Toward a comprehensive language for biological systems

Rule-based modeling has become a powerful approach for modeling intracellular networks, which are characterized by rich molecular diversity. Truly comprehensive models of cell behavior, however, must address spatial complexity at both the intracellular level and at the level of interacting populations of cells, and will require richer modeling languages and tools. A recent paper in BMC Systems Biology represents a signifcant step toward the development of a unified modeling language and software platform for the development of multi-level, multiscale biological models

Syntactic Markovian Bisimulation for Chemical Reaction Networks

In chemical reaction networks (CRNs) with stochastic semantics based on continuous-time Markov chains (CTMCs), the typically large populations of species cause combinatorially large state spaces. This makes the analysis very difficult in practice and represents the major bottleneck for the applicability of minimization techniques based, for instance, on lumpability. In this paper we present syntactic Markovian bisimulation (SMB), a notion of bisimulation developed in the Larsen-Skou style of probabilistic bisimulation, defined over the structure of a CRN rather than over its underlying CTMC. SMB identifies a lumpable partition of the CTMC state space a priori, in the sense that it is an equivalence relation over species implying that two CTMC states are lumpable when they are invariant with respect to the total population of species within the same equivalence class. We develop an efficient partition-refinement algorithm which computes the largest SMB of a CRN in polynomial time in the number of species and reactions. We also provide an algorithm for obtaining a quotient network from an SMB that induces the lumped CTMC directly, thus avoiding the generation of the state space of the original CRN altogether. In practice, we show that SMB allows significant reductions in a number of models from the literature. Finally, we study SMB with respect to the deterministic semantics of CRNs based on ordinary differential equations (ODEs), where each equation gives the time-course evolution of the concentration of a species. SMB implies forward CRN bisimulation, a recently developed behavioral notion of equivalence for the ODE semantics, in an analogous sense: it yields a smaller ODE system that keeps track of the sums of the solutions for equivalent species.Comment: Extended version (with proofs), of the corresponding paper published at KimFest 2017 (http://kimfest.cs.aau.dk/

Efficient Syntax-Driven Lumping of Differential Equations

We present an algorithm to compute exact aggregations of a class of systems of ordinary differential equations (ODEs). Our approach consists in an extension of Paige and Tarjan’s seminal solution to the coarsest refinement problem by encoding an ODE system into a suitable discrete-state representation. In particular, we consider a simple extension of the syntax of elementary chemical reaction networks because (i) it can express ODEs with derivatives given by polynomials of degree at most two, which are relevant in many applications in natural sciences and engineering; and (ii) we can build on two recently introduced bisimulations, which yield two complementary notions of ODE lumping. Our algorithm computes the largest bisimulations in O(r⋅s⋅logs)O(r⋅s⋅log⁡s) time, where r is the number of monomials and s is the number of variables in the ODEs. Numerical experiments on real-world models from biochemistry, electrical engineering, and structural mechanics show that our prototype is able to handle ODEs with millions of variables and monomials, providing significant model reductions

KaDE: A Tool to Compile Kappa Rules into (Reduced) ODE Models

Tools paper trackInternational audienceKappa is a formal language that can be used to model sys- tems of biochemical interactions among proteins. It offers several se- mantics to describe the behaviour of Kappa models at different levels of abstraction. Each Kappa model is a set of context-free rewrite rules. One way to understand the semantics of a Kappa model is to read its rules as an implicit description of a (potentially infinite) reaction net- work. KaDE is interpreting this definition to compile Kappa models into reaction networks (or equivalently into sets of ordinary differential equations). KaDE uses a static analysis that identifies pairs of sites that are indistinguishable from the rules point of view, to infer backward and forward bisimulations, hence reducing the size of the underlying reaction networks without having to generate them explicitly. In this paper, we describe the main current functionalities of KaDE and we give some benchmarks on case studies

The CD34-Related Molecule Podocalyxin Is a Potent Inducer of Microvillus Formation

BACKGROUND: Podocalyxin is a CD34-related transmembrane protein involved in hematopoietic cell homing, kidney morphogenesis, breast cancer progression, and epithelial cell polarization. Although this sialomucin has been shown to block cell adhesion, the mechanisms involved remain enigmatic. It has, however, been postulated that the adaptor proteins NHERF-1 and 2 could regulate apical targeting of Podocalyxin by linking it to the actin cytoskeleton. PRINCIPAL FINDINGS: Here, in contrast, we find that full-length Podocalyxin acts to recruit NHERF-1 to the apical domain. Moreover, we show that ectopic expression of Podocalyxin in epithelial cells leads to microvillus formation along an expanded apical domain that extends laterally to the junctional complexes. Removal of the C-terminal PDZ-binding domain of Podocalyxin abolishes NHERF-1 recruitment but, surprisingly, has no effect on the formation of microvilli. Instead, we find that the extracellular domain and transmembrane region of Podocalyxin are sufficient to direct recruitment of filamentous actin and ezrin to the plasma membrane and induce microvillus formation. CONCLUSIONS/SIGNIFICANCE: Our data suggest that this single molecule can modulate NHERF localization and, independently, act as a key orchestrator of apical cell morphology, thereby lending mechanistic insights into its multiple roles as a polarity regulator, tumor progression marker, and anti-adhesin

Rule-based modelling provides an extendable framework for comparing candidate mechanisms underpinning clathrin polymerisation

Abstract Polymerisation of clathrin is a key process that underlies clathrin-mediated endocytosis. Clathrin-coated vesicles are responsible for cell internalization of external substances required for normal homeostasis and life –sustaining activity. There are several hypotheses describing formation of closed clathrin structures. According to one of the proposed mechanisms cage formation may start from a flat lattice buildup on the cellular membrane, which is later transformed into a curved structure. Creation of the curved surface requires rearrangement of the lattice, induced by additional molecular mechanisms. Different potential mechanisms require a modeling framework that can be easily modified to compare between them. We created an extendable rule-based model that describes polymerisation of clathrin molecules and various scenarios of cage formation. Using Global Sensitivity Analysis (GSA) we obtained parameter sets describing clathrin pentagon closure and the emergence/production and closure of large-size clathrin cages/vesicles. We were able to demonstrate that the model can reproduce budding of the clathrin cage from an initial flat array

Statistical abstraction for multi-scale spatio-temporal systems

Spatio-temporal systems exhibiting multi-scale behaviour are common in applications ranging from cyber-physical systems to systems biology, yet they present formidable challenges for computational modelling and analysis. Here we consider a prototypic scenario where spatially distributed agents decide their movement based on external inputs and a fast-equilibrating internal computation. We propose a generally applicable strategy based on statistically abstracting the internal system using Gaussian Processes, a powerful class of non-parametric regression techniques from Bayesian Machine Learning. We show on a running example of bacterial chemotaxis that this approach leads to accurate and much faster simulations in a variety of scenarios.Comment: 14th International Conference on Quantitative Evaluation of SysTems (QEST 2017

Search for Gravitational Waves from Primordial Black Hole Binary Coalescences in the Galactic Halo

We use data from the second science run of the LIGO gravitational-wave detectors to search for the gravitational waves from primordial black hole (PBH) binary coalescence with component masses in the range 0.2--$1.0 M_\odot$. The analysis requires a signal to be found in the data from both LIGO observatories, according to a set of coincidence criteria. No inspiral signals were found. Assuming a spherical halo with core radius 5 kpc extending to 50 kpc containing non-spinning black holes with masses in the range 0.2--$1.0 M_\odot$, we place an observational upper limit on the rate of PBH coalescence of 63 per year per Milky Way halo (MWH) with 90% confidence.Comment: 7 pages, 4 figures, to be submitted to Phys. Rev.

The priming effect of extracellular UTP on human neutrophils: Role of calcium released from thapsigargin-sensitive intracellular stores

P2Y2 receptors, which are equally responsive to ATP and UTP, can trigger intracellular signaling events, such as intracellular calcium mobilization and mitogen-activated protein (MAP) kinase phosphorylation in polymorphonuclear leukocytes (PMN). Moreover, extracellular nucleotides have been shown to prime chemoattractant-induced superoxide production. The aim of our study was to investigate the mechanism responsible for the priming effect of extracellular nucleotides on reactive oxygen species (ROS) production induced in human neutrophils by two different chemoattractants: formyl-methionyl-leucyl-phenylalanine (fMLP) and interleukin-8 (IL-8). Nucleotide-induced priming of ROS production was concentration- and time-dependent. When UTP was added to neutrophil suspensions prior to chemoattractant, the increase of the response reached the maximum at 1 min of pre-incubation with the nucleotide. UTP potentiated the phosphorylation of p44/42 and p38 MAP kinases induced by chemoattractants, however the P2 receptor-mediated potentiation of ROS production was still detectable in the presence of a SB203580 or U0126, supporting the view that MAP kinases do not play a major role in regulating the nucleotide-induced effect. In the presence of thapsigargin, an inhibitor of the ubiquitous sarco-endoplasmic reticulum Ca2+-ATPases in mammalian cells, the effect of fMLP was not affected, but UTP-induced priming was abolished, suggesting that the release of calcium from thapsigargin-sensitive intracellular stores is essential for nucleotide-induced priming in human neutrophils

Machines vs. Ensembles: Effective MAPK Signaling through Heterogeneous Sets of Protein Complexes

A grant from the One-University Open Access Fund at the University of Kansas was used to defray the author’s publication fees in this Open Access journal. The Open Access Fund, administered by librarians from the KU, KU Law, and KUMC libraries, is made possible by contributions from the offices of KU Provost, KU Vice Chancellor for Research & Graduate Studies, and KUMC Vice Chancellor for Research. For more information about the Open Access Fund, please see http://library.kumc.edu/authors-fund.xml.Despite the importance of intracellular signaling networks, there is currently no consensus regarding the fundamental nature of the protein complexes such networks employ. One prominent view involves stable signaling machines with well-defined quaternary structures. The combinatorial complexity of signaling networks has led to an opposing perspective, namely that signaling proceeds via heterogeneous pleiomorphic ensembles of transient complexes. Since many hypotheses regarding network function rely on how we conceptualize signaling complexes, resolving this issue is a central problem in systems biology. Unfortunately, direct experimental characterization of these complexes has proven technologically difficult, while combinatorial complexity has prevented traditional modeling methods from approaching this question. Here we employ rule-based modeling, a technique that overcomes these limitations, to construct a model of the yeast pheromone signaling network. We found that this model exhibits significant ensemble character while generating reliable responses that match experimental observations. To contrast the ensemble behavior, we constructed a model that employs hierarchical assembly pathways to produce scaffold-based signaling machines. We found that this machine model could not replicate the experimentally observed combinatorial inhibition that arises when the scaffold is overexpressed. This finding provides evidence against the hierarchical assembly of machines in the pheromone signaling network and suggests that machines and ensembles may serve distinct purposes in vivo. In some cases, e.g. core enzymatic activities like protein synthesis and degradation, machines assembled via hierarchical energy landscapes may provide functional stability for the cell. In other cases, such as signaling, ensembles may represent a form of weak linkage, facilitating variation and plasticity in network evolution. The capacity of ensembles to signal effectively will ultimately shape how we conceptualize the function, evolution and engineering of signaling networks