Quantitative Biology

In the past years, many computational methods have been developed to infer the structure of gene regulatory networks from time-series data. However, the applicability and accuracy presumptions of such algorithms remain unclear due to experimental heterogeneity. This paper assesses the performance of recent and successful network inference strategies under a novel, multifactorial evaluation framework in order to highlight pragmatic tradeoffs in experimental design. The effects of data quantity and systems perturbations are addressed, thereby formulating guidelines for efficient resource management. Realistic data were generated from six widely used benchmark models of rhythmic and non-rhythmic gene regulatory systems with random perturbations mimicking the effect of gene knock-out or chemical treatments. Then, time-series data of increasing lengths were provided to five state-of-the-art network inference algorithms representing distinctive mathematical paradigms. The performances of such network reconstruction methodologies are uncovered under various experimental conditions. We report that the algorithms do not benefit equally from data increments. Furthermore, for rhythmic systems, it is more profitable for network inference strategies to be run on long time-series rather than short time-series with multiple perturbations. By contrast, for the non-rhythmic systems, increasing the number of perturbation experiments yielded better results than increasing the sampling frequency. We expect that future benchmark and algorithm design would integrate such multifactorial considerations to promote their widespread and conscientious usage.

Biological processes at the cellular level are stochastic in nature, and the immune response system is no different. Therefore, models that attempt to explain this system need to also incorporate noise or fluctuations that can account for the observed variability. In this work, a stochastic model of the immune response system is presented in terms of the dynamics of the T cells and the virus particles. Making use of the Green's function and the Wilemski-Fixman approximation, this model is then solved to obtain the analytical expression for the joint probability density function of these variables in the early and late stages of infection. This is then also used to calculate the average level of virus particles in the system. Upon comparing the theoretically predicted average virus levels to those of COVID-19 patients, it is hypothesized that the long lived dynamics that are characteristic of such viral infections are due to the long range correlations in the temporal fluctuations of the virions. This model therefore provides an insight into the effects of noise on viral dynamics.

Environmental contaminant exposure can pose significant risks to human health. Therefore, evaluating the impact of this exposure is of great importance; however, it is often difficult because both the molecular mechanism of disease and the mode of action of the contaminants are complex. We used network biology techniques to quantitatively assess the impact of environmental contaminants on the human interactome and diseases with a particular focus on seven major contaminant categories: persistent organic pollutants (POPs), dioxins, polycyclic aromatic hydrocarbons (PAHs), pesticides, perfluorochemicals (PFCs), metals, and pharmaceutical and personal care products (PPCPs). We integrated publicly available data on toxicogenomics, the diseasome, protein-protein interactions (PPIs), and gene essentiality and found that a few contaminants were targeted to many genes, and a few genes were targeted by many contaminants. The contaminant targets were hub proteins in the human PPI network, whereas the target proteins in most categories did not contain abundant essential proteins. Generally, contaminant targets and disease-associated proteins were closely associated with the PPI network, and the closeness of the associations depended on the disease type and chemical category. Network biology techniques were used to identify environmental contaminants with broad effects on the human interactome and contaminant-sensitive biomarkers. Moreover, this method enabled us to quantify the relationship between environmental contaminants and human diseases, which was supported by epidemiological and experimental evidence. These methods and findings have facilitated the elucidation of the complex relationship between environmental exposure and adverse health outcomes.

Heterogeneity is ubiquitous in stem cells (SC), cancer cells (CS), and cancer stem cells (CSC). SC and CSC heterogeneity is manifested as diverse sub-populations with self-renewing and unique regeneration capacity. Moreover, the CSC progeny possesses multiple plasticity and cancerous characteristics. Many studies have demonstrated that cancer heterogeneity is one of the greatest obstacle for therapy. This leads to the incomplete anti-cancer therapies and transitory efficacy. Furthermore, numerous micro-metastasis leads to the wide spread of the tumor cells across the body which is the beginning of metastasis. The epigenetic processes (DNA methylation or histone remodification etc.) can provide a source for certain heterogeneity. In this study, we develop a mathematical model to quantify the heterogeneity of SC, CSC and cancer taking both genetic and epigenetic effects into consideration. We uncovered the roles and physical mechanisms of heterogeneity from the three aspects (SC, CSC and cancer). In the adiabatic regime (relatively fast regulatory binding and effective coupling among genes), seven native states (SC, CSC, Cancer, Premalignant, Normal, Lesion and Hyperplasia) emerge. In non-adiabatic regime (relatively slow regulatory binding and effective weak coupling among genes), multiple meta-stable SC, CS, CSC and differentiated states emerged which can explain the origin of heterogeneity. In other words, the slow regulatory binding mimicking the epigenetics can give rise to heterogeneity. Elucidating the origin of heterogeneity and dynamical interrelationship between intra-tumoral cells has clear clinical significance in helping to understand the cellular basis of treatment response, therapeutic resistance, and tumor relapse.

For many stochastic models of interest in systems biology, such as those describing biochemical reaction networks, exact quantification of parameter uncertainty through statistical inference is intractable. Likelihood-free computational inference techniques enable parameter inference when the likelihood function for the model is intractable but the generation of many sample paths is feasible through stochastic simulation of the forward problem. The most common likelihood-free method in systems biology is approximate Bayesian computation that accepts parameters that result in low discrepancy between stochastic simulations and measured data. However, it can be difficult to assess how the accuracy of the resulting inferences are affected by the choice of acceptance threshold and discrepancy function. The pseudo-marginal approach is an alternative likelihood-free inference method that utilises a Monte Carlo estimate of the likelihood function. This approach has several advantages, particularly in the context of noisy, partially observed, time-course data typical in biochemical reaction network studies. Specifically, the pseudo-marginal approach facilitates exact inference and uncertainty quantification, and may be efficiently combined with particle filters for low variance, high-accuracy likelihood estimation. In this review, we provide a practical introduction to the pseudo-marginal approach using inference for biochemical reaction networks as a series of case studies. Implementations of key algorithms and examples are provided using the Julia programming language; a high performance, open source programming language for scientific computing.

The multiple futile cycle is a phosphorylation system in which a molecular substrate might be phosphorylated sequentially n times by means of an enzymatic mechanism. The system has been studied mathematically using reaction network theory and ordinary differential equations. It is known that the system might have at least as many as 2[n/2]+1 steady states (where [x] is the integer part of x) for particular choices of parameters. Furthermore, for the simple and dual futile cycles (n=1,2) the stability of the steady states has been determined in the sense that the only steady state of the simple futile cycle is globally stable, while there exist parameter values for which the dual futile cycle admits two asymptotically stable and one unstable steady state. For general n, evidence that the possible number of asymptotically stable steady states increases with n has been given, which has led to the conjecture that parameter values can be chosen such that [n/2]+1 out of 2[n/2]+1 steady states are asymptotically stable and the remaining steady states are unstable. We prove this conjecture here by first reducing the system to a smaller one, for which we find a choice of parameter values that give rise to a unique steady state with multiplicity 2[n/2]+1. Using arguments from geometric singular perturbation theory, and a detailed analysis of the centre manifold of this steady state, we achieve the desired result.

Pluripotent embryonic stem cells are of paramount importance for biomedical research thanks to their innate ability for self-renewal and differentiation into all major cell lines. The fateful decision to exit or remain in the pluripotent state is regulated by complex genetic regulatory network. Latest advances in transcriptomics have made it possible to infer basic topologies of pluripotency governing networks. The inferred network topologies, however, only encode boolean information while remaining silent about the roles of dynamics and molecular noise in gene expression. These features are widely considered essential for functional decision making. Herein we developed a framework for extending the boolean level networks into models accounting for individual genetic switches and promoter architecture which allows mechanistic interrogation of the roles of molecular noise, external signaling, and network topology. We demonstrate the pluripotent state of the network to be a broad attractor which is robust to variations of gene expression. Dynamics of exiting the pluripotent state, on the other hand, is significantly influenced by the molecular noise originating from genetic switching events which makes cells more responsive to extracellular signals. Lastly we show that steady state probability landscape can be significantly remodeled by global gene switching rates alone which can be taken as a proxy for how global epigenetic modifications exert control over stability of pluripotent states.

The notion of entropy is shared between statistics and thermodynamics, and is fundamental to both disciplines. This makes statistical problems particularly suitable for reaction network implementations. In this paper we show how to perform a statistical operation known as Information Projection or E projection with stochastic mass-action kinetics. Our scheme encodes desired conditional distributions as the equilibrium distributions of reaction systems. To our knowledge this is a first scheme to exploit the inherent stochasticity of reaction networks for information processing. We apply this to the problem of an artificial cell trying to infer its environment from partial observations.

In this paper, a system architecture is proposed that approximately models the functionality of metabolic networks. The AND/OR graph model is used to represent the metabolic network and each processing element in the system emulates the functionality of a metabolite. The system is implemented on a graphics processing unit (GPU) as the hardware platform using CUDA environment. The proposed architecture takes advantage of the inherent parallelism in the network structure in terms of both pathway and metabolite traversal. The function of each element is defined such that it can find flux-balanced pathways. Pathways in both small and large metabolic networks are applied to the proposed architecture and the results are discussed.

Genome-scale metabolic models have become a fundamental tool for examining metabolic principles. However, metabolism is not solely characterized by the underlying biochemical reactions and catalyzing enzymes, but also affected by regulatory events. Since the pioneering work of Covert and co-workers as well as Shlomi and co-workers it is debated, how regulation and metabolism synergistically characterize a coherent cellular state. The first approaches started from metabolic models which were extended by the regulation of the encoding genes of the catalyzing enzymes. By now, bioinformatics databases in principle allow addressing the challenge of integrating regulation and metabolism on a system-wide level. Collecting information from several databases we provide a network representation of the integrated gene regulatory and metabolic system for Escherichia coli, including major cellular processes, from metabolic processes via protein modification to a variety of regulatory events. Besides transcriptional regulation, we also take into account regulation of translation, enzyme activities and reactions. Our network model provides novel topological characterizations of system components based on their positions in the network. We show that network characteristics suggest a representation of the integrated system as three network domains (regulatory, metabolic and interface networks) instead of two. This new three-domain representation reveals the structural centrality of components with known high functional relevance. This integrated network can serve as a platform for understanding coherent cellular states as active subnetworks and to elucidate crossover effects between metabolism and gene regulation.