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arXiv2012

Positive feedback and temperature mediated molecular switch controls differential gene regulation in Bordetella pertussis

Based on the phosphorelay kinetics operative within BvgAS two component system we propose a mathematical framework for signal transduction and gene regulation of phenotypic phases in Bordetella pertussis. The proposed model identifies a novel mechanism of transcriptional interference between two promoters present in the bvg locus. To understand the system behavior under elevated temperature, the developed model has been studied in two different ways. First, a quasi-steady state analysis has been carried out for the two component system, comprising of sensor BvgS and response regulator BvgA. The quasi-steady state analysis reveals temperature induced sharp molecular switch, leading to amplification in the output of BvgA. Accumulation of a large pool of BvgA thus results into differential regulation of the downstream genes, including the gene encoding toxin. Numerical integration of the full network kinetics is then carried out to explore time dependent behavior of different system components, that qualitatively capture the essential features of experimental results performed in vivo. Furthermore, the developed model has been utilized to study mutants that are impaired in their ability to phosphorylate the transcription factor, BvgA, of the signaling network.

q-bio.MN↗

arXiv2012

Simplifying the Jacobian Criterion for precluding multistationarity in chemical reaction networks

Chemical reaction networks taken with mass-action kinetics are dynamical systems that arise in chemical engineering and systems biology. In general, determining whether a chemical reaction network admits multiple steady states is difficult, as this requires determining existence of multiple positive solutions to a large system of polynomials with unknown coefficients. However, in certain cases, various easy criteria can be applied. One such test is the Jacobian Criterion, due to Craciun and Feinberg, which gives sufficient conditions for ruling out the possibility of multiple steady states. A chemical reaction network is said to pass the Jacobian Criterion if all terms in the determinant expansion of its parametrized Jacobian matrix have the same sign. In this article, we present a procedure which simplifies the application of the Jacobian Criterion, and as a result, we identify a new class of networks for which multiple steady states is precluded: those in which all chemical species have total molecularity of at most two. The total molecularity of a species refers to the sum of all of its stoichiometric coefficients in the network. We illustrate our results by examining enzyme catalysis networks.

math.DS↗

arXiv2011

Protein Hypernetworks: a Logic Framework for Interaction Dependencies and Perturbation Effects in Protein Networks

Motivation: Protein interactions are fundamental building blocks of biochemical reaction systems underlying cellular functions. The complexity and functionality of such systems emerge not from the protein interactions themselves but from the dependencies between these interactions. Therefore, a comprehensive approach for integrating and using information about such dependencies is required. Results: We present an approach for endowing protein networks with interaction dependencies using propositional logic, thereby obtaining protein hypernetworks. First we demonstrate how this framework straightforwardly improves the prediction of protein complexes. Next we show that modeling protein perturbations in hypernetworks, rather than in networks, allows to better infer the functional necessity of proteins for yeast. Furthermore, hypernetworks improve the prediction of synthetic lethal interactions in yeast, indicating their capability to capture high-order functional relations between proteins. Conclusion: Protein hypernetworks are a consistent formal framework for modeling dependencies between protein interactions within protein networks. First applications of protein hypernetworks on the yeast interactome indicate their value for inferring functional features of complex biochemical systems.

q-bio.MN↗

arXiv2011

Stochastic analysis of a miRNA-protein toggle switch

Within systems biology there is an increasing interest in the stochastic behavior of genetic and biochemical reaction networks. An appropriate stochastic description is provided by the chemical master equation, which represents a continuous time Markov chain (CTMC). In this paper we consider the stochastic properties of a biochemical circuit, known to control eukaryotic cell cycle and possibly involved in oncogenesis, recently proposed in the literature within a deterministic framework. Due to the inherent stochasticity of biochemical processes and the small number of molecules involved, the stochastic approach should be more correct in describing the real system: we study the agreement between the two approaches by exploring the system parameter space. We address the problem by proposing a simplified version of the model that allows analytical treatment, and by performing numerical simulations for the full model. We observed optimal agreement between the stochastic and the deterministic description of the circuit in a large range of parameters, but some substantial differences arise in at least two cases: 1) when the deterministic system is in the proximity of a transition from a monostable to a bistable configuration, and 2) when bistability (in the deterministic system) is "masked" in the stochastic system by the distribution tails. The approach provides interesting estimates of the optimal number of molecules involved in the toggle. Our discussion of the points of strengths, potentiality and weakness of the chemical master equation in systems biology and the differences with respect to deterministic modeling are leveraged in order to provide useful advice for both the bioinformatician practitioner and the theoretical scientist.

physics.bio-ph↗

arXiv2011

Perturbed and Permuted: Signal Integration in Network-Structured Dynamic Systems

Biological systems (among others) may respond to a large variety of distinct external stimuli, or signals. These perturbations will generally be presented to the system not singly, but in various combinations, so that a proper understanding of the system response requires assessment of the degree to which the effects of one signal modulate the effects of another. This paper develops a pair of structural metrics for sparse differential equation models of complex dynamic systems and demonstrates that said metrics correlate with proxies of the susceptibility of one signal-response to be altered in the context of a second signal. One of these metrics may be interpreted as a normalized arc density in the neighborhood of certain influential nodes; this metric appears to correlate with increased independence of signal response.

q-bio.QM↗

arXiv2011

Computing fluxes and chemical potential distributions in biochemical networks: energy balance analysis of the human red blood cell

The analysis of non-equilibrium steady states of biochemical reaction networks relies on finding the configurations of fluxes and chemical potentials satisfying stoichiometric (mass balance) and thermodynamic (energy balance) constraints. Efficient methods to explore such states are crucial to predict reaction directionality, calculate physiologic ranges of variability, estimate correlations, and reconstruct the overall energy balance of the network from the underlying molecular processes. While different techniques for sampling the space generated by mass balance constraints are currently available, thermodynamics is generically harder to incorporate. Here we introduce a method to sample the free energy landscape of a reaction network at steady state. In its most general form, it allows to calculate distributions of fluxes and concentrations starting from trial functions that may contain prior biochemical information. We apply our method to the human red blood cell's metabolic network, whose space of mass-balanced flux states has been sampled extensively in recent years. Specifically, we profile its thermodynamically feasible flux configurations, characterizing in detail how fluctuations of fluxes and potentials are correlated. Based on this, we derive the cell's energy balance in terms of entropy production, chemical work done and thermodynamic efficiency.

q-bio.MN↗

arXiv2011

Variable elimination in post-translational modification reaction networks with mass-action kinetics

We define a subclass of Chemical Reaction Networks called Post-Translational Modification systems. Important biological examples of such systems include MAPK cascades and two-component systems which are well-studied experimentally as well as theoretically. The steady states of such a system are solutions to a system of polynomial equations with as many variables as equations. Even for small systems the task of finding the solutions is daunting. We develop a mathematical framework based on the notion of a cut, which provides a linear elimination procedure to reduce the number of variables in the system. The steady states are parameterized algebraically by a set of "core" variables, and the non-negative steady states correspond to non-negative values of the core variables. Further, minimal cuts are the connected components in the species graph and provide conservation laws. A criterion for when a set of independent conservation laws can be derived from cuts is given.

q-bio.MN↗

arXiv2011

Analysis of noise-induced bistability in Michaelis Menten single-step enzymatic cycle

In this paper we study noise-induced bistability in a specific circuit with many biological implications, namely a single-step enzymatic cycle described by Michaelis Menten equations with quasi-steady state assumption. We study the system both with a Master Equation formalism, and with the Fokker-Planck continuous approximation, characterizing the conditions in which the continuous approach is a good approximation of the exact discrete model. An analysis of the stationary distribution in both cases shows that bimodality can not occur in such a system. We discuss which additional requirements can generate stochastic bimodality, by coupling the system with a chemical reaction involving enzyme production and turnover. This extended system shows a bistable behaviour only in specific parameter windows depending on the number of molecules involved, providing hints about which should be a feasible system size in order that such a phenomenon could be exploited in real biological systems.

physics.bio-ph↗

arXiv2011

An iterative feature selection method for GRNs inference by exploring topological properties

An important problem in bioinformatics is the inference of gene regulatory networks (GRN) from temporal expression profiles. In general, the main limitations faced by GRN inference methods is the small number of samples with huge dimensionalities and the noisy nature of the expression measurements. In face of these limitations, alternatives are needed to get better accuracy on the GRNs inference problem. This work addresses this problem by presenting an alternative feature selection method that applies prior knowledge on its search strategy, called SFFS-BA. The proposed search strategy is based on the Sequential Floating Forward Selection (SFFS) algorithm, with the inclusion of a scale-free (Barabási-Albert) topology information in order to guide the search process to improve inference. The proposed algorithm explores the scale-free property by pruning the search space and using a power law as a weight for reducing it. In this way, the search space traversed by the SFFS-BA method combines a breadth-first search when the number of combinations is small ( <= 2) with a depth-first search when the number of combinations becomes explosive ( >= 3), being guided by the scale-free prior information. Experimental results show that the SFFS-BA provides a better inference similarities than SFS and SFFS, keeping the robustness of the SFS and SFFS methods, thus presenting very good results.

cs.CV↗

arXiv2011

Structure and Dynamics of Polynomial Dynamical Systems

Discrete models have a long tradition in engineering, including finite state machines, Boolean networks, Petri nets, and agent-based models. Of particular importance is the question of how the model structure constrains its dynamics. This paper discusses an algebraic framework to study such questions. The systems discussed here are given by mappings on an affine space over a finite field, whose coordinate functions are polynomials. They form a general class of models which can represent many discrete model types. Assigning to such a system its dependency graph, that is, the directed graph that indicates the variable dependencies, provides a mapping from systems to graphs. A basic property of this mapping is derived and used to prove that dynamical systems with an acyclic dependency graph can only have a unique fixed point in their phase space and no periodic orbits. This result is then applied to a published model of in vitro virus competition.

q-bio.MN↗

arXiv2011

Low probability Bid-Bax reaction generates heterogeneity in apoptosis resistance of cancer and cancer stem cells

Variability in the tumorigenic potential among cancer cells within a tumor population is an unresolved fundamental issue in cancer biology. It is important to know whether cancer cells with higher tumorigenic potential, such as cancer stem cells, are only a small subpopulation. We attempt to address the question of variability in tumorigenic potential based on the heterogeneity in apoptosis resistance of cancer cells. We use stochastic differential equations and kinetic Monte Carlo simulations to explore the mechanisms that generate cell-to-cell variability in apoptosis resistance of cancer cells. In our model, a simplified scheme of apoptosis signaling reactions is developed focusing on the proapoptotic Bid-Bax reaction and its inhibition by Bcl-2 like antiapoptotic proteins. We show how a combination of low probability Bid-Bax reaction along with overexpressed reactant molecules allows specific killing of cancer cells, especially under targeted therapy such as Bcl-2 inhibition. This low probability Bid-Bax reaction protects normal cells from accidental apoptosis but generates cell-to-cell stochastic variability in apoptotic activation of cells equipped with overexpressed Bid and Bax molecules. We further demonstrate that cellular variations in Bcl-2 / Bax ratio, within a cancer cell population, can affect the intrinsic fluctuations arising from the stochastic Bid-Bax reaction and thereby provides a mechanism for origin of cells with higher tumorigenic potential. We discuss the implications of our results for cancer therapy, such as, optimal strategies to minimize stochastic fluctuations in cancer cell death.

q-bio.MN↗

arXiv2011

Noise Propagation in Biological and Chemical Reaction Networks

We describe how noise propagates through a network by calculating the variance of the outputs. Using stochastic calculus and dynamical systems theory, we study the network topologies that accentuate or alleviate the effect of random variance in the network for both directed and undirected graphs. Given a linear tree network, the variance in the output is a convex function of the poles of the individual nodes. Cycles create correlations which in turn increase the variance in the output. Feedforward and feedback have a limited effect on noise propagation when the respective cycles is sufficiently long. Crosstalk between the elements of different pathways helps reduce the output noise, but makes the network slower. Next, we study the differences between disturbances in the inputs and disturbances in the network parameters, and how they propagate to the outputs. Finally, we show how noise correlations can affect the steady state of the system in chemical reaction networks with reactions of two or more reactants, each of which may be affected by independent or correlated noise sources.

q-bio.MN↗

arXiv2011

Environmental versatility promotes modularity in genome-scale metabolic networks

The ubiquity of modules in biological networks may result from an evolutionary benefit of a modular organization. For instance, modularity may increase the rate of adaptive evolution, because modules can be easily combined into new arrangements that may benefit their carrier. Conversely, modularity may emerge as a by-product of some trait. We here ask whether this last scenario may play a role in genome-scale metabolic networks that need to sustain life in one or more chemical environments. For such networks, we define a network module as a maximal set of reactions that are fully coupled, i.e., whose fluxes can only vary in fixed proportions. This definition overcomes limitations of purely graph based analyses of metabolism by exploiting the functional links between reactions. We call a metabolic network viable in a given chemical environment if it can synthesize all of an organism's biomass compounds from nutrients in this environment. An organism's metabolism is highly versatile if it can sustain life in many different chemical environments. We here ask whether versatility affects the modularity of metabolic networks.

q-bio.MN↗

arXiv2012

Atoms of multistationarity in chemical reaction networks

Chemical reaction systems are dynamical systems that arise in chemical engineering and systems biology. In this work, we consider the question of whether the minimal (in a precise sense) multistationary chemical reaction networks, which we propose to call `atoms of multistationarity,' characterize the entire set of multistationary networks. Our main result states that the answer to this question is `yes' in the context of fully open continuous-flow stirred-tank reactors (CFSTRs), which are networks in which all chemical species take part in the inflow and outflow. In order to prove this result, we show that if a subnetwork admits multiple steady states, then these steady states can be lifted to a larger network, provided that the two networks share the same stoichiometric subspace. We also prove an analogous result when a smaller network is obtained from a larger network by `removing species.' Our results provide the mathematical foundation for a technique used by Siegal-Gaskins et al. of establishing bistability by way of `network ancestry.' Additionally, our work provides sufficient conditions for establishing multistationarity by way of atoms and moreover reduces the problem of classifying multistationary CFSTRs to that of cataloging atoms of multistationarity. As an application, we enumerate and classify all 386 bimolecular and reversible two-reaction networks. Of these, exactly 35 admit multiple positive steady states. Moreover, each admits a unique minimal multistationary subnetwork, and these subnetworks form a poset (with respect to the relation of `removing species') which has 11 minimal elements (the atoms of multistationarity).

math.DS↗

arXiv2011

PUB-MS - a mass-spectrometry-based method to monitor protein-protein proximity in vivo

The common techniques to study protein-protein proximity in vivo are not well-adapted to the capabilities and the expertise of a standard proteomics laboratory, typically based on the use of mass spectrometry. With the aim of closing this gap, we have developed PUB-MS (for Proximity Utilizing Biotinylation and Mass Spectrometry), an approach to monitor protein-protein proximity, based on biotinylation of a protein fused to a biotin-acceptor peptide (BAP) by a biotin-ligase, BirA, fused to its interaction partner. The biotinylation status of the BAP can be further detected by either Western analysis or mass spectrometry. The BAP sequence was redesigned for easy monitoring of the biotinylation status by LC-MS/MS. In several experimental models, we demonstrate that the biotinylation in vivo is specifically enhanced when the BAP- and BirA- fused proteins are in proximity to each other. The advantage of mass spectrometry is demonstrated by using BAPs with different sequences in a single experiment (allowing multiplex analysis) and by the use of stable isotopes. Finally, we show that our methodology can be also used to study a specific subfraction of a protein of interest that was in proximity with another protein at a predefined time before the analysis.

q-bio.MN↗

arXiv2011

Biological network comparison via Ipsen-Mikhailov distance

Highlighting similarities and differences between networks is an informative task in investigating many biological processes. Typical examples are detecting differences between an inferred network and the corresponding gold standard, or evaluating changes in a dynamic network along time. Although fruitful insights can be drawn by qualitative or feature-based methods, a distance must be used whenever a quantitative assessment is required. Here we introduce the Ipsen-Mikhailov metric for biological network comparison, based on the difference of the distributions of the Laplacian eigenvalues of the compared graphs. Being a spectral measure, its focus is on the general structure of the net so it can overcome the issues affecting local metrics such as the edit distances. Relation with the classical Matthews Correlation Coefficient (MCC) is discussed, showing the finer discriminant resolution achieved by the Ipsen-Mikhailov metric. We conclude with three examples of application in functional genomic tasks, including stability of network reconstruction as robustness to data subsampling, variability in dynamical networks and differences in networks associated to a classification task.

q-bio.MN↗

arXiv2011

Stochastic modeling of p53-regulated apoptosis upon radiation damage

We develop and study the evolution of a model of radiation induced apoptosis in cells using stochastic simulations, and identified key protein targets for effective mitigation of radiation damage. We identified several key proteins associated with cellular apoptosis using an extensive literature survey. In particular, we focus on the p53 transcription dependent and p53 transcription independent pathways for mitochondrial apoptosis. Our model reproduces known p53 oscillations following radiation damage. The key, experimentally testable hypotheses that we generate are - inhibition of PUMA is an effective strategy for mitigation of radiation damage if the treatment is administered immediately, at later stages following radiation damage, inhibition of tBid is more effective.

physics.bio-ph↗

arXiv2011

A Formal Verification Approach to the Design of Synthetic Gene Networks

The design of genetic networks with specific functions is one of the major goals of synthetic biology. However, constructing biological devices that work "as required" remains challenging, while the cost of uncovering flawed designs experimentally is large. To address this issue, we propose a fully automated framework that allows the correctness of synthetic gene networks to be formally verified in silico from rich, high level functional specifications. Given a device, we automatically construct a mathematical model from experimental data characterizing the parts it is composed of. The specific model structure guarantees that all experimental observations are captured and allows us to construct finite abstractions through polyhedral operations. The correctness of the model with respect to temporal logic specifications can then be verified automatically using methods inspired by model checking. Overall, our procedure is conservative but it can filter through a large number of potential device designs and select few that satisfy the specification to be implemented and tested further experimentally. Illustrative examples of the application of our methods to the design of simple synthetic gene networks are included.

eess.SY↗