Modeling and Simulation of the Immune System as a Self-Regulating Network

Metabolomics meets systems immunology

Metabolic processes play a critical role in immune regulation. Metabolomics is the systematic analysis of small molecules (metabolites) in organisms or biological samples, providing an opportunity to comprehensively study interactions between metabolism and immunity in physiology and disease. Integrating metabolomics into systems immunology allows the exploration of the interactions of multilayered features in the biological system and the molecular regulatory mechanism of these features. Here, we provide an overview on recent technological developments of metabolomic applications in immunological research. To begin, two widely used metabolomics approaches are compared: targeted and untargeted metabolomics. Then, we provide a comprehensive overview of the analysis workflow and the computational tools available, including sample preparation, raw spectra data preprocessing, data processing, statistical analysis, and interpretation. Third, we describe how to integrate metabolomics with other omics approaches in immunological studies using available tools. Finally, we discuss new developments in metabolomics and its prospects for immunology research. This review provides guidance to researchers using metabolomics and multiomics in immunity research, thus facilitating the application of systems immunology to disease research.

Cancer immune control dynamics: a clinical data driven model of systemic immunity in patients with metastatic melanoma

Background

Recent clinical advances in cancer immuno-therapeutics underscore the need for improved understanding of the complex relationship between cancer and the multiple, multi-functional, inter-dependent, cellular and humoral mediators/regulators of the human immune system. This interdisciplinary effort exploits engineering analysis methods utilized to investigate anomalous physical system behaviors to explore immune system behaviors. Cancer Immune Control Dynamics (CICD), a systems analysis approach, attempts to identify differences between systemic immune homeostasis of 27 healthy volunteers versus 14 patients with metastatic malignant melanoma based on daily serial measurements of conventional peripheral blood biomarkers (15 cell subsets, 35 cytokines). The modeling strategy applies engineering control theory to analyze an individual’s immune system based on the biomarkers’ dynamic non-linear oscillatory behaviors. The reverse engineering analysis uses a Singular Value Decomposition (SVD) algorithm to solve the inverse problem and identify a solution profile of the active biomarker relationships. Herein, 28,605 biologically possible biomarker interactions are modeled by a set of matrix equations creating a system interaction model. CICD quantifies the model with a participant’s biomarker data then computationally solves it to measure each relationship’s activity allowing a visualization of the individual’s current state of immunity.

Results

CICD results provide initial evidence that this model-based analysis is consistent with identified roles of biomarkers in systemic immunity of cancer patients versus that of healthy volunteers. The mathematical computations alone identified a plausible network of immune cells, including T cells, natural killer (NK) cells, monocytes, and dendritic cells (DC) with cytokines MCP-1 [CXCL2], IP-10 [CXCL10], and IL-8 that play a role in sustaining the state of immunity in advanced cancer.

Conclusions

With CICD modeling capabilities, the complexity of the immune system is mathematically quantified through thousands of possible interactions between multiple biomarkers. Therefore, the overall state of an individual’s immune system regardless of clinical status, is modeled as reflected in their blood samples. It is anticipated that CICD-based capabilities will provide tools to specifically address cancer and treatment modulated (immune checkpoint inhibitors) parameters of human immunity, revealing clinically relevant biological interactions.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-021-04025-7.

Modeling Radioimmune Response-Current Status and Perspectives

The combination of immune therapy with radiation offers an exciting and promising treatment modality in cancer therapy. It has been hypothesized that radiation induces damage signals within the tumor, making it more detectable for the immune system. In combination with inhibiting immune checkpoints an effective anti-tumor immune response may be established. This inversion from tumor immune evasion raises numerous questions to be solved to support an effective clinical implementation: These include the optimum immune drug and radiation dose time courses, the amount of damage and associated doses required to stimulate an immune response, and the impact of lymphocyte status and dynamics. Biophysical modeling can offer unique insights, providing quantitative information addressing these factors and highlighting mechanisms of action. In this work we review the existing modeling approaches of combined ‘radioimmune’ response, as well as associated fields of study. We propose modeling attempts that appear relevant for an effective and predictive model. We emphasize the importance of the time course of drug and dose delivery in view to the time course of the triggered biological processes. Special attention is also paid to the dose distribution to circulating blood lymphocytes and the effect this has on immune competence.

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

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

Digital Pathology Analysis Quantifies Spatial Heterogeneity of CD3, CD4, CD8, CD20, and FoxP3 Immune Markers in Triple-Negative Breast Cancer

Overwhelming evidence has shown the significant role of the tumor microenvironment (TME) in governing the triple-negative breast cancer (TNBC) progression. Digital pathology can provide key information about the spatial heterogeneity within the TME using image analysis and spatial statistics. These analyses have been applied to CD8+ T cells, but quantitative analyses of other important markers and their correlations are limited. In this study, a digital pathology computational workflow is formulated for characterizing the spatial distributions of five immune markers (CD3, CD4, CD8, CD20, and FoxP3) and then the functionality is tested on whole slide images from patients with TNBC. The workflow is initiated by digital image processing to extract and colocalize immune marker-labeled cells and then convert this information to point patterns. Afterward invasive front (IF), central tumor (CT), and normal tissue (N) are characterized. For each region, we examine the intra-tumoral heterogeneity. The workflow is then repeated for all specimens to capture inter-tumoral heterogeneity. In this study, both intra- and inter-tumoral heterogeneities are observed for all five markers across all specimens. Among all regions, IF tends to have higher densities of immune cells and overall larger variations in spatial model fitting parameters and higher density in cell clusters and hotspots compared to CT and N. Results suggest a distinct role of IF in the tumor immuno-architecture. Though the sample size is limited in the study, the computational workflow could be readily reproduced and scaled due to its automatic nature. Importantly, the value of the workflow also lies in its potential to be linked to treatment outcomes and identification of predictive biomarkers for responders/non-responders, and its application to parameterization and validation of computational immuno-oncology models.

Modeling the Effect of Memory in the Adaptive Immune Response

It is well understood that there are key differences between a primary immune response and subsequent responses. Specifically, memory T cells that remain after a primary response drive the clearance of antigen in later encounters. While the existence of memory T cells is widely accepted, the specific mechanisms that govern their function are generally debated. In this paper, we develop a mathematical model of the immune response. This model follows the creation, activation, and regulation of memory T cells, which allows us to explore the differences between the primary and secondary immune responses. Through the incorporation of memory T cells, we demonstrate how the immune system can mount a faster and more effective secondary response. This mathematical model provides a quantitative framework for studying chronic infections and auto-immune diseases.

Dependence of CD8 T Cell Response upon Antigen Load During Primary Infection : Analysis of Data from Yellow Fever Vaccination

A major question in immunology is what role antigen load plays in determining the size of the CD8 immune response. Is the amount of antigen important during recruitment, proliferation, and/or memory formation? Animal studies have shown that antigen is only strictly required early during activation of T cells, but the importance of antigen at later timepoints is unclear. Using data from 24 volunteers infected with the yellow fever vaccine virus (YFV), we analyzed the dependence of T cell proliferation upon viral load. We found that volunteers with high viral load initially have greater T cell responses, but by 28 days post-vaccination those with lower viral load are able to 'catch-up.' Using differential equation modeling we show that this pattern is consistent with viral load only affecting recruitment (i.e., programmed proliferation) as opposed to affecting recruitment and proliferation (i.e., antigen-dependent proliferation). A quantitative understanding of the dependence of T cell dynamics on antigen load will be of use to modelers studying not only vaccination, but also cancer immunology and autoimmune disorders.

Multiscale Agent-Based and Hybrid Modeling of the Tumor Immune Microenvironment

Multiscale systems biology and systems pharmacology are powerful methodologies that are playing increasingly important roles in understanding the fundamental mechanisms of biological phenomena and in clinical applications. In this review, we summarize the state of the art in the applications of agent-based models (ABM) and hybrid modeling to the tumor immune microenvironment and cancer immune response, including immunotherapy. Heterogeneity is a hallmark of cancer; tumor heterogeneity at the molecular, cellular, and tissue scales is a major determinant of metastasis, drug resistance, and low response rate to molecular targeted therapies and immunotherapies. Agent-based modeling is an effective methodology to obtain and understand quantitative characteristics of these processes and to propose clinical solutions aimed at overcoming the current obstacles in cancer treatment. We review models focusing on intra-tumor heterogeneity, particularly on interactions between cancer cells and stromal cells, including immune cells, the role of tumor-associated vasculature in the immune response, immune-related tumor mechanobiology, and cancer immunotherapy. We discuss the role of digital pathology in parameterizing and validating spatial computational models and potential applications to therapeutics.

The Bayesian optimist's guide to adaptive immune receptor repertoire analysis

Probabilistic modeling is fundamental to the statistical analysis of complex data. In addition to forming a coherent description of the data-generating process, probabilistic models enable parameter inference about given datasets. This procedure is well developed in the Bayesian perspective, in which one infers probability distributions describing to what extent various possible parameters agree with the data. In this paper, we motivate and review probabilistic modeling for adaptive immune receptor repertoire data then describe progress and prospects for future work, from germline haplotyping to adaptive immune system deployment across tissues. The relevant quantities in immune sequence analysis include not only continuous parameters such as gene use frequency but also discrete objects such as B-cell clusters and lineages. Throughout this review, we unravel the many opportunities for probabilistic modeling in adaptive immune receptor analysis, including settings for which the Bayesian approach holds substantial promise (especially if one is optimistic about new computational methods). From our perspective, the greatest prospects for progress in probabilistic modeling for repertoires concern ancestral sequence estimation for B-cell receptor lineages, including uncertainty from germline genotype, rearrangement, and lineage development.

Combining Theoretical and Experimental Techniques to Study Murine Heart Transplant Rejection

The quality of life of organ transplant recipients is compromised by complications associated with life-long immunosuppression, such as hypertension, diabetes, opportunistic infections, and cancer. Moreover, the absence of established tolerance to the transplanted tissues causes limited long-term graft survival rates. Thus, there is a great medical need to understand the complex immune system interactions that lead to transplant rejection so that novel and effective strategies of intervention that redirect the system toward transplant acceptance (while preserving overall immune competence) can be identified. This study implements a systems biology approach in which an experimentally based mathematical model is used to predict how alterations in the immune response influence the rejection of mouse heart transplants. Five stages of conventional mouse heart transplantation are modeled using a system of 13 ordinary differential equations that tracks populations of both innate and adaptive immunity as well as proxies for pro- and anti-inflammatory factors within the graft and a representative draining lymph node. The model correctly reproduces known experimental outcomes, such as indefinite survival of the graft in the absence of CD4⁺ T cells and quick rejection in the absence of CD8⁺ T cells. The model predicts that decreasing the translocation rate of effector cells from the lymph node to the graft delays transplant rejection. Increasing the starting number of quiescent regulatory T cells in the model yields a significant but somewhat limited protective effect on graft survival. Surprisingly, the model shows that a delayed appearance of alloreactive T cells has an impact on graft survival that does not correlate linearly with the time delay. This computational model represents one of the first comprehensive approaches toward simulating the many interacting components of the immune system. Despite some limitations, the model provides important suggestions of experimental investigations that could improve the understanding of rejection. Overall, the systems biology approach used here is a first step in predicting treatments and interventions that can induce transplant tolerance while preserving the capacity of the immune system to protect against legitimate pathogens.

Mathematical Models for Immunology: Current State of the Art and Future Research Directions

The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales. To emphasise the use of mathematics in modelling in this area, we also review some of the mathematical tools used to investigate these models. Finally, we discuss some future trends in both experimental immunology and mathematical immunology for the upcoming years.

Modeling-Enabled Systems Nutritional Immunology

This review highlights the fundamental role of nutrition in the maintenance of health, the immune response, and disease prevention. Emerging global mechanistic insights in the field of nutritional immunology cannot be gained through reductionist methods alone or by analyzing a single nutrient at a time. We propose to investigate nutritional immunology as a massively interacting system of interconnected multistage and multiscale networks that encompass hidden mechanisms by which nutrition, microbiome, metabolism, genetic predisposition, and the immune system interact to delineate health and disease. The review sets an unconventional path to apply complex science methodologies to nutritional immunology research, discovery, and development through “use cases” centered around the impact of nutrition on the gut microbiome and immune responses. Our systems nutritional immunology analyses, which include modeling and informatics methodologies in combination with pre-clinical and clinical studies, have the potential to discover emerging systems-wide properties at the interface of the immune system, nutrition, microbiome, and metabolism.

Cancer-driven dynamics of immune cells in a microfluidic environment

Scope of the present work is to infer the migratory ability of leukocytes by stochastic processes in order to distinguish the spontaneous organization of immune cells against an insult (namely cancer). For this purpose, spleen cells from immunodeficient mice, selectively lacking the transcription factor IRF-8 (IRF-8 knockout; IRF-8 KO), or from immunocompetent animals (wild-type; WT), were allowed to interact, alternatively, with murine B16.F10 melanoma cells in an ad hoc microfluidic environment developed on a LabOnChip technology. In this setting, only WT spleen cells were able to establish physical interactions with melanoma cells. Conversely, IRF-8 KO immune cells exhibited poor dynamical reactivity towards the neoplastic cells. In the present study, we collected data on the motility of these two types of spleen cells and built a complete set of observables that recapitulate the biological complexity of the system in these experiments. With remarkable accuracy, we concluded that the IRF-8 KO cells performed pure uncorrelated random walks, while WT splenocytes were able to make singular drifted random walks that collapsed on a straight ballistic motion for the system as a whole, hence giving rise to a highly coordinate response. These results may provide a useful system to quantitatively analyse the real time cell-cell interactions and to foresee the behavior of immune cells with tumor cells at the tissue level.

A cognitive computational model inspired by the immune system response

The immune system has a cognitive ability to differentiate between healthy and unhealthy cells. The immune system response (ISR) is stimulated by a disorder in the temporary fuzzy state that is oscillating between the healthy and unhealthy states. However, modeling the immune system is an enormous challenge; the paper introduces an extensive summary of how the immune system response functions, as an overview of a complex topic, to present the immune system as a cognitive intelligent agent. The homogeneity and perfection of the natural immune system have been always standing out as the sought-after model we attempted to imitate while building our proposed model of cognitive architecture. The paper divides the ISR into four logical phases: setting a computational architectural diagram for each phase, proceeding from functional perspectives (input, process, and output), and their consequences. The proposed architecture components are defined by matching biological operations with computational functions and hence with the framework of the paper. On the other hand, the architecture focuses on the interoperability of main theoretical immunological perspectives (classic, cognitive, and danger theory), as related to computer science terminologies. The paper presents a descriptive model of immune system, to figure out the nature of response, deemed to be intrinsic for building a hybrid computational model based on a cognitive intelligent agent perspective and inspired by the natural biology. To that end, this paper highlights the ISR phases as applied to a case study on hepatitis C virus, meanwhile illustrating our proposed architecture perspective.

Reconceiving autoimmunity: An overview

Three interconnected positions are advocated: (1) although serving as a useful model, the immune self does not exist as such; (2) instead of a self/nonself demarcation, the immune system 'sees' itself, i.e., it does not ignore the 'self' or attack the 'other;' but exhibits a spectrum of responses, which when viewed from outside the system appear as discrimination of 'self' and 'nonself' based on certain criteria of reactivity. When immune reactions are conceived in terms of normal physiology and open exchange with the environment, where borders dividing host and foreign are elusive and changing, host defense is only part of the immune system's functions, which actually comprise two basic tasks: protection, i.e., to preserve host integrity, and maintenance of organismic identity. And thus (3) if the spectrum of immunity is enlarged, differentiating low reactive 'autoimmune' reactions from activated immune responses against the 'other' is only a matter of degree. Simply, all immunity is 'autoimmunity,' and the pathologic state of immunity directed at normal constituents of the organism is a particular case of dis-regulation, which appropriately is designated, autoimmune. Other uses of 'autoimmunity' and its congeners function as the semantic remnants of Burnet's original self/nonself theory and should be replaced. A new nomenclature is proposed, concinnity, which more accurately designates the physiology of the animal's ordinary housekeeping economy mediated by the immune system than 'autoimmunity' when used to describe such normal functions.

Spatiotemporal dynamics of intratumoral immune cells reveal the immune landscape in human cancer

The complex interactions between tumors and their microenvironment remain to be elucidated. Combining large-scale approaches, we examined the spatio-temporal dynamics of 28 different immune cell types (immunome) infiltrating tumors. We found that the immune infiltrate composition changed at each tumor stage and that particular cells had a major impact on survival. Densities of T follicular helper (Tfh) cells and innate cells increased, whereas most T cell densities decreased along with tumor progression. The number of B cells, which are key players in the core immune network and are associated with prolonged survival, increased at a late stage and showed a dual effect on recurrence and tumor progression. The immune control relevance was demonstrated in three endoscopic orthotopic colon-cancer mouse models. Genomic instability of the chemokine CXCL13 was a mechanism associated with Tfh and B cell infiltration. CXCL13 and IL21 were pivotal factors for the Tfh/B cell axis correlating with survival. This integrative study reveals the immune landscape in human colorectal cancer and the major hallmarks of the microenvironment associated with tumor progression and recurrence.

A quantitative assessment model of T-cell immune function for predicting risks of infection and rejection during the early stage after liver transplantation

Although more and more clinical studies indicated that ImmuKnow assay could efficiently assess the immune status of recipients, it still has the challenge to predict the occurrence of clinical adverse events. This study aimed to establish a quantitative assessment model, which could more efficiently predict immune function of T lymphocytes after liver transplantation based on three indexes: CD4+ T lymphocyte count (C), CD4+/CD8+ ratio (R), and ImmuKnow adenosine triphosphate (ATP) value (A). We selected 194 recipients and measured the A, C, and R index every week, then obtained the Fisher linear discriminant functions by SPSS 16.0. Next, we divided the recipients into three groups: infection, stable, and rejection groups according to clinical status. After calculating, the discriminant function, 0.012A + 0.019C + 1.322R (simplified into T = 2A + 3C + 200R), was selected to represent the T-cell-mediated immune function. Based on the model, the optimal cutoff T values for infection and rejection were 1415 (sensitivity = 80%, specificity = 79.9%,AUC = 92.3%) and 1939.5 (sensitivity = 93.9%, specificity = 77.6%, AUC = 88.6%), relatively (p < 0.001). In conclusion, this model may be a more feasible way to evaluate the cellular immune function status in liver transplantation recipients.

Investigating mathematical models of immuno-interactions with early-stage cancer under an agent-based modelling perspective

Many advances in research regarding immuno-interactions with cancer were developed with the help of ordinary differential equation (ODE) models. These models, however, are not effectively capable of representing problems involving individual localisation, memory and emerging properties, which are common characteristics of cells and molecules of the immune system. Agent-based modelling and simulation is an alternative paradigm to ODE models that overcomes these limitations. In this paper we investigate the potential contribution of agent-based modelling and simulation when compared to ODE modelling and simulation. We seek answers to the following questions: Is it possible to obtain an equivalent agent-based model from the ODE formulation? Do the outcomes differ? Are there any benefits of using one method compared to the other? To answer these questions, we have considered three case studies using established mathematical models of immune interactions with early-stage cancer. These case studies were re-conceptualised under an agent-based perspective and the simulation results were then compared with those from the ODE models. Our results show that it is possible to obtain equivalent agent-based models (i.e. implementing the same mechanisms); the simulation output of both types of models however might differ depending on the attributes of the system to be modelled. In some cases, additional insight from using agent-based modelling was obtained. Overall, we can confirm that agent-based modelling is a useful addition to the tool set of immunologists, as it has extra features that allow for simulations with characteristics that are closer to the biological phenomena.

Systems biology of complex symptom profiles: capturing interactivity across behavior, brain and immune regulation

As our thinking about the basic principles of biology and medicine continue to evolve, the importance of context and regulatory interaction is becoming increasingly obvious. Biochemical and physiological components do not exist in isolation but instead are part of a tightly integrated network of interacting elements that ensure robustness and support the emergence of complex behavior. This integration permeates all levels of biology from gene regulation, to immune cell signaling, to coordinated patterns of neuronal activity and the resulting psychosocial interaction. Systems biology is an emerging branch of science that sits as a translational catalyst at the interface of the life and computational sciences. While there is no universally accepted definition of systems biology, we attempt to provide an overview of some the basic unifying concepts and current efforts in the field as they apply to illnesses where brain and subsequent behavior are a chief component, for example autism, schizophrenia, depression, and others. Methods in this field currently constitute a broad mosaic that stretches across multiple scales of biology and physiological compartments. While this work by no means constitutes an exhaustive list of all these methods, this work highlights the principal sub-disciplines presently driving the field as well as future directions of progress.

Understanding natural killer cell regulation by mathematical approaches

The activity of natural killer (NK) cells is regulated by various processes including education/licensing, priming, integration of positive and negative signals through an array of activating and inhibitory receptors, and the development of memory-like functionality. These processes are often very complex due to the large number of different receptors and signaling pathways involved. Understanding these complex mechanisms is therefore a challenge, but is critical for understanding NK cell regulation. Mathematical approaches can facilitate the analysis and understanding of complex systems. Therefore, they may be instrumental for studies in NK cell biology. Here we provide a review of the different mathematical approaches to the analysis of NK cell signal integration, activation, proliferation, and the acquisition of inhibitory receptors. These studies show how mathematical methods can aid the analysis of NK cell regulation.

Models and methods for analysis of lymphocyte repertoire generation, development, selection and evolution

T and B cell receptor repertoires are diversified by variable region gene rearrangement and selected based on functionality and lack of self-reactivity. Repertoires can also be defined based on phenotype and function rather than receptor specificity - such as the diversity of T helper cell subsets. Natural killer (NK) cell repertoires, in which each cell expresses a randomly chosen subset of its inhibitory receptor genes, and is educated based on self-MHC recognition by yet unknown mechanisms, are also phenotypic repertoires. Studying the generation, development and selection of lymphocyte repertoires, and their functions during immune responses, is essential for understanding the function of the immune system in healthy individuals and in immune deficient, autoimmune or cancer patients. The study of lymphocyte repertoires will enable clinical immunologists to develop better therapeutic monoclonal antibodies, vaccines, transplantation donor-recipient matching protocols, and other immune intervention strategies. The recent development of high-throughput methods for repertoire data collection - from multicolor flow cytometry through single-cell imaging to deep sequencing - presents us now, for the first time, with the ability to analyze and compare large samples of lymphocyte repertoires in health, aging and disease. The exponential growth of these datasets, however, challenges the theoretical immunology community to develop methods for data organization and analysis. Furthermore, the need to test hypotheses regarding immune function, and generate predictions regarding the outcomes of medical interventions, necessitates the development of complex mathematical and computational models, covering processes on multiple scales, from the genetic and molecular to the cellular and system scales.

Systems biology: the next frontier for bioinformatics

Biochemical systems biology augments more traditional disciplines, such as genomics, biochemistry and molecular biology, by championing (i) mathematical and computational modeling; (ii) the application of traditional engineering practices in the analysis of biochemical systems; and in the past decade increasingly (iii) the use of near-comprehensive data sets derived from 'omics platform technologies, in particular "downstream" technologies relative to genome sequencing, including transcriptomics, proteomics and metabolomics. The future progress in understanding biological principles will increasingly depend on the development of temporal and spatial analytical techniques that will provide high-resolution data for systems analyses. To date, particularly successful were strategies involving (a) quantitative measurements of cellular components at the mRNA, protein and metabolite levels, as well as in vivo metabolic reaction rates, (b) development of mathematical models that integrate biochemical knowledge with the information generated by high-throughput experiments, and (c) applications to microbial organisms. The inevitable role bioinformatics plays in modern systems biology puts mathematical and computational sciences as an equal partner to analytical and experimental biology. Furthermore, mathematical and computational models are expected to become increasingly prevalent representations of our knowledge about specific biochemical systems.