Modelling heterogeneous intracellular networks at the cellular scale

Cell function relies on the coordinated action of heterogeneous interconnected networks of biomolecules. Mathematical models help us explore the dynamics and behaviour of these intracellular networks in greater detail. Models of increasing scale and complexity are being developed to probe cellular processes, often necessitating the use of several types of mathematical representation in hybrid models. Here we review recent efforts to incorporate the influences of stochasticity and spatial heterogeneity into cellular level models, ranging from abstract coarse-grained representations to large-scale hybrid models comprising thousands of biological components. We discuss the key challenges involved in, and recent mathematical advances enabling the development and analysis of mathematical models of complex intracellular processes

Model of host-pathogen Interaction dynamics links In vivo optical imaging and immune responses

Tracking disease progression in vivo is essential for the development of treatments against bacterial infection. Optical imaging has become a central tool for in vivo tracking of bacterial population development and therapeutic response. For a precise understanding of in vivo imaging results in terms of disease mechanisms derived from detailed postmortem observations, however, a link between the two is needed. Here, we develop a model that provides that link for the investigation of Citrobacter rodentium infection, a mouse model for enteropathogenic Escherichia coli (EPEC). We connect in vivo disease progression of C57BL/6 mice infected with bioluminescent bacteria, imaged using optical tomography and X-ray computed tomography, to postmortem measurements of colonic immune cell infiltration. We use the model to explore changes to both the host immune response and the bacteria and to evaluate the response to antibiotic treatment. The developed model serves as a novel tool for the identification and development of new therapeutic interventions

Mathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case Study

The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to showcase current mathematical and statistical techniques that enable modelers to gain insight into (models of) gene regulation, and generate testable predictions. We introduce a range of modeling frameworks, but focus on ordinary differential equation (ODE) models since they remain the most widely used approach in systems biology and medicine and continue to offer great potential. We present methods for the analysis of a single model, comprising applications of standard dynamical systems approaches such as nondimensionalization, steady state, asymptotic and sensitivity analysis, and more recent statistical and algebraic approaches to compare models with data. We present parameter estimation and model comparison techniques, focusing on Bayesian analysis and coplanarity via algebraic geometry. Our intention is that this (non exhaustive) review may serve as a useful starting point for the analysis of models in systems medicine.Comment: Submitted to 'Systems Medicine' as a book chapte

Probing the Mutational Interplay between Primary and Promiscuous Protein Functions: A Computational-Experimental Approach

Protein promiscuity is of considerable interest due its role in adaptive metabolic plasticity, its fundamental connection with molecular evolution and also because of its biotechnological applications. Current views on the relation between primary and promiscuous protein activities stem largely from laboratory evolution experiments aimed at increasing promiscuous activity levels. Here, on the other hand, we attempt to assess the main features of the simultaneous modulation of the primary and promiscuous functions during the course of natural evolution. The computational/experimental approach we propose for this task involves the following steps: a function-targeted, statistical coupling analysis of evolutionary data is used to determine a set of positions likely linked to the recruitment of a promiscuous activity for a new function; a combinatorial library of mutations on this set of positions is prepared and screened for both, the primary and the promiscuous activities; a partial-least-squares reconstruction of the full combinatorial space is carried out; finally, an approximation to the Pareto set of variants with optimal primary/promiscuous activities is derived. Application of the approach to the emergence of folding catalysis in thioredoxin scaffolds reveals an unanticipated scenario: diverse patterns of primary/promiscuous activity modulation are possible, including a moderate (but likely significant in a biological context) simultaneous enhancement of both activities. We show that this scenario can be most simply explained on the basis of the conformational diversity hypothesis, although alternative interpretations cannot be ruled out. Overall, the results reported may help clarify the mechanisms of the evolution of new functions. From a different viewpoint, the partial-least-squares-reconstruction/Pareto-set-prediction approach we have introduced provides the computational basis for an efficient directed-evolution protocol aimed at the simultaneous enhancement of several protein features and should therefore open new possibilities in the engineering of multi-functional enzymes

A Measure of the Promiscuity of Proteins and Characteristics of Residues in the Vicinity of the Catalytic Site That Regulate Promiscuity

Promiscuity, the basis for the evolution of new functions through ‘tinkering’ of residues in the vicinity of the catalytic site, is yet to be quantitatively defined. We present a computational method Promiscuity Indices Estimator (PROMISE) - based on signatures derived from the spatial and electrostatic properties of the catalytic residues, to estimate the promiscuity (PromIndex) of proteins with known active site residues and 3D structure. PromIndex reflects the number of different active site signatures that have congruent matches in close proximity of its native catalytic site, the quality of the matches and difference in the enzymatic activity. Promiscuity in proteins is observed to follow a lognormal distribution (μ = 0.28, σ = 1.1 reduced chi-square = 3.0E-5). The PROMISE predicted promiscuous functions in any protein can serve as the starting point for directed evolution experiments. PROMISE ranks carboxypeptidase A and ribonuclease A amongst the more promiscuous proteins. We have also investigated the properties of the residues in the vicinity of the catalytic site that regulates its promiscuity. Linear regression establishes a weak correlation (R2∼0.1) between certain properties of the residues (charge, polar, etc) in the neighborhood of the catalytic residues and PromIndex. A stronger relationship states that most proteins with high promiscuity have high percentages of charged and polar residues within a radius of 3 Å of the catalytic site, which is validated using one-tailed hypothesis tests (P-values∼0.05). Since it is known that these characteristics are key factors in catalysis, their relationship with the promiscuity index cross validates the methodology of PROMISE

Gene regulatory network inference from sngle-cell data using multivariate information measures

While single-cell gene expression experiments present new challenges for data processing, the cellto-cell variability observed also reveals statistical relationships that can be used by information theory. Here, we use multivariate information theory to explore the statistical dependencies between triplets of genes in single-cell gene expression datasets. We develop PIDC, a fast, efficient algorithm that uses partial information decomposition (PID) to identify regulatory relationships between genes. We thoroughly evaluate the performance of our algorithm and demonstrate that the higher-order information captured by PIDC allows it to outperform pairwise mutual information-based algorithms when recovering true relationships present in simulated data. We also infer gene regulatory networks from three experimental single-cell datasets and illustrate how network context, choices made during analysis, and sources of variability affect network inference. PIDC tutorials and open-source software for estimating PID are available. PIDC should facilitate the identification of putative functional relationships and mechanistic hypotheses from single-cell transcriptomic data

SYSTEMS BIOLOGY. Systems biology (un)certainties.

How can modelers restore confidence in systems and computational biology?</jats:p

Model of Host-Pathogen Interaction Dynamics Links In Vivo Optical Imaging and Immune Responses.

Tracking disease progression in vivo is essential for the development of treatments against bacterial infection. Optical imaging has become a central tool for in vivo tracking of bacterial population development and therapeutic response. For a precise understanding of in vivo imaging results in terms of disease mechanisms derived from detailed postmortem observations, however, a link between the two is needed. Here, we develop a model that provides that link for the investigation of Citrobacter rodentium infection, a mouse model for enteropathogenic Escherichia coli (EPEC). We connect in vivo disease progression of C57BL/6 mice infected with bioluminescent bacteria, imaged using optical tomography and X-ray computed tomography, to postmortem measurements of colonic immune cell infiltration. We use the model to explore changes to both the host immune response and the bacteria and to evaluate the response to antibiotic treatment. The developed model serves as a novel tool for the identification and development of new therapeutic interventions

MEANS: python package for Moment Expansion Approximation, iNference and Simulation.

MOTIVATION: Many biochemical systems require stochastic descriptions. Unfortunately these can only be solved for the simplest cases and their direct simulation can become prohibitively expensive, precluding thorough analysis. As an alternative, moment closure approximation methods generate equations for the time-evolution of the system's moments and apply a closure ansatz to obtain a closed set of differential equations; that can become the basis for the deterministic analysis of the moments of the outputs of stochastic systems. RESULTS: We present a free, user-friendly tool implementing an efficient moment expansion approximation with parametric closures that integrates well with the IPython interactive environment. Our package enables the analysis of complex stochastic systems without any constraints on the number of species and moments studied and the type of rate laws in the system. In addition to the approximation method our package provides numerous tools to help non-expert users in stochastic analysis. AVAILABILITY AND IMPLEMENTATION: https://github.com/theosysbio/means CONTACTS: [email protected] or [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online