Using Petri Net tools to study properties and dynamics of biological systems

Several supplementary concepts for applied category-theoretical states over an extended Petri net using an example relating to genetic coding: Toward an abstract algebraic formulation of molecular/genetic biology

algebraic concepts such as category are considered cornerstones on which logical consistency relies in any sophisticated study of natural phenomena. However, to the best of our knowledge, in molecular/genetic biology, their application is still severely limited because they capture neither the dynamics nor provide a visual form. The Petri net (PN) has often been used to illustrate visually parallel, asynchronous dynamic events in small data systems. A prototypal hybrid model combining both category theory and extended PNs may instead be indispensable for that purpose. This hybrid model incorporates 1) token-like elements of a group, 2) object-like places of a category, 3) square poles (rather than pentagon poles) that enable unique identifications of single-strand DNA sequences from the shape of its polygonal line, 4) creation/annihilation morphisms that generate/erase tokens, 5) Cartesian products 'Z5×Z2×…' that enable conversions between DNA and RNA sequences, 6) somatic recombinations (VDJ recombinations) for antibodies displayed concretely in category-theoretic form, 7) 'identity protein Δ' translated from a triplet of identity bases 'EEE' as an advanced concept from our previous display of the canonical central dogma, 8) illustrations of an incidence-matrix-like matrix A that includes operators as coordinates, and 9) basic topics concerning the canonical central dogma being displayed concretely using concepts of conventional category theory such as 'adjoint', 'adjoint functor', 'natural transformation', 'Yoneda's lemma' and 'Kan extension'. These ideas provide more advanced tools that expand our previous model concerning nucleic-acid-base sequences. Despite the nascent nature of our methodology, our hybrid model has potential in a variety of applications, illustrated using molecular/genetic sequences, in particular providing a simple dynamic/visual representation. With further improvements, this approach may prove effective in reducing the need for large data-storing systems.

Large-scale computational modelling of the M1 and M2 synovial macrophages in rheumatoid arthritis

Macrophages play an essential role in rheumatoid arthritis. Depending on their phenotype (M1 or M2), they can play a role in the initiation or resolution of inflammation. The M1/M2 ratio in rheumatoid arthritis is higher than in healthy controls. Despite this, no treatment targeting specifically macrophages is currently used in clinics. Thus, devising strategies to selectively deplete proinflammatory macrophages and promote anti-inflammatory macrophages could be a promising therapeutic approach. State-of-the-art molecular interaction maps of M1 and M2 macrophages in rheumatoid arthritis are available and represent a dense source of knowledge; however, these maps remain limited by their static nature. Discrete dynamic modelling can be employed to study the emergent behaviours of these systems. Nevertheless, handling such large-scale models is challenging. Due to their massive size, it is computationally demanding to identify biologically relevant states in a cell- and disease-specific context. In this work, we developed an efficient computational framework that converts molecular interaction maps into Boolean models using the CaSQ tool. Next, we used a newly developed version of the BMA tool deployed to a high-performance computing cluster to identify the models' steady states. The identified attractors are then validated using gene expression data sets and prior knowledge. We successfully applied our framework to generate and calibrate the M1 and M2 macrophage Boolean models for rheumatoid arthritis. Using KO simulations, we identified NFkB, JAK1/JAK2, and ERK1/Notch1 as potential targets that could selectively suppress proinflammatory macrophages and GSK3B as a promising target that could promote anti-inflammatory macrophages in rheumatoid arthritis.

Modeling and analyzing the action process of monoamine hormones in depression: a Petri nets-based intelligent approach

In contemporary society, the incidence of depression is increasing significantly around the world. At present, most of the treatment methods for depression are psychological counseling and drug therapy. However, this approach does not allow patients to visualize the logic of hormones at the pathological level. In order to better apply intelligence computing methods to the medical field, and to more easily analyze the relationship between norepinephrine and dopamine in depression, it is necessary to build an interpretable graphical model to analyze this relationship which is of great significance to help discover new treatment ideas and potential drug targets. Petri net (PN) is a mathematical and graphic tool used to simulate and study complex system processes. This article utilizes PN to study the relationship between norepinephrine and dopamine in depression. We use PN to model the relationship between the norepinephrine and dopamine, and then use the invariant method of PN to verify and analyze it. The mathematical model proposed in this article can explain the complex pathogenesis of depression and visualize the process of intracellular hormone-induced state changes. Finally, the experiment result suggests that our method provides some possible research directions and approaches for the development of antidepressant drugs.

A Community-of-Practice-based Evaluation Methodology for Knowledge Intensive Computational Methods and its Application to Multimorbidity Decision Support

OBJECTIVE

The study has dual objectives. Our first objective (1) is to develop a community-of-practice-based evaluation methodology for knowledge-intensive computational methods. We target a whitebox analysis of the computational methods to gain insight on their functional features and inner workings. In more detail, we aim to answer evaluation questions on (i) support offered by computational methods for functional features within the application domain; and (ii) in-depth characterizations of the underlying computational processes, models, data and knowledge of the computational methods. Our second objective (2) involves applying the evaluation methodology to answer questions (i) and (ii) for knowledge-intensive clinical decision support (CDS) methods, which operationalize clinical knowledge as computer interpretable guidelines (CIG); we focus on multimorbidity CIG-based clinical decision support (MGCDS) methods that target multimorbidity treatment plans.

MATERIALS AND METHODS

Our methodology directly involves the research community of practice in (a) identifying functional features within the application domain; (b) defining exemplar case studies covering these features; and (c) solving the case studies using their developed computational methods-research groups detail their solutions and functional feature support in solution reports. Next, the study authors (d) perform a qualitative analysis of the solution reports, identifying and characterizing common themes (or dimensions) among the computational methods. This methodology is well suited to perform whitebox analysis, as it directly involves the respective developers in studying inner workings and feature support of computational methods. Moreover, the established evaluation parameters (e.g., features, case studies, themes) constitute a re-usable benchmark framework, which can be used to evaluate new computational methods as they are developed. We applied our community-of-practice-based evaluation methodology on MGCDS methods.

RESULTS

Six research groups submitted comprehensive solution reports for the exemplar case studies. Solutions for two of these case studies were reported by all groups. We identified four evaluation dimensions: detection of adverse interactions, management strategy representation, implementation paradigms, and human-in-the-loop support.Based on our whitebox analysis, we present answers to the evaluation questions (i) and (ii) for MGCDS methods.

DISCUSSION

The proposed evaluation methodology includes features of illuminative and comparison-based approaches; focusing on understanding rather than judging/scoring or identifying gaps in current methods. It involves answering evaluation questions with direct involvement of the research community of practice, who participate in setting up evaluation parameters and solving exemplar case studies. Our methodology was successfully applied to evaluate six MGCDS knowledge-intensive computational methods. We established that, while the evaluated methods provide a multifaceted set of solutions with different benefits and drawbacks, no single MGCDS method currently provides a comprehensive solution for MGCDS.

CONCLUSION

We posit that our evaluation methodology, applied here to gain new insights into MGCDS, can be used to assess other types of knowledge-intensive computational methods and answer other types of evaluation questions. Our case studies can be accessed at our GitHub repository (https://github.com/william-vw/MGCDS).

Stochastic Petri net model describing the relationship between reported maternal and congenital syphilis cases in Brazil

INTRODUCTION

Syphilis is a sexually transmitted disease (STD) caused by Treponema pallidum subspecies pallidum. In 2016, it was declared an epidemic in Brazil due to its high morbidity and mortality rates, mainly in cases of maternal syphilis (MS) and congenital syphilis (CS) with unfavorable outcomes. This paper aimed to mathematically describe the relationship between MS and CS cases reported in Brazil over the interval from 2010 to 2020, considering the likelihood of diagnosis and effective and timely maternal treatment during prenatal care, thus supporting the decision-making and coordination of syphilis response efforts.

METHODS

The model used in this paper was based on stochastic Petri net (SPN) theory. Three different regressions, including linear, polynomial, and logistic regression, were used to obtain the weights of an SPN model. To validate the model, we ran 100 independent simulations for each probability of an untreated MS case leading to CS case (PUMLC) and performed a statistical t-test to reinforce the results reported herein.

RESULTS

According to our analysis, the model for predicting congenital syphilis cases consistently achieved an average accuracy of 93% or more for all tested probabilities of an untreated MS case leading to CS case.

CONCLUSIONS

The SPN approach proved to be suitable for explaining the Notifiable Diseases Information System (SINAN) dataset using the range of 75-95% for the probability of an untreated MS case leading to a CS case (PUMLC). In addition, the model's predictive power can help plan actions to fight against the disease.

Study of the bioenergetics to identify the novel pathways as a drug target against Mycobacterium tuberculosis using Petri net

Tuberculosis is one of the life-threatening diseases globally, caused by the bacteria Mycobacterium tuberculosis. In order to control this epidemic globally, there is an urgent need to discover new drugs with novel mechanism of action that can help in shortening the duration of treatment for both drug resistant and drug sensitive tuberculosis. Mycobacterium essentially depends on oxidative phosphorylation for its growth and establishment of pathogenesis. This pathway is unique in Mycobacterium tuberculosis as compared to host due to the differences in some of the enzyme complexes carrying electron transfer. Hence, it serves as an important drug target area. The uncouplers which inhibit adenosine triphosphate synthesis, could play a vital role in serving as antimycobacterial agents and thus could help in eradicating this deadly disease. In this article, the bioenergetics of Mycobacterium tuberculosis are studied with and without uncouplers using Petri net. Petri net is among the most widely used mathematical and computational tools to model and study the complex biochemical networks. We first represented the bioenergetic pathway as a Petri net which is then validated and analyzed using invariant analysis techniques of Petri net. The valid mathematical models presented here are capable to explain the molecular mechanism of uncouplers and the processes occurring within the electron transport chain of Mycobacterium tuberculosis. The results explained the net behavior in agreement with the biological results and also suggested some possible processes and pathways to be studied as a drug target for developing antimycobacterials.

Model-based pathway enrichment analysis applied to the TGF-beta regulation of autophagy in autism

To differentiate between conditions of health and disease, current pathway enrichment analysis methods detect the differential expression of distinct biological pathways. System-level model-driven approaches, however, are lacking. Here we present a new methodology that uses a dynamic model to suggest a unified subsystem to better differentiate between diseased and healthy conditions. Our methodology includes the following steps: 1) detecting connections between relevant differentially expressed pathways; 2) construction of a unified in silico model, a stochastic Petri net model that links these distinct pathways; 3) model execution to predict subsystem activation; and 4) enrichment analysis of the predicted subsystem. We apply our approach to the TGF-beta regulation of the autophagy system implicated in autism. Our model was constructed manually, based on the literature, to predict, using model simulation, the TGF-beta-to-autophagy active subsystem and downstream gene expression changes associated with TGF-beta, which go beyond the individual findings derived from literature. We evaluated the in silico predicted subsystem and found it to be co-expressed in the normative whole blood human gene expression data. Finally, we show our subsystem's gene set to be significantly differentially expressed in two independent datasets of blood samples of ASD (autistic spectrum disorders) individuals as opposed to controls. Our study demonstrates that dynamic pathway unification can define a new refined subsystem that can significantly differentiate between disease conditions.

A Pathway Analysis Approach Using Petri Net

Perturbation in the normal function of the cell signaling pathways often leads to diseases. One of the factors that help understand the mechanism of diseases is the precise identification and investigation of perturbed signaling pathways. Pathway analysis methods have been developed as their purpose is to identify perturbed signaling pathways in given conditions. Among these methods, some consider the pathways topologies in their analysis, which are referred to as topology-based methods. Most of the topology-based methods used simple graph-based models to incorporate topology in their analysis, which have some limitations. We describe a new Pathway Analysis method using Petri net (PAPet) that uses the Petri net to model the signaling pathways and then propose an algorithm to measure the perturbation on a given pathway under a given condition. Modeling with Petri net has some advantages and could overcome the shortcomings of the simple graph-based models. We illustrate the capabilities of the proposed method using sensitivity, prioritization, mean reciprocal rank, and false-positive rate metrics on 36 real datasets from various diseases. The results of comparing PAPet with five pathway analysis methods FoPA, PADOG, GSEA, CePa and SPIA show that PAPet is the best one that provides a good compromise between all metrics. In addition, the results of applying methods to gene expression profiles in normal and Pancreatic Ductal Adenocarcinoma cancer (PDAC) samples show that the PAPet method achieves the best rank among others in finding the pathways that have been previously reported for PDAC. The PAPet method is available at https://github.com/fmansoori/PAPET.

In silico clinical trials: concepts and early adoptions

Innovations in information and communication technology infuse all branches of science, including life sciences. Nevertheless, healthcare is historically slow in adopting technological innovation, compared with other industrial sectors. In recent years, new approaches in modelling and simulation have started to provide important insights in biomedicine, opening the way for their potential use in the reduction, refinement and partial substitution of both animal and human experimentation. In light of this evidence, the European Parliament and the United States Congress made similar recommendations to their respective regulators to allow wider use of modelling and simulation within the regulatory process. In the context of in silico medicine, the term 'in silico clinical trials' refers to the development of patient-specific models to form virtual cohorts for testing the safety and/or efficacy of new drugs and of new medical devices. Moreover, it could be envisaged that a virtual set of patients could complement a clinical trial (reducing the number of enrolled patients and improving statistical significance), and/or advise clinical decisions. This article will review the current state of in silico clinical trials and outline directions for a full-scale adoption of patient-specific modelling and simulation in the regulatory evaluation of biomedical products. In particular, we will focus on the development of vaccine therapies, which represents, in our opinion, an ideal target for this innovative approach.

Simplifying the Verification of Simulation Models through Petri Net to FlexSim Mapping

Simplifying the encoding of a simulation conceptual model representation reduces the number of errors that will be detected in the verification phase. In this paper, we present a mapping between Petri nets, a well-known formalism, and FlexSim, a well-known simulation tool. The proposal is illustrated through an example of how a model specified in a Petri net can be encoded easily, reducing the time needed to understand and verify the model. In the proposed methodology, the mapping must be defined at the initial stage of the encoding, starting from (in this case) a Petri net conceptual model, and ending at the encoding tool (FlexSim in this case). The main advantages of the proposed methodology are discussed.

Modelling and Simulation of Biochemical Processes Using Petri Nets

Systems composed of many components which interact with each other and lead to unpredictable global behaviour, are considered as complex systems. In a biological context, complex systems represent living systems composed of a large number of interacting elements. In order to study these systems, a precise mathematical modelling was typically used in this context. However, this modelling has limitations in the structural understanding and the behavioural study. In this sense, formal computational modelling is an approach that allows to model and to simulate dynamical properties of these particular systems. In this paper, we use Hybrid Functional Petri Net (HFPN), a Petri net extension dedicated to study and verify biopathways, to model and study the Methionine metabolic pathway. Methionine and its derivatives play significant roles in human bodies. We propose a set of simulations for the purpose of studying and analysing the Methionine pathway’s behaviour. Our simulation results have shown that several important abnormalities in this pathway are related to sever diseases such as Alzheimer’s disease, cardiovascular disease, cancers and others.

A graphical and computational modeling platform for biological pathways

A major endeavor of systems biology is the construction of graphical and computational models of biological pathways as a means to better understand their structure and function. Here, we present a protocol for a biologist-friendly graphical modeling scheme that facilitates the construction of detailed network diagrams, summarizing the components of a biological pathway (such as proteins and biochemicals) and illustrating how they interact. These diagrams can then be used to simulate activity flow through a pathway, thereby modeling its dynamic behavior. The protocol is divided into four sections: (i) assembly of network diagrams using the modified Edinburgh Pathway Notation (mEPN) scheme and yEd network editing software with pathway information obtained from published literature and databases of molecular interaction data; (ii) parameterization of the pathway model within yEd through the placement of 'tokens' on the basis of the known or imputed amount or activity of a component; (iii) model testing through visualization and quantitative analysis of the movement of tokens through the pathway, using the network analysis tool Graphia Professional and (iv) optimization of model parameterization and experimentation. This is the first modeling approach that combines a sophisticated notation scheme for depicting biological events at the molecular level with a Petri net-based flow simulation algorithm and a powerful visualization engine with which to observe the dynamics of the system being modeled. Unlike many mathematical approaches to modeling pathways, it does not require the construction of a series of equations or rate constants for model parameterization. Depending on a model's complexity and the availability of information, its construction can take days to months, and, with refinement, possibly years. However, once assembled and parameterized, a simulation run, even on a large model, typically takes only seconds. Models constructed using this approach provide a means of knowledge management, information exchange and, through the computation simulation of their dynamic activity, generation and testing of hypotheses, as well as prediction of a system's behavior when perturbed.

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.

Genetic Expression Level Prediction Based on Extended Fuzzy Petri Nets

With the advances in technique for high throughput data gathering such as microarrays, DNA sequencing machines and continuous development of human genome project, the traditional physical and chemical methods have been more difficult to meet the requests of time consuming and results accuracy. Exploring and understanding the causal relationship of complex gene regulatory networks and transforming the massive data of large-scale biological research to useful biological knowledge are the present challenge. As a result, there are two typical applications both the confidence value prediction of DNA sequence and influence degree prediction of gene expression which have become the hot issues in our daily life. In this paper, two extended fuzzy Petri nets approaches are proposed, based on the existing fuzzy Petri net model, to model and analyze for the hot issues respectively. One is the fuzzy colored Petri net, which combines fuzzy Petri net with colored Petri net to model fuzzy rule-based reasoning and determine confidence values for bases called in DNA sequence. The other is extended fuzzy Petri net, which integrates reverse reasoning into fuzzy Petri net and is proposed to model gene regulatory network. It can predict the change in expression level of target based on the input expression level of activator/repressor. Compared with the method of fuzzy Petri net, the two extended fuzzy Petri nets models perform more accurately in the following typical experiment reasoning outcomes and show that the proposed methods are feasible and available.

Biosystem models, generated from a complex rule/reaction/influence network and from two functionality prototypes

In this work we have further developed the Direct Computer Mapping (DCM) based modelling and simulation methodology. A unified, transition-based representation of complex rule, reaction and influence networks has been introduced and two prototypes (one general state- and another general transition-prototype) have been developed for the unified functional modelling of the state and transition nodes. Starting from the network and from the functional prototypes, an automatic generation method of the graphically editable and extensible GraphML description of biosystem models has been elaborated. The new developments have been implemented in the improved kernel of DCM models. The applied knowledge representation makes possible the unified generation and execution of the balance-based quantitative and influence- or rule-based qualitative, as well as optionally time-driven, multiscale biosystem models. Application of the developed methodology has been illustrated by the improved implementation of the formerly studied and upgraded example biosystem model for combining the detailed, quantitative p53/miR34a signalling system with the pathological model through an extended rule-based coupling model.

Systems pharmacology and enhanced pharmacodynamic models for understanding antibody-based drug action and toxicity

Pharmacokinetic (PK) and pharmacodynamic (PD) models seek to describe the temporal pattern of drug exposures and their associated pharmacological effects produced at micro- and macro-scales of organization. Antibody-based drugs have been developed for a large variety of diseases, with effects exhibited through a comprehensive range of mechanisms of action. Mechanism-based PK/PD and systems pharmacology models can play a major role in elucidating and integrating complex antibody pharmacological properties, such as nonlinear disposition and dynamical intracellular signaling pathways triggered by ligation to their cognate targets. Such complexities can be addressed through the use of robust computational modeling techniques that have proven powerful tools for pragmatic characterization of experimental data and for theoretical exploration of antibody efficacy and adverse effects. The primary objectives of such multi-scale mathematical models are to generate and test competing hypotheses and to predict clinical outcomes. In this review, relevant systems pharmacology and enhanced PD (ePD) models that are used as predictive tools for antibody-based drug action are reported. Their common conceptual features are highlighted, along with approaches used for modeling preclinical and clinically available data. Key examples illustrate how systems pharmacology and ePD models codify the interplay among complex biology, drug concentrations, and pharmacological effects. New hybrid modeling concepts that bridge cutting-edge systems pharmacology models with established PK/ePD models will be needed to anticipate antibody effects on disease in subpopulations and individual patients.

A methodological approach for using high-level Petri Nets to model the immune system response

BACKGROUND

Mathematical and computational models showed to be a very important support tool for the comprehension of the immune system response against pathogens. Models and simulations allowed to study the immune system behavior, to test biological hypotheses about diseases and infection dynamics, and to improve and optimize novel and existing drugs and vaccines. Continuous models, mainly based on differential equations, usually allow to qualitatively study the system but lack in description; conversely discrete models, such as agent based models and cellular automata, permit to describe in detail entities properties at the cost of losing most qualitative analyses. Petri Nets (PN) are a graphical modeling tool developed to model concurrency and synchronization in distributed systems. Their use has become increasingly marked also thanks to the introduction in the years of many features and extensions which lead to the born of "high level" PN.

RESULTS

We propose a novel methodological approach that is based on high level PN, and in particular on Colored Petri Nets (CPN), that can be used to model the immune system response at the cellular scale. To demonstrate the potentiality of the approach we provide a simple model of the humoral immune system response that is able of reproducing some of the most complex well-known features of the adaptive response like memory and specificity features.

CONCLUSIONS

The methodology we present has advantages of both the two classical approaches based on continuous and discrete models, since it allows to gain good level of granularity in the description of cells behavior without losing the possibility of having a qualitative analysis. Furthermore, the presented methodology based on CPN allows the adoption of the same graphical modeling technique well known to life scientists that use PN for the modeling of signaling pathways. Finally, such an approach may open the floodgates to the realization of multi scale models that integrate both signaling pathways (intra cellular) models and cellular (population) models built upon the same technique and software.

A model-driven methodology for exploring complex disease comorbidities applied to autism spectrum disorder and inflammatory bowel disease

We propose a model-driven methodology aimed to shed light on complex disorders. Our approach enables exploring shared etiologies of comorbid diseases at the molecular pathway level. The method, Comparative Comorbidities Simulation (CCS), uses stochastic Petri net simulation for examining the phenotypic effects of perturbation of a network known to be involved in comorbidities to predict new roles for mutations in comorbid conditions. To demonstrate the utility of our novel methodology, we investigated the molecular convergence of autism spectrum disorder (ASD) and inflammatory bowel disease (IBD) on the autophagy pathway. In addition to validation by domain experts, we used formal analyses to demonstrate the model's self-consistency. We then used CCS to compare the effects of loss of function (LoF) mutations previously implicated in either ASD or IBD on the autophagy pathway. CCS identified similar dynamic consequences of these mutations in the autophagy pathway. Our method suggests that two LoF mutations previously implicated in IBD may contribute to ASD, and one ASD-implicated LoF mutation may play a role in IBD. Future targeted genomic or functional studies could be designed to directly test these predictions.

An Integrated Qualitative and Quantitative Biochemical Model Learning Framework Using Evolutionary Strategy and Simulated Annealing

Both qualitative and quantitative model learning frameworks for biochemical systems have been studied in computational systems biology. In this research, after introducing two forms of pre-defined component patterns to represent biochemical models, we propose an integrative qualitative and quantitative modelling framework for inferring biochemical systems. In the proposed framework, interactions between reactants in the candidate models for a target biochemical system are evolved and eventually identified by the application of a qualitative model learning approach with an evolution strategy. Kinetic rates of the models generated from qualitative model learning are then further optimised by employing a quantitative approach with simulated annealing. Experimental results indicate that our proposed integrative framework is feasible to learn the relationships between biochemical reactants qualitatively and to make the model replicate the behaviours of the target system by optimising the kinetic rates quantitatively. Moreover, potential reactants of a target biochemical system can be discovered by hypothesising complex reactants in the synthetic models. Based on the biochemical models learned from the proposed framework, biologists can further perform experimental study in wet laboratory. In this way, natural biochemical systems can be better understood.

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.

Altering physiological networks using drugs: steps towards personalized physiology

Background

The rise of personalized medicine has reminded us that each patient must be treated as an individual. One factor in making treatment decisions is the physiological state of each patient, but definitions of relevant states and methods to visualize state-related physiologic changes are scarce. We constructed correlation networks from physiologic data to demonstrate changes associated with pressor use in the intensive care unit.

Methods

We collected 29 physiological variables at one-minute intervals from nineteen trauma patients in the intensive care unit of an academic hospital and grouped each minute of data as receiving or not receiving pressors. For each group we constructed Spearman correlation networks of pairs of physiologic variables. To visualize drug-associated changes we split the networks into three components: an unchanging network, a network of connections with changing correlation sign, and a network of connections only present in one group.

Results

Out of a possible 406 connections between the 29 physiological measures, 64, 39, and 48 were present in each of the three component networks. The static network confirms expected physiological relationships while the network of associations with changed correlation sign suggests putative changes due to the drugs. The network of associations present only with pressors suggests new relationships that could be worthy of study.

Conclusions

We demonstrated that visualizing physiological relationships using correlation networks provides insight into underlying physiologic states while also showing that many of these relationships change when the state is defined by the presence of drugs. This method applied to targeted experiments could change the way critical care patients are monitored and treated.

Modeling metabolic networks for mammalian cell systems: general considerations, modeling strategies, and available tools

Over the past decades, the availability of large amounts of information regarding cellular processes and reaction rates, along with increasing knowledge about the complex mechanisms involved in these processes, has changed the way we approach the understanding of cellular processes. We can no longer rely only on our intuition for interpreting experimental data and evaluating new hypotheses, as the information to analyze is becoming increasingly complex. The paradigm for the analysis of cellular systems has shifted from a focus on individual processes to comprehensive global mathematical descriptions that consider the interactions of metabolic, genomic, and signaling networks. Analysis and simulations are used to test our knowledge by refuting or validating new hypotheses regarding a complex system, which can result in predictive capabilities that lead to better experimental design. Different types of models can be used for this purpose, depending on the type and amount of information available for the specific system. Stoichiometric models are based on the metabolic structure of the system and allow explorations of steady state distributions in the network. Detailed kinetic models provide a description of the dynamics of the system, they involve a large number of reactions with varied kinetic characteristics and require a large number of parameters. Models based on statistical information provide a description of the system without information regarding structure and interactions of the networks involved. The development of detailed models for mammalian cell metabolism has only recently started to grow more strongly, due to the intrinsic complexities of mammalian systems, and the limited availability of experimental information and adequate modeling tools. In this work we review the strategies, tools, current advances, and recent models of mammalian cells, focusing mainly on metabolism, but discussing the methodology applied to other types of networks as well.

A rigorous approach to facilitate and guarantee the correctness of the genetic testing management in human genome information systems

Background

Recent medical and biological technology advances have stimulated the development of new testing systems that have been providing huge, varied amounts of molecular and clinical data. Growing data volumes pose significant challenges for information processing systems in research centers. Additionally, the routines of genomics laboratory are typically characterized by high parallelism in testing and constant procedure changes.

Results

This paper describes a formal approach to address this challenge through the implementation of a genetic testing management system applied to human genome laboratory. We introduced the Human Genome Research Center Information System (CEGH) in Brazil, a system that is able to support constant changes in human genome testing and can provide patients updated results based on the most recent and validated genetic knowledge. Our approach uses a common repository for process planning to ensure reusability, specification, instantiation, monitoring, and execution of processes, which are defined using a relational database and rigorous control flow specifications based on process algebra (ACP). The main difference between our approach and related works is that we were able to join two important aspects: 1) process scalability achieved through relational database implementation, and 2) correctness of processes using process algebra. Furthermore, the software allows end users to define genetic testing without requiring any knowledge about business process notation or process algebra.

Conclusions

This paper presents the CEGH information system that is a Laboratory Information Management System (LIMS) based on a formal framework to support genetic testing management for Mendelian disorder studies. We have proved the feasibility and showed usability benefits of a rigorous approach that is able to specify, validate, and perform genetic testing using easy end user interfaces.

MODELING AND ANALYZING THE METABOLISM OF RIBOFLAVIN PRODUCTION USING PETRI NETS

A number of recent studies have focused on structural and functional analysis and simulation of biochemical pathways, and it suggested that these structure-oriented analysis methods could be greatly helpful for the understanding of the metabolism. Among several structural analysis methods, Petri nets analysis (PNA) has a visual representation that facilitates users' comprehension and thus is employed in this study. The main results in the present paper are: (1) an in silico model of the metabolism of riboflavin production in bacillus subtilis based on PNA; and (2) a study with structural analysis. The obtained invariants are analyzed and classified based on their structural and functional capabilities.

Probabilistic polynomial dynamical systems for reverse engineering of gene regulatory networks

Elucidating the structure and/or dynamics of gene regulatory networks from experimental data is a major goal of systems biology. Stochastic models have the potential to absorb noise, account for un-certainty, and help avoid data overfitting. Within the frame work of probabilistic polynomial dynamical systems, we present an algorithm for the reverse engineering of any gene regulatory network as a discrete, probabilistic polynomial dynamical system. The resulting stochastic model is assembled from all minimal models in the model space and the probability assignment is based on partitioning the model space according to the likeliness with which a minimal model explains the observed data. We used this method to identify stochastic models for two published synthetic network models. In both cases, the generated model retains the key features of the original model and compares favorably to the resulting models from other algorithms.

Some aspects of the anemia of chronic disorders modeled and analyzed by petri net based approach

Anemia of chronic disorders is a very important phenomenon and iron is a crucial factor of this complex process. To better understand this process and its influence on some other factors we have built a mathematical model of the human body iron homeostasis, which possibly most exactly would reflect the metabolism of iron in the case of anemia and inflammation. The model has been formulated in the language of Petri net theory, which allows for its simulation and precise analysis. The obtained results of the analysis of the model’s behavior, concerning the influence of anemia and inflammation on the transferrin receptors, and hepcidin concentration changes are the valuable complements to the knowledge following from clinical research. This analysis is one of the first attempts to investigate properties and behavior of a not fully understood biological system on a basis of its Petri net based model.

Petri Nets - A Mathematical Formalism to Analyze Chemical Reaction Networks

In this review we introduce and discuss Petri nets - a mathematical formalism to describe and analyze chemical reaction networks. Petri nets were developed to describe concurrency in general systems. We find most applications to technical and financial systems, but since about twenty years also in systems biology to model biochemical systems. This review aims to give a short informal introduction to the basic formalism illustrated by a chemical example, and to discuss possible applications to the analysis of chemical reaction networks, including cheminformatics. We give a short overview about qualitative as well as quantitative modeling Petri net techniques useful in systems biology, summarizing the state-of-the-art in that field and providing the main literature references. Finally, we discuss advantages and limitations of Petri nets and give an outlook to further development.

Simulation of a Petri net-based model of the terpenoid biosynthesis pathway

Background

The development and simulation of dynamic models of terpenoid biosynthesis has yielded a systems perspective that provides new insights into how the structure of this biochemical pathway affects compound synthesis. These insights may eventually help identify reactions that could be experimentally manipulated to amplify terpenoid production. In this study, a dynamic model of the terpenoid biosynthesis pathway was constructed based on the Hybrid Functional Petri Net (HFPN) technique. This technique is a fusion of three other extended Petri net techniques, namely Hybrid Petri Net (HPN), Dynamic Petri Net (HDN) and Functional Petri Net (FPN).

Results

The biological data needed to construct the terpenoid metabolic model were gathered from the literature and from biological databases. These data were used as building blocks to create an HFPNe model and to generate parameters that govern the global behaviour of the model. The dynamic model was simulated and validated against known experimental data obtained from extensive literature searches. The model successfully simulated metabolite concentration changes over time (pt) and the observations correlated with known data. Interactions between the intermediates that affect the production of terpenes could be observed through the introduction of inhibitors that established feedback loops within and crosstalk between the pathways.

Conclusions

Although this metabolic model is only preliminary, it will provide a platform for analysing various high-throughput data, and it should lead to a more holistic understanding of terpenoid biosynthesis.

Predicting drug side-effects by chemical systems biology

New approaches to predicting ligand similarity and protein interactions can explain unexpected observations of drug inefficacy or side-effects.

Modeling the temporal evolution of the Drosophila gene expression from DNA microarray time series

The time evolution of gene expression across the developmental stages of the host organism can be inferred from appropriate DNA microarray time series. Modeling this evolution aims eventually at improving the understanding and prediction of the complex phenomena that are the basis of life. We focus on the embryonic-to-adult development phases of Drosophila melanogaster, and chose to model the expression network with the help of a system of differential equations with constant coefficients, which are nonlinear in the transcript concentrations but linear in their logarithms. To reduce the dimensionality of the problem, genes having similar expression profiles are grouped into 17 clusters. We show that a simple linear model is able to reproduce the experimental data with very good precision, owing to the large number of parameters that represent the connections between the clusters. Remarkably, the parameter reduction allowed elimination of up to 80-85% of these connections while keeping fairly good precision. This result supports the low-connectivity hypothesis of gene expression networks, with about three connections per cluster, without introducing a priori hypotheses. The core of the network shows a few gene clusters with negative self-regulation, and some highly connected clusters involving proteins with crucial functions.

Rapidly exploring structural and dynamic properties of signaling networks using PathwayOracle

BACKGROUND

In systems biology the experimentalist is presented with a selection of software for analyzing dynamic properties of signaling networks. These tools either assume that the network is in steady-state or require highly parameterized models of the network of interest. For biologists interested in assessing how signal propagates through a network under specific conditions, the first class of methods does not provide sufficiently detailed results and the second class requires models which may not be easily and accurately constructed. A tool that is able to characterize the dynamics of a signaling network using an unparameterized model of the network would allow biologists to quickly obtain insights into a signaling network's behavior.

RESULTS

We introduce PathwayOracle, an integrated suite of software tools for computationally inferring and analyzing structural and dynamic properties of a signaling network. The feature which differentiates PathwayOracle from other tools is a method that can predict the response of a signaling network to various experimental conditions and stimuli using only the connectivity of the signaling network. Thus signaling models are relatively easy to build. The method allows for tracking signal flow in a network and comparison of signal flows under different experimental conditions. In addition, PathwayOracle includes tools for the enumeration and visualization of coherent and incoherent signaling paths between proteins, and for experimental analysis - loading and superimposing experimental data, such as microarray intensities, on the network model.

CONCLUSION

PathwayOracle provides an integrated environment in which both structural and dynamic analysis of a signaling network can be quickly conducted and visualized along side experimental results. By using the signaling network connectivity, analyses and predictions can be performed quickly using relatively easily constructed signaling network models. The application has been developed in Python and is designed to be easily extensible by groups interested in adding new or extending existing features. PathwayOracle is freely available for download and use.

Stochastic Petri Net extension of a yeast cell cycle model

This paper presents the definition, solution and validation of a stochastic model of the budding yeast cell cycle, based on Stochastic Petri Nets (SPN). A specific family of SPNs is selected for building a stochastic version of a well-established deterministic model. We describe the procedure followed in defining the SPN model from the deterministic ODE model, a procedure that can be largely automated. The validation of the SPN model is conducted with respect to both the results provided by the deterministic one and the experimental results available from literature. The SPN model catches the behavior of the wild type budding yeast cells and a variety of mutants. We show that the stochastic model matches some characteristics of budding yeast cells that cannot be found with the deterministic model. The SPN model fine-tunes the simulation results, enriching the breadth and the quality of its outcome.

Hierarchical coordinate systems for understanding complexity and its evolution, with applications to genetic regulatory networks

Beyond complexity measures, sometimes it is worthwhile in addition to investigate how complexity changes structurally, especially in artificial systems where we have complete knowledge about the evolutionary process. Hierarchical decomposition is a useful way of assessing structural complexity changes of organisms modeled as automata, and we show how recently developed computational tools can be used for this purpose, by computing holonomy decompositions and holonomy complexity. To gain insight into the evolution of complexity, we investigate the smoothness of the landscape structure of complexity under minimal transitions. As a proof of concept, we illustrate how the hierarchical complexity analysis reveals symmetries and irreversible structure in biological networks by applying the methods to the lac operon mechanism in the genetic regulatory network of Escherichia coli.

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.

Computational systems biology in drug discovery and development: methods and applications

Computational systems biology is an emerging field in biological simulation that attempts to model or simulate intra- and intercellular events using data gathered from genomic, proteomic or metabolomic experiments. The need to model complex temporal and spatiotemporal processes at many different scales has led to the emergence of numerous techniques, including systems of differential equations, Petri nets, cellular automata simulators, agent-based models and pi calculus. This review provides a brief summary and an assessment of most of these approaches. It also provides examples of how these methods are being used to facilitate drug discovery and development.

Conceptual-level workflow modeling of scientific experiments using NMR as a case study

Background

Scientific workflows improve the process of scientific experiments by making computations explicit, underscoring data flow, and emphasizing the participation of humans in the process when intuition and human reasoning are required. Workflows for experiments also highlight transitions among experimental phases, allowing intermediate results to be verified and supporting the proper handling of semantic mismatches and different file formats among the various tools used in the scientific process. Thus, scientific workflows are important for the modeling and subsequent capture of bioinformatics-related data. While much research has been conducted on the implementation of scientific workflows, the initial process of actually designing and generating the workflow at the conceptual level has received little consideration.

Results

We propose a structured process to capture scientific workflows at the conceptual level that allows workflows to be documented efficiently, results in concise models of the workflow and more-correct workflow implementations, and provides insight into the scientific process itself. The approach uses three modeling techniques to model the structural, data flow, and control flow aspects of the workflow. The domain of biomolecular structure determination using Nuclear Magnetic Resonance spectroscopy is used to demonstrate the process. Specifically, we show the application of the approach to capture the workflow for the process of conducting biomolecular analysis using Nuclear Magnetic Resonance (NMR) spectroscopy.

Conclusion

Using the approach, we were able to accurately document, in a short amount of time, numerous steps in the process of conducting an experiment using NMR spectroscopy. The resulting models are correct and precise, as outside validation of the models identified only minor omissions in the models. In addition, the models provide an accurate visual description of the control flow for conducting biomolecular analysis using NMR spectroscopy experiment.

Qualitative networks: a symbolic approach to analyze biological signaling networks

BACKGROUND

A central goal of Systems Biology is to model and analyze biological signaling pathways that interact with one another to form complex networks. Here we introduce Qualitative networks, an extension of Boolean networks. With this framework, we use formal verification methods to check whether a model is consistent with the laboratory experimental observations on which it is based. If the model does not conform to the data, we suggest a revised model and the new hypotheses are tested in-silico.

RESULTS

We consider networks in which elements range over a small finite domain allowing more flexibility than Boolean values, and add target functions that allow to model a rich set of behaviors. We propose a symbolic algorithm for analyzing the steady state of these networks, allowing us to scale up to a system consisting of 144 elements and state spaces of approximately 10(86) states. We illustrate the usefulness of this approach through a model of the interaction between the Notch and the Wnt signaling pathways in mammalian skin, and its extensive analysis.

CONCLUSION

We introduce an approach for constructing computational models of biological systems that extends the framework of Boolean networks and uses formal verification methods for the analysis of the model. This approach can scale to multicellular models of complex pathways, and is therefore a useful tool for the analysis of complex biological systems. The hypotheses formulated during in-silico testing suggest new avenues to explore experimentally. Hence, this approach has the potential to efficiently complement experimental studies in biology.

Qualitatively modelling and analysing genetic regulatory networks: a Petri net approach

MOTIVATION

New developments in post-genomic technology now provide researchers with the data necessary to study regulatory processes in a holistic fashion at multiple levels of biological organization. One of the major challenges for the biologist is to integrate and interpret these vast data resources to gain a greater understanding of the structure and function of the molecular processes that mediate adaptive and cell cycle driven changes in gene expression. In order to achieve this biologists require new tools and techniques to allow pathway related data to be modelled and analysed as network structures, providing valuable insights which can then be validated and investigated in the laboratory.

RESULTS

We propose a new technique for constructing and analysing qualitative models of genetic regulatory networks based on the Petri net formalism. We take as our starting point the Boolean network approach of treating genes as binary switches and develop a new Petri net model which uses logic minimization to automate the construction of compact qualitative models. Our approach addresses the shortcomings of Boolean networks by providing access to the wide range of existing Petri net analysis techniques and by using non-determinism to cope with incomplete and inconsistent data. The ideas we present are illustrated by a case study in which the genetic regulatory network controlling sporulation in the bacterium Bacillus subtilis is modelled and analysed.

AVAILABILITY

The Petri net model construction tool and the data files for the B. subtilis sporulation case study are available at http://bioinf.ncl.ac.uk/gnapn.