Searcharxiv⌕ Search

arXiv subjects

Ilya Nemenman

Publications and source records attributed to Ilya Nemenman.

At least 91 records · Page 5Linked to original sources
arXiv2008

Quantifying evolvability in small biological networks

We introduce a quantitative measure of the capacity of a small biological network to evolve. We apply our measure to a stochastic description of the experimental setup of Guet et al. (Science 296:1466, 2002), treating chemical inducers as functional inputs to biochemical networks and the expression of a reporter gene as the functional output. We take an information-theoretic approach, allowing the system to set parameters that optimize signal processing ability, thus enumerating each network's highest-fidelity functions. We find that all networks studied are highly evolvable by our measure, meaning that change in function has little dependence on change in parameters. Moreover, we find that each network's functions are connected by paths in the parameter space along which information is not significantly lowered, meaning a network may continuously change its functionality without losing it along the way. This property further underscores the evolvability of the networks.

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

Serially-regulated biological networks fully realize a constrained set of functions

We show that biological networks with serial regulation (each node regulated by at most one other node) are constrained to {\it direct functionality}, in which the sign of the effect of an environmental input on a target species depends only on the direct path from the input to the target, even when there is a feedback loop allowing for multiple interaction pathways. Using a stochastic model for a set of small transcriptional regulatory networks that have been studied experimentally, we further find that all networks can achieve all functions permitted by this constraint under reasonable settings of biochemical parameters. This underscores the functional versatility of the networks.

q-bio.MN↗
arXiv2008

Determinants of bistability in induction of the Escherichia coli lac operon

We have developed a mathematical model of regulation of expression of the Escherichia coli lac operon, and have investigated bistability in its steady-state induction behavior in the absence of external glucose. Numerical analysis of equations describing regulation by artificial inducers revealed two natural bistability parameters that can be used to control the range of inducer concentrations over which the model exhibits bistability. By tuning these bistability parameters, we found a family of biophysically reasonable systems that are consistent with an experimentally determined bistable region for induction by thio-methylgalactoside (Ozbudak et al. Nature 427:737, 2004). The model predicts that bistability can be abolished when passive transport or permease export becomes sufficiently large; the former case is especially relevant to induction by isopropyl-beta, D-thiogalactopyranoside. To model regulation by lactose, we developed similar equations in which allolactose, a metabolic intermediate in lactose metabolism and a natural inducer of lac, is the inducer. For biophysically reasonable parameter values, these equations yield no bistability in response to induction by lactose; however, systems with an unphysically small permease-dependent export effect can exhibit small amounts of bistability for limited ranges of parameter values. These results cast doubt on the relevance of bistability in the lac operon within the natural context of E. coli, and help shed light on the controversy among existing theoretical studies that address this issue. The results also suggest an experimental approach to address the relevance of bistability in the lac operon within the natural context of E. coli.

q-bio.CB↗
arXiv2007

Reconstruction of metabolic networks from high-throughput metabolite profiling data: in silico analysis of red blood cell metabolism

We investigate the ability of algorithms developed for reverse engineering of transcriptional regulatory networks to reconstruct metabolic networks from high-throughput metabolite profiling data. For this, we generate synthetic metabolic profiles for benchmarking purposes based on a well-established model for red blood cell metabolism. A variety of data sets is generated, accounting for different properties of real metabolic networks, such as experimental noise, metabolite correlations, and temporal dynamics. These data sets are made available online. We apply ARACNE, a mainstream transcriptional networks reverse engineering algorithm, to these data sets and observe performance comparable to that obtained in the transcriptional domain, for which the algorithm was originally designed.

q-bio.MN↗
arXiv2007

The Berry phase and the pump flux in stochastic chemical kinetics

We study a classical two-state stochastic system in a sea of substrates and products (absorbing states), which can be interpreted as a single Michaelis-Menten catalyzing enzyme or as a channel on a cell surface. We introduce a novel general method and use it to derive the expression for the full counting statistics of transitions among the absorbing states. For the evolution of the system under a periodic perturbation of the kinetic rates, the latter contains a term with a purely geometrical (the Berry phase) interpretation. This term gives rise to a pump current between the absorbing states, which is due entirely to the stochastic nature of the system. We calculate the first two cumulants of this current, and we argue that it is observable experimentally.

q-bio.QM↗
arXiv2006

Neural coding of a natural stimulus ensemble: Uncovering information at sub-millisecond resolution

Our knowledge of the sensory world is encoded by neurons in sequences of discrete, identical pulses termed action potentials or spikes. There is persistent controversy about the extent to which the precise timing of these spikes is relevant to the function of the brain. We revisit this issue, using the motion-sensitive neurons of the fly visual system as a test case. New experimental methods allow us to deliver more nearly natural visual stimuli, comparable to those which flies encounter in free, acrobatic flight, and new mathematical methods allow us to draw more reliable conclusions about the information content of neural responses even when the set of possible responses is very large. We find that significant amounts of visual information are represented by details of the spike train at millisecond and sub-millisecond precision, even though the sensory input has a correlation time of ~60ms; different patterns of spike timing represent distinct motion trajectories, and the absolute timing of spikes points to particular features of these trajectories with high precision. Under these naturalistic conditions, the system continues to transmit more information at higher photon flux, even though individual photoreceptors are counting more than one million photons per second, and removes redundancy in the stimulus to generate a more efficient neural code.

q-bio.NC↗
arXiv2006

Optimal signal processing in small stochastic biochemical networks

We quantify the influence of the topology of a transcriptional regulatory network on its ability to process environmental signals. By posing the problem in terms of information theory, we may do this without specifying the function performed by the network. Specifically, we study the maximum mutual information between the input (chemical) signal and the output (genetic) response attainable by the network in the context of an analytic model of particle number fluctuations. We perform this analysis for all biochemical circuits, including various feedback loops, that can be built out of 3 chemical species, each under the control of one regulator. We find that a generic network, constrained to low molecule numbers and reasonable response times, can transduce more information than a simple binary switch and, in fact, manages to achieve close to the optimal information transmission fidelity. These high-information solutions are robust to tenfold changes in most of the networks' biochemical parameters; moreover they are easier to achieve in networks containing cycles with an odd number of negative regulators (overall negative feedback) due to their decreased molecular noise (a result which we derive analytically). Finally, we demonstrate that a single circuit can support multiple high-information solutions. These findings suggest a potential resolution of the "cross-talk" dilemma as well as the previously unexplained observation that transcription factors which undergo proteolysis are more likely to be auto-repressive.

q-bio.MN↗
arXiv2006

Genome-wide discovery of modulators of transcriptional interactions in human B lymphocytes

Transcriptional interactions in a cell are modulated by a variety of mechanisms that prevent their representation as pure pairwise interactions between a transcription factor and its target(s). These include, among others, transcription factor activation by phosphorylation and acetylation, formation of active complexes with one or more co-factors, and mRNA/protein degradation and stabilization processes. This paper presents a first step towards the systematic, genome-wide computational inference of genes that modulate the interactions of specific transcription factors at the post-transcriptional level. The method uses a statistical test based on changes in the mutual information between a transcription factor and each of its candidate targets, conditional on the expression of a third gene. The approach was first validated on a synthetic network model, and then tested in the context of a mammalian cellular system. By analyzing 254 microarray expression profiles of normal and tumor related human B lymphocytes, we investigated the post transcriptional modulators of the MYC proto-oncogene, an important transcription factor involved in tumorigenesis. Our method discovered a set of 100 putative modulator genes, responsible for modulating 205 regulatory relationships between MYC and its targets. The set is significantly enriched in molecules with function consistent with their activities as modulators of cellular interactions, recapitulates established MYC regulation pathways, and provides a notable repertoire of novel regulators of MYC function. The approach has broad applicability and can be used to discover modulators of any other transcription factor, provided that adequate expression profile data are available.

q-bio.MN↗
arXiv2005

ARACNE: An Algorithm for the Reconstruction of Gene Regulatory Networks in a Mammalian Cellular Context

Background: Elucidating gene regulatory networks is crucial for understanding normal cell physiology and complex pathologic phenotypes. Existing computational methods for the genome-wide ``reverse engineering'' of such networks have been successful only for lower eukaryotes with simple genomes. Here we present ARACNE, a novel algorithm, using microarray expression profiles, specifically designed to scale up to the complexity of regulatory networks in mammalian cells, yet general enough to address a wider range of network deconvolution problems. This method uses an information theoretic approach to eliminate the majority of indirect interactions inferred by co-expression methods. Results: We prove that ARACNE reconstructs the network exactly (asymptotically) if the effect of loops in the network topology is negligible, and we show that the algorithm works well in practice, even in the presence of numerous loops and complex topologies. We assess ARACNE's ability to reconstruct transcriptional regulatory networks using both a realistic synthetic dataset and a microarray dataset from human B cells. On synthetic datasets ARACNE achieves very low error rates and outperforms established methods, such as Relevance Networks and Bayesian Networks. Application to the deconvolution of genetic networks in human B cells demonstrates ARACNE's ability to infer validated transcriptional targets of the c MYC proto-oncogene. We also study the effects of mis estimation of mutual information on network reconstruction, and show that algorithms based on mutual information ranking are more resilient to estimation errors.

q-bio.MN↗
arXiv2004

Conditional Network Analysis Identifies Candidate Regulator Genes in Human B Cells

Cellular phenotypes are determined by the dynamical activity of networks of co-regulated genes. Elucidating such networks is crucial for the understanding of normal cell physiology as well as for the dissection of complex pathologic phenotypes. Existing methods for such "reverse engineering" of genetic networks from microarray expression data have been successful only in prokaryotes (E. coli) and lower eukaryotes (S. cerevisiae) with relatively simple genomes. Additionally, they have mostly attempted to reconstruct average properties about the network connectivity without capturing the highly conditional nature of the interactions. In this paper we extend the ARACNE algorithm, which we recently introduced and successfully applied to the reconstruction of whole-genome transcriptional networks from mammalian cells, precisely to link the existence of specific network structures to the expression or lack thereof of specific regulator genes. This is accomplished by analyzing thousands of alternative network topologies generated by constraining the data set on the presence or absence of putative regulator genes. By considering interactions that are consistently supported across several such constraints, we identify many transcriptional interactions that would not have been detectable by the original method. By selecting genes that produce statistically significant changes in network topology, we identify novel candidate regulator genes. Further analysis shows that transcription factors, kinases, phosphatases, and other gene families known to effect biochemical interactions, are significantly overrepresented among the set of candidate regulator genes identified in silico, indirectly supporting the validity of the approach.

q-bio.MN↗
arXiv2004

Fluctuation-dissipation theorem and models of learning

Advances in statistical learning theory have resulted in a multitude of different designs of learning machines. But which ones are implemented by brains and other biological information processors? We analyze how various abstract Bayesian learners perform on different data and argue that it is difficult to determine which learning-theoretic computation is performed by a particular organism using just its performance in learning a stationary target (learning curve). Basing on the fluctuation-dissipation relation in statistical physics, we then discuss a different experimental setup that might be able to solve the problem.

q-bio.NC↗
arXiv2004

Information theory, multivariate dependence, and genetic network inference

We define the concept of dependence among multiple variables using maximum entropy techniques and introduce a graphical notation to denote the dependencies. Direct inference of information theoretic quantities from data uncovers dependencies even in undersampled regimes when the joint probability distribution cannot be reliably estimated. The method is tested on synthetic data. We anticipate it to be useful for inference of genetic circuits and other biological signaling networks.

q-bio.QM↗
arXiv2004

Entropy and information in neural spike trains: Progress on the sampling problem

The major problem in information theoretic analysis of neural responses and other biological data is the reliable estimation of entropy--like quantities from small samples. We apply a recently introduced Bayesian entropy estimator to synthetic data inspired by experiments, and to real experimental spike trains. The estimator performs admirably even very deep in the undersampled regime, where other techniques fail. This opens new possibilities for the information theoretic analysis of experiments, and may be of general interest as an example of learning from limited data.

physics.data-an↗
arXiv2003

Potential and field singularity at a surface point charge

The behavior of the magnetic potential near a point charge (fluxon) located at a curved regular boundary surface is shown to be essentially different from that of a volume point charge. In addition to the usual inverse distance singularity, two singular terms are generally present. The first of them, a logarithmic one, is axially symmetric with respect to the boundary normal at the charge location, and proportional to the sum of the two principal curvatures of the boundary surface at this point, that is, to the local mean curvature. The second term is asymmetric and proportional to the difference of the two principal curvatures in question; it is also bounded at the charge location. Both terms vanish, apparently, if the charge is at a planar point of the boundary, and only in this case. The field in the charge vicinity behaves accordingly, featuring generally two singular terms proportional to the inverse distance, in addition to the main inverse distance squared singularity. This result is significant, in particular, for studying the interaction of magnetic vortices in type II superconductors.

math-ph↗
arXiv2002

Inference of entropies of discrete random variables with unknown cardinalities

We examine the recently introduced NSB estimator of entropies of severely undersampled discrete variables and devise a procedure for calculating the involved integrals. We discover that the output of the estimator has a well defined limit for large cardinalities of the variables being studied. Thus one can estimate entropies with no a priori assumptions about these cardinalities, and a closed form solution for such estimates is given.

physics.data-an↗
arXiv2002

Process Pathway Inference via Time Series Analysis

Motivated by recent experimental developments in functional genomics, we construct and test a numerical technique for inferring it process pathways, in which one process calls another process, from time series data. We validate using a case in which data are readily available and formulate an extension, appropriate for genetic regulatory networks, which exploits Bayesian inference and in which the present--day undersampling is compensated for by prior understanding of genetic regulation.

physics.bio-ph↗