# Quantitative Biology - Molecular Networks Publications (50)

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## Quantitative Biology - Molecular Networks Publications

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

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 equa- tions 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 distribu- tions 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

Astrocytes affect neural transmission by a tight control via glutamate transporters on glutamate concentrations in direct vicinity to the synaptic cleft and by extracellular glutamate. Their relevance for information representation has been supported by in-vivo studies in ferret and mouse primary visual cortex. In ferret blocking glutamate transport pharmacologically broadened tuning curves and enhanced the response at preferred orientation. Read More

Many biochemical reactions involve a stream of chemical reactants (ligand molecules) flowing over a surface to which other reactants (receptors) are confined. Scientists measure rate constants associated with these reactions in an optical biosensor: an instrument in which ligand molecules are convected through a flow cell, over a surface on which receptors are immobilized. In applications such as DNA damage repair multiple simultaneous reactions occur on the surface of the biosensor. Read More

P-values are being computed for increasingly complicated statistics but lacking evaluations on their quality. Meanwhile, accurate p-values enable significance comparison across batches of hypothesis tests and consequently unified false discover rate (FDR) control. This article discusses two related questions in this setting. Read More

We introduce an in silico model for the initial spread of an aberrant phenotype with Warburg-like overflow metabolism within a healthy homeostatic tissue in contact with a nutrient reservoir (the blood), aimed at characterizing the role of the microenvironment for aberrant growth. Accounting for cellular metabolic activity, competition for nutrients, spatial diffusion and their feedbacks on aberrant replication and death rates, we obtain a phase portrait where distinct asymptotic whole-tissue states are found upon varying the tissue-blood turnover rate and the level of blood-borne primary nutrient. Over a broad range of parameters, the spreading dynamics is bistable as random fluctuations can impact the final state of the tissue. Read More

Cancer complexome comprises a heterogeneous and multifactorial milieu that varies in cytology, physiology, signaling mechanisms and response to therapy. The combined framework of network theory and spectral graph theory along with the multilayer anal- ysis provides a comprehensive approach to analyze the proteomic data of seven different cancers, namely, breast, oral, ovarian, cervical, lung, colon and prostate. Our analysis demonstrates that the protein-protein interaction networks of the normal and the cancerous tissues associated with the seven cancers have overall similar structural and spectral properties. Read More

Signal transducers and activators of transcription (STATs) are key molecular determinants of T cell fate and effector function. A number of inflammatory diseases are characterized by an altered balance of T cell phenotypes and cytokine secretion. STATs, therefore, represent viable therapeutic targets in numerous pathologies. Read More

Competition to bind microRNAs induces an effective positive crosstalk between their targets, therefore known as `competing endogenous RNAs' or ceRNAs. While such an effect is known to play a significant role in specific conditions, estimating its strength from data and, experimentally, in physiological conditions appears to be far from simple. Here we show that the susceptibility of ceRNAs to different types of perturbations affecting their competitors (and hence their tendency to crosstalk) can be encoded in quantities as intuitive and as simple to measure as correlation functions. Read More

About half of human cancers show normal TP53 gene and aberrant overexpression of Mdm2 and/or MdmX. This fact promotes a promising cancer therapeutic strategy which targeting the interactions between p53 and Mdm2/MdmX. For developing the inhibitors to disrupt the p53-Mdm2/MdmX interactions, we systematically investigate structural and interaction characteristics of p53 and inhibitors with Mdm2 and MdmX from atomistic level by exploiting stochastic molecular dynamics simulations. Read More

**Affiliations:**

^{1}Michigan State University,

^{2}Michigan State University,

^{3}Michigan State University,

^{4}Michigan State University

While all organisms on Earth descend from a common ancestor, there is no consensus on whether the origin of this ancestral self-replicator was a one-off event or whether it was only the final survivor of multiple origins. Here we use the digital evolution system Avida to study the origin of self-replicating computer programs. By using a computational system, we avoid many of the uncertainties inherent in any biochemical system of self-replicators (while running the risk of ignoring a fundamental aspect of biochemistry). Read More

We introduce diffusively coupled networks where the dynamical system at each vertex is planar Hamiltonian. The problems we address are synchronisation and an analogue of diffusion-driven Turing instability for time-dependent homogeneous states. As a consequence of the underlying Hamiltonian structure there exist unusual behaviours compared with networks of coupled limit cycle oscillators or activator-inhibitor systems. Read More

We prove a sample path Large Deviation Principle (LDP) for a class of jump processes whose rates are not uniformly Lipschitz continuous in phase space. Building on it we further establish the corresponding Wentzell-Freidlin (W-F) (infinite time horizon) asymptotic theory. These results apply to jump Markov processes that model the dynamics of chemical reaction networks under mass action kinetics, on a microscopic scale. Read More

Background: The Epithelial-Mesenchymal Transition (EMT) endows epithelial-looking cells with enhanced migratory ability during embryonic development and tissue repair. EMT can also be co-opted by cancer cells to acquire metastatic potential and drug-resistance. Recent research has argued that epithelial (E) cells can undergo either a partial EMT to attain a hybrid epithelial/mesenchymal (E/M) phenotype that typically displays collective migration, or a complete EMT to adopt a mesenchymal (M) phenotype that shows individual migration. Read More

Genetic and environmental perturbation experiments have been used to study microbes in a bid to gain insight into transcriptional regulation, adaptive evolution, and other cellular dynamics. These studies have potential in enabling rational strain design. Unfortunately, experimentally determined intracellular flux distribution are often inconsistent or incomparable due to different experimental conditions and methodologies. Read More

A cell has the ability to convert an environmental change into the expression of genetic information through a chain of intracellular signal transduction reactions. Here, we aimed to develop a method for quantifying this signal transduction. We showed that the channel capacities of individual steps in a given general model cascade were equivalent in an independent manner, and were given by the entropy production rate. Read More

In order to function reliably, synthetic molecular circuits require mechanisms that allow them to adapt to environmental disturbances. Least mean squares (LMS) schemes, such as commonly encountered in signal processing and control, provide a powerful means to accomplish that goal. In this paper we show how the traditional LMS algorithm can be implemented at the molecular level using only a few elementary biomolecular reactions. Read More

Complex diseases can be modeled as damage to intracellular networks that results in abnormal cell behaviors. Network-based dynamic models such as Boolean models have been employed to model a variety of biological systems including those corresponding to disease. Previous work designed compensatory interactions to stabilize an attractor of a Boolean network after single node damage. Read More

We introduce a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and we prove general results based on the network structure. Many post-translational modification networks are MESSI systems. For example: the motifs in Feliu-Wiuf'12, sequential distributive multisite phosphorylation networks, sequential processive multisite phosphorylation networks, most of the examples in Angeli et al. Read More

Circadian clocks must be able to entrain to time-varying signals to keep their oscillations in phase with the day-night rhythm. On the other hand, they must also exhibit input compensation: their period must remain about one day in different constant environments. The post-translational oscillator of the Kai system can be entrained by transient or oscillatory changes in the ATP fraction, yet is insensitive to constant changes in this fraction. Read More

We introduce a tensor-based algebraic clustering method to extract sparse, low-dimensional structure from multidimensional arrays of experimental data. Our methodology is applicable to high dimensional data structures that arise across the sciences. Specifically we introduce a new way to cluster data subject to multi-indexed structural constraints via integer programming. Read More

Gene expression levels carry information about signals that have functional significance for the organism. Using the gap gene network in the fruit fly embryo as an example, we show how this information can be decoded, building a dictionary that translates expression levels into a map of implied positions. The optimal decoder makes use of graded variations in absolute expression level, resulting in positional estimates that are precise to ~1% of the embryo's length. Read More