NERDSS: A Nonequilibrium Simulator for Multibody Self-Assembly at the Cellular Scale

Currently, a significant barrier to building predictive models of cellular self-assembly processes is that molecular models cannot capture minutes-long dynamics that couple distinct components with active processes, whereas reaction-diffusion models cannot capture structures of molecular assembly. Here, we introduce the nonequilibrium reaction-diffusion self-assembly simulator (NERDSS), which addresses this spatiotemporal resolution gap. NERDSS integrates efficient reaction-diffusion algorithms into generalized software that operates on user-defined molecules through diffusion, binding and orientation, unbinding, chemical transformations, and spatial localization. By connecting the fast processes of binding with the slow timescales of large-scale assembly, NERDSS integrates molecular resolution with reversible formation of ordered, multisubunit complexes. NERDSS encodes models using rule-based formatting languages to facilitate model portability, usability, and reproducibility. Applying NERDSS to steps in clathrin-mediated endocytosis, we design multicomponent systems that can form lattices in solution or on the membrane, and we predict how stochastic but localized dephosphorylation of membrane lipids can drive lattice disassembly. The NERDSS simulations reveal the spatial constraints on lattice growth and the role of membrane localization and cooperativity in nucleating assembly. By modeling viral lattice assembly and recapitulating oscillations in protein expression levels for a circadian clock model, we illustrate the adaptability of NERDSS. NERDSS simulates user-defined assembly models that were previously inaccessible to existing software tools, with broad applications to predicting self-assembly in vivo and designing high-yield assemblies in vitro.     

An integrated modeling-experimental strategy for the analysis of metabolic pathways

An inherent problem in studying the behavior of a metabolic pathway is the impossibility of developing a complete, detailed model that includes all the cellular processes that have an impact on the set of fluxes in such a pathway. Lacking this, one requires some means of modeling the interactions between a metabolic pathway and other cellular processes for the purpose of analyzing pathway characteristics within the cell (e.g., determining sensitivity coefficients for various steps in the pathway) with a minimal amount of time and effort. A general framework is developed for studying these issues in a rigorous manner. Using this framework, detailed knowledge about a metabolic pathway (i.e., a set of rate expressions for steps in the pathway) can be combined with the results from a relatively simple set of experiments in order to obtain estimates for the sensitivity of the pathway to enzyme activities, inhibition constants, and other parameters that determine the pathway's behavior, while accounting for the pathway's interaction with the rest of the cellular metabolism. A model system representing amino acid production is used to illustrate the problem and to provide results based on computational experiments. The modeling strategy described here should be useful in genetic design to improve pathway fluxes and metabolic network selectivity.     

Hybrid computational modeling demonstrates the utility of simulating complex cellular networks in type 1 diabetes

Persistent destruction of pancreatic β-cells in type 1 diabetes (T1D) results from multifaceted pancreatic cellular interactions in various phase progressions. Owing to the inherent heterogeneity of coupled nonlinear systems, computational modeling based on T1D etiology help achieve a systematic understanding of biological processes and T1D health outcomes. The main challenge is to design such a reliable framework to analyze the highly orchestrated biology of T1D based on the knowledge of cellular networks and biological parameters. We constructed a novel hybrid in-silico computational model to unravel T1D onset, progression, and prevention in a non-obese-diabetic mouse model. The computational approach that integrates mathematical modeling, agent-based modeling, and advanced statistical methods allows for modeling key biological parameters and time-dependent spatial networks of cell behaviors. By integrating interactions between multiple cell types, model results captured the individual-specific dynamics of T1D progression and were validated against experimental data for the number of infiltrating CD8⁺T-cells. Our simulation results uncovered the correlation between five auto-destructive mechanisms identifying a combination of potential therapeutic strategies: the average lifespan of cytotoxic CD8⁺T-cells in islets; the initial number of apoptotic β-cells; recruitment rate of dendritic-cells (DCs); binding sites on DCs for naïve CD8⁺T-cells; and time required for DCs movement. Results from therapy-directed simulations further suggest the efficacy of proposed therapeutic strategies depends upon the type and time of administering therapy interventions and the administered amount of therapeutic dose. Our findings show modeling immunogenicity that underlies autoimmune T1D and identifying autoantigens that serve as potential biomarkers are two pressing parameters to predict disease onset and progression.     

Discrete event, multi-level simulation of metabolite channeling

Typically differential equations are employed to simulate cellular dynamics. To develop a valid continuous model based on differential equations requires accurate parameter estimations; an accuracy which is often difficult to achieve, due to the lack of data. In addition, processes in metabolic pathways, e.g. metabolite channeling, seem to be of a rather qualitative and discrete nature. With respect to the available data and to the perception of the underlying system, a discrete rather than a continuous approach to modeling and simulation seems more adequate. A discrete approach does not necessarily imply a more abstract view on the system. If we move from macro to micro and multi-level modeling, aspects of subsystems and their interactions, which have been only implicitly represented, become an explicit part of the model. To start exploring discrete event phenomena within metabolite channeling we choose the tryptophan synthase. Based on a continuous macro model, a discrete event, multi-level model is developed which allows us to analyze the interrelation between structural and functional characteristics of the enzymes.     

Kinetic modeling of microbial growth,enzyme activity,and gene deletions: An integrated model of β-glucosidase function in Cellvibrio japonicus

Understanding the complex growth and metabolic dynamics in microorganisms requires advanced kinetic models containing both metabolic reactions and enzymatic regulation to predict phenotypic behaviors under different conditions and perturbations. Most current kinetic models lack gene expression dynamics and are separately calibrated to distinct media, which consequently makes them unable to account for genetic perturbations or multiple substrates. This challenge limits our ability to gain a comprehensive understanding of microbial processes towards advanced metabolic optimizations that are desired for many biotechnology applications. Here, we present an integrated computational and experimental approach for the development and optimization of mechanistic kinetic models for microbial growth and metabolic and enzymatic dynamics. Our approach integrates growth dynamics, gene expression, protein secretion, and gene-deletion phenotypes. We applied this methodology to build a dynamic model of the growth kinetics in batch culture of the bacterium Cellvibrio japonicus grown using either cellobiose or glucose media. The model parameters were inferred from an experimental data set using an evolutionary computation method. The resulting model was able to explain the growth dynamics of C. japonicus using either cellobiose or glucose media and was also able to accurately predict the metabolite concentrations in the wild-type strain as well as in β-glucosidase gene deletion mutant strains. We validated the model by correctly predicting the non-diauxic growth and metabolite consumptions of the wild-type strain in a mixed medium containing both cellobiose and glucose, made further predictions of mutant strains growth phenotypes when using cellobiose and glucose media, and demonstrated the utility of the model for designing industrially-useful strains. Importantly, the model is able to explain the role of the different β-glucosidases and their behavior under genetic perturbations. This integrated approach can be extended to other metabolic pathways to produce mechanistic models for the comprehensive understanding of enzymatic functions in multiple substrates.     

Large-scale in silico modeling of metabolic interactions between cell types in the human brain

Metabolic interactions between multiple cell types are difficult to model using existing approaches. Here we present a workflow that integrates gene expression data, proteomics data and literature-based manual curation to model human metabolism within and between different types of cells. Transport reactions are used to account for the transfer of metabolites between models of different cell types via the interstitial fluid. We apply the method to create models of brain energy metabolism that recapitulate metabolic interactions between astrocytes and various neuron types relevant to Alzheimer's disease. Analysis of the models identifies genes and pathways that may explain observed experimental phenomena, including the differential effects of the disease on cell types and regions of the brain. Constraint-based modeling can thus contribute to the study and analysis of multicellular metabolic processes in the human tissue microenvironment and provide detailed mechanistic insight into high-throughput data analysis.     

A multi-approach and multi-scale platform to model CD4+ T cells responding to infections

Immune responses rely on a complex adaptive system in which the body and infections interact at multiple scales and in different compartments. We developed a modular model of CD4+ T cells, which uses four modeling approaches to integrate processes at three spatial scales in different tissues. In each cell, signal transduction and gene regulation are described by a logical model, metabolism by constraint-based models. Cell population dynamics are described by an agent-based model and systemic cytokine concentrations by ordinary differential equations. A Monte Carlo simulation algorithm allows information to flow efficiently between the four modules by separating the time scales. Such modularity improves computational performance and versatility and facilitates data integration. We validated our technology by reproducing known experimental results, including differentiation patterns of CD4+ T cells triggered by different combinations of cytokines, metabolic regulation by IL2 in these cells, and their response to influenza infection. In doing so, we added multi-scale insights to single-scale studies and demonstrated its predictive power by discovering switch-like and oscillatory behaviors of CD4+ T cells that arise from nonlinear dynamics interwoven across three scales. We identified the inflamed lymph node’s ability to retain naive CD4+ T cells as a key mechanism in generating these emergent behaviors. We envision our model and the generic framework encompassing it to serve as a tool for understanding cellular and molecular immunological problems through the lens of systems immunology.     

Dynamic simulation of the human red blood cell metabolic network

We have developed a Mathematica application package to perform dynamic simulations of the red blood cell (RBC) metabolic network. The package relies on, and integrates, many years of mathematical modeling and biochemical work on red blood cell metabolism. The extensive data regarding the red blood cell metabolic network and the previous kinetic analysis of all the individual components makes the human RBC an ideal 'model' system for mathematical metabolic models. The Mathematica package can be used to understand the dynamics and regulatory characteristics of the red blood cell.     

Hypothesis testing via integrated computer modeling and digital fluorescence microscopy

Computational modeling has the potential to add an entirely new approach to hypothesis testing in yeast cell biology. Here, we present a method for seamless integration of computational modeling with quantitative digital fluorescence microscopy. This integration is accomplished by developing computational models based on hypotheses for underlying cellular processes that may give rise to experimentally observed fluorescent protein localization patterns. Simulated fluorescence images are generated from the computational models of underlying cellular processes via a "model-convolution" process. These simulated images can then be directly compared to experimental fluorescence images in order to test the model. This method provides a framework for rigorous hypothesis testing in yeast cell biology via integrated mathematical modeling and digital fluorescence microscopy.     

A computational modeling and analysis in cell biological dynamics using electric cell-substrate impedance sensing (ECIS)

In this paper, a study of computational modeling and multi-scale analysis in cell dynamics is presented. Our study aims at: (1) deriving and validating a mathematical model for cell growth, and (2) quantitatively detecting and analyzing the biological interdependencies across multiple observational scales with a variety of time and frequency resolutions. This research was conducted using the time series data practically measured from a novel on-line cell monitoring technique, referred to as electric cell-substrate impedance sensing (ECIS), which allows continuously tracking the cellular behavior such as adhesion, proliferation, spreading and micromotion. First, comparing our ECIS-based cellular growth modeling analysis results with those determined by hematocytometer measurement using different time intervals, we found that the results obtained from both experimental methods consistently agreed. However, our study demonstrated that it is much easier and more convenient to operate with the ECIS system for on-line cellular growth monitoring. Secondly, for multi-scale analysis our results showed that the proposed wavelet-based methodology can effectively quantify the fluctuations associated with cell micromotions and quantitatively capture the biological interdependencies across multiple observational scales. Note that although the wavelet method is well known, its application into the ECIS time series analysis is novel and unprecedented in computational cell biology. Our analyses indicated that the proposed study on ECIS time series could provide a hopeful start and great potentials in both modeling and elucidating the complex mechanisms of cell biological systems.     

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.     

Comparative proteomic study reveals the involvement of diurnal cycle in cell division, enlargement, and starch accumulation in developing endosperm of Oryza sativa

The development and starch accumulation of cereal endosperms rely on the sugar supply of leaves, which is subject to diurnal cycles, and the endosperm itself also experiences a light/dark switch. However, revealing how the cereal endosperm responds to diurnal input remains a major challenge. We used comparative proteomic approaches to probe diurnally affected processes in rice endosperm (Oryza sativa) 10 days after flowering under 12-h light/12-h dark. Starch granules in rice endosperm showed a growth ring structure under a normal light/dark cycle but not under constant light. Sucrose showed a high level in light and low level in dark. Two-dimensional (2-D) differential in-gel electrophoresis-based proteomic analysis revealed 101 protein spots diurnally changed and 91 identities, which were involved in diverse processes with preferred distribution in stress response, protein synthesis/destination and metabolism. Proteins involved in cell division showed high expression in light and those in cell enlargement and cell wall synthesis high in dark, while starch synthesis proteins were light-downregulated and dark-upregulated. Redox homeostasis-associated proteins showed in-phase peaks under light and dark. These data demonstrate diurnal input-regulated diverse cellular and metabolic processes in rice endosperm, and coordination among these processes is essential for development and starch accumulation with diurnal input.     

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.     

Organellar vs cellular control of mitochondrial dynamics

Mitochondrial dynamics, the fusion and fission of individual mitochondrial units, is critical to the exchange of the metabolic, genetic and proteomic contents of individual mitochondria. In this regard, fusion and fission events have been shown to modulate mitochondrial bioenergetics, as well as several cellular processes including fuel sensing, ATP production, autophagy, apoptosis, and the cell cycle. Regulation of the dynamic events of fusion and fission occur at two redundant and interactive levels. Locally, the microenvironment of the individual mitochondrion can alter its ability to fuse, divide or move through the cell. Globally, nuclear-encoded processes and cellular ionic and second messenger systems can alter or activate mitochondrial proteins, regulate mitochondrial dynamics and concomitantly change the condition of the mitochondrial population. In this review we investigate the different global and local signals that control mitochondrial biology. This discussion is carried out to clarify the different signals that impact the status of the mitochondrial population.     

Dynamic Redox Regulation of IL-4 Signaling

Quantifying the magnitude and dynamics of protein oxidation during cell signaling is technically challenging. Computational modeling provides tractable, quantitative methods to test hypotheses of redox mechanisms that may be simultaneously operative during signal transduction. The interleukin-4 (IL-4) pathway, which has previously been reported to induce reactive oxygen species and oxidation of PTP1B, may be controlled by several other putative mechanisms of redox regulation; widespread proteomic thiol oxidation observed via 2D redox differential gel electrophoresis upon IL-4 treatment suggests more than one redox-sensitive protein implicated in this pathway. Through computational modeling and a model selection strategy that relied on characteristic STAT6 phosphorylation dynamics of IL-4 signaling, we identified reversible protein tyrosine phosphatase (PTP) oxidation as the primary redox regulatory mechanism in the pathway. A systems-level model of IL-4 signaling was developed that integrates synchronous pan-PTP oxidation with ROS-independent mechanisms. The model quantitatively predicts the dynamics of IL-4 signaling over a broad range of new redox conditions, offers novel hypotheses about regulation of JAK/STAT signaling, and provides a framework for interrogating putative mechanisms involving receptor-initiated oxidation.     

Metabolic modeling of Saccharomyces cerevisiae using the optimal control of homeostasis: a cybernetic model definition

A model is presented to describe the observed behavior of microorganisms that aim at metabolic homeostasis while growing and adapting to their environment in an optimal way. The cellular metabolism is seen as a network with a multiple controller system with both feedback and feedforward control, i.e., a model based on a dynamic optimal metabolic control. The dynamic network consists of aggregated pathways, each having a control setpoint for the metabolic states at a given growth rate. This set of strategies of the cell forms a true cybernetic model with a minimal number of assumptions. The cellular strategies and constraints were derived from metabolic flux analysis using an identified, biochemically relevant, stoichiometry matrix derived from experimental data on the cellular composition of continuous cultures of Saccharomyces cerevisiae. Based on these data a cybernetic model was developed to study its dynamic behavior. The growth rate of the cell is determined by the structural compounds and fluxes of compounds related to central metabolism. In contrast to many other cybernetic models, the minimal model does not consist of any assumed internal kinetic parameters or interactions. This necessitates the use of a stepwise integration with an optimization of the fluxes at every time interval. Some examples of the behavior of this model are given with respect to steady states and pulse responses. This model is very suitable for describing semiquantitatively dynamics of global cellular metabolism and may form a useful framework for including structured and more detailed kinetic models.     

Descriptive proteomic analysis shows protein variability between closely related clinical isolates of Mycobacterium tuberculosis

The use of isobaric tags such as iTRAQ allows the relative and absolute quantification of hundreds of proteins in a single experiment for up to eight different samples. More classical techniques such as 2‐DE can offer a complimentary approach for the analysis of complex protein samples. In this study, the proteomes of secreted and cytosolic proteins of genetically closely related strains of Mycobacterium tuberculosis were analyzed. Analysis of 2‐D gels afforded 28 spots with variations in protein abundance between strains. These were identified by MS/MS. Meanwhile, a rigorous statistical analysis of iTRAQ data allowed the identification and quantification of 101 and 137 proteins in the secreted and cytosolic fractions, respectively. Interestingly, several differences in protein levels were observed between the closely related strains BE, C28 and H6. Seven proteins related to cell wall and cell processes were more abundant in BE, while enzymes related to metabolic pathways (GltA2, SucC, Gnd1, Eno) presented lower levels in the BE strain. Proteins involved in iron and sulfur acquisition (BfrB, ViuB, TB15.3 and SseC2) were more abundant in C28 and H6. In general, iTRAQ afforded rapid identification of fine differences between protein levels such as those presented between closely related strains. This provides a platform from which the relevance of these differences can be assessed further using complimentary proteomic and biological modeling methods.