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arXiv2008

When correlations matter - response of dynamical networks to small perturbations

We systematically study and compare damage spreading for random Boolean and threshold networks under small external perturbations (damage), a problem which is relevant to many biological networks. We identify a new characteristic connectivity $K_s$, at which the average number of damaged nodes after a large number of dynamical updates is independent of the total number of nodes $N$. We estimate the critical connectivity for finite $N$ and show that it systematically deviates from the annealed approximation. Extending the approach followed in a previous study, we present new results indicating that internal dynamical correlations tend to increase not only the probability for small, but also for very large damage events, leading to a broad, fat-tailed distribution of damage sizes. These findings indicate that the descriptive and predictive value of averaged order parameters for finite size networks - even for biologically highly relevant sizes up to several thousand nodes - is limited.

cond-mat.dis-nn↗

arXiv2008

Network Structure and Dynamics, and Emergence of Robustness by Stabilizing Selection in an Artificial Genome

Genetic regulation is a key component in development, but a clear understanding of the structure and dynamics of genetic networks is not yet at hand. In this work we investigate these properties within an artificial genome model originally introduced by Reil. We analyze statistical properties of randomly generated genomes both on the sequence- and network level, and show that this model correctly predicts the frequency of genes in genomes as found in experimental data. Using an evolutionary algorithm based on stabilizing selection for a phenotype, we show that robustness against single base mutations, as well as against random changes in initial network states that mimic stochastic fluctuations in environmental conditions, can emerge in parallel. Evolved genomes exhibit characteristic patterns on both sequence and network level.

q-bio.MN↗

arXiv2008

The Dynamics of Conjunctive and Disjunctive Boolean Networks

The relationship between the properties of a dynamical system and the structure of its defining equations has long been studied in many contexts. Here we study this problem for the class of conjunctive (resp. disjunctive) Boolean networks, that is, Boolean networks in which all Boolean functions are constructed with the AND (resp. OR) operator only. The main results of this paper describe network dynamics in terms of the structure of the network dependency graph (topology). For a given such network, all possible limit cycle lengths are computed and lower and upper bounds for the number of cycles of each length are given. In particular, the exact number of fixed points is obtained. The bounds are in terms of structural features of the dependency graph and its partially ordered set of strongly connected components. For networks with strongly connected dependency graph, the exact cycle structure is computed.

math.CO↗

arXiv2008

A comparative evolutionary study of transcription networks

We present a comparative analysis of large-scale topological and evolutionary properties of transcription networks in three species, the two distant bacteria E. coli and B. subtilis, and the yeast S. cerevisiae. The study focuses on the global aspects of feedback and hierarchy in transcriptional regulatory pathways. While confirming that gene duplication has a significant impact on the shaping of all the analyzed transcription networks, our results point to distinct trends between the bacteria, where time constraints in the transcription of downstream genes might be important in shaping the hierarchical structure of the network, and yeast, which seems able to sustain a higher wiring complexity, that includes the more feedback, intricate hierarchy, and the combinatorial use of heterodimers made of duplicate transcription factors.

q-bio.MN↗

arXiv2008

Elucidation of differential response networks from toxicogenomics data

We describe a novel approach to the analysis of toxicogenomics data and elucidation of biological networks affected by drug treatments. In this method approximately 15,000 linear pathway modules were generated from manually assembled pathway maps from MetaCore (GeneGo, Inc.). Microarray expression data from livers of rat exposed to phenobarbital, mestranol and tamoxifen were mapped onto these modules. Using different analytical techniques we have identified sets of "differential" pathways featuring highly correlated expression among multiple repeats of the same treatment while showing strong anti-correlation across different treatments. Network modules distinguishing chemical treatments were re-assembled based on these pathways. Unlike traditional statistical and clustering procedures in expression profiling, our method takes into account both network connectivity and gene expression in the course of the analysis. We demonstrate that it enables identification of important cellular mechanisms involved in drug response that would have been missed by the analysis based on individual gene expression profiles.

q-bio.MN↗

arXiv2008

Reliability of regulatory networks and its evolution

The problem of reliability of the dynamics in biological regulatory networks is studied in the framework of a generalized Boolean network model with continuous timing and noise. Using well-known artificial genetic networks such as the repressilator, we discuss concepts of reliability of rhythmic attractors. In a simple evolution process we investigate how overall network structure affects the reliability of the dynamics. In the course of the evolution, networks are selected for reliable dynamics. We find that most networks can be easily evolved towards reliable functioning while preserving the original function.

q-bio.MN↗

arXiv2008

Sensitivity Regulation based on Noise Propagation in Stochastic Reaction Networks

In this work we focus on how noise propagates in biochemical reaction networks and affects sensitivities of the system. We discover that the stochastic fluctuations can enhance sensitivities in one region of the value of control parameters by reducing sensitivities in another region. Based on this compensation principle, we designed a concentration detector in which enhanced amplification is achieved by an incoherent feedforward reaction network.

q-bio.MN↗

arXiv2008

A dynamic logic method for determining behaviors of biological networks

A dynamic logic method was developed to analyze molecular networks of cells by combining Kauffman and Thomas's logic operations with molecular interaction parameters. The logic operations characterize the discrete interactions between biological components. The interaction parameters (e.g. response times) describe the quantitative kinetics. The combination of the two quantitatively characterizes the discrete biological interactions. A number of simple networks were analyzed. The main results include: we proved the theorems to determine bistable states and oscillation behaviors of networks, we showed that time delays are essential for oscillation structures, we proved that single variable networks do not have chaotic behaviors, and we explained why one signal can have multiply responses. In addition, we applied the present method to the analysis of the MAPK cascade, feed-forward loops, and mitosis cycle of budding yeast cells.

q-bio.QM↗

arXiv2008

Optimal Control of Evolutionary Dynamics

Elucidating the fitness measures optimized during the evolution of complex biological systems is a major challenge in evolutionary theory. We present experimental evidence and an analytical framework demonstrating how biochemical networks exploit optimal control strategies in their evolutionary dynamics. Optimal control theory explains a striking pattern of extremization in the redox potentials of electron transport proteins, assuming only that their fitness measure is a control objective functional with bounded controls.

q-bio.MN↗

arXiv2008

A fast and efficient gene-network reconstruction method from multiple over-expression experiments

Reverse engineering of gene regulatory networks presents one of the big challenges in systems biology. Gene regulatory networks are usually inferred from a set of single-gene over-expressions and/or knockout experiments. Functional relationships between genes are retrieved either from the steady state gene expressions or from respective time series. We present a novel algorithm for gene network reconstruction on the basis of steady-state gene-chip data from over-expression experiments. The algorithm is based on a straight forward solution of a linear gene-dynamics equation, where experimental data is fed in as a first predictor for the solution. We compare the algorithm's performance with the NIR algorithm, both on the well known E.Coli experimental data and on in-silico experiments. We show superiority of the proposed algorithm in the number of correctly reconstructed links and discuss computational time and robustness. The proposed algorithm is not limited by combinatorial explosion problems and can be used in principle for large networks of thousands of genes.

q-bio.MN↗

arXiv2008

Multi-Scale, Multi-Resolution Brain Cancer Modeling

In advancing discrete-based computational cancer models towards clinical applications, one faces the dilemma of how to deal with an ever growing amount of biomedical data that ought to be incorporated eventually in one form or another. Model scalability becomes of paramount interest. In an effort to start addressing this critical issue, here, we present a novel multi-scale and multi-resolution agent-based in silico glioma model. While "multi-scale" refers to employing an epidermal growth factor receptor (EGFR)-driven molecular network to process cellular phenotypic decisions within the micro-macroscopic environment, "multi-resolution" is achieved through algorithms that classify cells to either active or inactive spatial clusters, which determine the resolution they are simulated at. The aim is to assign computational resources where and when they matter most for maintaining or improving the predictive power of the algorithm, onto specific tumor areas and at particular times. Using a previously described 2D brain tumor model, we have developed four different computational methods for achieving the multi-resolution scheme, three of which are designed to dynamically train on the high-resolution simulation that serves as control. To quantify the algorithms' performance, we rank them by weighing the distinct computational time savings of the simulation runs versus the methods' ability to accurately reproduce the high-resolution results of the control. Finally, to demonstrate the flexibility of the underlying concept, we show the added value of combining the two highest-ranked methods.

q-bio.CB↗

arXiv2008

Cancer Cell Motility: Optimizing Spatial Search Strategies

Aberrantly regulated cell motility is a hallmark of cancer cells. A hybrid agent-based model has been developed to investigate the synergistic and antagonistic cell motility-impacting effects of three microenvironment variables simultaneously: chemoattraction, haptotactic permission, and biomechanical constraint or resistance. Reflecting distinct cell-specific intracellular machinery, the cancer cells are modelled as processing a variety of spatial search strategies that respond to these three influencing factors with differential weights attached to each. While responding exclusively to chemoattraction optimizes cell displacement effectiveness, incorporating permission and resistance components becomes increasingly important with greater distance to the chemoattractant source and/or after reducing the ligand's effective diffusion coefficient. Extending this to a heterogeneous population of cells shows that displacement effectiveness increases with clonal diversity as characterized by the Shannon index. However, the resulting data can be fit best to an exponential function, suggesting that there is a level of population heterogeneity beyond which its added value to the cancer system becomes minimal as directionality ceases to increase. Possible experimental extensions and potential clinical implications are discussed.

q-bio.CB↗

arXiv2008

From differential equations to Boolean networks: A Case Study in modeling regulatory networks

Methods of modeling cellular regulatory networks as diverse as differential equations and Boolean networks co-exist, however, without any closer correspondence to each other. With the example system of the fission yeast cell cycle control network, we here set the two approaches in relation to each other. We find that the Boolean network can be formulated as a specific coarse-grained limit of the more detailed differential network model for this system. This lays the mathematical foundation on which Boolean networks can be applied to biological regulatory networks in a controlled way.

q-bio.MN↗

arXiv2008

Constructing a Knowledge Base for Gene Regulatory Dynamics by Formal Concept Analysis Methods

Our aim is to build a set of rules, such that reasoning over temporal dependencies within gene regulatory networks is possible. The underlying transitions may be obtained by discretizing observed time series, or they are generated based on existing knowledge, e.g. by Boolean networks or their nondeterministic generalization. We use the mathematical discipline of formal concept analysis (FCA), which has been applied successfully in domains as knowledge representation, data mining or software engineering. By the attribute exploration algorithm, an expert or a supporting computer program is enabled to decide about the validity of a minimal set of implications and thus to construct a sound and complete knowledge base. From this all valid implications are derivable that relate to the selected properties of a set of genes. We present results of our method for the initiation of sporulation in Bacillus subtilis. However the formal structures are exhibited in a most general manner. Therefore the approach may be adapted to signal transduction or metabolic networks, as well as to discrete temporal transitions in many biological and nonbiological areas.

q-bio.MN↗

arXiv2008

The Invention of Proteomic Code and mRNA Assisted Protein Folding

Background The theoretical requirements for a genetic code were well defined and modeled by George Gamow and Francis Crick in the 50-es. Their models failed. However the valid Genetic Code, provided by Nirenberg and Matthaei in 1961, ignores many theoretical requirements for a perfect Code. Something is simply missing from the canonical Code. Results The 3x redundancy of the Genetic code is usually explained as a necessity to increase the resistance of the mutation resistance of the genetic information. However it has many additional roles. 1.) It has a periodical structure which corresponds to the physico-chemical and structural properties of amino acids. 2.) It provides physico-chemical definition of codon boundaries. 3.) It defines a code for amino acid co-locations (interactions) in the coded proteins. 4.) It regulates, through wobble bases the free folding energy (and structure) of mRNAs. I shortly review the history of the Genetic Code as well as my own published observations to provide a novel, original explanation of its redundancy. Conclusions The redundant Genetic Code contains biological information which is additional to the 64/20 definition of amino acids. This additional information is used to define the 3D structure of coding nucleic acids as well as the coded proteins and it is called the Proteomic Code and mRNA Assisted Protein Folding.

q-bio.BM↗

arXiv2008

Towards Kinetic Modeling of Global Metabolic Networks with Incomplete Experimental Input on Kinetic Parameters

This is the first report, to our knowledge, on a systematic method for constructing a large scale kinetic metabolic model with incomplete information on kinetic parametersr, and its initial application to the modeling of central metabolism of Methylobacterium extorquens AM1, a methylotrophic and environmental important bacterium, with all necessary constraints. Through a systematic and consistent procedure of finding a set of parameters in the physiological range we overcome an outstanding difficulty in large scale kinetic modeling: the requirement for a massive number of enzymatic reaction parameters. We are able to construct the kinetic model based on general biological considerations and incomplete experimental kinetic parameters. The success of our approach with incompletely input information is guaranteed by two known principles in biology, the robustness of the system and the cooperation among its various parts. (Will be pleased to be informed on other methodologies dealing with same type of problems: aoping@u.washington.edu)

q-bio.MN↗

arXiv2008

Coarse-graining stochastic biochemical networks: quasi-stationary approximation and fast simulations using a stochastic path integral technique

We propose a universal approach for analysis and fast simulations of stiff stochastic biochemical kinetics networks, which rests on elimination of fast chemical species without a loss of information about mesoscopic, non-Poissonian fluctuations of the slow ones. Our approach, which is similar to the Born-Oppenheimer approximation in quantum mechanics, follows from the stochastic path integral representation of the full counting statistics of reaction events (also known as the cumulant generating function). In applications with a small number of chemical reactions, this approach produces analytical expressions for moments of chemical fluxes between slow variables. This allows for a low-dimensional, interpretable representation of the biochemical system, that can be used for coarse-grained numerical simulation schemes with a small computational complexity and yet high accuracy. As an example, we consider a chain of biochemical reactions, derive its coarse-grained description, and show that the Gillespie simulations of the original stiff system, the coarse-grained simulations, and the full analytical treatment are in an agreement, but the coarse-grained simulations are three orders of magnitude faster than the Gillespie analogue.

q-bio.MN↗

arXiv2008

A quantitative comparison of sRNA-based and protein-based gene regulation

Small, non-coding RNAs (sRNAs) play important roles as genetic regulators in prokaryotes. sRNAs act post-transcriptionally via complementary pairing with target mRNAs to regulate protein expression. We use a quantitative approach to compare and contrast sRNAs with conventional transcription factors (TFs) to better understand the advantages of each form of regulation. In particular, we calculate the steady-state behavior, noise properties, frequency-dependent gain (amplification), and dynamical response to large input signals of both forms of regulation. While the mean steady-state behavior of sRNA-regulated proteins exhibits a distinctive tunable threshold-linear behavior, our analysis shows that transcriptional bursting leads to significantly higher intrinsic noise in sRNA-based regulation than in TF-based regulation in a large range of expression levels and limits the ability of sRNAs to perform quantitative signaling. Nonetheless, we find that sRNAs are better than TFs at filtering noise in input signals. Additionally, we find that sRNAs allow cells to respond rapidly to large changes in input signals. These features suggest a niche for sRNAs in allowing cells to transition quickly yet reliably between distinct states. This functional niche is consistent with the widespread appearance of sRNAs in stress-response and quasi-developmental networks in prokaryotes.

q-bio.MN↗