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Two long-standing challenges in theoretical population genetics and evolution are predicting the distribution of phenotype diversity generated by mutation and available for selection, and determining the interaction of mutation, selection and drift to characterize evolutionary equilibria and dynamics. More fundamental for enabling such predictions is the current inability to causally link genotype to phenotype. There are three major mechanistic mappings required for such a linking - genetic sequence to kinetic parameters of the molecular processes, kinetic parameters to biochemical system phenotypes, and biochemical phenotypes to organismal phenotypes. This article introduces a theoretical framework, the Phenotype Design Space (PDS) framework, for addressing these challenges by focusing on the mapping of kinetic parameters to biochemical system phenotypes. It provides a quantitative theory whose key features include (1) a mathematically rigorous definition of phenotype based on biochemical kinetics, (2) enumeration of the full phenotypic repertoire, and (3) functional characterization of each phenotype independent of its context-dependent selection or fitness contributions. This framework is built on Design Space methods that relate system phenotypes to genetically determined parameters and environmentally determined variables. It also has the potential to automate prediction of phenotype-specific mutation rate constants and equilibrium distributions of phenotype diversity in microbial populations undergoing steady-state exponential growth, which provides an ideal reference to which more realistic cases can be compared. Although the framework is quite general and flexible, the details will undoubtedly differ for different functions, organisms and contexts. Here a hypothetical case study involving a small molecular system, a primordial circadian clock, is used to introduce this framework and to illustrate its use in a particular case. The framework is built on fundamental biochemical kinetics. Thus, the foundation is based on linear algebra and reasonable physical assumptions, which provide numerous opportunities for experimental testing and further elaboration to deal with complex multicellular organisms that are currently beyond its scope. The discussion provides a comparison of results from the PDS framework with those from other approaches in theoretical population genetics.

Mathematical models of biochemical systems provide a means to elucidate the link between the genotype, environment, and phenotype. A subclass of mathematical models, known as mechanistic models, quantitatively describe the complex non-linear mechanisms that capture the intricate interactions between biochemical components. However, the study of mechanistic models is challenging because most are analytically intractable and involve large numbers of system parameters. Conventional methods to analyze them rely on local analyses about a nominal parameter set and they do not reveal the vast majority of potential phenotypes possible for a given system design. We have recently developed a new modeling approach that does not require estimated values for the parameters initially and inverts the typical steps of the conventional modeling strategy. Instead, this approach relies on architectural features of the model to identify the phenotypic repertoire and then predict values for the parameters that yield specific instances of the system that realize desired phenotypic characteristics. Here, we present a collection of software tools, the Design Space Toolbox V2 based on the System Design Space method, that automates (1) enumeration of the repertoire of model phenotypes, (2) prediction of values for the parameters for any model phenotype, and (3) analysis of model phenotypes through analytical and numerical methods. The result is an enabling technology that facilitates this radically new, phenotype-centric, modeling approach. We illustrate the power of these new tools by applying them to a synthetic gene circuit that can exhibit multi-stability. We then predict values for the system parameters such that the design exhibits 2, 3, and 4 stable steady states. In one example, inspection of the basins of attraction reveals that the circuit can count between three stable states by transient stimulation through one of two input channels: a positive channel that increases the count, and a negative channel that decreases the count. This example shows the power of these new automated methods to rapidly identify behaviors of interest and efficiently predict parameter values for their realization. These tools may be applied to understand complex natural circuitry and to aid in the rational design of synthetic circuits.

Coronavirus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection is a systemic disease affecting not only the lungs but also multiple organ systems. Clinical studies implicate that SARS-CoV-2 infection causes imbalance of cellular homeostasis and immune response that trigger cytokine storm, oxidative stress, thrombosis, and insulin resistance. Mathematical modeling can offer in-depth understanding of the SARS-CoV-2 infection and illuminate how subcellular mechanisms and feedback loops underpin disease progression and multiorgan failure. We report here a mathematical model of SARS-CoV-2 infection pathway network with cytokine storm, oxidative stress, thrombosis, insulin resistance, and nitric oxide (NO) pathways. The biochemical systems theory model shows autocrine loops with positive feedback enabling excessive immune response, cytokines, transcription factors, and interferons, which can imbalance homeostasis of the system. The simulations suggest that changes in immune response led to uncontrolled release of cytokines and chemokines, including interleukin (IL)-1β, IL-6, and tumor necrosis factor α (TNFα), and affect insulin, coagulation, and NO signaling pathways. Increased production of NETs (neutrophil extracellular traps), thrombin, PAI-1 (plasminogen activator inhibitor-1), and other procoagulant factors led to thrombosis. By analyzing complex biochemical reactions, this model forecasts the key intermediates, potential biomarkers, and risk factors at different stages of COVID-19. These insights can be useful for drug discovery and development, as well as precision treatment of multiorgan implications of COVID-19 as seen in systems medicine. [ABSTRACT FROM AUTHOR]

• I briefly summarize Michael Savageau's "Biochemical Systems Analysis" papers, published in volumes 25 and 26 of the journal. • These papers kickstarted Biochemical Systems Theory, which originated many of the core concepts and tools of Systems Biology. • I identify the most relevant developments in Biochemical Systems Theory since 1969. Michael Savageau's Biochemical Systems Analysis I, II, III papers, published in volumes 25 and 26 of the journal, kickstarted a research programme that originated many of the core concepts and tools of Systems Biology. This article briefly summarizes these papers and discusses the most relevant developments in Biochemical Systems Theory since their publication. [ABSTRACT FROM AUTHOR]

Disease represents a specific case of malfunctioning within a complex system. Whereas it is often feasible to observe and possibly treat the symptoms of a disease, it is much more challenging to identify and characterize its molecular root causes. Even in infectious diseases that are caused by a known parasite, it is often impossible to pinpoint exactly which molecular profiles of components or processes are directly or indirectly altered. However, a deep understanding of such profiles is a prerequisite for rational, efficacious treatments. Modern omics methodologies are permitting large-scale scans of some molecular profiles, but these scans often yield results that are not intuitive and difficult to interpret. For instance, the comparison of healthy and diseased transcriptome profiles may point to certain sets of involved genes, but a host of post-transcriptional processes and regulatory mechanisms renders predictions regarding metabolic or physiological consequences of the observed changes in gene expression unreliable. Here we present proof of concept that dynamic models of metabolic pathway systems may offer a tool for interpreting transcriptomic profiles measured during disease. We illustrate this strategy with the interpretation of expression data of genes coding for enzymes associated with purine metabolism. These data were obtained during infections of rhesus macaques ( Macaca mulatta ) with the malaria parasite Plasmodium cynomolgi or P. coatneyi . The model-based interpretation reveals clear patterns of flux redistribution within the purine pathway that are consistent between the two malaria pathogens and are even reflected in data from humans infected with P. falciparum . This article is part of a Special Issue entitled: Accelerating Precision Medicine through Genetic and Genomic Big Data Analysis edited by Yudong Cai & Tao Huang. [ABSTRACT FROM AUTHOR]

Enormous advances in genetics andmetabolic engineering havemade it possible, in principle, to create new plants and crops with improved yield through targeted molecular alterations. However, while the potential is beyond doubt, the actual implementation of envisioned new strains is often difficult, due to the diverse and complex nature of plants. Indeed, the intrinsic complexity of plants makes intuitive predictions difficult and often unreliable. The hope for overcoming this challenge is that methods of data mining and computational systems biology may become powerful enough that they could serve as beneficial tools for guiding future experimentation. In the first part of this article, we review the complexities of plants, as well as some of the mathematical and computational methods that have been used in the recent past to deepen our understanding of crops and their potential yield improvements. In the second part, we present a specific case study that indicates how robust models may be employed for crop improvements. This case study focuses on the biosynthesis of lignin in switchgrass (Panicum virgatum). Switchgrass is considered one of themost promising candidates for the second generation of bioenergy production, which does not use edible plant parts. Lignin is important in this context, because it impedes the use of cellulose in such inedible plant materials. The dynamic model offers a platform for investigating the pathway behavior in transgenic lines. In particular, it allows predictions of lignin content and composition in numerous genetic perturbation scenarios. [ABSTRACT FROM AUTHOR]

Parkinson's disease (PD), a neurodegenerative disorder, affects millions of people and has gained attention because of its clinical roles affecting behaviors related to motor and nonmotor symptoms. Although studies on PD from various aspects are becoming popular, few rely on predictive systems modeling approaches. Using Biochemical Systems Theory (BST), this article attempts to model and characterize dopaminergic cell death and understand pathophysiology of progression of PD. PD pathways were modeled using stochastic differential equations incorporating law of mass action, and initial concentrations for the modeled proteins were obtained from literature. Simulations suggest that dopamine levels were reduced significantly due to an increase in dopaminergic quinones and 3,4-dihydroxyphenylacetaldehyde (DOPAL) relating to imbalances compared to control during PD progression. Associating to clinically observed PD-related cell death, simulations show abnormal parkin and reactive oxygen species levels with an increase in neurofibrillary tangles. While relating molecular mechanistic roles, the BST modeling helps predicting dopaminergic cell death processes involved in the progression of PD and provides a predictive understanding of neuronal dysfunction for translational neuroscience. [ABSTRACT FROM AUTHOR]

The time-scale hierarchies of a very general class of models in differential equations is analyzed. Classical methods for model reduction and time-scale analysis have been adapted to this formalism and a complementary method is proposed. A unified theoretical treatment shows how the structure of the system can be much better understood by inspection of two sets of singular values: one related to the stoichiometric structure of the system and another to its kinetics. The methods are exemplified first through a toy model, then a large synthetic network and finally with numeric simulations of three classical benchmark models of real biological systems.

Mathematical models of biochemical systems provide a means to elucidate the link between the genotype, environment and phenotype. A subclass of mathematical models, known as mechanistic models, quantitatively describe the complex non-linear mechanisms that capture the intricate interactions between biochemical components. However, the study of mechanistic models is challenging because most are analytically intractable and involve large numbers of system parameters. Conventional methods to analyze them rely on local analyses about a nominal parameter set and they do not reveal the vast majority of potential phenotypes possible for a given system design. We have recently developed a new modeling approach that does not require estimated values for the parameters initially and inverts the typical steps of the conventional modeling strategy. Instead, this approach relies on architectural features of the model to identify the phenotypic repertoire and then predict values for the parameters that yield specific instances of the system that realize desired phenotypic characteristics. Here, we present a collection of software tools, the Design Space Toolbox V2 based on the System Design Space method, that automates (1) enumeration of the repertoire of model phenotypes, (2) prediction of values for the parameters for any model phenotype and (3) analysis of model phenotypes through analytical and numerical methods. The result is an enabling technology that facilitates this radically new, phenotype-centric, modeling approach. We illustrate the power of these new tools by applying them to a synthetic gene circuit that can exhibit multi-stability. We then predict values for the system parameters such that the design exhibits 2, 3 and 4 stable steady states. In one example, inspection of the basins of attraction reveals that the circuit can count between 3 stable states by transient stimulation through one of two input channels: a positive channel that increases the count, and a negative channel that decreases the count. This example shows the power of these new automated methods to rapidly identify behaviors of interest and efficiently predict parameter values for their realization. These tools may be applied to understand complex natural circuitry and to aid in the rational design of synthetic circuits.

The high-throughput acquisition of metabolome data is greatly anticipated for the complete understanding of cellular metabolism in living organisms. A variety of analytical technologies have been developed to acquire large-scale metabolic profiles under different biological or environmental conditions. Time series data are useful for predicting the most likely metabolic pathways because they provide important information regarding the accumulation of metabolites, which implies causal relationships in the metabolic reaction network. Considerable effort has been undertaken to utilize these data for constructing a mathematical model merging system properties and quantitatively characterizing a whole metabolic system in toto. However, there are technical difficulties between benchmarking the provision and utilization of data. Although hundreds of metabolites can be measured, which provide information on the metabolic reaction system, simultaneous measurement of thousands of metabolites is still challenging. In addition, it is nontrivial to logically predict the dynamic behaviors of unmeasurable metabolite concentrations without sufficient information on the metabolic reaction network. Yet, consolidating the advantages of advancements in both metabolomics and mathematical modeling remain to be accomplished. This review outlines the conceptual basis of and recent advances in technologies in both the research fields. It also highlights the potential for constructing a large-scale mathematical model by estimating model parameters from time series metabolome data in order to comprehensively understand metabolism at the systems level.

Heat is one of the most fundamental and ancient environmental stresses, and response mechanisms are found in prokaryotes and shared among most eukaryotes. In the budding yeast Saccharomyces cerevisiae, the heat stress response involves coordinated changes at all biological levels, from gene expression to protein and metabolite abundances, and to temporary adjustments in physiology. Due to its integrative multi-level-multi-scale nature, heat adaptation constitutes a complex dynamic process, which has forced most experimental and modeling analyses in the past to focus on just one or a few of its aspects. Here we review the basic components of the heat stress response in yeast and outline what has been done, and what needs to be done, to merge the available information into computational structures that permit comprehensive diagnostics, interrogation, and interpretation. We illustrate the process in particular with the coordination of two metabolic responses, namely the dramatic accumulation of the protective disaccharide trehalose and the substantial change in the profile of sphingolipids, which in turn affect gene expression. The proposed methods primarily use differential equations in the canonical modeling framework of Biochemical Systems Theory (BST), which permits the relatively easy construction of coarse, initial models even in systems that are incompletely characterized.

Abstract Cryptococcus neoformans (Cn) is the most common cause of fungal meningitis worldwide. In infected patients, growth of the fungus can occur within the phagolysosome of phagocytic cells, especially in non‐activated macrophages of immunocompromised subjects. Since this environment is characteristically acidic, Cn must adapt to low pH to survive and efficiently cause disease. In the present work, we designed, tested, and experimentally validated a theoretical model of the sphingolipid biochemical pathway in Cn under acidic conditions. Simulations of metabolic fluxes and enzyme deletions or downregulation led to predictions that show good agreement with experimental results generated post hoc and reconcile intuitively puzzling results. This study demonstrates how biochemical modeling can yield testable predictions and aid our understanding of fungal pathogenesis through the design and computational simulation of hypothetical experiments.

The time-scale hierarchies of a very general class of models in differential equations is analyzed. Classical methods for model reduction and time-scale analysis have been adapted to this formalism and a complementary method is proposed. A unified theoretical treatment shows how the structure of the system can be much better understood by inspection of two sets of singular values: one related to the stoichiometric structure of the system and another to its kinetics. The methods are exemplified first through a toy model, then a large synthetic network and finally with numeric simulations of three classical benchmark models of real biological systems. [ABSTRACT FROM AUTHOR]

Background: Switchgrass is a prime target for biofuel production from inedible plant parts and has been the subject of numerous investigations in recent years. Yet, one of the main obstacles to effective biofuel production remains to be the major problem of recalcitrance. Recalcitrance emerges in part from the 3-D structure of lignin as a polymer in the secondary cell wall. Lignin limits accessibility of the sugars in the cellulose and hemicellulose polymers to enzymes and ultimately decreases ethanol yield. Monolignols, the building blocks of lignin polymers, are synthesized in the cytosol and translocated to the plant cell wall, where they undergo polymerization. The biosynthetic pathway leading to monolignols in switchgrass is not completely known, and difficulties associated with in vivo measurements of these intermediates pose a challenge for a true understanding of the functioning of the pathway. Results: In this study, a systems biological modeling approach is used to address this challenge and to elucidate the structure and regulation of the lignin pathway through a computational characterization of alternate candidate topologies. The analysis is based on experimental data characterizing stem and tiller tissue of four transgenic lines (knockdowns of genes coding for key enzymes in the pathway) as well as wild-type switchgrass plants. These data consist of the observed content and composition of monolignols. The possibility of a G-lignin specific metabolic channel associated with the production and degradation of coniferaldehyde is examined, and the results support previous findings from another plant species. The computational analysis suggests regulatory mechanisms of product inhibition and enzyme competition, which are well known in biochemistry, but so far had not been reported in switchgrass. By including these mechanisms, the pathway model is able to represent all observations. Conclusions: The results show that the presence of the coniferaldehyde channel is necessary and that product inhibition and competition over cinnamoyl-CoA-reductase (CCR1) are essential for matching the model to observed increases in H-lignin levels in 4-coumarate:CoA-ligase (4CL) knockdowns. Moreover, competition for 4-coumarate:CoA-ligase (4CL) is essential for matching the model to observed increases in the pathway metabolites in caffeic acid O-methyltransferase (COMT) knockdowns. As far as possible, the model was validated with independent data. [ABSTRACT FROM AUTHOR]

Matching experimental and theoretical approaches have often been fruitful in the investigation of complex biological processes. Here we develop a novel non-conventional model for the denitrification of waste water. Earlier models of the denitrification process were compiled by the International Association on Water Quality group. The Activated Sludge Models 1-3, which are the most frequently used all over the world, are presently not adapted towards the integration of both nitrous and nitric oxide emissions during the denitrification process. In the present work, a Generalized Mass Action model, based on Biochemical Systems Theory, was designed to simulate the nitrate reduction observed in specific experimental conditions. The model was implemented and analysed with the software package PLAS. Data from a representative experiment were chosen ( T=10°C, pH=7, C/N=3, with acetate as carbon source) to simulate greenhouse NO and N2O gas emissions, in order to test hypotheses about the corresponding bacterial metabolic pathways. The results show that the reduction of nitrate and nitrite is kinetically limiting and that nitrate reduction is limited by diffusion and support that distinct microbial subpopulations are involved in the denitrification pathway, which has consequences for NO emissions. [ABSTRACT FROM AUTHOR]

The availability of large-scale datasets has led to more effort being made to understand characteristics of metabolic reaction networks. However, because the large-scale data are semi-quantitative, and may contain biological variations and/or analytical errors, it remains a challenge to construct a mathematical model with precise parameters using only these data. The present work proposes a simple method, referred to as PENDISC ([InlineEquation not available: see fulltext.]arameter [InlineEquation not available: see fulltext.]stimation in a [InlineEquation not available: see fulltext.]on-[InlineEquation not available: see fulltext.]mensionalized [InlineEquation not available: see fulltext.]-system with [InlineEquation not available: see fulltext.]onstraints), to assist the complex process of parameter estimation in the construction of a mathematical model for a given metabolic reaction system. The PENDISC method was evaluated using two simple mathematical models: a linear metabolic pathway model with inhibition and a branched metabolic pathway model with inhibition and activation. The results indicate that a smaller number of data points and rate constant parameters enhances the agreement between calculated values and time-series data of metabolite concentrations, and leads to faster convergence when the same initial estimates are used for the fitting. This method is also shown to be applicable to noisy time-series data and to unmeasurable metabolite concentrations in a network, and to have a potential to handle metabolome data of a relatively large-scale metabolic reaction system. Furthermore, it was applied to aspartate-derived amino acid biosynthesis in Arabidopsis thaliana plant. The result provides confirmation that the mathematical model constructed satisfactorily agrees with the time-series datasets of seven metabolite concentrations. [ABSTRACT FROM AUTHOR]

Abstract: Probably the most prominent expectation associated with systems biology is the computational support of personalized medicine and predictive health. At least some of this anticipated support is envisioned in the form of disease simulators that will take hundreds of personalized biomarker data as input and allow the physician to explore and optimize possible treatment regimens on a computer before the best treatment is applied to the actual patient in a custom-tailored manner. The key prerequisites for such simulators are mathematical and computational models that not only manage the input data and implement the general physiological and pathological principles of organ systems but also integrate the myriads of details that affect their functionality to a significant degree. Obviously, the construction of such models is an overwhelming task that suggests the long-term development of hierarchical or telescopic approaches representing the physiology of organs and their diseases, first coarsely and over time with increased granularity. This article illustrates the rudiments of such a strategy in the context of cystic fibrosis (CF) of the lung. The starting point is a very simplistic, generic model of inflammation, which has been shown to capture the principles of infection, trauma, and sepsis surprisingly well. The adaptation of this model to CF contains as variables healthy and damaged cells, as well as different classes of interacting cytokines and infectious microbes that are affected by mucus formation, which is the hallmark symptom of the disease (Perez-Vilar and Boucher, 2004) [1]. The simple model represents the overall dynamics of the disease progression, including so-called acute pulmonary exacerbations, quite well, but of course does not provide much detail regarding the specific processes underlying the disease. In order to launch the next level of modeling with finer granularity, it is desirable to determine which components of the coarse model contribute most to the disease dynamics. The article introduces for this purpose the concept of module gains or ModGains, which quantify the sensitivity of key disease variables in the higher-level system. In reality, these variables represent complex modules at the next level of granularity, and the computation of ModGains therefore allows an importance ranking of variables that should be replaced with more detailed models. The “hot-swapping” of such detailed modules for former variables is greatly facilitated by the architecture and implementation of the overarching, coarse model structure, which is here formulated with methods of biochemical systems theory (BST). This article is part of a Special Issue entitled: Computational Proteomics, Systems Biology & Clinical Implications. Guest Editor: Yudong Cai. [Copyright &y& Elsevier]

Background: Advances in modern high-throughput techniques of molecular biology have enabled top-down approaches for the estimation of parameter values in metabolic systems, based on time series data. Special among them is the recent method of dynamic flux estimation (DFE), which uses such data not only for parameter estimation but also for the identification of functional forms of the processes governing a metabolic system. DFE furthermore provides diagnostic tools for the evaluation of model validity and of the quality of a model fit beyond residual errors. Unfortunately, DFE works only when the data are more or less complete and the system contains as many independent fluxes as metabolites. These drawbacks may be ameliorated with other types of estimation and information. However, such supplementations incur their own limitations. In particular, assumptions must be made regarding the functional forms of some processes and detailed kinetic information must be available, in addition to the time series data. Results: The authors propose here a systematic approach that supplements DFE and overcomes some of its shortcomings. Like DFE, the approach is model-free and requires only minimal assumptions. If sufficient time series data are available, the approach allows the determination of a subset of fluxes that enables the subsequent applicability of DFE to the rest of the flux system. The authors demonstrate the procedure with three artificial pathway systems exhibiting distinct characteristics and with actual data of the trehalose pathway in Saccharomyces cerevisiae. Conclusions: The results demonstrate that the proposed method successfully complements DFE under various situations and without a priori assumptions regarding the model representation. The proposed method also permits an examination of whether at all, to what degree, or within what range the available time series data can be validly represented in a particular functional format of a flux within a pathway system. Based on these results, further experiments may be designed to generate data points that genuinely add new information to the structure identification and parameter estimation tasks at hand. [ABSTRACT FROM AUTHOR]

Modern systems biology and synthetic bioengineering face two major challenges in relating properties of the genetic components of a natural or engineered system to its integrated behavior. The first is the fundamental unsolved problem of relating the digital representation of the genotype to the analog representation of the parameters for the molecular components. For example, knowing the DNA sequence does not allow one to determine the kinetic parameters of an enzyme. The second is the fundamental unsolved problem of relating the parameters of the components and the environment to the phenotype of the global system. For example, knowing the parameters does not tell one how many qualitatively distinct phenotypes are in the organism's repertoire or the relative fitness of the phenotypes in different environments. These also are challenges for biomedical engineers as they attempt to develop therapeutic strategies to treat pathology or to redirect normal cellular functions for biotechnological purposes. In this article, the second of these fundamental challenges will be addressed, and the notion of a 'system design space' for relating the parameter space of components to the phenotype space of bioengineering systems will be focused upon. First, the concept of a system design space will be motivated by introducing one of its key components from an intuitive perspective. Second, a simple linear example will be used to illustrate a generic method for constructing the design space in which qualitatively distinct phenotypes can be identified and counted, their fitness analyzed and compared, and their tolerance to change measured. Third, two examples of nonlinear systems from different areas of biomedical engineering will be presented. Finally, after giving reference to a few other applications that have made use of the system design space approach to reveal important design principles, some concluding remarks concerning challenges and opportunities for further development will be made. [ABSTRACT FROM AUTHOR]

Abstract: Pathway models in biotechnology are customarily designed with metabolite concentrations as the primary, dependent variables, whereas fluxes are derived quantities that are secondarily computed from the primary variables. In other fields of mathematics, such as graph theory and linear systems analysis, it has proven useful to complement primal network model designs in terms of vertices (pools) and edges (processes) with dual designs, where the roles of the primary and secondary quantities are interchanged. The conversion from primal to dual systems is fairly easy in linear systems, but it is unclear to what degree it is possible in nonlinear systems. In this article, we present a method to transform nonlinear primal models of pathways or other biotechnological processes that conform to the Generalized Mass Action (GMA) structure within the formalism of Biochemical Systems Theory (BST) into dual models that focus on fluxes, rather than pools. Interestingly, this transformation is relatively straightforward, once some notational issues are streamlined, and the resulting dual system is again in the format of a GMA system. The transformation is illustrated with the example of glycolysis in Saccharomyces cerevisiae, a well known organism in the food industry. The results suggest how rewriting a model in terms of its fluxes helps bridge the gap between flux balance and dynamic models and also offers a view of the investigated system that is complementary to that of the original model. This dual view is important, because fluxes are sometimes more relevant for the behavior of a biotechnological system than (metabolite) pools. The dual system furthermore offers a systematic approach toward understanding the dynamical constraints under which the system operates. [ABSTRACT FROM AUTHOR]

Abstract: Recent trends suggest that future biotechnology will increasingly rely on mathematical models of the biological systems under investigation. In particular, metabolic engineering will make wider use of metabolic pathway models in stoichiometric or fully kinetic format. A significant obstacle to the use of pathway models is the identification of suitable process descriptions and their parameters. We recently showed that, at least under favorable conditions, Dynamic Flux Estimation (DFE) permits the numerical characterization of fluxes from sets of metabolic time series data. However, DFE does not prescribe how to convert these numerical results into functional representations. In some cases, Michaelis–Menten rate laws or canonical formats are well suited, in which case the estimation of parameter values is easy. However, in other cases, appropriate functional forms are not evident, and exhaustive searches among all possible candidate models are not feasible. We show here how piecewise power-law functions of one or more variables offer an effective default solution for the almost unbiased representation of uni- and multivariate time series data. The results of an automated algorithm for their determination are piecewise power-law fits, whose accuracy is only limited by the available data. The individual power-law pieces may lead to discontinuities at break points or boundaries between sub-domains. In many practical applications, these boundary gaps do not cause problems. Potential smoothing techniques, based on differential inclusions and Filippov''s theory, are discussed in . [Copyright &y& Elsevier]

Abstract: Mathematical modeling has become an integral component in biotechnology, in which these models are frequently used to design and optimize bioprocesses. Canonical models, like power-laws within the Biochemical Systems Theory, offer numerous mathematical and numerical advantages, including built-in flexibility to simulate general nonlinear behavior. The construction of such models relies on the estimation of unknown case-specific model parameters by way of experimental data fitting, also known as inverse modeling. Despite the large number of publications on this topic, this task remains the bottleneck in canonical modeling of biochemical systems. The focus of this paper concerns with the question of identifiability of power-law models from dynamic data, that is, whether the parameter values can be uniquely and accurately identified from time-series data. Existing and newly developed parameter identifiability methods were applied to two power-law models of biochemical systems, and the results pointed to the lack of parametric identifiability as the root cause of the difficulty faced in the inverse modeling. Despite the focus on power-law models, the analyses and conclusions are extendable to other canonical models, and the issue of parameter identifiability is expected to be a common problem in biochemical system modeling. [ABSTRACT FROM AUTHOR]

Abstract: We analyze the growth dynamics of Saccharomyces diastaticus LORRE 316 utilizing mixed-sugar to produce ethanol and glycerol, using three alternative modeling frameworks, namely S-system, lin-log model and Monod''s model. The S-system and lin-log model have identical steady-state solutions, but differ in their representation of transients. The global/local optimization method was applied to determine optimal parameter values for each model. Hybrid differential evolution with data collocation was first applied to determine a satisfied solution. Such a global search phase could avoid yielding a premature estimate and alleviate computational burden. The optimal estimate obtained from the global search phase was then served as the initial starting point for a local optimization method to obtain the refined solution. From experimental observation, the dynamical prediction using the S-system is more acceptable than those of the lin-log model and Monod''s model. [Copyright &y& Elsevier]

Abstract: The FNR (fumarate nitrate reduction) protein plays a central role in the global oxygen response of a variety of bacteria. In Escherichia coli, FNR is the master transcriptional regulator of the transition between aerobic and anaerobic growth. Regulation of FNR is achieved by cycling the molecule between three states in a process dependent on oxygen. In an effort to better understand the nature of this post-transcriptional cyclic regulatory mechanism, we formulated a kinetic model of the FNR protein and its regulation in E. coli. The values for the parameters of the model were fit to experimental data for the wild-type organism, and the model was validated by successfully predicting the behavior of fnr mutant strains characterized in the literature. We characterized the steady-state behavior of the FNR system by determining its sensitivity to changes in parameter values and its response to changes in the concentration of iron–sulfur cluster assembly proteins and the protease ClpXP. We also determined the steady-state induction characteristic that provides a direct estimate for the levels of the active form of FNR as a function of oxygen concentration. This result, in combination with reporter assays for expression of FNR target operons, gives an estimate for the equilibrium dissociation constant for the binding of active FNR to its recognition sequences in the DNA. Finally, we predicted the dynamics of the aerobic-to-anaerobic transition and determined distinct contributions to the dynamic profile of regulatory mechanisms operating at the transcriptional and post-translational levels. [Copyright &y& Elsevier]

Abstract: Although characterization of the genotype has undergone revolutionary advances as a result of the successful genome projects, the chasm between our understanding of a fully characterized gene sequence and the phenotypic repertoire of the organism is as broad and deep as it was in the pre-genomic era. There are two fundamental unsolved problems that provide the context for the challenges in relating genotype to phenotype. We address one of these and describe a generic method for constructing a system design space in which qualitatively distinct phenotypes can be identified and counted, their relative fitness analyzed and compared, and their tolerance to change measured. [Copyright &y& Elsevier]

Abstract: Sensitivity analysis plays an important role in the study of biological systems. Biochemical systems theory (BST) as well as metabolic control analysis (MCA) has had great success in describing the control and regulation of biological systems at steady state. However, there are notable exceptions, such as signal transduction or cell cycle regulation systems where the transient or oscillatory behavior of interest is often found in the temporal response. Some extensions of BST and MCA to non-steady behavior have appeared in the literature. However, there requires to have a unified methodology to efficiently solve biological system models described by the BST or MCA formulation. In this work, the modified collocation method is applied to solve transient responses and its corresponding dynamic sensitivities for the non-linear biological systems described by the GMA formulation. The method could simultaneously compute both solutions and dynamic sensitivities of the system equations element-by-element. Any MCA formulations could be recast into a GMA model so the Jacobian matrix and the partial derivatives with respect to the model parameters could be analytically evaluated while the solution is in progress. In this study, we have presented three biological systems to illustrate the efficiency of the proposed algorithm. [Copyright &y& Elsevier]

One of the major unsolved problems of modern biology is deep understanding of the complex relationship between the information encoded in the genome of an organism and the phenotypic properties manifested by that organism. Fundamental advances must be made before we can begin to approach the goal of predicting the phenotypic consequences of a given mutation or an organism's response to a novel environmental challenge. Although this problem is often portrayed as if the task were to find a more or less direct link between genotypic and phenotypic levels, on closer examination the relationship is far more layered and complex. Although there are some intuitive notions of what is meant by phenotype at the level of the organism, it is far from clear what this term means at the biochemical level. We have described design principles that are readily revealed by representation of molecular systems in an appropriate design space. Here, we first describe a generic approach to the construction of such a design space in which qualitatively distinct phenotypes can be identified and counted. Second, we show how the boundaries between these phenotypic regions provide a method of characterizing a system's tolerance to large changes in the values of its parameters. Third, we illustrate the approach for one of the most basic modules, of biochemical networks and describe an associated design principle. Finally, we discuss the scaling of this approach to large systems. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a detailed systems model of Parkinson''s disease (PD), developed utilizing a pragmatic application of biochemical systems theory (BST) intended to assist experimentalists in the study of system behavior. This approach utilizes relative values as a reasonable initial estimate for BST and provides a theoretical means of applying numerical solutions to qualitative and semi-quantitative understandings of cellular pathways and mechanisms. The approach allows for the simulation of human disease through its ability to organize and integrate existing information about metabolic pathways without having a full quantitative description of those pathways, so that hypotheses about individual processes may be tested in a systems environment. Incorporating this method, the PD model describes α-synuclein aggregation as mediated by dopamine metabolism, the ubiquitin–proteasome system, and lysosomal degradation, allowing for the examination of dynamic pathway interactions and the evaluation of possible toxic mechanisms in the aggregation process. Four system perturbations: elevated α-synuclein aggregation, impaired dopamine packaging, increased neurotoxins, and α-synuclein overexpression, were analyzed for correlation to qualitative PD system hypotheses present in the literature, with the model demonstrating a high level of agreement with these hypotheses. Additionally, various PD treatment methods, including levadopa and monoamine oxidase inhibition (MAOI) therapy, were applied to the disease models to examine their effects on the system. Future additions and refinements to the model may further the understanding of the emergent behaviors of the disease, helping in the identification of system sensitivities and possible therapeutic targets. [Copyright &y& Elsevier]

Most biological systems are by nature hybrids consist of interacting discrete and continuous components, which may even operate on different time scales. Therefore, it is desirable to establish modeling frameworks that are capable of combining deterministic and stochastic, discrete and continuous, as well as multi-timescale features. In the context of molecular systems biology, an example for the need of such a combination is the investigation of integrated biological pathways that contain gene regulatory, metabolic and signaling components, which may operate on different time scales and involve on-off switches as well as stochastic effects. The implementation of integrated hybrid systems is not trivial because most software is limited to one or the other of the dichotomies above. In this study, we first review the motivation for hybrid modeling. Secondly, by using the example of a toggle switch model, we illustrate a recently developed modeling framework that is based on the combination of biochemical systems theory (BST) and hybrid functional Petri nets (HFPN). Finally, we discuss remaining challenges and future opportunities. [ABSTRACT FROM AUTHOR]

Many biological systems are genuinely hybrids consisting of interacting discrete and continuous components and processes that often operate at different time scales. It is therefore desirable to create modeling frameworks capable of combining differently structured processes and permitting their analysis over multiple time horizons. During the past 40 years, Biochemical Systems Theory (BST) has been a very successful approach to elucidating metabolic, gene regulatory, and signaling systems. However, its foundation in ordinary differential equations has precluded BST from directly addressing problems containing switches, delays, and stochastic effects. In this study, we extend BST to hybrid modeling within the framework of Hybrid Functional Petri Nets (HFPN). First, we show how the canonical GMA and S-system models in BST can be directly implemented in a standard Petri Net framework. In a second step we demonstrate how to account for different types of time delays as well as for discrete, stochastic, and switching effects. Using representative test cases, we validate the hybrid modeling approach through comparative analyses and simulations with other approaches and highlight the feasibility, quality, and efficiency of the hybrid method. [ABSTRACT FROM AUTHOR]

Oscillations exist at all levels of biological systems and are often crucial for their proper functioning. Among the various types of oscillations, limit cycles have received particular attention for more than one hundred years. Specifically, theorems have been established that characterize whether a system might have the capability of exhibiting limit cycles. However, the practical application of these theorems is usually cumbersome and there are hardly any guidelines for devising de novo models that exhibit limit cycles of a desired form. In this paper, we propose a simple method for constructing and customizing stable limit cycles in two-dimensional systems according to desired features, including frequency, amplitude, and phase shift between system variables. The method is based on "inverting" a criterion proposed by Lewis for characterizing oscillations in two-dimensional S-system models. First, we execute comprehensive simulations that result in a set of over 2000 prototype limit cycles. Second, we show with examples how these prototypes can be further customized to adhere to predetermined specifications. This two-step process is fast and efficacious, especially when one considers the paucity of alternative methods. Finally, we illustrate how one may create systems with more complex dynamics by modulating the prototypes with external input signals. [ABSTRACT FROM AUTHOR]

Abstract: Mathematical modeling for dynamic biological systems is a central theme in systems biology. There are still many challenges in using time-course data to obtain an inverse problem of nonlinear dynamic biological systems. In this study, a multi-objective optimization technique is introduced to determine kinetic parameter values of biochemical reaction systems. The multi-objective parameter estimation was converted into the minimax problem through the satisfying trade-off method. The aspiration value was assigned as the minimum solution to the corresponding single objective estimation. The aim of this trade-off estimation was to obtain a compromised result by simultaneously minimizing both concentration and slope error criteria. Hybrid differential evolution was applied to solve the minimax problem and to yield a global estimation. [Copyright &y& Elsevier]

Cryptococcus neoformans (Cn) is the most common cause of fungal meningitis worldwide. In infected patients, growth of the fungus can occur within the phagolysosome of phagocytic cells, especially in non-activated macrophages of immunocompromised subjects. Since this environment is characteristically acidic, Cn must adapt to low pH to survive and efficiently cause disease. In the present work, we designed, tested, and experimentally validated a theoretical model of the sphingolipid biochemical pathway in Cn under acidic conditions. Simulations of metabolic fluxes and enzyme deletions or downregulation led to predictions that show good agreement with experimental results generated post hoc and reconcile intuitively puzzling results. This study demonstrates how biochemical modeling can yield testable predictions and aid our understanding of fungal pathogenesis through the design and computational simulation of hypothetical experiments. [ABSTRACT FROM AUTHOR]

Abstract: We analyze the growth dynamics and production of an industrially interesting amino acid in a recombinant Escherichia coli strain, using in parallel two alternative modeling frameworks, namely S-systems and lin-log models. These models have identical steady-state solutions, but differ in their representation of transients. The models were parameterized with data from two bioprocesses that differed in their initial culture concentrations and then used to predict responses under yet a different initial culture regimen. Among the S-system models, several alternatives representing slightly different pathway structures, were tested. All were found to be capable of capturing the dynamics of all variables in the test systems and also of predicting the dynamic responses under new conditions. The lin-log models also captured the dynamics, but not as well as the S-system models. A probable reason for the inferior performance of lin-log models is their intrinsic property of not representing situations well where variable concentrations are moderately small. [Copyright &y& Elsevier]

The combination of high-throughput methods of molecular biology with advanced mathematical and computational techniques has propelled the emergent field of systems biology into a position of prominence. Unthinkable a decade ago, it has become possible to screen and analyze the expression of entire genomes, simultaneously assess large numbers of proteins and their prevalence, and characterize in detail the metabolic state of a cell population. Although very important, the focus on comprehensive networks of biological components is only one side of systems biology. Complementing large-scale assessments, and sometimes at the risk of being forgotten, are more subtle analyses that rationalize the design and functioning of biological modules in exquisite detail. This intricate side of systems biology aims at identifying the specific roles of processes and signals in smaller, fully regulated systems by computing what would happen if these signals were lacking or organized in a different fashion. We exemplify this type of approach with a detailed analysis of the regulation of glucose utilization in Lactococcus lactis. This organism is exposed to alternating periods of glucose availability and starvation. During starvation, it accumulates an intermediate of glycolysis, which allows it to take up glucose immediately upon availability. This notable accumulation poses a nontrivial control task that is solved with an unusual, yet ingeniously designed and timed feedforward activation system. The elucidation of this control system required high-precision, dynamic in vivo metabolite data, combined with methods of nonlinear systems analysis, and may serve as a paradigm for multidisciplinary approaches to fine-scaled systems biology. [ABSTRACT FROM AUTHOR]

Novel high-throughput measurement techniques in vivo are beginning to produce dense high-quality time series which can be used to investigate the structure and regulation of biochemical networks. We propose an automated information extraction procedure which takes advantage of the unique S-system structure and supports model building from time traces, curve fitting, model selection, and structure identification based on parameter estimation. The procedure comprises of three modules: model Generation, parameter estimation or model Fitting, and model Selection (GFS algorithm).The GFS algorithm has been implemented in MATLAB and returns a list of candidate S-systems which adequately explain the data and guides the search to the most plausible model for the time series under study. By combining two strategies (namely decoupling and limiting connectivity) with methods of data smoothing, the proposed algorithm is scalable up to realistic situations of moderate size. We illustrate the proposed methodology with a didactic example. [ABSTRACT FROM AUTHOR]