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arXiv2012

Spatial organization of proteomes: A low-rank approximation

We investigate the problem of signal transduction via a descriptive analysis of the spatial organization of the complement of proteins exerting a certain function within a cellular compartment. We propose a scheme to assign a numerical value to individual proteins in a protein interaction network by means of a simple optimization algorithm. We test our procedure against datasets focusing on the proteomes in the neurite and soma compartments.

q-bio.MN↗

arXiv2012

Stochastic simulation of biochemical systems with randomly fluctuating rate constants

In an experimental study of single enzyme reactions, it has been proposed that the rate constants of the enzymatic reactions fluctuate randomly, according to a given distribution. To quantify the uncertainty arising from random rate constants, it is necessary to investigate how one can simulate such a biochemical system. To do this, we will take the Gillespie's stochastic simulation algorithm for simulating the evolution of the state of a chemical system, and study a modification of the algorithm that incorporates the random rate constants. In addition to simulating the waiting time of each reaction step, the modified algorithm also involves simulating the random fluctuation of the rate constant at each reaction time. We consider the modified algorithm in a general framework, then specialize it to two contrasting physical models, one in which the fluctuations occur on a much faster time scale than the reaction step, and the other in which the fluctuations occur much more slowly. The latter case was applied to the single enzyme reaction system, using in part the Metropolis-Hastings algorithm to enact the given distribution on the random rate constants. The modified algorithm is shown to produce simulation outputs that are corroborated by the experimental results. It is hoped that this modified algorithm can subsequently be used as a tool for the estimation or calibration of parameters in the system using experimental data.

q-bio.QM↗

arXiv2012

Topological effects of data incompleteness of gene regulatory networks

The topological analysis of biological networks has been a prolific topic in network science during the last decade. A persistent problem with this approach is the inherent uncertainty and noisy nature of the data. One of the cases in which this situation is more marked is that of transcriptional regulatory networks (TRNs) in bacteria. The datasets are incomplete because regulatory pathways associated to a relevant fraction of bacterial genes remain unknown. Furthermore, direction, strengths and signs of the links are sometimes unknown or simply overlooked. Finally, the experimental approaches to infer the regulations are highly heterogeneous, in a way that induces the appearance of systematic experimental-topological correlations. And yet, the quality of the available data increases constantly. In this work we capitalize on these advances to point out the influence of data (in)completeness and quality on some classical results on topological analysis of TRNs, specially regarding modularity at different levels. In doing so, we identify the most relevant factors affecting the validity of previous findings, highlighting important caveats to future prokaryotic TRNs topological analysis.

physics.bio-ph↗

arXiv2013

Power-law Kinetics and Determinant Criteria for the Preclusion of Multistationarity in Networks of Interacting Species

We present determinant criteria for the preclusion of non-degenerate multiple steady states in networks of interacting species. A network is modeled as a system of ordinary differential equations in which the form of the species formation rate function is restricted by the reactions of the network and how the species influence each reaction. We characterize families of so-called power-law kinetics for which the associated species formation rate function is injective within each stoichiometric class and thus the network cannot exhibit multistationarity. The criterion for power-law kinetics is derived from the determinant of the Jacobian of the species formation rate function. Using this characterization we further derive similar determinant criteria applicable to general sets of kinetics. The criteria are conceptually simple, computationally tractable and easily implemented. Our approach embraces and extends previous work on multistationarity, such as work in relation to chemical reaction networks with dynamics defined by mass-action or non-catalytic kinetics, and also work based on graphical analysis of the interaction graph associated to the system. Further, we interpret the criteria in terms of circuits in the so-called DSR-graph

math.DS↗

arXiv2013

Deformed Toric Ideal Constraints for Stoichiometric Networks

We discuss chemical reaction networks and metabolic pathways based on stoichiometric network analysis, and introduce deformed toric ideal constraints by the algebraic geometrical approach. This paper concerns steady state flux of chemical reaction networks and metabolic pathways. With the deformed toric ideal constraints, the linear combination parameters of extreme pathways are automatically constrained without introducing ad hoc constraints. To illustrate the effectiveness of such constraints, we discuss two examples of chemical reaction network and metabolic pathway; in the former the flux and the concentrations are constrained completely by deformed toric ideal constraints, and in the latter, it is shown the deformed toric ideal constrains the linear combination parameters of flux at least partially. Even in the latter case, the flux and the concentrations are constrained completely with the additional constraint that the total amount of enzyme is constant.

q-bio.MN↗

arXiv2012

Predicting effects of structural stress in a genome-reduced model bacterial metabolism

We studied in silico effects of structural stress in Mycoplasma pneumoniae, a genome-reduced model bacterial organism, by tracking the damage propagating on its metabolic network after a deleterious perturbation. First, we analyzed failure cascades spreading from individual reactions and pairs of reactions and compared the results to those in Staphylococcus aureus and Escherichia coli. To alert to the potential damage caused by the failure of individual reactions, we propose a generic predictor based on local information that identifies target reactions for structural vulnerability. With respect to the simultaneous failure of pairs of reactions, we detected strong non-linear amplification effects that can be predicted by the presence of specific motifs in the intersection of single cascades. We further connected the metabolic and gene co-expression networks of M. pneumoniae through enzyme activities, and studied the consequences of knocking out individual genes and clusters of genes. Damage caused by single gene knockouts reveals a strong correlation between genome-scale cascades of large impact and gene essentiality. At the same time, we found that genes controlling high-damage reactions tend to operate in functional isolation, as a metabolic protection mechanism. We conclude that the architecture of M. pneumoniae, both at the level of metabolism and genome, seems to have evolved towards increased structural robustness, similarly to other more complex model bacterial organisms, despite its reduced genome size and its greater metabolic network linearity. Our approach, although motivated biochemically, is generic enough to be of potential use toward analyzing and predicting spreading of structural stress in any bipartite complex network.

q-bio.MN↗

arXiv2012

A new mechanism of development and differentiation through slow binding/unbinding of regulatory proteins to the genes

Understanding the differentiation, a biological process from a multipotent stem or progenitor state to a mature cell is critically important. We develop a theoretical framework to quantify the underlying potential landscape and biological paths for cell development and differentiation. We propose a new mechanism of differentiation and development through binding/unbinding of regulatory proteins to the gene promoters. We found indeed the differentiated states can emerge from the slow promoter binding/unbinding processes. Furthermore, under slow promoter binding/unbinding, we found multiple meta-stable differentiated states. This can explain the origin of multiple states observed in the recent experiments. In addition, the kinetic time quantified by mean first passage transition time for the differentiation and reprogramming strongly depends on the time scale of the promoter binding/unbinding processes. We discovered an optimal speed for differentiation for certain binding/unbinding rates of regulatory proteins to promoters. More experiments in the future might be able to tell if cells differentiate at at that optimal speed. In addition, we quantify kinetic pathways for the differentiation and reprogramming. We found that they are irreversible. This captures the non-equilibrium dynamics in multipotent stem or progenitor cells. Such inherent time-asymmetry as a result of irreversibility of state transition pathways as shown may provide the origin of time arrow for cell development.

q-bio.MN↗

arXiv2012

Flexible and robust networks

We consider networks with two types of nodes. The v-nodes, called centers, are hyper- connected and interact one to another via many u-nodes, called satellites. This central- ized architecture, widespread in gene networks, possesses two fundamental properties. Namely, this organization creates feedback loops that are capable to generate practically any prescribed patterning dynamics, chaotic or periodic, or having a number of equilib- rium states. Moreover, this organization is robust with respect to random perturbations of the system.

q-bio.MN↗

arXiv2012

Inference of Temporally Varying Bayesian Networks

When analysing gene expression time series data an often overlooked but crucial aspect of the model is that the regulatory network structure may change over time. Whilst some approaches have addressed this problem previously in the literature, many are not well suited to the sequential nature of the data. Here we present a method that allows us to infer regulatory network structures that may vary between time points, utilising a set of hidden states that describe the network structure at a given time point. To model the distribution of the hidden states we have applied the Hierarchical Dirichlet Process Hideen Markov Model, a nonparametric extension of the traditional Hidden Markov Model, that does not require us to fix the number of hidden states in advance. We apply our method to exisiting microarray expression data as well as demonstrating is efficacy on simulated test data.

q-bio.MN↗

arXiv2012

Computational modeling of neuronal networks

Human brain contains about 10 billion neurons, each of which has about 10~10,000 nerve endings from which neurotransmitters are released in response to incoming spikes, and the released neurotransmitters then bind to receptors located in the postsynaptic neurons. However, individually, neurons are noisy and synaptic release is in general unreliable. But groups of neurons that are arranged in specialized modules can collectively perform complex information processing tasks robustly and reliably. How functionally groups of neurons perform behavioural related tasks crucial rely on a coherent organization of dynamics from membrane ionic kinetics to synaptic coupling of the network and dynamics of rhythmic oscillations that are tightly linked to behavioural state. To capture essential features of the biological system at multiple spatial-temporal scales, it is important to construct a suitable computational model that is closely or solely based on experimental data. Depending on what one wants to understand, these models can either be very functional and biologically realistic descriptions with thousands of coupled differential equations (Hodgkin-Huxley type) or greatly simplified caricatures (integrate-and-fire type) which are useful for studying large interconnected networks.

q-bio.NC↗

arXiv2012

The collective oscillation period of inter-coupled Goodwin oscillators

Many biological oscillators are arranged in networks composed of many inter-coupled cellular oscillators. However, results are still lacking on the collective oscillation period of inter-coupled gene regulatory oscillators, which, as has been reported, may be different from the oscillation period of an autonomous cellular oscillator. Based on the Goodwin oscillator, we analyze the collective oscillation pattern of coupled cellular oscillator networks. First we give a condition under which the oscillator network exhibits oscillatory and synchronized behavior, then we estimate the collective oscillation period based on a multivariable harmonic balance technique. Analytical results are derived in terms of biochemical parameters, thus giving insight into the basic mechanism of biological oscillation and providing guidance in synthetic biology design. Simulation results are given to confirm the theoretical predictions.

eess.SY↗

arXiv2012

Biological Circuits: Analysis of a Biological Oscillator

The simple circadian oscillator found in cyanobacteria can be reconstituted in vitro using three proteins-KaiA, KaiB and KaiC. The total phosphorylation level of KaiC oscillates with a circadian period. Recent experiments elucidated the structure and function of the cyanobacterial circadian oscillator, which is driven by sunlight intensity variation and therefore by Earth's rotation. In this paper, we derive the oscillator's equation of motion directly from experimental data, couple it with Earth's rotation and compute its natural periods and resonance curve. Finally, we propose the use of a quantum circuit that is capable of describing the function of the oscillator.

q-bio.MN↗

arXiv2012

Fixed-points in Random Boolean Networks: The impact of parallelism in the scale-free topology case

Fixed points are fundamental states in any dynamical system. In the case of gene regulatory networks (GRNs) they correspond to stable genes profiles associated to the various cell types. We use Kauffman's approach to model GRNs with random Boolean networks (RBNs). We start this paper by proving that, if we fix the values of the source nodes (nodes with in-degree 0), the expected number of fixed points of any RBN is one (independently of the topology we choose). For finding such fixed points we use the α-asynchronous dynamics (where every node is updated independently with probability 0 < α < 1). In fact, it is well-known that asynchrony avoids the cycle attractors into which parallel dynamics tends to fall. We perform simulations and we show the remarkable property that, if for a given RBN with scale-free topology and α-asynchronous dynamics an initial configuration reaches a fixed point, then every configuration also reaches a fixed point. By contrast, in the parallel regime, the percentage of initial configurations reaching a fixed point (for the same networks) is dramatically smaller. We contrast the results of the simulations on scale-free networks with the classical Erdos-Renyi model of random networks. Everything indicates that scale-free networks are extremely robust. Finally, we study the mean and maximum time/work needed to reach a fixed point when starting from randomly chosen initial configurations.

q-bio.CB↗

arXiv2012

Reconstruction of Network Evolutionary History from Extant Network Topology and Duplication History

Genome-wide protein-protein interaction (PPI) data are readily available thanks to recent breakthroughs in biotechnology. However, PPI networks of extant organisms are only snapshots of the network evolution. How to infer the whole evolution history becomes a challenging problem in computational biology. In this paper, we present a likelihood-based approach to inferring network evolution history from the topology of PPI networks and the duplication relationship among the paralogs. Simulations show that our approach outperforms the existing ones in terms of the accuracy of reconstruction. Moreover, the growth parameters of several real PPI networks estimated by our method are more consistent with the ones predicted in literature.

q-bio.PE↗

arXiv2012

Growth efficiency as a cellular objective in Eschericia coli

The identification of cellular objectives is one of the central topics in the research of microbial metabolic networks. In particular, the information about a cellular objective is needed in flux balance analysis which is a commonly used constrained-based metabolic network analysis method for the prediction of cellular phenotypes. The cellular objective may vary depending on the organism and its growth conditions. It is probable that nutritionally scarce conditions are very common in the nature and, in order to survive in those conditions, cells exhibit various highly efficient nutrient processing systems like enzymes. In this study, we explore the efficiency of a metabolic network in transformation of substrates to new biomass, and we introduce a new objective function simulating growth efficiency. We examined the properties of growth efficiency using a metabolic model for Eschericia coli. We found that the maximal growth efficiency is obtained at a finite nutrient uptake rate. The rate is substrate-dependent and it typically does not exceed 20 mmol/h/gDW. We further examined whether the maximal growth efficiency could serve as a cellular objective function in metabolic network analysis, and found that cellular growth in batch cultivation can be predicted reasonably well under this assumption. The fit to experimental data was found slightly better than with the commonly used objective function of maximal growth rate. Based on our results, we suggest that the maximal growth efficiency can be considered as a plausible optimization criterion in metabolic modeling for E. coli. In the future, it would be interesting to study growth efficiency as a cellular objective also in other cellular systems and under different cultivation conditions.

q-bio.MN↗

arXiv2012

Computing Weakly Reversible Linearly Conjugate Chemical Reaction Networks with Minimal Deficiency

Mass-action kinetics is frequently used in systems biology to model the behaviour of interacting chemical species. Many important dynamical properties are known to hold for such systems if they are weakly reversible and have a low deficiency. In particular, the Deficiency Zero and Deficiency One Theorems guarantee strong regularity with regards to the number and stability of positive equilibrium states. It is also known that chemical reaction networks with disparate reaction structure can exhibit the same qualitative dynamics. The theory of linear conjugacy encapsulates the cases where this relationship is captured by a linear transformation. In this paper, we propose a mixed-integer linear programming algorithm capable of determining weakly reversible reaction networks with a minimal deficiency which are linearly conjugate to a given reaction network.

math.DS↗

arXiv2012

On the relation between reactions and complexes of (bio)chemical reaction networks

Robustness of biochemical systems has become one of the central questions in systems biology although it is notoriously difficult to formally capture its multifaceted nature. Maintenance of normal system function depends not only on the stoichiometry of the underlying interrelated components, but also on a multitude of kinetic parameters. Invariant flux ratios, obtained within flux coupling analysis, as well as invariant complex ratios, derived within chemical reaction network theory, can characterize robust properties of a system at steady state. However, the existing formalisms for the description of these invariants do not provide full characterization as they either only focus on the flux-centric or the concentration-centric view. Here we develop a novel mathematical framework which combines both views and thereby overcomes the limitations of the classical methodologies. Our unified framework will be helpful in analyzing biologically important system properties.

q-bio.MN↗

arXiv2012

Concordant Chemical Reaction Networks and the Species-Reaction Graph

In a recent paper it was shown that, for chemical reaction networks possessing a subtle structural property called concordance, dynamical behavior of a very circumscribed (and largely stable) kind is enforced, so long as the kinetics lies within the very broad and natural weakly monotonic class. In particular, multiple equilibria are precluded, as are degenerate positive equilibria. Moreover, under certain circumstances, also related to concordance, all real eigenvalues associated with a positive equilibrium are negative. Although concordance of a reaction network can be decided by readily available computational means, we show here that, when a nondegenerate network's Species-Reaction Graph satisfies certain mild conditions, concordance and its dynamical consequences are ensured. These conditions are weaker than earlier ones invoked to establish kinetic system injectivity, which, in turn, is just one ramification of network concordance. Because the Species-Reaction Graph resembles pathway depictions often drawn by biochemists, results here expand the possibility of inferring signicant dynamical information directly from standard biochemical reaction diagrams.

q-bio.MN↗