Deterministic models and stochastic simulations in multiple reaction models in systems biology

Fine-Grained Parallel and Distributed Spatial Stochastic Simulation of Biological Reactions

Calcific aortic valve disease (CAVD) arises from coupled interactions between blood flow, tissue mechanics, and cellular signaling. Hemodynamic forces influence endothelial and interstitial cell behavior, while the resulting tissue remodeling alters valve motion and flow patterns. Capturing this two-way feedback requires models that integrate fluid-structure mechanics with biochemical regulation, yet such multiscale coupling remains technically challenging. Previous computational models have focused on isolated aspects of the disease: fluid-structure interaction (FSI) simulations reproduce valve deformation and flow, and systems biology (SB) models describe molecular signaling that drives fibrosis and calcification. However, without coupling, these approaches cannot predict how mechanical dysfunction initiates biochemical remodeling or how biochemical changes feed back on mechanics. Here, we present a multi-physics computational framework that couples three-dimensional FSI simulations of aortic valve dynamics with a mechanistic SB model of calcification signaling. The FSI module resolves pulsatile blood flow and leaflet deformation, yielding local wall shear stresses and tissue strains throughout the cardiac cycle. These mechanical quantities are used as inputs to the SB module, which represents key biochemical pathways governing inflammation, TGF- β /SMAD signaling, and nitric-oxide (NO)-mediated inhibition within valvular cells. Simulations predict long-term calcification trajectories for valves of varying thickness, showing that fibrosis-induced stiffening lowers shear stress, reduces NO synthesis, and enhances TGF- β activation, thereby accelerating calcification. The framework is modular and extensible, allowing future incorporation of additional pathways, as well as implementation of full two-way coupling between the FSI and SB models. By integrating physics-based hemodynamics with systems-level biochemistry, this study provides a proof-of-principle demonstration of a next-generation, multi-scale modeling platform for studying cardiovascular disease that unites blood flow dynamics and biochemical signaling.

In this review, we describe technology and use of single-fluorophore imaging and detection in living cells with regard to application in systems biology and medicine. Because all biological reactions occur under aqueous conditions, the realization of single-fluorophore imaging using an optical microscope has led to the direct observation of biological molecules at work. Today, we can observe single molecules in individual living cells and even higher multicellular organisms. Using single-molecule imaging, we can determine the absolute values of kinetic and dynamic parameters of molecular reactions as a whole and during fluctuations and distribution. In addition, identification of the coordinate of single molecules has enabled super-localization techniques to virtually improve spatial resolution of optical microscopy. Single-molecule detection that depends on point detection instead of imaging is also useful in detecting concentrations, diffusive movements, and molecular interactions in living cells, especially in the cytoplasm. The precise and absolute values of positional, kinetic, and dynamic parameters that are determined by single-molecule imaging and detection in living cells constitute valuable data on unitary biological reactions, because they are obtained without destroying the integrity of complex cellular systems. Moreover, most parameters that are determined by single-molecule measurements can be substituted directly into equations that describe kinetic and dynamic models in systems biology and medicine.

Prediction and control sufficient for reliable medical and other interventions are prominent aims of modeling in systems biology. The short-term attainment of these goals has played a strong role in projecting the importance and value of the field. In this paper I identify the standard models must meet to achieve these objectives as predictive robustness—predictive reliability over large domains. Drawing on the results of an ethnographic investigation and various studies in the systems biology literature, I explore four current obstacles to achieving predictive robustness; data constraints, parameter uncertainty, collaborative constraints and system-scale requirements. I use a case study and the commentary of systems biologists themselves to show that current practices in the field, rather than pursuing these goals, frequently use models heuristically to investigate and build understanding of biological systems that do not meet standards of predictive robustness but are nonetheless effective uses of computation. A more heuristic conception of modeling allows us to interpret current practices as ways that manage these obstacles more effectively, particularly collaborative constraints, such that modelers can in the long-run at least work towards prediction and control.

The exploding number of computational models produced by Systems Biologists over the last years is an invitation to structure and exploit this new wealth of information. Researchers would like to trace models relevant to specific scientific questions, to explore their biological content, to align and combine them, and to match them with experimental data. To automate these processes, it is essential to consider semantic annotations, which describe their biological meaning. As a prerequisite for a wide range of computational methods, we propose general and flexible similarity measures for Systems Biology models computed from semantic annotations. By using these measures and a large extensible ontology, we implement a platform that can retrieve, cluster, and align Systems Biology models and experimental data sets. At present, its major application is the search for relevant models in the BioModels Database, starting from initial models, data sets, or lists of biological concepts. Beyond similarity searches, the representation of models by semantic feature vectors may pave the way for visualisation, exploration, and statistical analysis of large collections of models and corresponding data.

In this article I address the interactions between biological knowledge and ideas about the kinds of entity that are suited to appropriation. I start by arguing that commodification and reductionism are closely linked, and that patenting suits entities that are discrete and isolable, such as those that are the focus of molecular biology. I then turn to the new field of systems biology, which recognizes that traditional reductionist approaches to biology are no longer adequate and attempts to provide a more integrative understanding of biological systems. In doing this, systems biology has to deal with emergent phenomena. But patenting does not suit the dynamic and interactive complexity that is the object of study in systems biology. If systems biology rejects reductionism where does that leave commodification? I examine attempts to commodify predictive computational models in systems biology. I then turn to systems biology's sister discipline, synthetic biology, which deals with emergence by reducing the complexity of biological systems. By factoring out messy contingencies, synthetic biology is, in theory, well suited to commodification. Drawing on both these examples I explore how ideas about appropriation, including open source, are influencing the nature and course of research in biology.

A First Course in Systems Biology is intended to serve as the textbook for a semester-long course in systems biology directed toward advanced undergraduate or graduate students. The book meets this goal admirably. Eberhard O. Voit writes in a style that is both interesting to read and highly informational. A First Course in Systems Biology manages to combine the fields of mathematics, engineering, and biology in a textbook that could be read and assimilated (with varying degrees of difficulty) by students of all three disciplines. The text is broken into three main sections: mathematical modeling, “molecular inventories” of the requisite biological systems, and case studies. Despite the extensive mathematical component, A First Course in Systems Biology is not set up like a traditional mathematics textbook. Instead of long proofs and stark equations, concepts are first introduced intuitively before the equations are formalized, and readers are walked through a concrete example. A number of plots and descriptive images accompany the math, ensuring that even a novice number-cruncher can grasp the basics of Boolean network models, stability analysis, and parameter estimation. The middle third of the text covers the most pertinent biological details required for studying gene regulatory systems, protein interaction networks, metabolic pathways, and cell signaling cascades from a systems biology perspective. The book closes with a series of case studies that focus on the proper selection and application of biological models. For example, in Chapter 12, Voit demonstrates the type of experimental data and computational simulation that would be required for modeling several aspects of heart function, from a physiological model of blood flow through the atria and ventricles to one that examines oscillations of calcium signaling. Throughout, Voit provides clear and concise explanations of the most important and basic modeling and biological concepts without resorting to oversimplification, though explanations can sometimes be vague. Further, some topics, particularly that of epigenetics, are disappointingly terse. However, the brevity is always compensated for with extensive references for the curious reader. Indeed, despite the approachability of the text, this book requires great concentration and interaction on the part of the reader. Frequently, Voit urges that “the reader should confirm” the mathematical conclusions stated in the text. Extensive and open-ended exercises are given at the end of each chapter. These problems are not for the faint of heart and often require additional research, computer coding, or essay writing to complete. While A First Course in Systems Biology does not teach students precisely how to code mathematical models or provide protocols for biological experiments, the book does grant students an entry into the proper mindset of systems biologists. The continual emphasis on determining how to choose an appropriate model for a given problem and understanding what type of information disparate models could provide prepares readers well for generating systems biology questions and models of their own.

Computational models are becoming more and more the central scientific paradigm for understanding the complexity of living systems. With the increasing number and size of these models there is a growing need for model reuse and exchange. Furthermore, detailed models are not manageable without computer support. There are efforts to formalise the mathematical structure of models (e.g. SBML) and to standardise the kinetic and biological meaning of model components (e.g. SBO, GO, UniProt). However, formalising only the structure of computational models is not sufficient to easily exchange and reuse models and to achieve full computer support for modelling. We also need to formalise the pragmatical and dynamical aspects of models.For this purpose we propose two ontologies: The Kinetic Simulation Algorithm Ontology (KiSAO) and the TErminology for the Description of DYnamics (TEDDY). KiSAO covers algorithms used for simulation of computational models. The ontology classifies and puts into context existing simulation algorithms. For the classification, it uses several criteria such as deterministic/stochastic or spatial/nonspatial. The aim of TEDDY is to provide terms for describing and characterising dynamical behaviours, observable dynamical phenomena, and control elements of biological models and biological systems in Systems Biology and Synthetic Biology.We demonstrate how these new ontologies can extend the formalisation of models beyond structure, using the well-known repressilator model as an example. The simulation results depend pragmatically on the used algorithm: We compare the simulation results of the deterministic Livermore solver for ordinary differential equations (KiSAO:0000071) to the simulation results of the stochastic Gibson and Bruck’s next reaction method (KiSAO:0000027). The simulation results depend dynamically on the parameter setting: While parameter * (maximum number of produced proteins per promotor) is increased the modelled dynamical system undergoes a Supercritical Hopf Bifurcation (TEDDY_0000074). Below the critical value of * the system exhibits _Damped Oscillation_ (TEDDY_0000063) converging to a Stable Spiral Point (TEDDY_0000126). Above the bifurcation the system possesses a Stable _Limit Cycle_ (TEDDY_0000114), i.e. it shows Sustained Oscillation. The Negative Feedback (TEDDY_0000034) of the system is a necessary precondition for the ability of the system to oscillate.For details on KiSAO see the "MIASE project page":http://sourceforge.net/projects/miase, for details on TEDDY see the "project page":http://sourceforge.net/projects/teddyontology.

We propose React(C), an expressive programming language for stochastic modeling and simulation in systems biology that is based on biochemical reactions with constraints. We prove that React(C) can express the stochastic π-calculus, in contrast to previous rule-based programming languages, and further illustrate the high expressiveness of React(C). We present a stochastic simulator for React(C) independently of the choice of the constraint language C. Our simulator decides for a given reaction rule whether it can be applied to the current biochemical solution. We show that this decision problem is NP-complete for arbitrary constraint systems C and that it can be solved in polynomial time for rules of bounded arity. In practice, we propose to solve this problem by constraint programming.

Biochemical systems can be described by biochemical reactions. Biochemical reactions can be investigated through mathematical modeling and stochastic simulations. Deterministic and stochastic models are two basic categories of models for biochemical reactions. Due to transmembrane transportation of biochemical species and delayed degradation, time delays are ubiquitous in coupled biochemical systems. Therefore, models for biochemical reactions can be further classified into delayed and un-delayed ones. For biochemical systems without delays, researchers have established the connections between deterministic models and stochastic models directly from the deterministic ones. For delayed biochemical systems, researchers have proposed some stochastic simulation methods to cope with biochemical reactions with time delays. However, the existing delayed stochastic simulation algorithms (SSA) are all incapable of realizing the comparison between highly nonlinear deterministic delayed models and stochastic models directly from the the deterministic ones. In this paper, we proposed a delayed SSA, which can realize the comparison between deterministic models and its stochastic counterparts. Furthermore, one can also use the algorithm to investigate intrinsic noise-induced behaviors, and the effect of system volumes. Several numerical examples show the effectiveness and correctness of our algorithm.

A selection of papers prepared by participants of 7th Young Scientists School SBB’15 is presented in three Supplementary Issues to the journals of BMC series, namely, BMC Genomics, BMC Genetics and BMC Microbiology. SBB’15 took place June 22nd-25th in Novosibirsk, Russia (http://conf.nsc.ru/sbb2015). The series of Young Scientists Schools in Systems Biology and Bioinformatics (SBB) started several years ago, in 2008, as educational workshop associated with the large international conference series on bioinformatics known as BGRS\SB (Bioinformatics of Genome Regulation and Structure\Systems Biology) (http://conf.bionet.nsc.ru/bgrssb2016). After its inauguration year of 1998, BGRS/SBB held biannually at the Institute of Cytology and Genetics SB RAS in Novosibirsk. In a recent decade, it became a prime meeting venue for biologists, computer scientists, physicists, mathematicians and biochemists working in an interdisciplinary field of systems biology and computer genomics. Being the largest system biology meeting series in Russia, BGRS\SB-14 attracted participants from 27 countries. In the past BioMedCentral had published series of special issues based on best materials presented at the conference in BMC Genomics (http://www.biomedcentral.com/bmcgenomics/supplements/15/S12), BMC Evolutionary Biology (http://www.biomedcentral.com/bmcevolbiol/supplements/15/S1), BMC Genetics (http://www.biomedcentral.com/bmcgenet/supplements/16/S1) and BMC Systems biology (http://www.biomedcentral.com/bmcsystbiol/supplements/9/S2). In addition, the protein structure related studies presented by BGRS/SBB participants were collated as special issues in Journal of Bioinformatics and Computational Biology (http://www.worldscientific.com/toc/jbcb/4113/01; http://www.worldscientific.com/toc/jbcb/11/01). [1] In addition, the SBB School series has its own history to be proud of. The first generation of its participants already matured enough to substantially advance in the field. A majority of the participants graduated with PhDs, and now are contributing to the school as the lecturers and to a number of world universities as professors. For some students, the conference became instrumental in obtaining their post-doc or first independent position in academic world. In many cases, the informal atmosphere of the school helped to spark a collaboration that later led to publications in leading journals or the dramatic changes in their science career. The Program Committee of the conference and SBB Schools series includes data analysis, bioinformatics and computational biology professionals from different countries. For the last decade, the SBB conference was co-chaired by Academician Prof. Nikolay A. Kolchanov of the Institute of Cytology and Genetics SB RAS, Russia and Prof. Dr. Ralf Hofestadt of Bielefeld University, Germany. System biology and bioinformatics are rapidly developing and wide fields of science knowledge. For Young Scientists Schools, every year is different as it comprises the topics for the trainings that are the hottest at the time of the event. In 2015, the SBB School concentrated on the modern genomics and an analysis of high-throughput sequencing data. The materials presented in the current special issue provide examples of seamless integration of experimental studies performed in the lab and the computer-assisted inquiries into in the complex patterns of the organization and the functioning of biologic systems at the molecular, cell, tissue, organ, and body levels. The scientific topics discussed in 2015 were presented at the following sections: Next generation sequencing (NGS) and data analysis Evolutionary bioinformatics Systems biology and gene network modeling In SBB’15 Supplements to BMC journals Genomics, we collected the best studies presented at the conference. Due to the general breadth of the field of Systems Biology and Bioinformatic, the manuscripts were accepted into three separate tracks, thus forming three Supplementary Issues, BMC Genomics, BMC Genetics and BMC Microbiology. Below we will describe contents of these issues.

The biological process and molecular functions involved in the cancer progression remain difficult to understand for biologists and clinical doctors. Recent developments in high-throughput technologies urge the systems biology to achieve more precise models for complex diseases. Computational and mathematical models are gradually being used to help us understand the omics data produced by high-throughput experimental techniques. The use of computational models in systems biology allows us to explore the pathogenesis of complex diseases, improve our understanding of the latent molecular mechanisms, and promote treatment strategy optimization and new drug discovery. Currently, it is urgent to bridge the gap between the developments of high-throughput technologies and systemic modeling of the biological process in cancer research. In this review, we firstly studied several typical mathematical modeling approaches of biological systems in different scales and deeply analyzed their characteristics, advantages, applications, and limitations. Next, three potential research directions in systems modeling were summarized. To conclude, this review provides an update of important solutions using computational modeling approaches in systems biology.

Practical identifiability of Systems Biology models has received a lot of attention in recent scientific research. It addresses the crucial question for models' predictability: how accurately can the models' parameters be recovered from available experimental data. The methods based on profile likelihood are among the most reliable methods of practical identification. However, these methods are often computationally demanding or lead to inaccurate estimations of parameters' confidence intervals. Development of methods, which can accurately produce parameters' confidence intervals in reasonable computational time, is of utmost importance for Systems Biology and QSP modeling. We propose an algorithm Confidence Intervals by Constraint Optimization (CICO) based on profile likelihood, designed to speed-up confidence intervals estimation and reduce computational cost. The numerical implementation of the algorithm includes settings to control the accuracy of confidence intervals estimates. The algorithm was tested on a number of Systems Biology models, including Taxol treatment model and STAT5 Dimerization model, discussed in the current article. The CICO algorithm is implemented in a software package freely available in Julia (https://github.com/insysbio/LikelihoodProfiler.jl) and Python (https://github.com/insysbio/LikelihoodProfiler.py).

With the recent rising application of mathematical models in the field of computational systems biology, the interest in sensitivity analysis methods had increased. The stochastic approach, based on chemical master equations, and the deterministic approach, based on ordinary differential equations (ODEs), are the two main approaches for analyzing mathematical models of biochemical systems. In this work, the performance of these approaches to compute sensitivity coefficients is explored in situations where stochastic and deterministic simulation can potentially provide different results (systems with unstable steady states, oscillators with population extinction and bistable systems). We consider two methods in the deterministic approach, namely the direct differential method and the finite difference method, and five methods in the stochastic approach, namely the Girsanov transformation, the independent random number method, the common random number method, the coupled finite difference method and the rejection-based finite difference method. The reviewed methods are compared in terms of sensitivity values and computational time to identify differences in outcome that can highlight conditions in which one approach performs better than the other.

An Application of Conditional Robust Calibration (CRC) to The Lotka-Volterra Predator-Prey model in computational systems biology: a comparison of two sampling strategies