# Quantitative Biology - Molecular Networks Publications (50)

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## Quantitative Biology - Molecular Networks Publications

A computation-oriented representation of uncertain kinetic systems is introduced and analysed in this paper. It is assumed that the monomial coefficients of the ODEs belong to a polytopic set, which defines a set of dynamical systems for an uncertain model. An optimization-based computation model is proposed for the structural analysis of uncertain models. Read More

We propose new activity-dependent adaptive Boolean networks inspired by the cis-regulatory mechanism in gene regulatory networks. We analytically show that our model can be solved for stationary in-degree distribution for a wide class of update rules by employing the annealed approximation of Boolean network dynamics and that evolved Boolean networks have a preassigned average sensitivity that can be set independently of update rules. In particular, when it is set to 1, our theory predicts that the proposed network rewiring algorithm drives Boolean networks towards criticality. Read More

A central goal in cancer genomics is to identify the somatic alterations that underpin tumor initiation and progression. This task is challenging as the mutational profiles of cancer genomes exhibit vast heterogeneity, with many alterations observed within each individual, few shared somatically mutated genes across individuals, and important roles in cancer for both frequently and infrequently mutated genes. While commonly mutated cancer genes are readily identifiable, those that are rarely mutated across samples are difficult to distinguish from the large numbers of other infrequently mutated genes. Read More

We consider the problem of inferring the probability distribution of flux configurations in metabolic network models from empirical flux data. For the simple case in which experimental averages are to be retrieved, data are described by a Boltzmann-like distribution ($\propto e^{F/T}$) where $F$ is a linear combination of fluxes and the `temperature' parameter $T\geq 0$ allows for fluctuations. The zero-temperature limit corresponds to a Flux Balance Analysis scenario, where an objective function ($F$) is maximized. Read More

Model-based prediction of stochastic noise in biomolecular reactions often resorts to approximation with unknown precision. As a result, unexpected stochastic fluctuation causes a headache for the designers of biomolecular circuits. This paper proposes a convex optimization approach to quantifying the steady state moments of molecular copy counts with theoretical rigor. Read More

Signaling in enzymatic networks is typically triggered by environmental fluctuations, resulting in a series of stochastic chemical reactions, leading to corruption of the signal by noise. For example, information flow is initiated by binding of extracellular ligands to receptors, which is transmitted through a {cascade involving} kinase-phosphatase stochastic chemical reactions. For a class of such networks, we develop a general field-theoretic approach in order to calculate the error in signal transmission as a function of an appropriate control variable. Read More

Given a conjunctive Boolean network (CBN) with $n$ state-variables, we consider the problem of finding a minimal set of state-variables to directly affect with an input so that the resulting conjunctive Boolean control network (CBCN) is controllable. We give a necessary and sufficient condition for controllability of a CBCN; an $O(n^2)$-time algorithm for testing controllability; and prove that nonetheless the minimal controllability problem for CBNs is NP-hard. Read More

Boolean networks is a well-established formalism for modelling biological systems. A vital challenge for analysing a Boolean network is to identify all the attractors. This becomes more challenging for large asynchronous Boolean networks, due to the asynchronous updating scheme. Read More

Biochemical reaction networks frequently consist of species evolving on multiple timescales. Stochastic simulations of such networks are often computationally challenging and therefore various methods have been developed to obtain sensible stochastic approximations on the timescale of interest. One of the rigorous and popular approaches is the multiscale approximation method for continuous time Markov processes. Read More

Understanding gene regulation is a fundamental step towards understanding of how cells function and respond to environmental cues and perturbations. An important step in this direction is to infer the transcription factor-gene regulatory network (GRN). However gene regulatory networks are typically constructed disregarding the fact that regulatory programs are conditioned on tissue type, developmental stage, sex, and other factors. Read More

Hyperamylinemia, a condition characterized by above-normal blood levels of the pancreas-derived peptide amylin, accompanies obesity and precedes type II diabetes. Human amylin oligomerizes easily and can deposit in the pancreas, brain, and heart, where they have been associated with calcium dysregulation. In the heart, accumulating evidence suggests that human amylin oligomers form modestly cation-selective, voltage-dependent ion channels that embed in the cell sarcolemma (SL). Read More

Cells receive signaling molecules by receptors and relay the information via sensory networks so that they can respond properly depending on the type of signals. Recent studies show that cells can extract multi-dimensional information from dynamical concentration patterns of signaling molecules. Here we study how cells generally and optimally process multi-dimensional information embedded in dynamical patterns through biochemical networks. Read More

We study an optimal control problem arising from a resource allocation problem in cellular metabolism. A minimalistic model that describes the production of enzymatic vs. non-enzymatic biomass components from a single nutrient source is introduced. Read More

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. Read More

Research of homogeneous (i.e., single node and edge type) biological networks (BNs) has received significant attention. Read More

Gene Ontology (GO) terms are frequently used to score alignments between protein-protein interaction (PPI) networks. Methods exist to measure the GO similarity between two proteins in isolation, but pairs of proteins in a network alignment are not isolated: each pairing is implicitly dependent upon every other pairing via the alignment itself. Current methods fail to take into account the frequency of GO terms across the networks, and attempt to account for common GO terms in an ad hoc fashion by imposing arbitrary rules on when to "allow" GO terms based on their location in the GO hierarchy, rather than using readily available frequency information in the PPI networks themselves. Read More

A stochastic version of the Barkai-Leibler model of chemotaxis receptors in {\it E. coli} is studied here to elucidate the effects of intrinsic network noise in their conformational dynamics. It was originally proposed to explain the robust and near-perfect adaptation of {\it E. Read More

In living cells, biochemical reactions are catalyzed by specific enzymes and connect to one another by sharing substrates and products, forming complex networks. In our previous studies, we established a framework determining the responses to enzyme perturbations only from network topology, and then proved a theorem, called the law of localization, explaining response patterns in terms of network topology. In this paper, we generalize these results to reaction networks with conserved concentrations, which allows us to study any reaction systems. Read More

Causal ordering of key events in the cell cycle is essential for proper functioning of an organism. Yet, it remains a mystery how a specific temporal program of events is maintained despite ineluctable stochasticity in the biochemical dynamics which dictate timing of cellular events. We propose that if a change of cell fate is triggered by the {\em time-integral} of the underlying stochastic biochemical signal, rather than the original signal, then a dramatic improvement in temporal specificity results. Read More

In discrete modelling of biological network, Boolean variables are mainly used and many tools and theorems are available for analysis of Boolean models. However, multilevel variables are often required to account for threshold effects, in which knowledge of the Boolean case does not generalise straightforwardly. This motivated the development of conversion methods for multilevel to Boolean models. Read More

We describe and analyse Levenberg-Marquardt methods for solving systems of nonlinear equations. More specifically, we first propose an adaptive formula for the Levenberg-Marquardt parameter and analyse the local convergence of the method under H\"{o}lder metric subregularity. We then introduce a bounded version of the Levenberg-Marquardt parameter and analyse the local convergence of the modified method under the \L ojasiewicz gradient inequality. Read More

Understanding the relationship between spontaneous stochastic fluctuations and the topology of the underlying gene regulatory network is fundamental for the study of gene expression, especially at the molecular level. Here by solving the analytical steady-state distribution of the protein copy number in a general kinetic model of gene expression, we reveal a quantitative relation between stochastic fluctuations and feedback regulation at the single-molecule level, which provides novel insights into how and to what extent a feedback loop can enhance or suppress molecular fluctuations. Based on such relation, we also develop an effective method to extract the topological information of gene regulatory networks from single-cell gene expression data. Read More

An Elementary Flux Mode (EFM) is a pathway with minimum set of reactions that are functional in steady-state constrained space. Due to the high computational complexity of calculating EFMs, different approaches have been proposed to find these flux-balanced pathways. In this paper, an approach to find a subset of EFMs is proposed based on a graph data model. Read More

Gene regulation is a series of processes that control gene expression and its extent. The connections among genes and their regulatory molecules, usually transcription factors, and a descriptive model of such connections, are known as gene regulatory networks (GRNs). Elucidating GRNs is crucial to understand the inner workings of the cell and the complexity of gene interactions. Read More

Biochemical feedback leads to dynamical transitions between cellular states, reminiscent of phase transitions in equilibrium systems. Yet cells are far from equilibrium. Here we show using a generic birth-death model that despite being far from equilibrium, biochemical feedback near a bifurcation point exhibits the scaling exponents of the mean-field universality class. Read More

In the immune system, T cells can quickly discriminate between foreign and self ligands with high accuracy. There is significant evidence T-cells achieve this remarkable performance utilizing a network architecture based on kinetic proofreading (KPR). KPR-based mechanisms actively consume energy to increase the specificity beyond what is possible in equilibrium. Read More

Gene expression is a noisy process and several mechanisms, both transcriptional and posttranscriptional, can stabilize protein levels in cells. Much work has focused on the role of miRNAs, showing in particular that miRNA-mediated regulation can buffer expression noise for lowly expressed genes. Here, using in silico simulations and mathematical modeling, we demonstrate that miRNAs can exert a much broader influence on protein levels by orchestrating competition-induced crosstalk between mRNAs. Read More

Which properties of metabolic networks can be derived solely from stoichiometric information about the network's constituent reactions? Predictive results have been obtained by Flux Balance Analysis (FBA), by postulating that cells set metabolic fluxes within the allowed stoichiometry so as to maximize their growth. Here, we generalize this framework to single cell level using maximum entropy models from statistical physics. We define and compute, for the core metabolism of Escherichia coli, a joint distribution over all fluxes that yields the experimentally observed growth rate. Read More

Microbial communities frequently communicate via quorum sensing (QS), where cells produce, secrete, and respond to a threshold level of an autoinducer (AI) molecule, thereby modulating gene expression. However, the biology of QS remains incompletely understood in heterogeneous communities, where variant bacterial strains possess distinct QS systems that produce chemically unique AIs. AI molecules bind to 'cognate' receptors, but also to 'non-cognate' receptors found in other strains, resulting in inter-strain crosstalk. Read More

In this work it is shown that scale free tails in metabolic flux distributions inferred from realistic large scale models can be simply an artefact due to reactions involved in thermodynamically unfeasible cycles, that are unbounded by physical constraints and would be able to perform work without expenditure of free energy. After correcting for thermodynamics, the metabolic space scales meaningfully with the physical limiting factors, acquiring in turn a richer multimodal structure potentially leading to symmetry breaking while optimizing for objective functions. Read More

Many microbial systems are known to actively reshape their proteomes in response to changes in growth conditions induced e.g. by nutritional stress or antibiotics. Read More

We quantify the amount of regulation required to control growth in living cells by a Maximum Entropy approach to the space of underlying metabolic states described by genome-scale models. Results obtained for E. coli and human cells are consistent with experiments and point to different regulatory strategies by which growth can be fostered or repressed. Read More

While we once thought of cancer as single monolithic diseases affecting a specific organ site, we now understand that there are many subtypes of cancer defined by unique patterns of gene mutations. These gene mutational data, which can be more reliably obtained than gene expression data, help to determine how the subtypes develop, evolve, and respond to therapies. Different from dense continuous-value gene expression data, which most existing cancer subtype discovery algorithms use, somatic mutational data are extremely sparse and heterogeneous, because there are less than 0. Read More

Oscillations in a stochastic dynamical system, whose deterministic counterpart has a stable steady state, are a widely reported phenomenon. Traditional methods of finding parameter regimes for stochastically-driven resonances are, however, cumbersome for any but the smallest networks. In this letter we show by example of the Brusselator how to use real root counting algorithms and graph theoretic tools to efficiently determine the number of resonant modes and parameter ranges for stochastic oscillations. Read More

This paper is concerned with the problem of stochastic control of gene regulatory networks (GRNs) observed indirectly through noisy measurements and with uncertainty in the intervention inputs. The partial observability of the gene states and uncertainty in the intervention process are accounted for by modeling GRNs using the partially-observed Boolean dynamical system (POBDS) signal model with noisy gene expression measurements. Obtaining the optimal infinite-horizon control strategy for this problem is not attainable in general, and we apply reinforcement learning and Gaussian process techniques to find a near-optimal solution. Read More

Partially-observed Boolean dynamical systems (POBDS) are a general class of nonlinear models with application in estimation and control of Boolean processes based on noisy and incomplete measurements. The optimal minimum mean square error (MMSE) algorithms for POBDS state estimation, namely, the Boolean Kalman filter (BKF) and Boolean Kalman smoother (BKS), are intractable in the case of large systems, due to computational and memory requirements. To address this, we propose approximate MMSE filtering and smoothing algorithms based on the auxiliary particle filter (APF) method from sequential Monte-Carlo theory. Read More

The learning rate is an information-theoretical quantity for bipartite Markov chains describing two coupled subsystems. It is defined as the rate at which transitions in the downstream subsystem tend to increase the mutual information between the two subsystems, and is bounded by the dissipation arising from these transitions. Its physical interpretation, however, is unclear, although it has been used as a metric for the sensing performance of the downstream subsystem. Read More

The stochastic dynamics of networks of biochemical reactions in living cells are typically modelled using chemical master equations (CMEs). The stationary distributions of CMEs are seldom solvable analytically, and few methods exist that yield numerical estimates with computable error bounds. Here, we present two such methods based on mathematical programming techniques. Read More

Assuming a steady-state condition within a cell, metabolic fluxes satisfy an under-determined linear system of stoichiometric equations. Characterizing the space of fluxes that satisfy such equations along with given bounds (and possibly additional relevant constraints) is considered of utmost importance for the understanding of cellular metabolism. Extreme values for each individual flux can be computed with Linear Programming (as Flux Balance Analysis), and their marginal distributions can be approximately computed with Monte-Carlo sampling. Read More

Signal transduction within biological cells is governed by networks of interacting proteins. Communication between these proteins is mediated by signaling molecules which bind to receptors and induce stochastic transitions between different conformational states. Signaling is typically a cooperative process which requires the occurrence of multiple binding events so that reaction rates have a nonlinear dependence on the amount of signaling molecule. Read More

Inverse problems in statistical physics are motivated by the challenges of `big data' in different fields, in particular high-throughput experiments in biology. In inverse problems, the usual procedure of statistical physics needs to be reversed: Instead of calculating observables on the basis of model parameters, we seek to infer parameters of a model based on observations. In this review, we focus on the inverse Ising problem and closely related problems, namely how to infer the interactions between spins given observed spin correlations, magnetisations, or other data. Read More

The study of Chemical Reaction Networks (CRN's) is a very active field. Earlier well-known results \cite{Feinberg:def_01:87, Anderson:product_dist:10} identify a topological quantity called deficiency, for any CRN, which, when exactly equal to zero, leads to a unique factorized steady-state for these networks. No results exist however for the steady states of non-zero-deficiency networks. Read More

Chemical reaction networks with generalized mass-action kinetics lead to power-law dynamical systems. As a simple example, we consider the Lotka reactions and the resulting planar ODE. We characterize the parameters (positive coefficients and real exponents) for which the unique positive equilibrium is a center. Read More

Improved understanding of molecular systems has only emphasised the sophistication of networks within the cell. Simultaneously, the advance of nucleic acid nanotechnology, a platform within which reactions can be exquisitely controlled, has made the development of artificial architectures and devices possible. Vital to this progress has been a solid foundation in the thermodynamics of molecular systems. Read More

The sampling of scale-free networks in Molecular Biology is usually achieved by growing networks from a seed using recursive algorithms with elementary moves which include the addition and deletion of nodes and bonds. These algorithms include the Barabasi-Albert algorithm. Later algorithms, such as the Duplication-Divergence algorithm, the Sol\'e algorithm and the iSite algorithm, were inspired by biological processes underlying the evolution of protein networks, and the networks they produce differ essentially from networks grown by the Barabasi-Albert algorithm. Read More

Background: MicroRNAs (miRNAs) play multiple roles in tumor biology [1]. Interestingly, reports from multiple groups suggest that miRNA targets may be coupled through competitive stoichiometric sequestration [2]. Specifically, computational models predicted [3, 4] and experimental assays confirmed [5, 6] that miRNA activity is dependent on miRNA target abundance, and consequently, changes to the abundance of some miRNA targets lead to changes to the regulation and abundance of their other targets. Read More

Computational techniques are required for narrowing down the vast space of possibilities to plausible prebiotic scenarios, since precise information on the molecular composition, the dominant reaction chemistry, and the conditions for that era are scarce. The exploration of large chemical reaction networks is a central aspect in this endeavour. While quantum chemical methods can accurately predict the structures and reactivities of small molecules, they are not efficient enough to cope with large-scale reaction systems. Read More

Genetic oscillators are present in the cells of many organisms and control several biological processes. The common feature of such oscillators is the presence of a protein which represses the transcription of its own gene. Recently, it has been shown that for many genes transcription is not a continuous process, but that it proceeds in bursts. Read More

The major biochemical networks of the living cell, the network of interacting genes and the network of biochemical reactions, are highly interdependent, however, they have been studied mostly as separate systems so far. In the last years an appropriate theoretical framework for studying interdependent networks has been developed in the context of statistical physics. Here we study the interdependent network of gene regulation and metabolism of the model organism Escherichia coli using the theoretical framework of interdependent networks. Read More

Networks can model real-world systems in a variety of domains. Network alignment (NA) aims to find a node mapping that conserves similar regions between compared networks. NA is applicable to many fields, including computational biology, where NA can guide the transfer of biological knowledge from well- to poorly-studied species across aligned network regions. Read More