We describe a computational protocol for the ARACNE algorithm, an information-theoretic method for identifying transcriptional interactions between gene products using microarray expression profile data. Similar to other algorithms, ARACNE predicts potential functional associations among genes, or novel functions for uncharacterized genes, by identifying statistical dependencies between gene products. However, based on biochemical validation, literature searches and DNA binding site enrichment analysis, ARACNE has also proven effective in identifying bona fide transcriptional targets, even in complex mammalian networks. Thus we envision that predictions made by ARACNE, especially when supplemented with prior knowledge or additional data sources, can provide appropriate hypotheses for the further investigation of cellular networks. While the examples in this protocol use only gene expression profile data, the algorithm's theoretical basis readily extends to a variety of other high-throughput measurements, such as pathway-specific or genome-wide proteomics, microRNA and metabolomics data. As these data become readily available, we expect that ARACNE might prove increasingly useful in elucidating the underlying interaction models. For a microarray data set containing approximately 10,000 probes, reconstructing the network around a single probe completes in several minutes using a desktop computer with a Pentium 4 processor. Reconstructing a genome-wide network generally requires a computational cluster, especially if the recommended bootstrapping procedure is used.

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.

We construct a unifying theory of geometric effects in mesoscopic stochastic kinetics. We demonstrate that the adiabatic pump and the reversible ratchet effects, as well as similar new phenomena in other domains, such as in epidemiology, all follow from very similar geometric phase contributions to the effective action in the stochastic path integral representation of the moment generating function. The theory provides the universal technique for identification, prediction, and calculation of pumplike phenomena in an arbitrary mesoscopic stochastic framework.

Dynamics of complex systems is often driven by large and intricate networks of microscopic interactions, whose sheer size obfuscates understanding. With limited experimental data, many parameters of such dynamics are unknown, and thus detailed, mechanistic models risk overfitting and making faulty predictions. At the other extreme, simple ad hoc models often miss defining features of the underlying systems. Here we develop an approach that instead constructs phenomenological, coarse-grained models of network dynamics that automatically adapt their complexity to the available data. Such adaptive models produce accurate predictions even when microscopic details are unknown. The approach is computationally tractable, even for a relatively large number of dynamical variables. Using simulated data, it correctly infers the phase space structure for planetary motion, avoids overfitting in a biological signalling system and produces accurate predictions for yeast glycolysis with tens of data points and over half of the interacting species unobserved.

Gradient sensing requires at least two measurements at different points in space. These measurements must then be communicated to a common location to be compared, which is unavoidably noisy. Although much is known about the limits of measurement precision by cells, the limits placed by the communication are not understood. Motivated by recent experiments, we derive the fundamental limits to the precision of gradient sensing in a multicellular system, accounting for communication and temporal integration. The gradient is estimated by comparing a "local" and a "global" molecular reporter of the external concentration, where the global reporter is exchanged between neighboring cells. Using the fluctuation-dissipation framework, we find, in contrast to the case when communication is ignored, that precision saturates with the number of cells independently of the measurement time duration, because communication establishes a maximum length scale over which sensory information can be reliably conveyed. Surprisingly, we also find that precision is improved if the local reporter is exchanged between cells as well, albeit more slowly than the global reporter. The reason is that whereas exchange of the local reporter weakens the comparison, it decreases the measurement noise. We term such a model "regional excitation-global inhibition." Our results demonstrate that fundamental sensing limits are necessarily sharpened when the need to communicate information is taken into account. C ells sense spatial gradients in environmental chemicals with remarkable precision. A single amoeba, for example, can respond to a difference of roughly 10 attractant molecules between the front and the back of the cell (1). Cells are even more sensitive when they are in a group: Cultures of many neurons respond to chemical gradients equivalent to a difference of only one molecule across an individual neuron's axonal growth cone (2), clusters of malignant lymphocytes have a wider chemotactic sensitivity than single cells (3), and groups of communicating epithelial cells detect gradients that are too weak for a single cell to detect (4). More generally, collective chemosensing properties are often very distinct from those in individual cells (3, 5-7). These observations have generated a renewed interest in the question of what sets the fundamental limit to the precision of gradient sensing in large, spatially extended, often collective sensory systems.Fundamentally, sensing a stationary gradient requires at least two measurements to be made at different points in space. The precision of these two or more individual measurements bounds the gradient sensing precision (8, 9). In its turn, each individual measurement is limited by the finite number of molecules within the detector volume and the ability of the detector to integrate over time, a point first made by Berg and Purcell (BP) (8). More detailed calculations of gradient sensing by specific geometries of receptors have since confirmed that the precision of gradient sensing remains limited by ...

A fundamental problem in neuroscience is understanding how sequences of action potentials ("spikes") encode information about sensory signals and motor outputs. Although traditional theories assume that this information is conveyed by the total number of spikes fired within a specified time interval (spike rate), recent studies have shown that additional information is carried by the millisecond-scale timing patterns of action potentials (spike timing). However, it is unknown whether or how subtle differences in spike timing drive differences in perception or behavior, leaving it unclear whether the information in spike timing actually plays a role in brain function. By examining the activity of individual motor units (the muscle fibers innervated by a single motor neuron) and manipulating patterns of activation of these neurons, we provide both correlative and causal evidence that the nervous system uses millisecond-scale variations in the timing of spikes within multispike patterns to control a vertebrate behavior-namely, respiration in the Bengalese finch, a songbird. These findings suggest that a fundamental assumption of current theories of motor coding requires revision.motor systems | neurophysiology | computational neuroscience | information theory | songbird T he brain uses sequences of spikes to encode sensory and motor signals. In principle, neurons can encode this information via their firing rates, the precise timing of their spikes, or both (1, 2). Although many studies have shown that spike timing contains information beyond that in the rate in sensory codes (3-5), these studies could not verify whether precise timing affects perception or behavior. In motor systems, rate coding approaches dominate (6, 7), but we recently showed that precise spike timing in motor cortex can predict upcoming behavior better than spike rates (8), showing that spike timing carries information in motor as well as sensory cortex. However, as in sensory systems, it remains unknown whether spike timing in motor systems actually controls variations in behavior (9, 10). Resolving this question, therefore, requires examining the spike code used by the neurons that innervate the muscles, because discovering an apparent spike timing code in any brain area upstream of motor neurons is subject to the same ambiguity about whether spike timing patterns actually affect behavior.A spike timing-based theory of motor production predicts that millisecond-scale fluctuations in spike timing, holding other spike train features constant, will causally influence behavior. We tested this prediction by analyzing the activity of single motor units (that is, the muscle fibers innervated by a single motor neuron), focusing largely on the minimal patterns that have variable spike timing but fixed firing rate, burst onset, and burst duration: sequences of three spikes ("triplets"), where the third spike is a fixed latency after the first, but the timing of the middle spike varies. We examined timing codes in songbirds by focusing on respiration, ...

The joint probability distribution of states of many degrees of freedom in biological systems, such as firing patterns in neural networks or antibody sequence compositions, often follows Zipf’s law, where a power law is observed on a rank-frequency plot. This behavior has been shown to imply that these systems reside near a unique critical point where the extensive parts of the entropy and energy are exactly equal. Here, we show analytically, and via numerical simulations, that Zipf-like probability distributions arise naturally if there is a fluctuating unobserved variable (or variables) that affects the system, such as a common input stimulus that causes individual neurons to fire at time-varying rates. In statistics and machine learning, these are called latent-variable or mixture models. We show that Zipf’s law arises generically for large systems, without fine-tuning parameters to a point. Our work gives insight into the ubiquity of Zipf’s law in a wide range of systems.

Collective cell responses to exogenous cues depend on cell-cell interactions. In principle, these can result in enhanced sensitivity to weak and noisy stimuli. However, this has not yet been shown experimentally, and, little is known about how multicellular signal processing modulates single cell sensitivity to extracellular signaling inputs, including those guiding complex changes in the tissue form and function. Here we explored if cell-cell communication can enhance the ability of cell ensembles to sense and respond to weak gradients of chemotactic cues. Using a combination of experiments with mammary epithelial cells and mathematical modeling, we find that multicellular sensing enables detection of and response to shallow Epidermal Growth Factor (EGF) gradients that are undetectable by single cells. However, the advantage of this type of gradient sensing is limited by the noisiness of the signaling relay, necessary to integrate spatially distributed ligand concentration information. We calculate the fundamental sensory limits imposed by this communication noise and combine them with the experimental data to estimate the effective size of multicellular sensory groups involved in gradient sensing. Functional experiments strongly implicated intercellular communication through gap junctions and calcium release from intracellular stores as mediators of collective gradient sensing. The resulting integrative analysis provides a framework for understanding the advantages and limitations of sensory information processing by relays of chemically coupled cells. Significance StatementWhat new properties may result from collective cell behavior, and how these emerging capabilities may influence shaping and function of tissues, in health and disease? Here, we explored these questions in the context of epithelial branching morphogenesis. We show experimentally that, while individual mammary epithelial cells are incapable of sensing extremely weak gradients of a growth factor, cellular collectives in organotypic cultures exhibit reliable, gradient driven, directional growth. This underscores a critical importance of collective cell-cell communication and computation in gradient sensing. We develop and verify a biophysical theory of such communication, and identify the mechanisms by which it is implemented in the mammary epithelium, quantitatively analyzing both advantages and limitations of biochemical cellular communication in collective decision making.All rights reserved. No reuse allowed without permission.(which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity.