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arXiv2011

Maximizing Output and Recognizing Autocatalysis in Chemical Reaction Networks is NP-Complete

Background: A classical problem in metabolic design is to maximize the production of desired compound in a given chemical reaction network by appropriately directing the mass flow through the network. Computationally, this problem is addressed as a linear optimization problem over the "flux cone". The prior construction of the flux cone is computationally expensive and no polynomial-time algorithms are known. Results: Here we show that the output maximization problem in chemical reaction networks is NP-complete. This statement remains true even if all reactions are monomolecular or bimolecular and if only a single molecular species is used as influx. As a corollary we show, furthermore, that the detection of autocatalytic species, i.e., types that can only be produced from the influx material when they are present in the initial reaction mixture, is an NP-complete computational problem. Conclusions: Hardness results on combinatorial problems and optimization problems are important to guide the development of computational tools for the analysis of metabolic networks in particular and chemical reaction networks in general. Our results indicate that efficient heuristics and approximate algorithms need to be employed for the analysis of large chemical networks since even conceptually simple flow problems are provably intractable.

q-bio.MN↗

arXiv2011

COLoR - Coordinated On-Line Rankers for Network Reconstruction

Predicting protein interactions is one of the more interesting challenges of the post-genomic era. Many algorithms address this problem as a binary classification problem: given two proteins represented as two vectors of features, predict if they interact or not. Importantly however, computational predictions are only one component of a larger framework for identifying PPI. The most promising candidate pairs can be validated experimentally by testing if they physical bind to each other. Since these experiments are more costly and error prone, the computational predictions serve as a filter, aimed to produce a small number of highly promising candidates. Here we propose to address this problem as a ranking problem: given a network with known interactions, rank all unknown pairs based on the likelihood of their interactions. In this paper we propose a ranking algorithm that trains multiple inter-connected models using a passive aggressive on-line approach. We show good results predicting protein-protein interactions for post synaptic density PPI network. We compare the precision of the ranking algorithm with local classifiers and classic support vector machine. Though the ranking algorithm outperforms the classic SVM classification, its performance is inferior compared to the local supervised method.

q-bio.MN↗

arXiv2011

The plasticity of TGF-beta signaling

The family of TGFb ligands is large and its members are involved in many different signaling processes. These signaling processes strongly differ in type with TGFb ligands eliciting both sustained or transient responses. Members of the TGFb family can also act as morphogen and cellular responses would then be expected to provide a direct read-out of the extracellular ligand concentration. We were interested to define the set of minimal modifications that are required to change the type of signal processing in the TGFb signaling network. To define the key aspects for signaling plasticity we focused on the core of the TGFb signaling network. With the help of a parameter screen we identified ranges of kinetic parameters and protein concentrations that give rise to transient, sustained, or oscillatory responses to constant stimuli, as well as those parameter ranges that enable a proportional response to time-varying ligand concentrations (as expected in the read-out of morphogens). A combination of a strong negative feedback and fast shuttling to the nucleus biases signaling to a transient rather than a sustained response, while oscillations were obtained if ligand binding to the receptor is weak and the turn-over of the I-Smad is fast. A proportional read-out required inefficient receptor activation in addition to a low affinity of receptor-ligand binding. We find that targeted modification of single parameters suffices to alter the response type. The architecture of the TGFb pathway enables the observed signaling plasticity. The observed range of signaling outputs to TGFb ligand in different cell types and under different conditions can be explained with differences in cellular protein concentrations and with changes in effective rate constants due to cross-talk with other signaling pathways.

q-bio.MN↗

arXiv2011

Nested canalyzing depth and network stability

We introduce the nested canalyzing depth of a function, which measures the extent to which it retains a nested canalyzing structure. We characterize the structure of functions with a given depth and compute the expected activities and sensitivities of the variables. This analysis quantifies how canalyzation leads to higher stability in Boolean networks. It generalizes the notion of nested canalyzing functions (NCFs), which are precisely the functions with maximum depth. NCFs have been proposed as gene regulatory network models, but their structure is frequently too restrictive and they are extremely sparse. We find that functions become decreasingly sensitive to input perturbations as the canalyzing depth increases, but exhibit rapidly diminishing returns in stability. Additionally, we show that as depth increases, the dynamics of networks using these functions quickly approach the critical regime, suggesting that real networks exhibit some degree of canalyzing depth, and that NCFs are not significantly better than functions of sufficient depth for many applications of the modeling and reverse engineering of biological networks.

q-bio.MN↗

arXiv2011

Global parameter identification of stochastic reaction networks from single trajectories

We consider the problem of inferring the unknown parameters of a stochastic biochemical network model from a single measured time-course of the concentration of some of the involved species. Such measurements are available, e.g., from live-cell fluorescence microscopy in image-based systems biology. In addition, fluctuation time-courses from, e.g., fluorescence correlation spectroscopy provide additional information about the system dynamics that can be used to more robustly infer parameters than when considering only mean concentrations. Estimating model parameters from a single experimental trajectory enables single-cell measurements and quantification of cell--cell variability. We propose a novel combination of an adaptive Monte Carlo sampler, called Gaussian Adaptation, and efficient exact stochastic simulation algorithms that allows parameter identification from single stochastic trajectories. We benchmark the proposed method on a linear and a non-linear reaction network at steady state and during transient phases. In addition, we demonstrate that the present method also provides an ellipsoidal volume estimate of the viable part of parameter space and is able to estimate the physical volume of the compartment in which the observed reactions take place.

q-bio.MN↗

arXiv2012

CytoITMprobe: a network information flow plugin for Cytoscape

To provide the Cytoscape users the possibility of integrating ITM Probe into their workflows, we developed CytoITMprobe, a new Cytoscape plugin. CytoITMprobe maintains all the desirable features of ITM Probe and adds additional flexibility not achievable through its web service version. It provides access to ITM Probe either through a web server or locally. The input, consisting of a Cytoscape network, together with the desired origins and/or destinations of information and a dissipation coefficient, is specified through a query form. The results are shown as a subnetwork of significant nodes and several summary tables. Users can control the composition and appearance of the subnetwork and interchange their ITM Probe results with other software tools through tab-delimited files. The main strength of CytoITMprobe is its flexibility. It allows the user to specify as input any Cytoscape network, rather than being restricted to the pre-compiled protein-protein interaction networks available through the ITM Probe web service. Users may supply their own edge weights and directionalities. Consequently, as opposed to ITM Probe web service, CytoITMprobe can be applied to many other domains of network-based research beyond protein-networks. It also enables seamless integration of ITM Probe results with other Cytoscape plugins having complementary functionality for data analysis.

q-bio.QM↗

arXiv2011

A Self-Replicating Peptide Nucleic Acid

We report on a case of autocatalytic feedback in a template directed synthesis of a self-complementary hexa-PNA from two trimeric building blocks. The course of the reaction was monitored in the presence of increasing initial concentrations of product by means of RP-HPLC. Kinetic modeling with the SimFit program revealed parabolic growth according to the so-called square-root law. The observed template effect, as well as the rate of the ligation, was significantly influenced by factors like nucleophilic catalysts, pH value, and uncharged co-solvents. Systematic optimization of the reaction conditions allowed us to increase the autocatalytic efficiency of the system by two orders of magnitude.

q-bio.MN↗

arXiv2011

Integration of cellular signals in chattering environments

Cells are constantly exposed to fluctuating environmental conditions. External signals are sensed, processed and integrated by cellular signal transduction networks, which translate input signals into specific cellular responses by means of biochemical reactions. These networks have a complex nature, and we are still far from having a complete characterization of the process through which they integrate information, specially given the noisy environment in which that information is embedded. Guided by the many instances of constructive influences of noise that have been reported in the physical sciences in the last decades, here we explore how multiple signals are integrated in an eukaryotic cell in the presence of background noise, or chatter. To that end, we use a Boolean model of a typical human signal transduction network. Despite its complexity, we find that the network is able to display simple patterns of signal integration. Furthermore, our computational analysis shows that these integration patterns depend on the levels of fluctuating background activity carried by other cell inputs. Taken together, our results indicate that signal integration is sensitive to environmental fluctuations, and that this background noise effectively determines the information integration capabilities of the cell.

q-bio.MN↗

arXiv2011

Robust and flexible response of Ostreococcus tauri circadian clock to light/dark cycles of varying photoperiod

The green microscopic alga Ostreococcus tauri has recently emerged as a promising model for understanding how circadian clocks, which drive the daily biological rythms of many organisms, synchronize to the day/night cycle in changing weather and seasons. Here, we analyze translational reporter time series data of its central clock genes CCA1 and TOC1 for a wide range of daylight durations (photoperiods). The variation of temporal profiles with day duration is complex, with the two actors tracking different moments of the day. Nevertheless, all profiles are accurately reproduced by a simple two-gene transcriptional loop model whose parameters are affected by light only through the photoperiod value. We show that this non-intuitive behavior allows the circadian clock to combine flexibility and robustness to daylight fluctuations.

q-bio.QM↗

arXiv2011

Positional information, in bits

Cells in a developing embryo have no direct way of "measuring" their physical position. Through a variety of processes, however, the expression levels of multiple genes come to be correlated with position, and these expression levels thus form a code for "positional information." We show how to measure this information, in bits, using the gap genes in the Drosophila embryo as an example. Individual genes carry nearly two bits of information, twice as much as expected if the expression patterns consisted only of on/off domains separated by sharp boundaries. Taken together, four gap genes carry enough information to define a cell's location with an error bar of ~1% along the anterior-posterior axis of the embryo. This precision is nearly enough for each cell to have a unique identity, which is the maximum information the system can use, and is nearly constant along the length of the embryo. We argue that this constancy is a signature of optimality in the transmission of information from primary morphogen inputs to the output of the gap gene network.

q-bio.MN↗

arXiv2012

Mathematics of the NFAT signalling pathway

This paper is a mathematical study of some aspects of the signalling pathway leading to the activation of the transcription factor NFAT (nuclear factor of activated T cells). Activation takes place by dephosphorylation at multiple sites. This has been modelled by Salazar and Höfer using a large system of ordinary differential equations depending on many parameters. With the help of chemical reaction network theory we show that for any choice of the parameters this system has a unique stationary solution for each value of the conserved quantity given by the total amount of NFAT and that all solutions converge to this stationary solution at late times. The dephosphorylation is carried out by calcineurin, which in turn is activated by a rise in calcium concentration. We study the way in which the dynamics of the calcium concentration influences NFAT activation, an issue also considered by Salazar and Höfer with the help of a model arising from work of Somogyi and Stucki. Criteria are obtained for convergence to equilibrium of solutions of the model for the calcium concentration.

q-bio.MN↗

arXiv2012

Mapping of Affymetrix probe sets to groups of transcripts using transcriptional networks

Motivation: Usefulness of analysis derived from Affymetrix microarrays depends largely upon the reliability of files describing the correspondence between probe sets, genes and transcripts. In particular, in case a gene is targeted by two probe sets, one must be able to assess if the corresponding signals measure a group of common transcripts or two groups of transcripts with little or no overlap. Results: Probe sets that effectively target the same group of transcripts have specific properties in the trancriptional networks we constructed. We found indeed that such probe sets had a very low negative correlation, a high positive correlation and a similar neighbourhood. Taking advantage of these properties, we devised a test allowing to group probe sets which target the same group of transcripts in a particular network. By considering several networks, additional information concerning the frequency of these associations was obtained. Availability and Implementation: The programs developed in Python (PSAWNpy) and in Matlab (PSAWNml) are freely available, and can be downloaded at http://code.google.com/p/arraymatic/. Tutorials and reference manuals are available at http://bns.crbm.cnrs.fr/softwares.html. Contact: mbellis@crbm.cnrs.fr. Supplementary information: Supplementary data are available at http://bns.crbm.cnrs.fr/download.html.

q-bio.MN↗

arXiv2012

Piecewise linear models of chemical reaction networks

We show that certain non-linear dynamical systems with non-linearities in the form of Hill functions, can be approximated by piecewise linear dynamical systems. The resulting piecewise systems have closed form solutions that can be used to understand the behavior of the fully nonlinear system. We justify the reduction using geometric singular perturbation theory, and illustrate the results in networks modeling a genetic switch and a genetic oscillator.

q-bio.MN↗

arXiv2012

A race model for singular olfactory receptor expression

In vertebrates, olfactory sensory neurons choose only one olfactory receptor to produce out of ~2000 possibilities. The mechanism for how this singular receptor expression occurs is unknown. Here we propose a mechanism that can stochastically select a single gene out of a large number of possibilities. In this model, receptor genes compete for a limited pool of transcription factors (TFs). The gene that recruits a target number of TFs is selected for expression. To support this mechanism, we have attempted to detect repeated motifs within known sequences of mouse olfactory receptor promoters. We find motifs that are significantly overrepresented in olfactory versus other gene promoters. We identify possible TFs that can target these motifs. Our model suggests that a small number of TFs can control the selection of a single gene out of ~2000 possibilities.

q-bio.MN↗

arXiv2012

Evaluating sources of variability in pathway profiling

A bioinformatics platform is introduced aimed at identifying models of disease-specific pathways, as well as a set of network measures that can quantify changes in terms of global structure or single link disruptions.The approach integrates a network comparison framework with machine learning molecular profiling. The platform includes different tools combined in one Open Source pipeline, supporting reproducibility of the analysis. We describe here the computational pipeline and explore the main sources of variability that can affect the results, namely the classifier, the feature ranking/selection algorithm, the enrichment procedure, the inference method and the networks comparison function. The proposed pipeline is tested on a microarray dataset of late stage Parkinsons' Disease patients together with healty controls. Choosing different machine learning approaches we get low pathway profiling overlapping in terms of common enriched elements. Nevertheless, they identify different but equally meaningful biological aspects of the same process, suggesting the integration of information across different methods as the best overall strategy. All the elements of the proposed pipeline are available as Open Source Software: availability details are provided in the main text.

q-bio.MN↗

arXiv2012

On Natural Genetic Engineering: Structural Dynamism in Random Boolean Networks

This short paper presents an abstract, tunable model of genomic structural change within the cell lifecycle and explores its use with simulated evolution. A well-known Boolean model of genetic regulatory networks is extended to include changes in node connectivity based upon the current cell state, e.g., via transposable elements. The underlying behaviour of the resulting dynamical networks is investigated before their evolvability is explored using a version of the NK model of fitness landscapes. Structural dynamism is found to be selected for in non-stationary environments and subsequently shown capable of providing a mechanism for evolutionary innovation when such reorganizations are inherited.

cs.CE↗

arXiv2012

Dramatic reduction of dimensionality in large biochemical networks due to strong pair correlations

Large multidimensionality of high-throughput datasets pertaining to cell signaling and gene regulation renders it difficult to extract mechanisms underlying the complex kinetics involving various biochemical compounds (e.g., proteins, lipids). Data-driven models often circumvent this difficulty by using pair correlations of the protein expression levels to produce a small numbers (<10) of principal components, each a linear combination of the concentrations, to successfully model how cells respond to different stimuli. However, it is not understood if this reduction is specific to a particular biological system or to nature of the stimuli used in these experiments. We study temporal changes in pair correlations described by the covariance matrix between different molecular species that evolve following deterministic mass action kinetics in large biologically relevant reaction networks and show that this dramatic reduction of dimensions (from hundreds to <5) arises from the strong correlations between different species at any time and is in sensitive of the form of the nonlinear interactions, network architecture and values of rate constants and concentrations over a wide range. We relate temporal changes in the eigenvalue spectrum of the covariance matrix to low-dimensional, local changes in directions of the trajectory embedded in much larger dimensions using elementary differential geometry. We illustrate how to extract biologically relevant insights such as identifying significant time scales and groups of correlated chemical species from our analysis. Our work provides for the first time a theoretical underpinning for the successful experimental analysis and points to way to extract mechanisms from large- scale high throughput data sets.

q-bio.QM↗

arXiv2012

Is the immune network a complex network?

Some years ago a cellular automata model was proposed to describe the evolution of the immune repertoire of B cells and antibodies based on Jerne's immune network theory and shape-space formalism. Here we investigate if the networks generated by this model in the different regimes can be classified as complex networks. We have found that in the chaotic regime the network has random characteristics with large, constant values of clustering coefficients, while in the ordered phase, the degree distribution of the network is exponential and the clustering coefficient exhibits power law behavior. In the transition region we observed a mixed behavior (random-like and exponential) of the degree distribution as opposed to the scale-free behavior reported for other biological networks. Randomness and low connectivity in the active sites allow for rapid changes in the connectivity distribution of the immune network in order to include and/or discard information and generate a dynamic memory. However it is the availability of the low concentration nodes to change rapidly without driving the system to pathological states that allow the generation of dynamic memory and consequently a reproduction of immune system behavior in mice. Although the overall behavior of degree correlation is positive, there is an interplay between assortative and disassortative mixing in the stable and transition regions regulated by a threshold value of the node degree, which achieves a maximum value on the transition region and becomes totally assortative in the chaotic regime.

physics.bio-ph↗