Background: Elucidating gene regulatory networks is crucial for understanding normal cell physiology and complex pathologic phenotypes. Existing computational methods for the genomewide "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 coexpression methods.

Molecular noise restricts the ability of an individual cell to resolve input signals of different strengths and gather information about the external environment. Transmitting information through complex signaling networks with redundancies can overcome this limitation. We developed an integrative theoretical and experimental framework, based on the formalism of information theory, to quantitatively predict and measure the amount of information transduced by molecular and cellular networks. Analyzing tumor necrosis factor (TNF) signaling revealed that individual TNF signaling pathways transduce information sufficient for accurate binary decisions, and an upstream bottleneck limits the information gained via multiple pathways together. Negative feedback to this bottleneck could both alleviate and enhance its limiting effect, despite decreasing noise. Bottlenecks likewise constrain information attained by networks signaling through multiple genes or cells.

We define predictive information I(pred)(T) as the mutual information between the past and the future of a time series. Three qualitatively different behaviors are found in the limit of large observation times T:I(pred)(T) can remain finite, grow logarithmically, or grow as a fractional power law. If the time series allows us to learn a model with a finite number of parameters, then I(pred)(T) grows logarithmically with a coefficient that counts the dimensionality of the model space. In contrast, power-law growth is associated, for example, with the learning of infinite parameter (or nonparametric) models such as continuous functions with smoothness constraints. There are connections between the predictive information and measures of complexity that have been defined both in learning theory and the analysis of physical systems through statistical mechanics and dynamical systems theory. Furthermore, in the same way that entropy provides the unique measure of available information consistent with some simple and plausible conditions, we argue that the divergent part of I(pred)(T) provides the unique measure for the complexity of dynamics underlying a time series. Finally, we discuss how these ideas may be useful in problems in physics, statistics, and biology.

Abstract. -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.Single molecule experiments [1] have led to a resurgence of work on the stochastic version of the classical Michaelis-Menten (MM) enzymatic mechanism that describes the enzymedriven catalytic conversion of a substrate into a product [2]. A lot of progress (analytical and numerical) has been made under various assumptions and for various internal enzyme structures [3][4][5][6][7]. Still, many questions linger. Specifically, linear signal transduction properties of biochemical networks, such as frequency dependent gains, are of a high interest [8][9][10]. These are studied by probing responses to periodic perturbations in the input signals (in our case, kinetic rates) due to fluctuations in chemical concentrations, in temperature, or due to other signals. However, such approaches usually disregard a phenomena known from the theory of stochastic ratchets [11], especially in the context of biological transport [12][13][14][15]. Namely, a system's symmetry may break, and, under an influence of a periodic or random zero-mean perturbation, the system may respond with a finite flux in a preferred direction. This, indeed, happens for the MM reaction [16], and we study the phenomenon in detail in this work.The ratchet or pump effect manifests itself during periodic driving of simple classical systems, such as a channel in a cell membrane, which is formally equivalent to the MM enzyme [16][17][18][19][20][21][22][23][24][25][26]. The prevalence of the transport terminology over the chemical one in the literature is grounded in experiments, where driving is achieved by application of periodic electric field or nonequilibrium noise that modulate barrier heights for different channel conformations. The resulting cross-membrane flux has contributions that have no analog in stationary conditions. p-1