duration of the early phase of infection, and variation between variants, arising from balancing the time the genome spends in the active state, the speed of incorporating new genomes into virions, and the production of viral components. Being a stochastic model, we can also assess other effects of mutations beyond just the mean number of virions produced, including the probability of aborted infections and the standard deviation of the number of virions produced. Our model provides a biologically interpretable framework for studying the stochastic nature of VSV replication, shedding light on the mechanisms underlying variation in virion production. In the future, this model could enable the design of more complex viral phenotypes when attenuating VSV, moving beyond solely considering the mean number of virions produced.

Searching for significant reactions and subprocesses in models of biological systems based on Petri nets

The primary aim of this research was to propose algorithms enabling the identification of significant reactions and subprocesses within models of biological systems constructed using classical Petri nets. These solutions allow to performance of two analysis methods: an importance analysis for identifying individual reactions critical to the functioning of the model and an occurrence analysis for finding essential subprocesses. To demonstrate the utility of these methods, analyses of an example model have been performed. In this case, it was a model related to the DNA damage response mechanism. It is worth noting that the proposed analyses can be applied to any biological phenomenon represented using the Petri net formalism. The presented analysis methods represent an extension of classical Petri net-based analyses. Their utility lies in their potential to enhance our comprehension of the biological phenomena under investigation. Furthermore, they can lead to the development of more effective medical therapies, as they can aid in the identification of potential molecular targets for drugs.

Expansions to the MGDrivE suite for simulating the efficacy of novel gene-drive constructs in the control of mosquito-borne diseases

OBJECTIVE

The MGDrivE (MGDrivE 1 and MGDrivE 2) modeling framework provides a flexible and expansive environment for testing the efficacy of novel gene-drive constructs for the control of mosquito-borne diseases. However, the existing model framework did not previously support several features necessary to simulate some types of intervention strategies. Namely, current MGDrivE versions do not permit modeling of small molecule inducible systems for controlling gene expression in gene drive designs or the inheritance patterns of self-eliminating gene drive mechanisms.

RESULTS

Here, we demonstrate a new MGDrivE 2 module that permits the simulation of gene drive strategies incorporating small molecule-inducible systems and self-eliminating gene drive mechanisms. Additionally, we also implemented novel sparsity-aware sampling algorithms for improved computational efficiency in MGDrivE 2 and supplied an analysis and plotting function applicable to the outputs of MGDrivE 1 and MGDrivE 2.

Energy transport between heat baths with oscillating temperatures

Energy transport is a fundamental physical process that plays a prominent role in the function and performance of myriad systems and technologies. Recent experimental measurements have shown that subjecting a macroscale system to a time-periodic temperature gradient can increase thermal conductivity in comparison to a static temperature gradient. Here, we theoretically examine this mechanism in a nanoscale model by applying a stochastic Langevin framework to describe the energy transport properties of a particle connecting two heat baths with different temperatures, where the temperature difference between baths is oscillating in time. Analytical expressions for the energy flux of each heat bath and for the system itself are derived for the case of a free particle and a particle in a harmonic potential. We find that dynamical effects in the energy flux induced by temperature oscillations give rise to complex energy transport hysteresis effects. The presented results suggest that applying time-periodic temperature modulations is a potential route to control energy storage and release in molecular devices and nanosystems.

Machine Learning Guided Batched Design of a Bacterial Ribosome Binding Site

Optimization of gene expression levels is an essential part of the organism design process. Fine control of this process can be achieved by engineering transcription and translation control elements, including the ribosome binding site (RBS). Unfortunately, the design of specific genetic parts remains challenging because of the lack of reliable design methods. To address this problem, we have created a machine learning guided Design-Build-Test-Learn (DBTL) cycle for the experimental design of bacterial RBSs to demonstrate how small genetic parts can be reliably designed using relatively small, high-quality data sets. We used Gaussian Process Regression for the Learn phase of the cycle and the Upper Confidence Bound multiarmed bandit algorithm for the Design of genetic variants to be tested in vivo. We have integrated these machine learning algorithms with laboratory automation and high-throughput processes for reliable data generation. Notably, by Testing a total of 450 RBS variants in four DBTL cycles, we have experimentally validated RBSs with high translation initiation rates equaling or exceeding our benchmark RBS by up to 34%. Overall, our results show that machine learning is a powerful tool for designing RBSs, and they pave the way toward more complicated genetic devices.

Kinetic Modeling of Saccharomyces cerevisiae Central Carbon Metabolism: Achievements, Limitations, and Opportunities

Central carbon metabolism comprises the metabolic pathways in the cell that process nutrients into energy, building blocks and byproducts. To unravel the regulation of this network upon glucose perturbation, several metabolic models have been developed for the microorganism Saccharomyces cerevisiae. These dynamic representations have focused on glycolysis and answered multiple research questions, but no commonly applicable model has been presented. This review systematically evaluates the literature to describe the current advances, limitations, and opportunities. Different kinetic models have unraveled key kinetic glycolytic mechanisms. Nevertheless, some uncertainties regarding model topology and parameter values still limit the application to specific cases. Progressive improvements in experimental measurement technologies as well as advances in computational tools create new opportunities to further extend the model scale. Notably, models need to be made more complex to consider the multiple layers of glycolytic regulation and external physiological variables regulating the bioprocess, opening new possibilities for extrapolation and validation. Finally, the onset of new data representative of individual cells will cause these models to evolve from depicting an average cell in an industrial fermenter, to characterizing the heterogeneity of the population, opening new and unseen possibilities for industrial fermentation improvement.

Mathematical Models of Plasmid Population Dynamics

With plasmid-mediated antibiotic resistance thriving and threatening to become a serious public health problem, it is paramount to increase our understanding of the forces that enable the spread and maintenance of drug resistance genes encoded in mobile genetic elements. The relevance of plasmids as vehicles for the dissemination of antibiotic resistance genes, in addition to the extensive use of plasmid-derived vectors for biotechnological and industrial purposes, has promoted the in-depth study of the molecular mechanisms controlling multiple aspects of a plasmids' life cycle. This body of experimental work has been paralleled by the development of a wealth of mathematical models aimed at understanding the interplay between transmission, replication, and segregation, as well as their consequences in the ecological and evolutionary dynamics of plasmid-bearing bacterial populations. In this review, we discuss theoretical models of plasmid dynamics that span from the molecular mechanisms of plasmid partition and copy-number control occurring at a cellular level, to their consequences in the population dynamics of complex microbial communities. We conclude by discussing future directions for this exciting research topic.

Comparison of modelling approaches demonstrated for p16-mediated signalling pathway in higher eukaryotes

Quantitative modelling of biological systems using Petri net technologies has experienced renaissance in the past couple of decades. The overwhelming majority of these models is deterministic though underlying biological systems are usually at the mesoscopic level and small, rather than large, and employ sparse molecular structure. Sparse biological systems are accompanied by randomness due to low molecular density, intrinsic random nature of phenomena and noise in an experiment. On the other hand, biochemical reactions are inherently uncertain due to imprecision and vagueness of kinetic parameters. Stochastic methods are used to cope with randomness while fuzzy methods are developed to deal with uncertainty of biological systems, but there is lack of common voice among researchers regarding the best choice of modelling approach for a particular biological system. The main issues addressed in this paper are the choice between deterministic, stochastic and fuzzy parameters and aspects; that is, which modelling approach to follow to reach the realistic approximation of an underlying biological system, and how to measure parallels and discrepancies between different quantitative paradigms. To this end, we use Petri nets with hybrid, stochastic and fuzzy parameters to create quantitative model of p16-mediated signalling pathway in higher eukaryotes, perform deterministic, pure stochastic and fuzzy stochastic simulations to predict the behaviour of major molecular regulators of p16-mediated pathway. In the meanwhile, we show how uncertain kinetic parameters can be precisely approximated in terms of α cuts. Then we perform statistical analysis of simulation results to measure similarity between the three modelling approaches. The statistical analysis reveals significant deviations between deterministic, pure stochastic and fuzzy stochastic approaches for most of the biological components. Due to rather small size of underlying biological system, it turns out that fuzzy stochastic approach is the most appropriate for modelling of p16-mediated signalling pathway because it successfully deals with both randomness and uncertainty and produces quantitative results with biological relevance.

Nets-within-nets for modeling emergent patterns in ontogenetic processes

Ontogenesis is the development of an organism from its earliest stage to maturity, including homeostasis maintenance throughout adulthood despite environmental perturbations. Almost all cells of a multicellular organism share the same genomic information. Nevertheless, phenotypic diversity and complex supra-cellular architectures emerge at every level, starting from tissues and organs. This is possible thanks to a robust and dynamic interplay of regulative mechanisms. To study ontogenesis, it is necessary to consider different levels of regulation, both genetic and epigenetic. Each cell undergoes a specific path across a landscape of possible regulative states affecting both its structure and its functions during development. This paper proposes using the Nets-Within-Nets formalism, which combines Petri Nets' simplicity with the capability to represent and simulate the interplay between different layers of regulation connected by non-trivial and context-dependent hierarchical relations. In particular, this work introduces a modeling strategy based on Nets-Within-Nets that can model several critical processes involved in ontogenesis. Moreover, it presents a case study focusing on the first phase of Vulval Precursor Cells specification in C.Elegans. The case study shows that the proposed model can simulate the emergent morphogenetic pattern corresponding to the observed developmental outcome of that phase, in both the physiological case and different mutations. The model presented in the results section is available online at https://github.com/sysbio-polito/NWN_CElegans_VPC_model/.

HM, Dolgert AJ, León TM, Marshall JM. MGDrivE 2: A simulation framework for gene drive systems incorporating seasonality and epidemiological dynamics

Interest in gene drive technology has continued to grow as promising new drive systems have been developed in the lab and discussions are moving towards implementing field trials. The prospect of field trials requires models that incorporate a significant degree of ecological detail, including parameters that change over time in response to environmental data such as temperature and rainfall, leading to seasonal patterns in mosquito population density. Epidemiological outcomes are also of growing importance, as: i) the suitability of a gene drive construct for release will depend on its expected impact on disease transmission, and ii) initial field trials are expected to have a measured entomological outcome and a modeled epidemiological outcome. We present MGDrivE 2 (Mosquito Gene Drive Explorer 2): a significant development from the MGDrivE 1 simulation framework that investigates the population dynamics of a variety of gene drive architectures and their spread through spatially-explicit mosquito populations. Key strengths and fundamental improvements of the MGDrivE 2 framework are: i) the ability of parameters to vary with time and induce seasonal population dynamics, ii) an epidemiological module accommodating reciprocal pathogen transmission between humans and mosquitoes, and iii) an implementation framework based on stochastic Petri nets that enables efficient model formulation and flexible implementation. Example MGDrivE 2 simulations are presented to demonstrate the application of the framework to a CRISPR-based split gene drive system intended to drive a disease-refractory gene into a population in a confinable and reversible manner, incorporating time-varying temperature and rainfall data. The simulations also evaluate impact on human disease incidence and prevalence. Further documentation and use examples are provided in vignettes at the project’s CRAN repository. MGDrivE 2 is freely available as an open-source R package on CRAN (https://CRAN.R-project.org/package=MGDrivE2). We intend the package to provide a flexible tool capable of modeling gene drive constructs as they move closer to field application and to infer their expected impact on disease transmission.

Malaria, dengue and other mosquito-borne diseases continue to pose a major global health burden through much of the world. Currently available tools, such as insecticides and antimalarial drugs, are not expected to be sufficient to eliminate these diseases from highly-endemic areas, hence there is interest in novel strategies including genetics-based approaches. In recent years, the advent of CRISPR-based gene-editing has greatly expanded the range of genetic control tools available, and MGDrivE 1 (Mosquito Gene Drive Explorer 1) was proposed to simulate the dynamics of these systems through spatially-structured mosquito populations. As the technology has advanced and potential field trials are being discussed, models are now needed that incorporate additional details, such as life history parameters that respond to daily and seasonal environmental fluctuations, and transmission of pathogens between mosquito and vertebrate hosts. Here, we present MGDrivE 2, a gene drive simulation framework that significantly improves upon MGDrivE 1 by addressing these modeling needs. MGDrivE 2 has also been reformulated as a stochastic Petri net, enabling model specification to be decoupled from simulation, making it easier to adapt the model for application to other insect and mammalian species.

Modelling Cell Metabolism: A Review on Constraint-Based Steady-State and Kinetic Approaches

Studying cell metabolism serves a plethora of objectives such as the enhancement of bioprocess performance, and advancement in the understanding of cell biology, of drug target discovery, and in metabolic therapy. Remarkable successes in these fields emerged from heuristics approaches, for instance, with the introduction of effective strategies for genetic modifications, drug developments and optimization of bioprocess management. However, heuristics approaches have showed significant shortcomings, such as to describe regulation of metabolic pathways and to extrapolate experimental conditions. In the specific case of bioprocess management, such shortcomings limit their capacity to increase product quality, while maintaining desirable productivity and reproducibility levels. For instance, since heuristics approaches are not capable of prediction of the cellular functions under varying experimental conditions, they may lead to sub-optimal processes. Also, such approaches used for bioprocess control often fail in regulating a process under unexpected variations of external conditions. Therefore, methodologies inspired by the systematic mathematical formulation of cell metabolism have been used to address such drawbacks and achieve robust reproducible results. Mathematical modelling approaches are effective for both the characterization of the cell physiology, and the estimation of metabolic pathways utilization, thus allowing to characterize a cell population metabolic behavior. In this article, we present a review on methodology used and promising mathematical modelling approaches, focusing primarily to investigate metabolic events and regulation. Proceeding from a topological representation of the metabolic networks, we first present the metabolic modelling approaches that investigate cell metabolism at steady state, complying to the constraints imposed by mass conservation law and thermodynamics of reactions reversibility. Constraint-based models (CBMs) are reviewed highlighting the set of assumed optimality functions for reaction pathways. We explore models simulating cell growth dynamics, by expanding flux balance models developed at steady state. Then, discussing a change of metabolic modelling paradigm, we describe dynamic kinetic models that are based on the mathematical representation of the mechanistic description of nonlinear enzyme activities. In such approaches metabolic pathway regulations are considered explicitly as a function of the activity of other components of metabolic networks and possibly far from the metabolic steady state. We have also assessed the significance of metabolic model parameterization in kinetic models, summarizing a standard parameter estimation procedure frequently employed in kinetic metabolic modelling literature. Finally, some optimization practices used for the parameter estimation are reviewed.

Tracing the footsteps of autophagy in computational biology

Autophagy plays a crucial role in maintaining cellular homeostasis through the degradation of unwanted materials like damaged mitochondria and misfolded proteins. However, the contribution of autophagy toward a healthy cell environment is not only limited to the cleaning process. It also assists in protein synthesis when the system lacks the amino acids’ inflow from the extracellular environment due to diet consumptions. Reduction in the autophagy process is associated with diseases like cancer, diabetes, non-alcoholic steatohepatitis, etc., while uncontrolled autophagy may facilitate cell death. We need a better understanding of the autophagy processes and their regulatory mechanisms at various levels (molecules, cells, tissues). This demands a thorough understanding of the system with the help of mathematical and computational tools. The present review illuminates how systems biology approaches are being used for the study of the autophagy process. A comprehensive insight is provided on the application of computational methods involving mathematical modeling and network analysis in the autophagy process. Various mathematical models based on the system of differential equations for studying autophagy are covered here. We have also highlighted the significance of network analysis and machine learning in capturing the core regulatory machinery governing the autophagy process. We explored the available autophagic databases and related resources along with their attributes that are useful in investigating autophagy through computational methods. We conclude the article addressing the potential future perspective in this area, which might provide a more in-depth insight into the dynamics of autophagy.

Domain-Specific Programming Languages for Computational Nucleic Acid Systems

The construction of models of system behavior is of great importance throughout science and engineering. In bioengineering and bionanotechnology, these often take the form of dynamic models that specify the evolution of different species over time. To ensure that scientific observations and conclusions are consistent and that systems can be reliably engineered on the basis of model predictions, it is important that models of biomolecular systems can be constructed in a reliable, principled, and efficient manner. This review focuses on efforts to address this need by using domain-specific programming languages as the basis for custom design tools for researchers working on computational nucleic acid devices, where a domain-specific language is simply a programming language tailored to a particular application domain. The underlying thesis of our review is that there is a continuum of practical implementation strategies for computational nucleic acid systems, which can all benefit from appropriate domain-specific languages and software design tools. We emphasize the need for specialized yet flexible tools that can be realized using domain-specific languages that compile to more general-purpose representations.

A Role of Inflammation and Immunity in Essential Hypertension-Modeled and Analyzed Using Petri Nets

Recent studies have shown that the innate and adaptive immune system, together with low-grade inflammation, may play an important role in essential hypertension. In this work, to verify the importance of selected factors for the development of essential hypertension, we created a Petri net-based model and analyzed it. The analysis was based mainly on t-invariants, knockouts of selected fragments of the net and its simulations. The blockade of the renin-angiotensin (RAA) system revealed that the most significant effect on the emergence of essential hypertension has RAA activation. This blockade affects: (1) the formation of angiotensin II, (2) inflammatory process (by influencing C-reactive protein (CRP)), (3) the initiation of blood coagulation, (4) bradykinin generation via the kallikrein-kinin system, (5) activation of lymphocytes in hypertension, (6) the participation of TNF alpha in the activation of the acute phase response, and (7) activation of NADPH oxidase-a key enzyme of oxidative stress. On the other hand, we found that the blockade of the activation of the RAA system may not eliminate hypertension that can occur due to disturbances associated with the osmotically independent binding of Na in the interstitium. Moreover, we revealed that inflammation alone is not enough to trigger primary hypertension, but it can coexist with it. We believe that our research may contribute to a better understanding of the pathology of hypertension. It can help identify potential subprocesses, which blocking will allow better control of essential hypertension.

Biological Network Visualization for Targeted Proteomics Based on Mean First-Passage Time in Semi-Lazy Random Walks

Experimental data from protein microarrays or other targeted assays are often analyzed using network-based visualization and modeling approaches. Reference networks, such as a graph of known protein-protein interactions, can be used to place experimental data in the context of biological pathways, making the results more interpretable. The first step in network-based visualization and modeling involves mapping the measured experimental endpoints to network nodes, but in targeted assays many network nodes have no corresponding measured endpoints. This leads to a novel problem – given full network structure and a subset of vertices that correspond to measured protein endpoints, infer connectivity between those vertices. We solve the problem by defining a semi-lazy random walk in directed graphs, and quantifying the mean first-passage time for graph nodes. Using simulated and real networks and data, we show that the graph connectivity structure inferred by the proposed method has higher agreement with underlying biology than two alternative strategies.

Cloning the λ Switch: Digital and Markov Representations

The lysis-lysogeny switch in E. coli due to infection from lambda phage has been extensively studied and explained by scientists of molecular biology. The bacterium either survives with the viral strand of deoxyribonucleic acid (DNA) or dies producing hundreds of viruses for propagation of infection. Many proteins transcribed after infection by λ phage take part in determining the fate of the bacterium, but two proteins that play a key role in this regard are the cI and cro dimers, which are transcribed off the viral DNA. This paper presents a novel modeling mechanism for the lysis-lysogeny switch, by transferring the interactions of the main proteins, the lambda right operator and promoter regions and the ribonucleic acid (RNA) polymerase, to a finite state machine (FSM), to determine cell fate. The FSM, and thus derived is implemented in field-programmable gate array (FPGA), and simulations have been run in random conditions. A Markov model has been created for the same mechanism. Steady state analysis has been conducted for the transition matrix of the Markov model, and the results have been generated to show the steady state probability of lysis with various model values. In this paper, it is hoped to lay down guidelines to convert biological processes into computing machines.

Recent advances in biomedical simulations: a manifesto for model engineering

Biomedical simulations are widely used to understand disease, engineer cells, and model cellular processes. In this article, we explore how to improve the quality of biomedical simulations by developing simulation models using tools and practices employed in software engineering. We refer to this direction as model engineering. Not all techniques used by software engineers are directly applicable to model engineering, and so some adaptations are required. That said, we believe that simulation models can benefit from software engineering practices for requirements, design, and construction as well as from software engineering tools for version control, error checking, and testing. Here we survey current efforts to improve simulation quality and discuss promising research directions for model engineering.

Modeling and Simulating the Aerobic Carbon Metabolism of a Green Microalga Using Petri Nets and New Concepts of VANESA

In this work we present new concepts of VANESA, a tool for modeling and simulation in systems biology. We provide a convenient way to handle mathematical expressions and take physical units into account. Simulation and result management has been improved, and syntax and consistency checks, based on physical units, reduce modeling errors. As a proof of concept, essential components of the aerobic carbon metabolism of the green microalga Chlamydomonas reinhardtii are modeled and simulated. The modeling process is based on xHPN Petri net formalism and simulation is performed with OpenModelica, a powerful environment and compiler for Modelica. VANESA, as well as OpenModelica, is open source, free-of-charge for non-commercial use, and is available at: http://agbi.techfak.uni-bielefeld.de/vanesa.

Analyzing the Behavior of Neuronal Pathways in Alzheimer's Disease Using Petri Net Modeling Approach

Alzheimer's Disease (AD) is the most common neuro-degenerative disorder in the elderly that leads to dementia. The hallmark of AD is senile lesions made by abnormal aggregation of amyloid beta in extracellular space of brain. One of the challenges in AD treatment is to better understand the mechanism of action of key proteins and their related pathways involved in neuronal cell death in order to identify adequate therapeutic targets. This study focuses on the phenomenon of aggregation of amyloid beta into plaques by considering the signal transduction pathways of Calpain-Calpastatin (CAST) regulation system and Amyloid Precursor Protein (APP) processing pathways along with Ca2+ channels. These pathways are modeled and analyzed individually as well as collectively through Stochastic Petri Nets for comprehensive analysis and thorough understating of AD. The model predicts that the deregulation of Calpain activity, disruption of Calcium homeostasis, inhibition of CAST and elevation of abnormal APP processing are key cytotoxic events resulting in an early AD onset and progression. Interestingly, the model also reveals that plaques accumulation start early (at the age of 40) in life but symptoms appear late. These results suggest that the process of neuro-degeneration can be slowed down or paused by slowing down the degradation rate of Calpain-CAST Complex. In the light of this study, the suggestive therapeutic strategy might be the prevention of the degradation of Calpain-CAST complexes and the inhibition of Calpain for the treatment of neurodegenerative diseases such as AD.

Handling variability and incompleteness of biological data by flexible nets: a case study for Wilson disease

Mathematical models that combine predictive accuracy with explanatory power are central to the progress of systems and synthetic biology, but the heterogeneity and incompleteness of biological data impede our ability to construct such models. Furthermore, the robustness displayed by many biological systems means that they have the flexibility to operate under a range of physiological conditions and this is difficult for many modeling formalisms to handle. Flexible nets (FNs) address these challenges and represent a paradigm shift in model-based analysis of biological systems. FNs can: (i) handle uncertainties, ranges and missing information in concentrations, stoichiometry, network topology, and transition rates without having to resort to statistical approaches; (ii) accommodate different types of data in a unified model that integrates various cellular mechanisms; and (iii) be employed for system optimization and model predictive control. We present FNs and illustrate their capabilities by modeling a well-established system, the dynamics of glucose consumption by a microbial population. We further demonstrate the ability of FNs to take control actions in response to genetic or metabolic perturbations. Having bench-marked the system, we then construct the first quantitative model for Wilson disease—a rare genetic disorder that impairs copper utilization in the liver. We used this model to investigate the feasibility of using vitamin E supplementation therapy for symptomatic improvement. Our results indicate that hepatocytic inflammation caused by copper accumulation was not aggravated by limitations on endogenous antioxidant supplies, which means that treating patients with antioxidants is unlikely to be effective.

In order to study complex dynamical systems, appropriate mathematical models that capture the system features are necessary. Biological systems, in particular, require flexible modeling approaches for their study since they exhibit variable quantifiable responses under different conditions. Moreover, data about a given biological system are often uncertain or unavailable. Here, a group of scientists from the University of Cambridge introduce Flexible Nets (FNs), a novel approach for the modeling, analysis, and control of biological systems. After presenting the FN approach, they show how a well-known system of glucose consumption and utilization by yeast can be modeled, analyzed and controlled. Then, FNs are used to build and analyze the first quantitative and predictive model of Wilson disease (a heritable defect in copper utilization). They demonstrate that FN simulations permit an evaluation of the relative efficacy of different therapeutic options.

Computational Systems Biology in Cancer: Modeling Methods and Applications

In recent years it has become clear that carcinogenesis is a complex process, both at the molecular and cellular levels. Understanding the origins, growth and spread of cancer, therefore requires an integrated or system-wide approach. Computational systems biology is an emerging sub-discipline in systems biology that utilizes the wealth of data from genomic, proteomic and metabolomic studies to build computer simulations of intra and intercellular processes. Several useful descriptive and predictive models of the origin, growth and spread of cancers have been developed in an effort to better understand the disease and potential therapeutic approaches. In this review we describe and assess the practical and theoretical underpinnings of commonly-used modeling approaches, including ordinary and partial differential equations, petri nets, cellular automata, agent based models and hybrid systems. A number of computer-based formalisms have been implemented to improve the accessibility of the various approaches to researchers whose primary interest lies outside of model development. We discuss several of these and describe how they have led to novel insights into tumor genesis, growth, apoptosis, vascularization and therapy.

The best models of metabolism

Biochemical systems are among of the oldest application areas of mathematical modeling. Spanning a time period of over one hundred years, the repertoire of options for structuring a model and for formulating reactions has been constantly growing, and yet, it is still unclear whether or to what degree some models are better than others and how the modeler is to choose among them. In fact, the variety of options has become overwhelming and difficult to maneuver for novices and experts alike. This review outlines the metabolic model design process and discusses the numerous choices for modeling frameworks and mathematical representations. It tries to be inclusive, even though it cannot be complete, and introduces the various modeling options in a manner that is as unbiased as that is feasible. However, the review does end with personal recommendations for the choices of default models. WIREs Syst Biol Med 2017, 9:e1391. doi: 10.1002/wsbm.1391 For further resources related to this article, please visit the WIREs website.

Integration of Genome Scale Metabolic Networks and Gene Regulation of Metabolic Enzymes With Physiologically Based Pharmacokinetics

The scope of physiologically based pharmacokinetic (PBPK) modeling can be expanded by assimilation of the mechanistic models of intracellular processes from systems biology field. The genome scale metabolic networks (GSMNs) represent a whole set of metabolic enzymes expressed in human tissues. Dynamic models of the gene regulation of key drug metabolism enzymes are available. Here, we introduce GSMNs and review ongoing work on integration of PBPK, GSMNs, and metabolic gene regulation. We demonstrate example models.

Manatee invariants reveal functional pathways in signaling networks

Background

Signal transduction pathways are important cellular processes to maintain the cell’s integrity. Their imbalance can cause severe pathologies. As signal transduction pathways feature complex regulations, they form intertwined networks. Mathematical models aim to capture their regulatory logic and allow an unbiased analysis of robustness and vulnerability of the signaling network. Pathway detection is yet a challenge for the analysis of signaling networks in the field of systems biology. A rigorous mathematical formalism is lacking to identify all possible signal flows in a network model.

Results

In this paper, we introduce the concept of Manatee invariants for the analysis of signal transduction networks. We present an algorithm for the characterization of the combinatorial diversity of signal flows, e.g., from signal reception to cellular response. We demonstrate the concept for a small model of the TNFR1-mediated NF- κB signaling pathway. Manatee invariants reveal all possible signal flows in the network. Further, we show the application of Manatee invariants for in silico knockout experiments. Here, we illustrate the biological relevance of the concept.

Conclusions

The proposed mathematical framework reveals the entire variety of signal flows in models of signaling systems, including cyclic regulations. Thereby, Manatee invariants allow for the analysis of robustness and vulnerability of signaling networks. The application to further analyses such as for in silico knockout was shown. The new framework of Manatee invariants contributes to an advanced examination of signaling systems.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0448-7) contains supplementary material, which is available to authorized users.

Formal reasoning about systems biology using theorem proving

System biology provides the basis to understand the behavioral properties of complex biological organisms at different levels of abstraction. Traditionally, analysing systems biology based models of various diseases have been carried out by paper-and-pencil based proofs and simulations. However, these methods cannot provide an accurate analysis, which is a serious drawback for the safety-critical domain of human medicine. In order to overcome these limitations, we propose a framework to formally analyze biological networks and pathways. In particular, we formalize the notion of reaction kinetics in higher-order logic and formally verify some of the commonly used reaction based models of biological networks using the HOL Light theorem prover. Furthermore, we have ported our earlier formalization of Zsyntax, i.e., a deductive language for reasoning about biological networks and pathways, from HOL4 to the HOL Light theorem prover to make it compatible with the above-mentioned formalization of reaction kinetics. To illustrate the usefulness of the proposed framework, we present the formal analysis of three case studies, i.e., the pathway leading to TP53 Phosphorylation, the pathway leading to the death of cancer stem cells and the tumor growth based on cancer stem cells, which is used for the prognosis and future drug designs to treat cancer patients.

A hybrid stochastic model of folate-mediated one-carbon metabolism: Effect of the common C677T MTHFR variant on de novo thymidylate biosynthesis

Folate-mediated one-carbon metabolism (FOCM) is an interconnected network of metabolic pathways, including those required for the de novo synthesis of dTMP and purine nucleotides and for remethylation of homocysteine to methionine. Mouse models of folate-responsive neural tube defects (NTDs) indicate that impaired de novo thymidylate (dTMP) synthesis through changes in SHMT expression is causative in folate-responsive NTDs. We have created a hybrid computational model comprised of ordinary differential equations and stochastic simulation. We investigated whether the de novo dTMP synthesis pathway was sensitive to perturbations in FOCM that are known to be associated with human NTDs. This computational model shows that de novo dTMP synthesis is highly sensitive to the common MTHFR C677T polymorphism and that the effect of the polymorphism on FOCM is greater in folate deficiency. Computational simulations indicate that the MTHFR C677T polymorphism and folate deficiency interact to increase the stochastic behavior of the FOCM network, with the greatest instability observed for reactions catalyzed by serine hydroxymethyltransferase (SHMT). Furthermore, we show that de novo dTMP synthesis does not occur in the cytosol at rates sufficient for DNA replication, supporting empirical data indicating that impaired nuclear de novo dTMP synthesis results in uracil misincorporation into DNA.

Mathematical Modelling of Bacterial Quorum Sensing: A Review

Bacterial quorum sensing (QS) refers to the process of cell-to-cell bacterial communication enabled through the production and sensing of the local concentration of small molecules called autoinducers to regulate the production of gene products (e.g. enzymes or virulence factors). Through autoinducers, bacteria interact with individuals of the same species, other bacterial species, and with their host. Among QS-regulated processes mediated through autoinducers are aggregation, biofilm formation, bioluminescence, and sporulation. Autoinducers are therefore "master" regulators of bacterial lifestyles. For over 10 years, mathematical modelling of QS has sought, in parallel to experimental discoveries, to elucidate the mechanisms regulating this process. In this review, we present the progress in mathematical modelling of QS, highlighting the various theoretical approaches that have been used and discussing some of the insights that have emerged. Modelling of QS has benefited almost from the onset of the involvement of experimentalists, with many of the papers which we review, published in non-mathematical journals. This review therefore attempts to give a broad overview of the topic to the mathematical biology community, as well as the current modelling efforts and future challenges.

Computational modeling in melanoma for novel drug discovery

INTRODUCTION

There is a growing body of evidence highlighting the applications of computational modeling in the field of biomedicine. It has recently been applied to the in silico analysis of cancer dynamics. In the era of precision medicine, this analysis may allow the discovery of new molecular targets useful for the design of novel therapies and for overcoming resistance to anticancer drugs. According to its molecular behavior, melanoma represents an interesting tumor model in which computational modeling can be applied. Melanoma is an aggressive tumor of the skin with a poor prognosis for patients with advanced disease as it is resistant to current therapeutic approaches.

AREAS COVERED

This review discusses the basics of computational modeling in melanoma drug discovery and development. Discussion includes the in silico discovery of novel molecular drug targets, the optimization of immunotherapies and personalized medicine trials.

EXPERT OPINION

Mathematical and computational models are gradually being used to help understand biomedical data produced by high-throughput analysis. The use of advanced computer models allowing the simulation of complex biological processes provides hypotheses and supports experimental design. The research in fighting aggressive cancers, such as melanoma, is making great strides. Computational models represent the key component to complement these efforts. Due to the combinatorial complexity of new drug discovery, a systematic approach based only on experimentation is not possible. Computational and mathematical models are necessary for bringing cancer drug discovery into the era of omics, big data and personalized medicine.

Fuzzy Stochastic Petri Nets for Modeling Biological Systems with Uncertain Kinetic Parameters

Stochastic Petri nets (SPNs) have been widely used to model randomness which is an inherent feature of biological systems. However, for many biological systems, some kinetic parameters may be uncertain due to incomplete, vague or missing kinetic data (often called fuzzy uncertainty), or naturally vary, e.g., between different individuals, experimental conditions, etc. (often called variability), which has prevented a wider application of SPNs that require accurate parameters. Considering the strength of fuzzy sets to deal with uncertain information, we apply a specific type of stochastic Petri nets, fuzzy stochastic Petri nets (FSPNs), to model and analyze biological systems with uncertain kinetic parameters. FSPNs combine SPNs and fuzzy sets, thereby taking into account both randomness and fuzziness of biological systems. For a biological system, SPNs model the randomness, while fuzzy sets model kinetic parameters with fuzzy uncertainty or variability by associating each parameter with a fuzzy number instead of a crisp real value. We introduce a simulation-based analysis method for FSPNs to explore the uncertainties of outputs resulting from the uncertainties associated with input parameters, which works equally well for bounded and unbounded models. We illustrate our approach using a yeast polarization model having an infinite state space, which shows the appropriateness of FSPNs in combination with simulation-based analysis for modeling and analyzing biological systems with uncertain information.

Auxin-driven patterning with unidirectional fluxes

The plant hormone auxin plays an essential role in the patterning of plant structures. Biological hypotheses supported by computational models suggest that auxin may fulfil this role by regulating its own transport, but the plausibility of previously proposed models has been questioned. We applied the notion of unidirectional fluxes and the formalism of Petri nets to show that the key modes of auxin-driven patterning-the formation of convergence points and the formation of canals-can be implemented by biochemically plausible networks, with the fluxes measured by dedicated tally molecules or by efflux and influx carriers themselves. Common elements of these networks include a positive feedback of auxin efflux on the allocation of membrane-bound auxin efflux carriers (PIN proteins), and a modulation of this allocation by auxin in the extracellular space. Auxin concentration in the extracellular space is the only information exchanged by the cells. Canalization patterns are produced when auxin efflux and influx act antagonistically: an increase in auxin influx or concentration in the extracellular space decreases the abundance of efflux carriers in the adjacent segment of the membrane. In contrast, convergence points emerge in networks in which auxin efflux and influx act synergistically. A change in a single reaction rate may result in a dynamic switch between these modes, suggesting plausible molecular implementations of coordinated patterning of organ initials and vascular strands predicted by the dual polarization theory.

Stochastic S-system modeling of gene regulatory network

Microarray gene expression data can provide insights into biological processes at a system-wide level and is commonly used for reverse engineering gene regulatory networks (GRN). Due to the amalgamation of noise from different sources, microarray expression profiles become inherently noisy leading to significant impact on the GRN reconstruction process. Microarray replicates (both biological and technical), generated to increase the reliability of data obtained under noisy conditions, have limited influence in enhancing the accuracy of reconstruction . Therefore, instead of the conventional GRN modeling approaches which are deterministic, stochastic techniques are becoming increasingly necessary for inferring GRN from noisy microarray data. In this paper, we propose a new stochastic GRN model by investigating incorporation of various standard noise measurements in the deterministic S-system model. Experimental evaluations performed for varying sizes of synthetic network, representing different stochastic processes, demonstrate the effect of noise on the accuracy of genetic network modeling and the significance of stochastic modeling for GRN reconstruction . The proposed stochastic model is subsequently applied to infer the regulations among genes in two real life networks: (1) the well-studied IRMA network, a real-life in-vivo synthetic network constructed within the Saccharomyces cerevisiae yeast, and (2) the SOS DNA repair network in Escherichia coli.

Using Petri nets for experimental design in a multi-organ elimination pathway

Genistein is a soy metabolite with estrogenic activity that may result in (un)favorable effects on human health. Elucidation of the mechanisms through which food additives such as genistein exert their beneficiary effects is a major challenge for the food industry. A better understanding of the genistein elimination pathway could shed light on such mechanisms. We developed a Petri net model that represents this multi-organ elimination pathway and which assists in the design of future experiments. Using this model we show that metabolic profiles solely measured in venous blood are not sufficient to uniquely parameterize the model. Based on simulations we suggest two solutions that provide better results: parameterize the model using gut epithelium profiles or add additional biological constrains in the model.

Methodologies for the modeling and simulation of biochemical networks, illustrated for signal transduction pathways: a primer

Biochemical networks depict the chemical interactions that take place among elements of living cells. They aim to elucidate how cellular behavior and functional properties of the cell emerge from the relationships between its components, i.e. molecules. Biochemical networks are largely characterized by dynamic behavior, and exhibit high degrees of complexity. Hence, the interest in such networks is growing and they have been the target of several recent modeling efforts. Signal transduction pathways (STPs) constitute a class of biochemical networks that receive, process, and respond to stimuli from the environment, as well as stimuli that are internal to the organism. An STP consists of a chain of intracellular signaling processes that ultimately result in generating different cellular responses. This primer presents the methodologies used for the modeling and simulation of biochemical networks, illustrated for STPs. These methodologies range from qualitative to quantitative, and include structural as well as dynamic analysis techniques. We describe the different methodologies, outline their underlying assumptions, and provide an assessment of their advantages and disadvantages. Moreover, publicly and/or commercially available implementations of these methodologies are listed as appropriate. In particular, this primer aims to provide a clear introduction and comprehensive coverage of biochemical modeling and simulation methodologies for the non-expert, with specific focus on relevant literature of STPs.

CN: a consensus algorithm for inferring gene regulatory networks using the SORDER algorithm and conditional mutual information test

Inferring Gene Regulatory Networks (GRNs) from gene expression data is a major challenge in systems biology. The Path Consistency (PC) algorithm is one of the popular methods in this field. However, as an order dependent algorithm, PC algorithm is not robust because it achieves different network topologies if gene orders are permuted. In addition, the performance of this algorithm depends on the threshold value used for independence tests. Consequently, selecting suitable sequential ordering of nodes and an appropriate threshold value for the inputs of PC algorithm are challenges to infer a good GRN. In this work, we propose a heuristic algorithm, namely SORDER, to find a suitable sequential ordering of nodes. Based on the SORDER algorithm and a suitable interval threshold for Conditional Mutual Information (CMI) tests, a network inference method, namely the Consensus Network (CN), has been developed. In the proposed method, for each edge of the complete graph, a weighted value is defined. This value is considered as the reliability value of dependency between two nodes. The final inferred network, obtained using the CN algorithm, contains edges with a reliability value of dependency of more than a defined threshold. The effectiveness of this method is benchmarked through several networks from the DREAM challenge and the widely used SOS DNA repair network in Escherichia coli. The results indicate that the CN algorithm is suitable for learning GRNs and it considerably improves the precision of network inference. The source of data sets and codes are available at .

An introduction to systems toxicology

Systems toxicology combines novel and historical experimental data to generate increasingly complex models of the biological response to chemical exposure.

esyN: network building, sharing and publishing

The construction and analysis of networks is increasingly widespread in biological research. We have developed esyN ("easy networks") as a free and open source tool to facilitate the exchange of biological network models between researchers. esyN acts as a searchable database of user-created networks from any field. We have developed a simple companion web tool that enables users to view and edit networks using data from publicly available databases. Both normal interaction networks (graphs) and Petri nets can be created. In addition to its basic tools, esyN contains a number of logical templates that can be used to create models more easily. The ability to use previously published models as building blocks makes esyN a powerful tool for the construction of models and network graphs. Users are able to save their own projects online and share them either publicly or with a list of collaborators. The latter can be given the ability to edit the network themselves, allowing online collaboration on network construction. esyN is designed to facilitate unrestricted exchange of this increasingly important type of biological information. Ultimately, the aim of esyN is to bring the advantages of Open Source software development to the construction of biological networks.

Genome scale modeling in systems biology: algorithms and resources

In recent years, in silico studies and trial simulations have complemented experimental procedures. A model is a description of a system, and a system is any collection of interrelated objects; an object, moreover, is some elemental unit upon which observations can be made but whose internal structure either does not exist or is ignored. Therefore, any network analysis approach is critical for successful quantitative modeling of biological systems. This review highlights some of most popular and important modeling algorithms, tools, and emerging standards for representing, simulating and analyzing cellular networks in five sections. Also, we try to show these concepts by means of simple example and proper images and graphs. Overall, systems biology aims for a holistic description and understanding of biological processes by an integration of analytical experimental approaches along with synthetic computational models. In fact, biological networks have been developed as a platform for integrating information from high to low-throughput experiments for the analysis of biological systems. We provide an overview of all processes used in modeling and simulating biological networks in such a way that they can become easily understandable for researchers with both biological and mathematical backgrounds. Consequently, given the complexity of generated experimental data and cellular networks, it is no surprise that researchers have turned to computer simulation and the development of more theory-based approaches to augment and assist in the development of a fully quantitative understanding of cellular dynamics.

Cancer systems biology and modeling: microscopic scale and multiscale approaches

Cancer has become known as a complex and systematic disease on macroscopic, mesoscopic and microscopic scales. Systems biology employs state-of-the-art computational theories and high-throughput experimental data to model and simulate complex biological procedures such as cancer, which involves genetic and epigenetic, in addition to intracellular and extracellular complex interaction networks. In this paper, different systems biology modeling techniques such as systems of differential equations, stochastic methods, Boolean networks, Petri nets, cellular automata methods and agent-based systems are concisely discussed. We have compared the mentioned formalisms and tried to address the span of applicability they can bear on emerging cancer modeling and simulation approaches. Different scales of cancer modeling, namely, microscopic, mesoscopic and macroscopic scales are explained followed by an illustration of angiogenesis in microscopic scale of the cancer modeling. Then, the modeling of cancer cell proliferation and survival are examined on a microscopic scale and the modeling of multiscale tumor growth is explained along with its advantages.

QSSPN: dynamic simulation of molecular interaction networks describing gene regulation, signalling and whole-cell metabolism in human cells

MOTIVATION

Dynamic simulation of genome-scale molecular interaction networks will enable the mechanistic prediction of genotype-phenotype relationships. Despite advances in quantitative biology, full parameterization of whole-cell models is not yet possible. Simulation methods capable of using available qualitative data are required to develop dynamic whole-cell models through an iterative process of modelling and experimental validation.

RESULTS

We formulate quasi-steady state Petri nets (QSSPN), a novel method integrating Petri nets and constraint-based analysis to predict the feasibility of qualitative dynamic behaviours in qualitative models of gene regulation, signalling and whole-cell metabolism. We present the first dynamic simulations including regulatory mechanisms and a genome-scale metabolic network in human cell, using bile acid homeostasis in human hepatocytes as a case study. QSSPN simulations reproduce experimentally determined qualitative dynamic behaviours and permit mechanistic analysis of genotype-phenotype relationships.

AVAILABILITY AND IMPLEMENTATION

The model and simulation software implemented in C++ are available in supplementary material and at http://sysbio3.fhms.surrey.ac.uk/qsspn/.

Animal models of enteroaggregative Escherichia coli infection

Enteroaggregative Escherichia coli (EAEC) has been acknowledged as an emerging cause of gastroenteritis worldwide for over two decades. Epidemiologists are revealing the role of EAEC in diarrheal outbreaks as a more common occurrence than ever suggested before. EAEC induced diarrhea is most commonly associated with travelers, children and immunocompromised individuals however its afflictions are not limited to any particular demographic. Many attributes have been discovered and characterized surrounding the capability of EAEC to provoke a potent pro-inflammatory immune response, however cellular and molecular mechanisms underlying initiation, progression and outcomes are largely unknown. This limited understanding can be attributed to heterogeneity in strains and the lack of adequate animal models. This review aims to summarize current knowledge about EAEC etiology, pathogenesis and clinical manifestation. Additionally, current animal models and their limitations will be discussed along with the value of applying systems-wide approaches such as computational modeling to study host-EAEC interactions.

Multi-level model for the investigation of oncoantigen-driven vaccination effect

Background

Cancer stem cell theory suggests that cancers are derived by a population of cells named Cancer Stem Cells (CSCs) that are involved in the growth and in the progression of tumors, and lead to a hierarchical structure characterized by differentiated cell population. This cell heterogeneity affects the choice of cancer therapies, since many current cancer treatments have limited or no impact at all on CSC population, while they reveal a positive effect on the differentiated cell populations.

Results

In this paper we investigated the effect of vaccination on a cancer hierarchical structure through a multi-level model representing both population and molecular aspects. The population level is modeled by a system of Ordinary Differential Equations (ODEs) describing the cancer population's dynamics. The molecular level is modeled using the Petri Net (PN) formalism to detail part of the proliferation pathway. Moreover, we propose a new methodology which exploits the temporal behavior derived from the molecular level to parameterize the ODE system modeling populations. Using this multi-level model we studied the ErbB2-driven vaccination effect in breast cancer.

Conclusions

We propose a multi-level model that describes the inter-dependencies between population and genetic levels, and that can be efficiently used to estimate the efficacy of drug and vaccine therapies in cancer models, given the availability of molecular data on the cancer driving force.

Approaches to modeling gene regulatory networks: a gentle introduction

This chapter is split into two main sections; first, I will present an introduction to gene networks. Second, I will discuss various approaches to gene network modeling which will include some examples for using different data sources. Computational modeling has been used for many different biological systems and many approaches have been developed addressing the different needs posed by the different application fields. The modeling approaches presented here are not limited to gene regulatory networks and occasionally I will present other examples. The material covered here is an update based on several previous publications by Thomas Schlitt and Alvis Brazma (FEBS Lett 579(8),1859-1866, 2005; Philos Trans R Soc Lond B Biol Sci 361(1467), 483-494, 2006; BMC Bioinformatics 8(suppl 6), S9, 2007) that formed the foundation for a lecture on gene regulatory networks at the In Silico Systems Biology workshop series at the European Bioinformatics Institute in Hinxton.

A proposal for augmenting biological model construction with a semi-intelligent computational modeling assistant

The translational challenge in biomedical research lies in the effective and efficient transfer of mechanistic knowledge from one biological context to another. Implicit in this process is the establishment of causality from correlation in the form of mechanistic hypotheses. Effectively addressing the translational challenge requires the use of automated methods, including the ability to computationally capture the dynamic aspect of putative hypotheses such that they can be evaluated in a high throughput fashion. Ontologies provide structure and organization to biomedical knowledge; converting these representations into executable models/simulations is the next necessary step. Researchers need the ability to map their conceptual models into a model specification that can be transformed into an executable simulation program. We suggest this mapping process, which approximates certain steps in the development of a computational model, can be expressed as a set of logical rules, and a semi-intelligent computational agent, the Computational Modeling Assistant (CMA), can perform reasoning to develop a plan to achieve the construction of an executable model. Presented herein is a description and implementation for a model construction reasoning process between biomedical and simulation ontologies that is performed by the CMA to produce the specification of an executable model that can be used for dynamic knowledge representation.

Automatic identification of model reductions for discrete stochastic simulation

Multiple time scales in cellular chemical reaction systems present a challenge for the efficiency of stochastic simulation. Numerous model reductions have been proposed to accelerate the simulation of chemically reacting systems by exploiting time scale separation. However, these are often identified and deployed manually, requiring expert knowledge. This is time-consuming, prone to error, and opportunities for model reduction may be missed, particularly for large models. We propose an automatic model analysis algorithm using an adaptively weighted Petri net to dynamically identify opportunities for model reductions for both the stochastic simulation algorithm and tau-leaping simulation, with no requirement of expert knowledge input. Results are presented to demonstrate the utility and effectiveness of this approach.

Understanding cancer mechanisms through network dynamics

Cancer is a complex, multifaceted disease. Cellular systems are perturbed both during the onset and development of cancer, and the behavioural change of tumour cells usually involves a broad range of dynamic variations. To an extent, the difficulty of monitoring the systemic change has been alleviated by recent developments in the high-throughput technologies. At both the genomic as well as proteomic levels, the technological advances in microarray and mass spectrometry, in conjunction with computational simulations and the construction of human interactome maps have facilitated the progress of identifying disease-associated genes. On a systems level, computational approaches developed for network analysis are becoming especially useful for providing insights into the mechanism behind tumour development and metastasis. This review emphasizes network approaches that have been developed to study cancer and provides an overview of our current knowledge of protein-protein interaction networks, and how their systemic perturbation can be analysed by two popular network simulation methods: Boolean network and ordinary differential equations.

Specification, construction, and exact reduction of state transition system models of biochemical processes

Biochemical reaction systems may be viewed as discrete event processes characterized by a number of states and state transitions. These systems may be modeled as state transition systems with transitions representing individual reaction events. Since they often involve a large number of interactions, it can be difficult to construct such a model for a system, and since the resulting state-level model can involve a huge number of states, model analysis can be difficult or impossible. Here, we describe methods for the high-level specification of a system using hypergraphs, for the automated generation of a state-level model from a high-level model, and for the exact reduction of a state-level model using information from the high-level model. Exact reduction is achieved through the automated application to the high-level model of the symmetry reduction technique and reduction by decomposition by independent subsystems, allowing potentially significant reductions without the need to generate a full model. The application of the method to biochemical reaction systems is illustrated by models describing a hypothetical ion-channel at several levels of complexity. The method allows for the reduction of the otherwise intractable example models to a manageable size.

Accurate estimation of nucleic acids by amplification efficiency dependent PCR

Accurate estimation of template - DNA or RNA by real time PCR is dependent on the amplification efficiency (F) of the reaction. The analytical equation describing the kinetics of PCR that is influenced by template re-annealing is formulated. It predicts the gradual reduction of F - from its initial value of 2, leading to template saturation. From an experimental standpoint, due to the exponential nature of the reaction a minute change in F can lead to a large error in the estimation of the initial template concentration. On the basis of individual variation in the amplification efficiency we have formulated a simple mathematical model and an MS Excel based data analysis software that allows accurate and automated quantification of initial template concentration. This method which does not require any normalisation with housekeeping genes was validated by transcript profiling of the genes in the TCA/glyoxylate cycle of E. coli. Consistent with published reports, we observed a precise and specific induction of the glyoxylate shunt genes when the bacteria was shifted from a six carbon glucose media to a two carbon source like acetate.