Modeling and simulation of biological systems with stochasticity

Mathematical modeling is a powerful approach for understanding the complexity of biological systems. Recently, several successful attempts have been made for simulating complex biological processes like metabolic pathways, gene regulatory networks and cell signaling pathways. The pathway models have not only generated experimentally verifiable hypothesis but have also provided valuable insights into the behavior of complex biological systems. Many recent studies have confirmed the phenotypic variability of organisms to an inherent stochasticity that operates at a basal level of gene expression. Due to this reason, development of novel mathematical representations and simulations algorithms are critical for successful modeling efforts in biological systems. The key is to find a biologically relevant representation for each representation. Although mathematically rigorous and physically consistent, stochastic algorithms are computationally expensive, they have been successfully used to model probabilistic events in the cell. This paper offers an overview of various mathematical and computational approaches for modeling stochastic phenomena in cellular systems.     

Bridging the gaps in systems biology

Systems biology aims at creating mathematical models, i.e., computational reconstructions of biological systems and processes that will result in a new level of understanding—the elucidation of the basic and presumably conserved “design” and “engineering” principles of biomolecular systems. Thus, systems biology will move biology from a phenomenological to a predictive science. Mathematical modeling of biological networks and processes has already greatly improved our understanding of many cellular processes. However, given the massive amount of qualitative and quantitative data currently produced and number of burning questions in health care and biotechnology needed to be solved is still in its early phases. The field requires novel approaches for abstraction, for modeling bioprocesses that follow different biochemical and biophysical rules, and for combining different modules into larger models that still allow realistic simulation with the computational power available today. We have identified and discussed currently most prominent problems in systems biology: (1) how to bridge different scales of modeling abstraction, (2) how to bridge the gap between topological and mechanistic modeling, and (3) how to bridge the wet and dry laboratory gap. The future success of systems biology largely depends on bridging the recognized gaps.     

Modularization of biochemical networks based on classification of Petri net t-invariants

Background  

Structural analysis of biochemical networks is a growing field in bioinformatics and systems biology. The availability of an increasing amount of biological data from molecular biological networks promises a deeper understanding but confronts researchers with the problem of combinatorial explosion. The amount of qualitative network data is growing much faster than the amount of quantitative data, such as enzyme kinetics. In many cases it is even impossible to measure quantitative data because of limitations of experimental methods, or for ethical reasons. Thus, a huge amount of qualitative data, such as interaction data, is available, but it was not sufficiently used for modeling purposes, until now. New approaches have been developed, but the complexity of data often limits the application of many of the methods. Biochemical Petri nets make it possible to explore static and dynamic qualitative system properties. One Petri net approach is model validation based on the computation of the system's invariant properties, focusing on t-invariants. T-invariants correspond to subnetworks, which describe the basic system behavior.     

Systems analysis of cellular networks under uncertainty

Besides the often-quoted complexity of cellular networks, the prevalence of uncertainties about components, interactions, and their quantitative features provides a largely underestimated hallmark of current systems biology. This uncertainty impedes the development of mechanistic mathematical models to achieve a true systems-level understanding. However, there is increasing evidence that theoretical approaches from diverse scientific domains can extract relevant biological knowledge efficiently, even from poorly characterized biological systems. As a common denominator, the methods focus on structural, rather than more detailed, kinetic network properties. A deeper understanding, better scaling, and the ability to combine the approaches pose formidable challenges for future theory developments.     

Analyzing protein–protein interactions in the post-interactomic era. Are we ready for the endgame?

Mapping protein–protein interactions in genome-wide scales revealed thousands of novel binding partners in each of the explored model organisms. Organizing these hits in comprehensive ways is becoming increasingly important for systems biology approaches to understand complex cellular processes and diseases. However, proteome wide interaction techniques and their resulting global networks are not revealing the topologies of networks that are truly operating in the cell. In this short review I will discuss which prerequisites have to be fulfilled and which experimental methods might be practicable to translate primary protein interaction data into network presentations that help in understanding cellular processes.     

计算系统生物学:理论、方法及在药物研发中的应用

计算系统生物学是一个多学科交叉的新兴领域,旨在通过整合海量数据建立其生物系统相互作用的复杂网络。数据的整合和模型的建立需要发展合适的数学方法和软件工具,这也是计算系统生物学的主要任务。生物系统模型有助于从整体上理解生物体的内在功能和特性。同时,生物网络模型在药物研发中的应用也越来越受到制药企业以及新药研发机构的重视,如用于特异性药物作用靶点的预测和药物毒性评估等。该文简要介绍计算系统生物学的常见网络和计算模型,以及建立模型所用的研究方法,并阐述其在建模和分析中的作用及面临的问题和挑战。     

Mechanistic systems models of cell signaling networks: a case study of myocyte adrenergic regulation

Signal transduction networks coordinate a wide variety of cellular functions, including gene expression, metabolism, and cell fate processes. Understanding biological networks quantitatively is a major challenge to post-genomic biology, and mechanistic systems models will be crucial for this task. Here, we review approaches towards developing mechanistic systems models of established cell signaling networks. The ability of mechanistic system models to generate testable biological hypotheses and experimental strategies is discussed. As a case study of model development and analysis, we examined the functional roles of phospholamban, the L-type calcium channel, the ryanodine receptor, and troponin I phosphorylation upon β-adrenergic stimulation in the rat ventricular myocyte. Model analysis revealed that while protein kinase A-mediated phosphorylation of the ryanodine receptor greatly increases its calcium sensitivity, calcium autoregulation may adapt quickly by negating potential increases in contractility. Systematic combinations of in silico perturbations supported the conclusion that phospholamban phosphoregulation is the primary mechanism for increased sarcoplasmic reticulum load and calcium relaxation rate during β-adrenergic stimulation, while both phospholamban and the L-type calcium channel contribute to increased systolic calcium. Combined with detailed experimental studies, mechanistic systems models will be valuable for developing a quantitative understanding of cell signaling networks.     

Systems biology of cellular rhythms

Rhythms abound in biological systems, particularly at the cellular level where they originate from the feedback loops present in regulatory networks. Cellular rhythms can be investigated both by experimental and modeling approaches, and thus represent a prototypic field of research for systems biology. They have also become a major topic in synthetic biology. We review advances in the study of cellular rhythms of biochemical rather than electrical origin by considering a variety of oscillatory processes such as Ca++ oscillations, circadian rhythms, the segmentation clock, oscillations in p53 and NF-κB, synthetic oscillators, and the oscillatory dynamics of cyclin-dependent kinases driving the cell cycle. Finally we discuss the coupling between cellular rhythms and their robustness with respect to molecular noise.     

Integration of Boolean models exemplified on hepatocyte signal transduction

The number of mathematical models for biological pathways is rapidly growing. In particular, Boolean modelling proved to be suited to describe large cellular signalling networks. Systems biology is at the threshold to holistic understanding of comprehensive networks. In order to reach this goal, connection and integration of existing models of parts of cellular networks into more comprehensive network models is necessary. We discuss model combination approaches for Boolean models. Boolean modelling is qualitative rather than quantitative and does not require detailed kinetic information. We show that these models are useful precursors for large-scale quantitative models and that they are comparatively easy to combine. We propose modelling standards for Boolean models as a prerequisite for smooth model integration. Using these standards, we demonstrate the coupling of two logical models on two different examples concerning cellular interactions in the liver. In the first example, we show the integration of two Boolean models of two cell types in order to describe their interaction. In the second example, we demonstrate the combination of two models describing different parts of the network of a single cell type. Combination of partial models into comprehensive network models will take systems biology to the next level of understanding. The combination of logical models facilitated by modelling standards is a valuable example for the next step towards this goal.     

Understanding biological functions through molecular networks

The completion of genome sequences and subsequent high-throughput mapping of molecular networks have allowed us to study biology from the network perspective. Experimental, statistical and mathematical modeling approaches have been employed to study the structure, function and dynamics of molecular networks, and begin to reveal important links of various network properties to the functions of the biological systems. In agreement with these functional links, evolutionary selection of a network is apparently based on the function, rather than directly on the structure of the network. Dynamic modularity is one of the prominent features of molecular networks. Taking advantage of such a feature may simplify network-based biological studies through construction of process-specific modular networks and provide functional and mechanistic insights linking genotypic variations to complex traits or diseases, which is likely to be a key approach in the next wave of understanding complex human diseases. With the development of ready-to-use network analysis and modeling tools the networks approaches will be infused into everyday biological research in the near future.     

Network-based functional modeling of genomics, transcriptomics and metabolism in bacteria

Molecular entities present in a cell (mRNA, proteins, metabolites,…) do not act in isolation, but rather in cooperation with each other to define an organisms form and function. Their concerted action can be viewed as networks of interacting entities that are active under certain conditions within the cell or upon certain environmental signals. A main challenge in systems biology is to model these networks, or in other words studying which entities interact to form cellular systems or accomplish similar functions. On the contrary, viewing a single entity or an experimental dataset in the light of an interaction network can reveal previous unknown insights in biological processes. In this review we give an overview of how integrated networks can be reconstructed from multiple omics data and how they can subsequently be used for network-based modeling of cellular function in bacteria.     

Making the right connections: biological networks in the light of evolution

Our understanding of how evolution acts on biological networks remains patchy, as is our knowledge of how that action is best identified, modelled and understood. Starting with network structure and the evolution of protein–protein interaction networks, we briefly survey the ways in which network evolution is being addressed in the fields of systems biology, development and ecology. The approaches highlighted demonstrate a movement away from a focus on network topology towards a more integrated view, placing biological properties centre‐stage. We argue that there remains great potential in a closer synergy between evolutionary biology and biological network analysis, although that may require the development of novel approaches and even different analogies for biological networks themselves.     

Genetic network inference: from co-expression clustering to reverse engineering

MOTIVATION: Advances in molecular biological, analytical and computational technologies are enabling us to systematically investigate the complex molecular processes underlying biological systems. In particular, using high-throughput gene expression assays, we are able to measure the output of the gene regulatory network. We aim here to review datamining and modeling approaches for conceptualizing and unraveling the functional relationships implicit in these datasets. Clustering of co-expression profiles allows us to infer shared regulatory inputs and functional pathways. We discuss various aspects of clustering, ranging from distance measures to clustering algorithms and multiple-cluster memberships. More advanced analysis aims to infer causal connections between genes directly, i.e. who is regulating whom and how. We discuss several approaches to the problem of reverse engineering of genetic networks, from discrete Boolean networks, to continuous linear and non-linear models. We conclude that the combination of predictive modeling with systematic experimental verification will be required to gain a deeper insight into living organisms, therapeutic targeting and bioengineering.     

A conceptual review on systems biology in health and diseases: from biological networks to modern therapeutics

Human physiology is an ensemble of various biological processes spanning from intracellular molecular interactions to the whole body phenotypic response. Systems biology endures to decipher these multi-scale biological networks and bridge the link between genotype to phenotype. The structure and dynamic properties of these networks are responsible for controlling and deciding the phenotypic state of a cell. Several cells and various tissues coordinate together to generate an organ level response which further regulates the ultimate physiological state. The overall network embeds a hierarchical regulatory structure, which when unusually perturbed can lead to undesirable physiological state termed as disease. Here, we treat a disease diagnosis problem analogous to a fault diagnosis problem in engineering systems. Accordingly we review the application of engineering methodologies to address human diseases from systems biological perspective. The review highlights potential networks and modeling approaches used for analyzing human diseases. The application of such analysis is illustrated in the case of cancer and diabetes. We put forth a concept of cell-to-human framework comprising of five modules (data mining, networking, modeling, experimental and validation) for addressing human physiology and diseases based on a paradigm of system level analysis. The review overtly emphasizes on the importance of multi-scale biological networks and subsequent modeling and analysis for drug target identification and designing efficient therapies.