Modelling cellular behaviour

A charged existence: A century of transmembrane ion transport in plants

If the past century marked the birth of membrane transport as a focus for research in plants, the past 50 years has seen the field mature from arcane interest to a central pillar of plant physiology. Ion transport across plant membranes accounts for roughly 30% of the metabolic energy consumed by a plant cell, and it underpins virtually every aspect of plant biology, from mineral nutrition, cell expansion, and development to auxin polarity, fertilization, plant pathogen defense, and senescence. The means to quantify ion flux through individual transporters, even single channel proteins, became widely available as voltage clamp methods expanded from giant algal cells to the fungus Neurospora crassa in the 1970s and the cells of angiosperms in the 1980s. Here, I touch briefly on some key aspects of the development of modern electrophysiology with a focus on the guard cells of stomata, now without dispute the premier plant cell model for ion transport and its regulation. Guard cells have proven to be a crucible for many technical and conceptual developments that have since emerged into the mainstream of plant science. Their study continues to provide fundamental insights and carries much importance for the global challenges that face us today.

OnGuard3e: A predictive, ecophysiology-ready tool for gas exchange and photosynthesis research

Gas exchange across the stomatal pores of leaves is a focal point in studies of plant-environmental relations. Stomata regulate atmospheric exchange with the inner air spaces of the leaf. They open to allow CO2 entry for photosynthesis and close to minimize water loss. Models that focus on the phenomenology of stomatal conductance generally omit the mechanics of the guard cells that regulate the pore aperture. The OnGuard platform fills this gap and offers a truly mechanistic approach with which to analyse stomatal gas exchange, whole-plant carbon assimilation and water-use efficiency. Previously, OnGuard required specialist knowledge of membrane transport, signalling and metabolism. Here we introduce OnGuard3e, a software package accessible to ecophysiologists and membrane biologists alike. We provide a brief guide to its use and illustrate how the package can be applied to explore and analyse stomatal conductance, assimilation and water use efficiencies, addressing a range of experimental questions with truly predictive outputs.

Engineering tRNA abundances for synthetic cellular systems

Routinizing the engineering of synthetic cells requires specifying beforehand how many of each molecule are needed. Physics-based tools for estimating desired molecular abundances in whole-cell synthetic biology are missing. Here, we use a colloidal dynamics simulator to make predictions for how tRNA abundances impact protein synthesis rates. We use rational design and direct RNA synthesis to make 21 synthetic tRNA surrogates from scratch. We use evolutionary algorithms within a computer aided design framework to engineer translation systems predicted to work faster or slower depending on tRNA abundance differences. We build and test the so-specified synthetic systems and find qualitative agreement between expected and observed systems. First principles modeling combined with bottom-up experiments can help molecular-to-cellular scale synthetic biology realize design-build-work frameworks that transcend tinker-and-test.

Estimation of Ordinary Differential Equation Models for Gene Regulatory Networks Through Data Cloning

Ordinary differential equations (ODEs) are widely used for elucidating dynamic processes in various fields. One of the applications of ODEs is to describe dynamics of gene regulatory networks (GRNs), which is a critical step in understanding disease mechanisms. However, estimation of ODE models for GRNs is challenging because of inflexibility of the model and noisy data with complex error structures such as heteroscedasticity, correlations between genes, and time dependency. In addition, either a likelihood or Bayesian approach is commonly used for estimation of ODE models, but both approaches have benefits and drawbacks in their own right. Data cloning is a maximum likelihood (ML) estimation method through the Bayesian framework. Since it works in the Bayesian framework, it is free from local optimum problems that are common drawbacks of ML methods. Also, its inference is invariant for the selection of prior distributions, which is a major issue in Bayesian methods. This study proposes an estimation method of ODE models for GRNs through data cloning. The proposed method is demonstrated through simulation and it is applied to real gene expression time-course data.

Colloidal Physics Modeling Reveals How Per-Ribosome Productivity Increases with Growth Rate in Escherichia coli

Faster-growing cells must synthesize proteins more quickly. Increased ribosome abundance only partly accounts for increases in total protein synthesis rates. The productivity of individual ribosomes must increase too, almost doubling by an unknown mechanism. Prior models point to diffusive transport as a limiting factor but raise a paradox: faster-growing cells are more crowded, yet crowding slows diffusion. We suspected that physical crowding, transport, and stoichiometry, considered together, might reveal a more nuanced explanation. To investigate, we built a first-principles physics-based model of Escherichia coli cytoplasm in which Brownian motion and diffusion arise directly from physical interactions between individual molecules of finite size, density, and physiological abundance. Using our microscopically detailed model, we predicted that physical transport of individual ternary complexes accounts for ~80% of translation elongation latency. We also found that volumetric crowding increases during faster growth even as cytoplasmic mass density remains relatively constant. Despite slowed diffusion, we predicted that improved proximity between ternary complexes and ribosomes wins out, illustrating a simple physics-based mechanism for how individual elongating ribosomes become more productive. We speculate that crowding imposes a physical limit on growth rate and undergirds cellular behavior more broadly. Unfitted colloidal-scale modeling offers systems biology a complementary "physics engine" for exploring how cellular-scale behaviors arise from physical transport and reactions among individual molecules. IMPORTANCE Ribosomes are the factories in cells that synthesize proteins. When cells grow faster, there are not enough ribosomes to keep up with the demand for faster protein synthesis without individual ribosomes becoming more productive. Yet, faster-growing cells are more crowded, seemingly making it harder for each ribosome to do its work. Our computational model of the physics of translation elongation reveals the underlying mechanism for how individual ribosomes become more productive: proximity and stoichiometry of translation molecules overcome crowding. Our model also suggests a universal physical limitation of cell growth rates.

What can mechanistic models tell us about guard cells, photosynthesis, and water use efficiency?

Stomatal pores facilitate gaseous exchange between the inner air spaces of the leaf and the atmosphere. The pores open to enable CO₂ entry for photosynthesis and close to reduce transpirational water loss. How stomata respond to the environment has long attracted interest in modeling as a tool to understand the consequences for the plant and for the ecosystem. Models that focus on stomatal conductance for gas exchange make intuitive sense, but such models need also to connect with the mechanics of the guard cells that regulate pore aperture if we are to understand the 'decisions made' by stomata, their impacts on the plant and on the global environment.

Guard cell endomembrane Ca2+-ATPases underpin a 'carbon memory' of photosynthetic assimilation that impacts on water-use efficiency

Stomata of most plants close to preserve water when the demand for CO₂ by photosynthesis is reduced. Stomatal responses are slow compared with photosynthesis, and this kinetic difference erodes assimilation and water-use efficiency under fluctuating light. Despite a deep knowledge of guard cells that regulate the stoma, efforts to enhance stomatal kinetics are limited by our understanding of its control by foliar CO₂. Guided by mechanistic modelling that incorporates foliar CO₂ diffusion and mesophyll photosynthesis, here we uncover a central role for endomembrane Ca²⁺ stores in guard cell responsiveness to fluctuating light and CO₂. Modelling predicted and experiments demonstrated a delay in Ca²⁺ cycling that was enhanced by endomembrane Ca²⁺-ATPase mutants, altering stomatal conductance and reducing assimilation and water-use efficiency. Our findings illustrate the power of modelling to bridge the gap from the guard cell to whole-plant photosynthesis, and they demonstrate an unforeseen latency, or 'carbon memory', of guard cells that affects stomatal dynamics, photosynthesis and water-use efficiency.

Are There Biomimetic Lessons from Genetic Regulatory Networks for Developing a Lunar Industrial Ecology?

We examine the prospect for employing a bio-inspired architecture for a lunar industrial ecology based on genetic regulatory networks. The lunar industrial ecology resembles a metabolic system in that it comprises multiple chemical processes interlinked through waste recycling. Initially, we examine lessons from factory organisation which have evolved into a bio-inspired concept, the reconfigurable holonic architecture. We then examine genetic regulatory networks and their application in the biological cell cycle. There are numerous subtleties that would be challenging to implement in a lunar industrial ecology but much of the essence of biological circuitry (as implemented in synthetic biology, for example) is captured by traditional electrical engineering design with emphasis on feedforward and feedback loops to implement robustness.

BiPSim: a flexible and generic stochastic simulator for polymerization processes

Detailed whole-cell modeling requires an integration of heterogeneous cell processes having different modeling formalisms, for which whole-cell simulation could remain tractable. Here, we introduce BiPSim, an open-source stochastic simulator of template-based polymerization processes, such as replication, transcription and translation. BiPSim combines an efficient abstract representation of reactions and a constant-time implementation of the Gillespie’s Stochastic Simulation Algorithm (SSA) with respect to reactions, which makes it highly efficient to simulate large-scale polymerization processes stochastically. Moreover, multi-level descriptions of polymerization processes can be handled simultaneously, allowing the user to tune a trade-off between simulation speed and model granularity. We evaluated the performance of BiPSim by simulating genome-wide gene expression in bacteria for multiple levels of granularity. Finally, since no cell-type specific information is hard-coded in the simulator, models can easily be adapted to other organismal species. We expect that BiPSim should open new perspectives for the genome-wide simulation of stochastic phenomena in biology.

High-Performance Whole-Cell Simulation Exploiting Modular Cell Biology Principles

One of the grand challenges of this century is modeling and simulating a whole cell. Extreme regulation of an extensive quantity of model and simulation data during whole-cell modeling and simulation renders it a computationally expensive research problem in systems biology. In this article, we present a high-performance whole-cell simulation exploiting modular cell biology principles. We prepare the simulation by dividing the unicellular bacterium, Escherichia coli (E. coli), into subcells utilizing the spatially localized densely connected protein clusters/modules. We set up a Brownian dynamics-based parallel whole-cell simulation framework by utilizing the Hamiltonian mechanics-based equations of motion. Though the velocity Verlet integration algorithm possesses the capability of solving the equations of motion, it lacks the ability to capture and deal with particle-collision scenarios. Hence, we propose an algorithm for detecting and resolving both elastic and inelastic collisions and subsequently modify the velocity Verlet integrator by incorporating our algorithm into it. Also, we address the boundary conditions to arrest the molecules' motion outside the subcell. For efficiency, we define one hashing-based data structure called the cellular dictionary to store all of the subcell-related information. A benchmark analysis of our CUDA C/C++ simulation code when tested on E. coli using the CPU-GPU cluster indicates that the computational time requirement decreases with the increase in the number of computing cores and becomes stable at around 128 cores. Additional testing on higher organisms such as rats and humans informs us that our proposed work can be extended to any organism and is scalable for high-end CPU-GPU clusters.

A new hierarchical approach to multi-level model abstraction for simplifying ODE models of biological networks and a case study: The G1/S Checkpoint/DNA damage signalling pathways of mammalian cell cycle

Model reduction is an important topic in studies of biological systems. By reducing the complexity of large models through multi-level models while keeping the essence (biological meaning) of the model, model reduction can help answer many important questions about these systems. In this paper, we present a new reduction method based on hierarchical representation and a lumping approach. We used G1/S checkpoint pathway represented in Ordinary Differential Equations (ODE) in Iwamoto et al. (2011) as a case study to present this reduction method. The approach consists of two parts; the first part represents the biological network as a hierarchy (multiple levels) based on protein binding relations, which allowed us to model the biological network at different levels of abstraction. The second part applies different levels (level 1, 2 and 3) of lumping the species together depending on the level of the hierarchy, resulting in a reduced and transformed model for each level. The model at each level is a representation of the whole system and can address questions pertinent to that level. We develop and simulate reduced models for levels-1, 2 and 3 of lumping for the G1/S checkpoint pathway and evaluate the biological plausibility of the proposed method by comparing the results with the original ODE model of Iwamoto et al. (2011). The results for continuous dynamics of the G1/S checkpoint pathway with or without DNA-damage for reduced models of level- 1, 2 and 3 of lumping are in very good agreement and consistent with the original model results and with biological findings. Therefore, the reduced models (level-1, 2 and 3) can be used to study cell cycle progression in G1 and the effects of DNA damage on it. It is suitable for reducing complex ODE biological network models while retaining accurate continuous dynamics of the system. The 3 levels of the reduced models respectively achieved 20%, 26% and 31% reduction of the base model. Moreover, the reduced model is more efficient to run (30%, 44% and 52% time reduction for the three levels) and generate solutions than the original ODE model. Simplification of complex mathematical models is possible and the proposed reduction method has the potential to make an impact across many fields of biomedical research.

Heat flow random walks in biomolecular systems using symbolic transfer entropy and graph theory

This study combines the information- and graph-theoretic measures to investigate the cluster modulation of the amino acid residues and nucleotides at complex biomolecular interfaces. The symbolic transfer entropy is used as an information-theoretic measure. I also used graph theory to obtain information and heat flow weighted digraph models used to study the topology of information and heat flow paths at complex biomolecular interfaces. I introduce the graph-theoretic measures, such as the influence score and betweenness centrality, to identify the most influential amino acid and nucleotide sequences as sources of the information and absorb centers of the structure's heat flow. PageRank-like random walks algorithm is used to analyze the network of amino acid and nucleotide sequences at the protein-RNA interface combined with weighted digraph models. The cluster analysis using graph-theoretic measures revealed the modular molecular structure and the mechanism of the binding interface. In this study, the first benchmark system is an intuitive directed information flow network used to test the algorithms, and the second benchmark is a protein-RNA complex system. The approach was able to identify the most influential amino acid residues and nucleotides. Furthermore, the statistical cluster analysis using graph-theoretic measures revealed the modular molecular structure and the binding mechanism at the interface.

Novel Tunable Spatio-Temporal Patterns From a Simple Genetic Oscillator Circuit

Multicellularity, the coordinated collective behavior of cell populations, gives rise to the emergence of self-organized phenomena at many different spatio-temporal scales. At the genetic scale, oscillators are ubiquitous in regulation of multicellular systems, including during their development and regeneration. Synthetic biologists have successfully created simple synthetic genetic circuits that produce oscillations in single cells. Studying and engineering synthetic oscillators in a multicellular chassis can therefore give us valuable insights into how simple genetic circuits can encode complex multicellular behaviors at different scales. Here we develop a study of the coupling between the repressilator synthetic genetic ring oscillator and constraints on cell growth in colonies. We show in silico how mechanical constraints generate characteristic patterns of growth rate inhomogeneity in growing cell colonies. Next, we develop a simple one-dimensional model which predicts that coupling the repressilator to this pattern of growth rate via protein dilution generates traveling waves of gene expression. We show that the dynamics of these spatio-temporal patterns are determined by two parameters; the protein degradation and maximum expression rates of the repressors. We derive simple relations between these parameters and the key characteristics of the traveling wave patterns: firstly, wave speed is determined by protein degradation and secondly, wavelength is determined by maximum gene expression rate. Our analytical predictions and numerical results were in close quantitative agreement with detailed individual based simulations of growing cell colonies. Confirming published experimental results we also found that static ring patterns occur when protein stability is high. Our results show that this pattern can be induced simply by growth rate dilution and does not require transition to stationary phase as previously suggested. Our method generalizes easily to other genetic circuit architectures thus providing a framework for multi-scale rational design of spatio-temporal patterns from genetic circuits. We use this method to generate testable predictions for the synthetic biology design-build-test-learn cycle.

Predicting the unexpected in stomatal gas exchange: not just an open-and-shut case

Plant membrane transport, like transport across all eukaryotic membranes, is highly non-linear and leads to interactions with characteristics so complex that they defy intuitive understanding. The physiological behaviour of stomatal guard cells is a case in point in which, for example, mutations expected to influence stomatal closing have profound effects on stomatal opening and manipulating transport across the vacuolar membrane affects the plasma membrane. Quantitative mathematical modelling is an essential tool in these circumstances, both to integrate the knowledge of each transport process and to understand the consequences of their manipulation in vivo. Here, we outline the OnGuard modelling environment and its use as a guide to predicting the emergent properties arising from the interactions between non-linear transport processes. We summarise some of the recent insights arising from OnGuard, demonstrate its utility in interpreting stomatal behaviour, and suggest ways in which the OnGuard environment may facilitate 'reverse-engineering' of stomata to improve water use efficiency and carbon assimilation.

Cytomorphic Electronics With Memristors for Modeling Fundamental Genetic Circuits

Cytomorphic engineering attempts to study the cellular behavior of biological systems using electronics. As such, it can be considered analogous to the study of neurobiological concepts for neuromorphic engineering applications. To date, digital and analog translinear electronics have commonly been used in the design of cytomorphic circuits; Such circuits could greatly benefit from lowering the area of the digital memory via memristive circuits. In this article, we propose a novel approach that utilizes the Boltzmann-exponential stochastic transport of ionic species through insulators to naturally model the nonlinear and stochastic behavior of biochemical reactions. We first show that two-terminal memristive devices can capture the non-linear and stochastic behavior of biochemical reactions. Then, we present the design of several building blocks based on analog memristive circuits that inherently model the biophysical mechanisms of gene expression. The circuits model induction by small molecules, activation and repression by transcription factors, biological promoters, cooperative binding, and transcriptional and translational regulation of gene expression. Finally, we utilize the building blocks to form complex mixed-signal networks that can simulate the delay-induced oscillator and the p53-mdm2 interaction in the cancer signaling pathway. Our approach can provide a fast and simple emulative framework for studying genetic circuits and arbitrary large-scale biological networks in systems and synthetic biology. Some challenges may be that memristive devices with frequent learning and programming do not have the same longevity as traditional transistor-based electron-transport devices, and operate with significantly slower time constants, which can limit emulation speed.

Enabling community-based metrology for wood-degrading fungi

BACKGROUND

Lignocellulosic biomass could support a greatly-expanded bioeconomy. Current strategies for using biomass typically rely on single-cell organisms and extensive ancillary equipment to produce precursors for downstream manufacturing processes. Alternative forms of bioproduction based on solid-state fermentation and wood-degrading fungi could enable more direct means of manufacture. However, basic methods for cultivating wood-degrading fungi are often ad hoc and not readily reproducible. Here, we developed standard reference strains, substrates, measurements, and methods sufficient to begin to enable reliable reuse of mycological materials and products in simple laboratory settings.

RESULTS

We show that a widely-available and globally-regularized consumer product (Pringles™) can support the growth of wood-degrading fungi, and that growth on Pringles™-broth can be correlated with growth on media made from a fully-traceable and compositionally characterized substrate (National Institute of Standards and Technology Reference Material 8492 Eastern Cottonwood Whole Biomass Feedstock). We also establish a Relative Extension Unit (REU) framework that is designed to reduce variation in quantification of radial growth measurements. So enabled, we demonstrate that five laboratories were able to compare measurements of wood-fungus performance via a simple radial extension growth rate assay, and that our REU-based approach reduced variation in reported measurements by up to ~ 75%.

CONCLUSIONS

Reliable reuse of materials, measures, and methods is necessary to enable distributed bioproduction processes that can be adopted at all scales, from local to industrial. Our community-based measurement methods incentivize practitioners to coordinate the reuse of standard materials, methods, strains, and to share information supporting work with wood-degrading fungi.

Transcript degradation and codon usage regulate gene expression in a lytic phage

Many viral genomes are small, containing only single- or double-digit numbers of genes and relatively few regulatory elements. Yet viruses successfully execute complex regulatory programs as they take over their host cells. Here, we propose that some viruses regulate gene expression via a carefully balanced interplay between transcription, translation, and transcript degradation. As our model system, we employ bacteriophage T7, whose genome of approximately sixty genes is well annotated and for which there is a long history of computational models of gene regulation. We expand upon prior modeling work by implementing a stochastic gene expression simulator that tracks individual transcripts, polymerases, ribosomes, and ribonucleases participating in the transcription, translation, and transcript-degradation processes occurring during a T7 infection. By combining this detailed mechanistic modeling of a phage infection with high-throughput gene expression measurements of several strains of bacteriophage T7, evolved and engineered, we can show that both the dynamic interplay between transcription and transcript degradation, and between these two processes and translation, appear to be critical components of T7 gene regulation. Our results point to targeted degradation as a generic gene regulation strategy that may have evolved in many other viruses. Further, our results suggest that detailed mechanistic modeling may uncover the biological mechanisms at work in both evolved and engineered virus variants.

Pleione: A tool for statistical and multi-objective calibration of Rule-based models

Mathematical models based on Ordinary Differential Equations (ODEs) are frequently used to describe and simulate biological systems. Nevertheless, such models are often difficult to understand. Unlike ODE models, Rule-Based Models (RBMs) utilise formal language to describe reactions as a cumulative number of statements that are easier to understand and correct. They are also gaining popularity because of their conciseness and simulation flexibility. However, RBMs generally lack tools to perform further analysis that requires simulation. This situation arises because exact and approximate simulations are computationally intensive. Translating RBMs into ODEs is commonly used to reduce simulation time, but this technique may be prohibitive due to combinatorial explosion. Here, we present the software called Pleione to calibrate RBMs. Parameter calibration is essential given the incomplete experimental determination of reaction rates and the goal of using models to reproduce experimental data. The software distributes stochastic simulations and calculations and incorporates equivalence tests to determine the fitness of RBMs compared with data. The primary features of Pleione were thoroughly tested on a model of gene regulation in Escherichia coli. Pleione yielded satisfactory results regarding calculation time and error reduction for multiple simulators, models, parameter search strategies, and computing infrastructures.

Use of molecular crowding for the detection of protein self-association by size-exclusion chromatography

The feasibility of employing molecular crowding cosolutes to facilitate the detection of protein self-association by zonal size exclusion chromatography is investigated. Theoretical considerations have established that although the cosolute-induced displacement of a self-association equilibrium towards the oligomeric state invariably occurs in the mobile phase of the column, that displacement is only manifested as a decreased protein elution volume for cosolutes sufficiently small to partition between the mobile and stationary phases. Indeed, the use of a crowding agent sufficiently large to be confined to the mobile phase gives rise to an increased elution volume that could be misconstrued as evidence of cosolute-induced protein dissociation. Those theoretical considerations are reinforced by experimental studies of α-chymotrypsin (a reversibly dimerizing enzyme) on Superdex 200. The use of cosolutes such as sucrose and small polyethylene glycol fractions such as PEG-2000 is therefore recommended for the detection of protein self-association by molecular crowding effects in size exclusion chromatography.

Algorithmic and Stochastic Representations of Gene Regulatory Networks and Protein-Protein Interactions

BACKGROUND

Latest studies reveal the importance of Protein-Protein interactions on physiologic functions and biological structures. Several stochastic and algorithmic methods have been published until now, for the modeling of the complex nature of the biological systems.

OBJECTIVE

Biological Networks computational modeling is still a challenging task. The formulation of the complex cellular interactions is a research field of great interest. In this review paper, several computational methods for the modeling of GRN and PPI are presented analytically.

METHODS

Several well-known GRN and PPI models are presented and discussed in this review study such as: Graphs representation, Boolean Networks, Generalized Logical Networks, Bayesian Networks, Relevance Networks, Graphical Gaussian models, Weight Matrices, Reverse Engineering Approach, Evolutionary Algorithms, Forward Modeling Approach, Deterministic models, Static models, Hybrid models, Stochastic models, Petri Nets, BioAmbients calculus and Differential Equations.

RESULTS

GRN and PPI methods have been already applied in various clinical processes with potential positive results, establishing promising diagnostic tools.

CONCLUSION

In literature many stochastic algorithms are focused in the simulation, analysis and visualization of the various biological networks and their dynamics interactions, which are referred and described in depth in this review paper.

A network-based zoning for parallel whole-cell simulation

Motivation

In Computational Cell Biology, whole-cell modeling and simulation is an absolute requirement to analyze and explore the cell of an organism. Despite few individual efforts on modeling, the prime obstacle hindering its development and progress is its compute-intensive nature. Towards this end, little knowledge is available on how to reduce the enormous computational overhead and which computational systems will be of use.

Results

In this article, we present a network-based zoning approach that could potentially be utilized in the parallelization of whole-cell simulations. Firstly, we construct the protein-protein interaction graph of the whole-cell of an organism using experimental data from various sources. Based on protein interaction information, we predict protein locality and allocate confidence score to the interactions accordingly. We then identify the modules of strictly localized interacting proteins by performing interaction graph clustering based on the confidence score of the interactions. By applying this method to Escherichia coli K12, we identified 188 spatially localized clusters. After a thorough Gene Ontology-based analysis, we proved that the clusters are also in functional proximity. We then conducted Principal Coordinates Analysis to predict the spatial distribution of the clusters in the simulation space. Our automated computational techniques can partition the entire simulation space (cell) into simulation sub-cells. Each of these sub-cells can be simulated on separate computing units of the High-Performance Computing (HPC) systems. We benchmarked our method using proteins. However, our method can be extended easily to add other cellular components like DNA, RNA and metabolites.

Availability and implementation

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Supplementary information

Supplementary data are available at Bioinformatics online.

When pain gets stuck: the evolution of pain chronification and treatment resistance

It is well-recognized that, despite similar pain characteristics, some people with chronic pain recover, whereas others do not. In this review, we discuss possible contributions and interactions of biological, social, and psychological perturbations that underlie the evolution of treatment-resistant chronic pain. Behavior and brain are intimately implicated in the production and maintenance of perception. Our understandings of potential mechanisms that produce or exacerbate persistent pain remain relatively unclear. We provide an overview of these interactions and how differences in relative contribution of dimensions such as stress, age, genetics, environment, and immune responsivity may produce different risk profiles for disease development, pain severity, and chronicity. We propose the concept of "stickiness" as a soubriquet for capturing the multiple influences on the persistence of pain and pain behavior, and their stubborn resistance to therapeutic intervention. We then focus on the neurobiology of reward and aversion to address how alterations in synaptic complexity, neural networks, and systems (eg, opioidergic and dopaminergic) may contribute to pain stickiness. Finally, we propose an integration of the neurobiological with what is known about environmental and social demands on pain behavior and explore treatment approaches based on the nature of the individual's vulnerability to or protection from allostatic load.

Generalizing Gillespie's Direct Method to Enable Network-Free Simulations

Gillespie's direct method for stochastic simulation of chemical kinetics is a staple of computational systems biology research. However, the algorithm requires explicit enumeration of all reactions and all chemical species that may arise in the system. In many cases, this is not feasible due to the combinatorial explosion of reactions and species in biological networks. Rule-based modeling frameworks provide a way to exactly represent networks containing such combinatorial complexity, and generalizations of Gillespie's direct method have been developed as simulation engines for rule-based modeling languages. Here, we provide both a high-level description of the algorithms underlying the simulation engines, termed network-free simulation algorithms, and how they have been applied in systems biology research. We also define a generic rule-based modeling framework and describe a number of technical details required for adapting Gillespie's direct method for network-free simulation. Finally, we briefly discuss potential avenues for advancing network-free simulation and the role they continue to play in modeling dynamical systems in biology.

Agent-based modelling in synthetic biology

Biological systems exhibit complex behaviours that emerge at many different levels of organization. These span the regulation of gene expression within single cells to the use of quorum sensing to co-ordinate the action of entire bacterial colonies. Synthetic biology aims to make the engineering of biology easier, offering an opportunity to control natural systems and develop new synthetic systems with useful prescribed behaviours. However, in many cases, it is not understood how individual cells should be programmed to ensure the emergence of a required collective behaviour. Agent-based modelling aims to tackle this problem, offering a framework in which to simulate such systems and explore cellular design rules. In this article, I review the use of agent-based models in synthetic biology, outline the available computational tools, and provide details on recently engineered biological systems that are amenable to this approach. I further highlight the challenges facing this methodology and some of the potential future directions.

An Investigation on the Aggregation and Rheodynamics of Human Red Blood Cells Using High Performance Computations

Studies on the haemodynamics of human circulation are clinically and scientifically important. In order to investigate the effect of deformation and aggregation of red blood cells (RBCs) in blood flow, a computational technique has been developed by coupling the interaction between the fluid and the deformable RBCs. Parallelization was carried out for the coupled code and a high speedup was achieved based on a spatial decomposition. In order to verify the code's capability of simulating RBC deformation and transport, simulations were carried out for a spherical capsule in a microchannel and multiple RBC transport in a Poiseuille flow. RBC transport in a confined tube was also carried out to simulate the peristaltic effects of microvessels. Relatively large-scale simulations were carried out of the motion of 49,512 RBCs in shear flows, which yielded a hematocrit of 45%. The large-scale feature of the simulation has enabled a macroscale verification and investigation of the overall characteristics of RBC aggregations to be carried out. The results are in excellent agreement with experimental studies and, more specifically, both the experimental and simulation results show uniform RBC distributions under high shear rates (60-100/s) whereas large aggregations were observed under a lower shear rate of 10/s.

MESOSCOPIC MODELING OF STOCHASTIC REACTION-DIFFUSION KINETICS IN THE SUBDIFFUSIVE REGIME

Subdiffusion has been proposed as an explanation of various kinetic phenomena inside living cells. In order to fascilitate large-scale computational studies of subdiffusive chemical processes, we extend a recently suggested mesoscopic model of subdiffusion into an accurate and consistent reaction-subdiffusion computational framework. Two different possible models of chemical reaction are revealed and some basic dynamic properties are derived. In certain cases those mesoscopic models have a direct interpretation at the macroscopic level as fractional partial differential equations in a bounded time interval. Through analysis and numerical experiments we estimate the macroscopic effects of reactions under subdiffusive mixing. The models display properties observed also in experiments: for a short time interval the behavior of the diffusion and the reaction is ordinary, in an intermediate interval the behavior is anomalous, and at long times the behavior is ordinary again.

Systems Medicine: Sketching the Landscape

To understand the meaning of the term Systems Medicine and to distinguish it from seemingly related other expressions currently in use, such as precision, personalized, -omics, or big data medicine, its underlying history and development into present time needs to be highlighted. Having this development in mind, it becomes evident that Systems Medicine is a genuine concept as well as a novel way of tackling the manifold complexity that occurs in nowadays clinical medicine-and not just a rebranding of what has previously been done in the past. So looking back it seems clear to many in the field that Systems Medicine has its origin in an integrative method to unravel biocomplexity, namely, Systems Biology. Here scientist by now gained useful experience that is on the verge toward implementation in clinical research and practice.Systems Medicine and Systems Biology have the same underlying theoretical principle in systems-based thinking-a methodology to understand complexity that can be traced back to ancient Greece. During the last decade, however, and due to a rapid methodological development in the life sciences and computing/IT technologies, Systems Biology has evolved from a scientific concept into an independent discipline most competent to tackle key questions of biocomplexity-with the potential to transform medicine and how it will be practiced in the future. To understand this process in more detail, the following section will thus give a short summary of the foundation of systems-based thinking and the different developmental stages including systems theory, the development of modern Systems Biology, and its transition into clinical practice. These are the components to pave the way toward Systems Medicine.

Time-Delayed Models of Gene Regulatory Networks

We discuss different mathematical models of gene regulatory networks as relevant to the onset and development of cancer. After discussion of alternative modelling approaches, we use a paradigmatic two-gene network to focus on the role played by time delays in the dynamics of gene regulatory networks. We contrast the dynamics of the reduced model arising in the limit of fast mRNA dynamics with that of the full model. The review concludes with the discussion of some open problems.

Detection and characterization of nonspecific, sparsely populated binding modes in the early stages of complexation

A method is proposed to study protein-ligand binding in a system governed by specific and nonspecific interactions. Strong associations lead to narrow distributions in the proteins configuration space; weak and ultraweak associations lead instead to broader distributions, a manifestation of nonspecific, sparsely populated binding modes with multiple interfaces. The method is based on the notion that a discrete set of preferential first-encounter modes are metastable states from which stable (prerelaxation) complexes at equilibrium evolve. The method can be used to explore alternative pathways of complexation with statistical significance and can be integrated into a general algorithm to study protein interaction networks. The method is applied to a peptide-protein complex. The peptide adopts several low-population conformers and binds in a variety of modes with a broad range of affinities. The system is thus well suited to analyze general features of binding, including conformational selection, multiplicity of binding modes, and nonspecific interactions, and to illustrate how the method can be applied to study these problems systematically. The equilibrium distributions can be used to generate biasing functions for simulations of multiprotein systems from which bulk thermodynamic quantities can be calculated.

Multi-state modeling of biomolecules

Multi-state modeling of biomolecules refers to a series of techniques used to represent and compute the behavior of biological molecules or complexes that can adopt a large number of possible functional states. Biological signaling systems often rely on complexes of biological macromolecules that can undergo several functionally significant modifications that are mutually compatible. Thus, they can exist in a very large number of functionally different states. Modeling such multi-state systems poses two problems: the problem of how to describe and specify a multi-state system (the “specification problem”) and the problem of how to use a computer to simulate the progress of the system over time (the “computation problem”). To address the specification problem, modelers have in recent years moved away from explicit specification of all possible states and towards rule-based formalisms that allow for implicit model specification, including the κ-calculus [1], BioNetGen [2]–[5], the Allosteric Network Compiler [6], and others [7], [8]. To tackle the computation problem, they have turned to particle-based methods that have in many cases proved more computationally efficient than population-based methods based on ordinary differential equations, partial differential equations, or the Gillespie stochastic simulation algorithm[9], [10]. Given current computing technology, particle-based methods are sometimes the only possible option. Particle-based simulators fall into two further categories: nonspatial simulators, such as StochSim [11], DYNSTOC [12], RuleMonkey [9], [13], and the Network-Free Stochastic Simulator (NFSim) [14], and spatial simulators, including Meredys [15], SRSim [16], [17], and MCell [18]–[20]. Modelers can thus choose from a variety of tools, the best choice depending on the particular problem. Development of faster and more powerful methods is ongoing, promising the ability to simulate ever more complex signaling processes in the future.

Exploring emergent properties in cellular homeostasis using OnGuard to model K+ and other ion transport in guard cells

It is widely recognized that the nature and characteristics of transport across eukaryotic membranes are so complex as to defy intuitive understanding. In these circumstances, quantitative mathematical modeling is an essential tool, both to integrate detailed knowledge of individual transporters and to extract the properties emergent from their interactions. As the first, fully integrated and quantitative modeling environment for the study of ion transport dynamics in a plant cell, OnGuard offers a unique tool for exploring homeostatic properties emerging from the interactions of ion transport, both at the plasma membrane and tonoplast in the guard cell. OnGuard has already yielded detail sufficient to guide phenotypic and mutational studies, and it represents a key step toward 'reverse engineering' of stomatal guard cell physiology, based on rational design and testing in simulation, to improve water use efficiency and carbon assimilation. Its construction from the HoTSig libraries enables translation of the software to other cell types, including growing root hairs and pollen. The problems inherent to transport are nonetheless challenging, and are compounded for those unfamiliar with conceptual 'mindset' of the modeler. Here we set out guidelines for the use of OnGuard and outline a standardized approach that will enable users to advance quickly to its application both in the classroom and laboratory. We also highlight the uncanny and emergent property of OnGuard models to reproduce the 'communication' evident between the plasma membrane and tonoplast of the guard cell.

Models of signalling networks - what cell biologists can gain from them and give to them

Computational models of cell signalling are perceived by many biologists to be prohibitively complicated. Why do math when you can simply do another experiment? Here, we explain how conceptual models, which have been formulated mathematically, have provided insights that directly advance experimental cell biology. In the past several years, models have influenced the way we talk about signalling networks, how we monitor them, and what we conclude when we perturb them. These insights required wet-lab experiments but would not have arisen without explicit computational modelling and quantitative analysis. Today, the best modellers are cross-trained investigators in experimental biology who work closely with collaborators but also undertake experimental work in their own laboratories. Biologists would benefit by becoming conversant in core principles of modelling in order to identify when a computational model could be a useful complement to their experiments. Although the mathematical foundations of a model are useful to appreciate its strengths and weaknesses, they are not required to test or generate a worthwhile biological hypothesis computationally.

A computational pipeline for identifying kinetic motifs to aid in the design and improvement of synthetic gene circuits

BACKGROUND

An increasing number of genetic components are available in several depositories of such components to facilitate synthetic biology research, but picking out those that will allow a designed circuit to achieve the specified function still requires multiple cycles of testing. Here, we addressed this problem by developing a computational pipeline to mathematically simulate a gene circuit for a comprehensive range and combination of the kinetic parameters of the biological components that constitute the gene circuit.

RESULTS

We showed that, using a well-studied transcriptional repression cascade as an example, the sets of kinetic parameters that could produce the specified system dynamics of the gene circuit formed clusters of recurrent combinations, referred to as kinetic motifs, which appear to be associated with both the specific topology and specified dynamics of the circuit. Furthermore, the use of the resulting "handbook" of performance-ranked kinetic motifs in finding suitable circuit components was illustrated in two application scenarios.

CONCLUSIONS

These results show that the computational pipeline developed here can provide a rational-based guide to aid in the design and improvement of synthetic gene circuits.

Information content and scalability in signal transduction network reconstruction formats

One of the first steps towards holistic understanding of cellular networks is the integration of the available information in a human and machine readable format. This network reconstruction process is well established for metabolic networks, and numerous genome wide metabolic reconstructions are already available. Extending these strategies to signalling networks has proven difficult, primarily due to the combinatorial nature of regulatory modifications. The combinatorial nature of possible protein-protein interactions and post translational modifications affects both network size and the correspondence between the reconstructed network and the underlying empirical data. Here, we discuss different approaches to reconstruction of signal transduction networks. We divide the current approaches into topological, specific state based and reaction-contingency based, and discuss their different information content and scalability. The discussion focusses on graphical formats but the points are in general applicable also to mathematical models and databases. While the formats have complementary strengths especially for small networks, reaction-contingency based formats have a number of advantages in the light of global network reconstruction. In particular, they minimise the need for assumptions, maximise the congruence with empirical data, and scale efficiently with network size.

ON MODELING OF LIVING ORGANISMS USING HIERARCHICAL COARSE-GRAINING ABSTRACTIONS OF KNOWLEDGE

High throughput technologies such as gene expression microarray, ChIP-chips, siRNA and protein arrays and high throughput mass spectrometry are enabling an ever increasing amount of data becoming available about DNA, RNA, proteins, metabolites as well as biological pathways and networks. The knowledge embedded in this data deluge needs to be recast in forms that lend themselves to analysis with the expectation of developing analytical instruments to gain insight and answer questions about life and living organisms. The powers of abstraction and model building are fundamental to the quest of making sense of the biological complexity embedded in these biological and clinical datasets. The modeling of living organisms is explored with a proposed framework for model representation of biological complexity. The principal foundational assumption of the proposed modeling philosophy recognizes the symbiotic relationship between information and energy flows, required for the transformation of matter, as a fundamental organizing force underlying the observable nature of living organisms. The use of the concept of regularities to refer to complexity of structure, function and dynamics alike provides a unified approach to the reasoning about the integration of knowledge representations of varying natures and scales of granularities. The application of the proposed modeling approach is illustrated in broad qualitative terms for the human organism.

Field Hypothesis on the Self-regulation of Gene Expression

The mechanism of the self-regulation of gene expression in living cells is generally explained by considering complicated networks of key-lock relationships, and in fact there is a large body of evidence on a hugenumber of key-lock relationships. However, in the present article we stress that with the network hypothesis alone it is impossible to fully explain the mechanism of self-regulation in life. Recently, it has been established that individual giant DNA molecules, larger than several tens of kilo base pairs, undergo a large discrete transition in their higher-order structure. It has become clear that nonspecific weak interactions with various chemicals, suchas polyamines, small salts, ATP and RNA, cause on/off switching in the higher-order structure of DNA. Thus, the field parameters of the cellular environment should play important roles in the mechanism of self-regulation, in addition to networks of key and locks. This conformational transition induced by field parameters may be related to rigid on/off regulation, whereas key-lock relationships may be involved in a more flexible control of gene expression.

BSim: an agent-based tool for modeling bacterial populations in systems and synthetic biology

Large-scale collective behaviors such as synchronization and coordination spontaneously arise in many bacterial populations. With systems biology attempting to understand these phenomena, and synthetic biology opening up the possibility of engineering them for our own benefit, there is growing interest in how bacterial populations are best modeled. Here we introduce BSim, a highly flexible agent-based computational tool for analyzing the relationships between single-cell dynamics and population level features. BSim includes reference implementations of many bacterial traits to enable the quick development of new models partially built from existing ones. Unlike existing modeling tools, BSim fully considers spatial aspects of a model allowing for the description of intricate micro-scale structures, enabling the modeling of bacterial behavior in more realistic three-dimensional, complex environments. The new opportunities that BSim opens are illustrated through several diverse examples covering: spatial multicellular computing, modeling complex environments, population dynamics of the lac operon, and the synchronization of genetic oscillators. BSim is open source software that is freely available from http://bsim-bccs.sf.net and distributed under the Open Source Initiative (OSI) recognized MIT license. Developer documentation and a wide range of example simulations are also available from the website. BSim requires Java version 1.6 or higher.

Complexity and the reductionism-holism debate in systems biology

Reductionism has largely influenced the development of science, culminating in its application to molecular biology. An increasing number of novel research findings have, however, shattered this view, showing how the molecular-reductionist approach cannot entirely handle the complexity of biological systems. Within this framework, the advent of systems biology as a new and more integrative field of research is described, along with the form which has taken on the debate of reductionism versus holism. Such an issue occupies a central position in systems biology, and nonetheless it is not always clearly delineated. This partly occurs because different dimensions (ontological, epistemological, methodological) are involved, and yet the concerned ones often remain unspecified. Besides, within systems biology different streams can be distinguished depending on the degree of commitment to embrace genuine systemic principles. Some useful insights into the future development of this discipline might be gained from the tradition of complexity and self-organization. This is especially true with regards the idea of self-reference, which incorporated into the organizational scheme is able to generate autonomy as an emergent property of the biological whole.

OnGuard, a computational platform for quantitative kinetic modeling of guard cell physiology

Stomatal guard cells play a key role in gas exchange for photosynthesis while minimizing transpirational water loss from plants by opening and closing the stomatal pore. Foliar gas exchange has long been incorporated into mathematical models, several of which are robust enough to recapitulate transpirational characteristics at the whole-plant and community levels. Few models of stomata have been developed from the bottom up, however, and none are sufficiently generalized to be widely applicable in predicting stomatal behavior at a cellular level. We describe here the construction of computational models for the guard cell, building on the wealth of biophysical and kinetic knowledge available for guard cell transport, signaling, and homeostasis. The OnGuard software was constructed with the HoTSig library to incorporate explicitly all of the fundamental properties for transporters at the plasma membrane and tonoplast, the salient features of osmolite metabolism, and the major controls of cytosolic-free Ca²⁺ concentration and pH. The library engenders a structured approach to tier and interrelate computational elements, and the OnGuard software allows ready access to parameters and equations 'on the fly' while enabling the network of components within each model to interact computationally. We show that an OnGuard model readily achieves stability in a set of physiologically sensible baseline or Reference States; we also show the robustness of these Reference States in adjusting to changes in environmental parameters and the activities of major groups of transporters both at the tonoplast and plasma membrane. The following article addresses the predictive power of the OnGuard model to generate unexpected and counterintuitive outputs.

Systems dynamic modeling of the stomatal guard cell predicts emergent behaviors in transport, signaling, and volume control

The dynamics of stomatal movements and their consequences for photosynthesis and transpirational water loss have long been incorporated into mathematical models, but none have been developed from the bottom up that are widely applicable in predicting stomatal behavior at a cellular level. We previously established a systems dynamic model incorporating explicitly the wealth of biophysical and kinetic knowledge available for guard cell transport, signaling, and homeostasis. Here we describe the behavior of the model in response to experimentally documented changes in primary pump activities and malate (Mal) synthesis imposed over a diurnal cycle. We show that the model successfully recapitulates the cyclic variations in H⁺, K⁺, Cl⁻, and Mal concentrations in the cytosol and vacuole known for guard cells. It also yields a number of unexpected and counterintuitive outputs. Among these, we report a diurnal elevation in cytosolic-free Ca²⁺ concentration and an exchange of vacuolar Cl⁻ with Mal, both of which find substantiation in the literature but had previously been suggested to require additional and complex levels of regulation. These findings highlight the true predictive power of the OnGuard model in providing a framework for systems analysis of stomatal guard cells, and they demonstrate the utility of the OnGuard software and HoTSig library in exploring fundamental problems in cellular physiology and homeostasis.

Fine-tuning tomato agronomic properties by computational genome redesign

Considering cells as biofactories, we aimed to optimize its internal processes by using the same engineering principles that large industries are implementing nowadays: lean manufacturing. We have applied reverse engineering computational methods to transcriptomic, metabolomic and phenomic data obtained from a collection of tomato recombinant inbreed lines to formulate a kinetic and constraint-based model that efficiently describes the cellular metabolism from expression of a minimal core of genes. Based on predicted metabolic profiles, a close association with agronomic and organoleptic properties of the ripe fruit was revealed with high statistical confidence. Inspired in a synthetic biology approach, the model was used for exploring the landscape of all possible local transcriptional changes with the aim of engineering tomato fruits with fine-tuned biotechnological properties. The method was validated by the ability of the proposed genomes, engineered for modified desired agronomic traits, to recapitulate experimental correlations between associated metabolites.

Stochastic simulation of chemically reacting systems using multi-core processors

In recent years, computer simulations have become increasingly useful when trying to understand the complex dynamics of biochemical networks, particularly in stochastic systems. In such situations stochastic simulation is vital in gaining an understanding of the inherent stochasticity present, as these models are rarely analytically tractable. However, a stochastic approach can be computationally prohibitive for many models. A number of approximations have been proposed that aim to speed up stochastic simulations. However, the majority of these approaches are fundamentally serial in terms of central processing unit (CPU) usage. In this paper, we propose a novel simulation algorithm that utilises the potential of multi-core machines. This algorithm partitions the model into smaller sub-models. These sub-models are then simulated, in parallel, on separate CPUs. We demonstrate that this method is accurate and can speed-up the simulation by a factor proportional to the number of processors available.

Analyzing protein-protein interaction networks

The advent of the "omics" era in biology research has brought new challenges and requires the development of novel strategies to answer previously intractable questions. Molecular interaction networks provide a framework to visualize cellular processes, but their complexity often makes their interpretation an overwhelming task. The inherently artificial nature of interaction detection methods and the incompleteness of currently available interaction maps call for a careful and well-informed utilization of this valuable data. In this tutorial, we aim to give an overview of the key aspects that any researcher needs to consider when working with molecular interaction data sets and we outline an example for interactome analysis. Using the molecular interaction database IntAct, the software platform Cytoscape, and its plugins BiNGO and clusterMaker, and taking as a starting point a list of proteins identified in a mass spectrometry-based proteomics experiment, we show how to build, visualize, and analyze a protein-protein interaction network.

A new approximate method for the stochastic simulation of chemical systems: the representative reaction approach

We have developed two new approximate methods for stochastically simulating chemical systems. The methods are based on the idea of representing all the reactions in the chemical system by a single reaction, i.e., by the "representative reaction approach" (RRA). Discussed in the article are the concepts underlying the new methods along with flowchart with all the steps required for their implementation. It is shown that the two RRA methods {with the reaction 2A −> B as the representative reaction (RR)} perform creditably with regard to accuracy and computational efficiency, in comparison to the exact stochastic simulation algorithm (SSA) developed by Gillespie and are able to successfully reproduce at least the first two moments of the probability distribution of each species in the systems studied. As such, the RRA methods represent a promising new approach for stochastically simulating chemical systems.

Modularity in protein complex and drug interactions reveals new polypharmacological properties

Recent studies have highlighted the importance of interconnectivity in a large range of molecular and human disease-related systems. Network medicine has emerged as a new paradigm to deal with complex diseases. Connections between protein complexes and key diseases have been suggested for decades. However, it was not until recently that protein complexes were identified and classified in sufficient amounts to carry out a large-scale analysis of the human protein complex system. We here present the first systematic and comprehensive set of relationships between protein complexes and associated drugs and analyzed their topological features. The network structure is characterized by a high modularity, both in the bipartite graph and in its projections, indicating that its topology is highly distinct from a random network and that it contains a rich and heterogeneous internal modular structure. To unravel the relationships between modules of protein complexes, drugs and diseases, we investigated in depth the origins of this modular structure in examples of particular diseases. This analysis unveils new associations between diseases and protein complexes and highlights the potential role of polypharmacological drugs, which target multiple cellular functions to combat complex diseases driven by gain-of-function mutations.

AN EFFECTIVE DATA MINING TECHNIQUE FOR RECONSTRUCTING GENE REGULATORY NETWORKS FROM TIME SERIES EXPRESSION DATA

Recent development in DNA microarray technologies has made the reconstruction of gene regulatory networks (GRNs) feasible. To infer the overall structure of a GRN, there is a need to find out how the expression of each gene can be affected by the others. Many existing approaches to reconstructing GRNs are developed to generate hypotheses about the presence or absence of interactions between genes so that laboratory experiments can be performed afterwards for verification. Since, they are not intended to be used to predict if a gene in an unseen sample has any interactions with other genes, statistical verification of the reliability of the discovered interactions can be difficult. Furthermore, since the temporal ordering of the data is not taken into consideration, the directionality of regulation cannot be established using these existing techniques. To tackle these problems, we propose a data mining technique here. This technique makes use of a probabilistic inference approach to uncover interesting dependency relationships in noisy, high-dimensional time series expression data. It is not only able to determine if a gene is dependent on another but also whether or not it is activated or inhibited. In addition, it can predict how a gene would be affected by other genes even in unseen samples. For performance evaluation, the proposed technique has been tested with real expression data. Experimental results show that it can be very effective. The discovered dependency relationships can reveal gene regulatory relationships that could be used to infer the structures of GRNs.

MODELING AND SIMULATION OF MOLECULAR BIOLOGY SYSTEMS USING PETRI NETS: MODELING GOALS OF VARIOUS APPROACHES

Petri nets are a discrete event simulation approach developed for system representation, in particular for their concurrency and synchronization properties. Various extensions to the original theory of Petri nets have been used for modeling molecular biology systems and metabolic networks. These extensions are stochastic, colored, hybrid and functional. This paper carries out an initial review of the various modeling approaches based on Petri net found in the literature, and of the biological systems that have been successfully modeled with these approaches. Moreover, the modeling goals and possibilities of qualitative analysis and system simulation of each approach are discussed.