Polarizability Plays a Decisive Role in Modulating Association Between Molecular Cations and Anions

Electrostatic interactions involving proteins depend not just on the ionic charges involved but also on their chemical identities. Here we examine the origins of incompletely understood differences in the strength of association of different pairs of monovalent molecular ions that are relevant to protein-protein and protein-ligand interactions. Cationic analogues of the basic amino acid side chains are simulated along with oxyanionic analogues of cation-exchange (CEX) ligands and acidic amino acids. Experimentally observed association trends with respect to the cations, but not anions, are captured by a non-polarizable model. A polarizable model proves decisive in capturing experimentally-suggested trends with respect to both cations and anions. Crucially, relative to a non-polarizable model, polarizability changes the free energy surface for ion-pair association, altering configurational sampling itself. An effective continuum correction to account for electronic polarizability can also capture the experimentally-suggested trends, but at the expense of fidelity to the underlying free energy surface

Singularly Perturbed Monotone Systems and an Application to Double Phosphorylation Cycles

The theory of monotone dynamical systems has been found very useful in the modeling of some gene, protein, and signaling networks. In monotone systems, every net feedback loop is positive. On the other hand, negative feedback loops are important features of many systems, since they are required for adaptation and precision. This paper shows that, provided that these negative loops act at a comparatively fast time scale, the main dynamical property of (strongly) monotone systems, convergence to steady states, is still valid. An application is worked out to a double-phosphorylation ``futile cycle'' motif which plays a central role in eukaryotic cell signaling.Comment: 21 pages, 3 figures, corrected typos, references remove

Exact model reduction of combinatorial reaction networks

Receptors and scaffold proteins usually possess a high number of distinct binding domains inducing the formation of large multiprotein signaling complexes. Due to combinatorial reasons the number of distinguishable species grows exponentially with the number of binding domains and can easily reach several millions. Even by including only a limited number of components and binding domains the resulting models are very large and hardly manageable. A novel model reduction technique allows the significant reduction and modularization of these models

An empirical Bayesian approach for model-based inference of cellular signaling networks

Background A common challenge in systems biology is to infer mechanistic descriptions of biological process given limited observations of a biological system. Mathematical models are frequently used to represent a belief about the causal relationships among proteins within a signaling network. Bayesian methods provide an attractive framework for inferring the validity of those beliefs in the context of the available data. However, efficient sampling of high-dimensional parameter space and appropriate convergence criteria provide barriers for implementing an empirical Bayesian approach. The objective of this study was to apply an Adaptive Markov chain Monte Carlo technique to a typical study of cellular signaling pathways. Results As an illustrative example, a kinetic model for the early signaling events associated with the epidermal growth factor (EGF) signaling network was calibrated against dynamic measurements observed in primary rat hepatocytes. A convergence criterion, based upon the Gelman-Rubin potential scale reduction factor, was applied to the model predictions. The posterior distributions of the parameters exhibited complicated structure, including significant covariance between specific parameters and a broad range of variance among the parameters. The model predictions, in contrast, were narrowly distributed and were used to identify areas of agreement among a collection of experimental studies. Conclusion In summary, an empirical Bayesian approach was developed for inferring the confidence that one can place in a particular model that describes signal transduction mechanisms and for inferring inconsistencies in experimental measurements

A Factor Graph Nested Effects Model To Identify Networks from Genetic Perturbations

Complex phenotypes such as the transformation of a normal population of cells into cancerous tissue result from a series of molecular triggers gone awry. We describe a method that searches for a genetic network consistent with expression changes observed under the knock-down of a set of genes that share a common role in the cell, such as a disease phenotype. The method extends the Nested Effects Model of Markowetz et al. (2005) by using a probabilistic factor graph to search for a network representing interactions among these silenced genes. The method also expands the network by attaching new genes at specific downstream points, providing candidates for subsequent perturbations to further characterize the pathway. We investigated an extension provided by the factor graph approach in which the model distinguishes between inhibitory and stimulatory interactions. We found that the extension yielded significant improvements in recovering the structure of simulated and Saccharomyces cerevisae networks. We applied the approach to discover a signaling network among genes involved in a human colon cancer cell invasiveness pathway. The method predicts several genes with new roles in the invasiveness process. We knocked down two genes identified by our approach and found that both knock-downs produce loss of invasive potential in a colon cancer cell line. Nested effects models may be a powerful tool for inferring regulatory connections and genes that operate in normal and disease-related processes

Regulation of early steps of GPVI signal transduction by phosphatases: a systems biology approach

We present a data-driven mathematical model of a key initiating step in platelet activation, a central process in the prevention of bleeding following Injury. In vascular disease, this process is activated inappropriately and causes thrombosis, heart attacks and stroke. The collagen receptor GPVI is the primary trigger for platelet activation at sites of injury. Understanding the complex molecular mechanisms initiated by this receptor is important for development of more effective antithrombotic medicines. In this work we developed a series of nonlinear ordinary differential equation models that are direct representations of biological hypotheses surrounding the initial steps in GPVI-stimulated signal transduction. At each stage model simulations were compared to our own quantitative, high-temporal experimental data that guides further experimental design, data collection and model refinement. Much is known about the linear forward reactions within platelet signalling pathways but knowledge of the roles of putative reverse reactions are poorly understood. An initial model, that includes a simple constitutively active phosphatase, was unable to explain experimental data. Model revisions, incorporating a complex pathway of interactions (and specifically the phosphatase TULA-2), provided a good description of the experimental data both based on observations of phosphorylation in samples from one donor and in those of a wider population. Our model was used to investigate the levels of proteins involved in regulating the pathway and the effect of low GPVI levels that have been associated with disease. Results indicate a clear separation in healthy and GPVI deficient states in respect of the signalling cascade dynamics associated with Syk tyrosine phosphorylation and activation. Our approach reveals the central importance of this negative feedback pathway that results in the temporal regulation of a specific class of protein tyrosine phosphatases in controlling the rate, and therefore extent, of GPVI-stimulated platelet activation

Noise Reduction by Diffusional Dissipation in a Minimal Quorum Sensing Motif

Cellular interactions are subject to random fluctuations (noise) in quantities of interacting molecules. Noise presents a major challenge for the robust function of natural and engineered cellular networks. Past studies have analyzed how noise is regulated at the intracellular level. Cell–cell communication, however, may provide a complementary strategy to achieve robust gene expression by enabling the coupling of a cell with its environment and other cells. To gain insight into this issue, we have examined noise regulation by quorum sensing (QS), a mechanism by which many bacteria communicate through production and sensing of small diffusible signals. Using a stochastic model, we analyze a minimal QS motif in Gram-negative bacteria. Our analysis shows that diffusion of the QS signal, together with fast turnover of its transcriptional regulator, attenuates low-frequency components of extrinsic noise. We term this unique mechanism “diffusional dissipation” to emphasize the importance of fast signal turnover (or dissipation) by diffusion. We further show that this noise attenuation is a property of a more generic regulatory motif, of which QS is an implementation. Our results suggest that, in a QS system, an unstable transcriptional regulator may be favored for regulating expression of costly proteins that generate public goods

Determination of Alkali and Halide Monovalent Ion Parameters for Use in Explicitly Solvated Biomolecular Simulations

Alkali (Li+, Na+, K+, Rb+, and Cs+) and halide (F−, Cl−, Br−, and I−) ions play an important role in many biological phenomena, roles that range from stabilization of biomolecular structure, to influence on biomolecular dynamics, to key physiological influence on homeostasis and signaling. To properly model ionic interaction and stability in atomistic simulations of biomolecular structure, dynamics, folding, catalysis, and function, an accurate model or representation of the monovalent ions is critically necessary. A good model needs to simultaneously reproduce many properties of ions, including their structure, dynamics, solvation, and moreover both the interactions of these ions with each other in the crystal and in solution and the interactions of ions with other molecules. At present, the best force fields for biomolecules employ a simple additive, nonpolarizable, and pairwise potential for atomic interaction. In this work, we describe our efforts to build better models of the monovalent ions within the pairwise Coulombic and 6-12 Lennard-Jones framework, where the models are tuned to balance crystal and solution properties in Ewald simulations with specific choices of well-known water models. Although it has been clearly demonstrated that truly accurate treatments of ions will require inclusion of nonadditivity and polarizability (particularly with the anions) and ultimately even a quantum mechanical treatment, our goal was to simply push the limits of the additive treatments to see if a balanced model could be created. The applied methodology is general and can be extended to other ions and to polarizable force-field models. Our starting point centered on observations from long simulations of biomolecules in salt solution with the AMBER force fields where salt crystals formed well below their solubility limit. The likely cause of the artifact in the AMBER parameters relates to the naive mixing of the Smith and Dang chloride parameters with AMBER-adapted Åqvist cation parameters. To provide a more appropriate balance, we reoptimized the parameters of the Lennard-Jones potential for the ions and specific choices of water models. To validate and optimize the parameters, we calculated hydration free energies of the solvated ions and also lattice energies (LE) and lattice constants (LC) of alkali halide salt crystals. This is the first effort that systematically scans across the Lennard-Jones space (well depth and radius) while balancing ion properties like LE and LC across all pair combinations of the alkali ions and halide ions. The optimization across the entire monovalent series avoids systematic deviations. The ion parameters developed, optimized, and characterized were targeted for use with some of the most commonly used rigid and nonpolarizable water models, specifically TIP3P, TIP4PEW, and SPC/E. In addition to well reproducing the solution and crystal properties, the new ion parameters well reproduce binding energies of the ions to water and the radii of the first hydration shells

Monotone and near-monotone biochemical networks

Monotone subsystems have appealing properties as components of larger networks, since they exhibit robust dynamical stability and predictability of responses to perturbations. This suggests that natural biological systems may have evolved to be, if not monotone, at least close to monotone in the sense of being decomposable into a “small” number of monotone components, In addition, recent research has shown that much insight can be attained from decomposing networks into monotone subsystems and the analysis of the resulting interconnections using tools from control theory. This paper provides an expository introduction to monotone systems and their interconnections, describing the basic concepts and some of the main mathematical results in a largely informal fashion

Integrin Clustering Is Driven by Mechanical Resistance from the Glycocalyx and the Substrate

Integrins have emerged as key sensory molecules that translate chemical and physical cues from the extracellular matrix (ECM) into biochemical signals that regulate cell behavior. Integrins function by clustering into adhesion plaques, but the molecular mechanisms that drive integrin clustering in response to interaction with the ECM remain unclear. To explore how deformations in the cell-ECM interface influence integrin clustering, we developed a spatial-temporal simulation that integrates the micro-mechanics of the cell, glycocalyx, and ECM with a simple chemical model of integrin activation and ligand interaction. Due to mechanical coupling, we find that integrin-ligand interactions are highly cooperative, and this cooperativity is sufficient to drive integrin clustering even in the absence of cytoskeletal crosslinking or homotypic integrin-integrin interactions. The glycocalyx largely mediates this cooperativity and hence may be a key regulator of integrin function. Remarkably, integrin clustering in the model is naturally responsive to the chemical and physical properties of the ECM, including ligand density, matrix rigidity, and the chemical affinity of ligand for receptor. Consistent with experimental observations, we find that integrin clustering is robust on rigid substrates with high ligand density, but is impaired on substrates that are highly compliant or have low ligand density. We thus demonstrate how integrins themselves could function as sensory molecules that begin sensing matrix properties even before large multi-molecular adhesion complexes are assembled