Biomedical subjects

William Bialek

Publications and source records attributed to William Bialek.

17 recordsLinked to original sources

PubMed2014

Mapping the stereotyped behaviour of freely moving fruit flies.

A frequent assumption in behavioural science is that most of an animal's activities can be described in terms of a small set of stereotyped motifs. Here, we introduce a method for mapping an animal's actions, relying only upon the underlying structure of postural movement data to organize and classify behaviours. Applying this method to the ground-based behaviour of the fruit fly, Drosophila melanogaster, we find that flies perform stereotyped actions roughly 50% of the time, discovering over 100 distinguishable, stereotyped behavioural states. These include multiple modes of locomotion and grooming. We use the resulting measurements as the basis for identifying subtle sex-specific behavioural differences and revealing the low-dimensional nature of animal motions.

Animals↗

PubMed2006

Weak pairwise correlations imply strongly correlated network states in a neural population.

Biological networks have so many possible states that exhaustive sampling is impossible. Successful analysis thus depends on simplifying hypotheses, but experiments on many systems hint that complicated, higher-order interactions among large groups of elements have an important role. Here we show, in the vertebrate retina, that weak correlations between pairs of neurons coexist with strongly collective behaviour in the responses of ten or more neurons. We find that this collective behaviour is described quantitatively by models that capture the observed pairwise correlations but assume no higher-order interactions. These maximum entropy models are equivalent to Ising models, and predict that larger networks are completely dominated by correlation effects. This suggests that the neural code has associative or error-correcting properties, and we provide preliminary evidence for such behaviour. As a first test for the generality of these ideas, we show that similar results are obtained from networks of cultured cortical neurons.

Action Potentials↗

PubMed2005

Information-based clustering.

In an age of increasingly large data sets, investigators in many different disciplines have turned to clustering as a tool for data analysis and exploration. Existing clustering methods, however, typically depend on several nontrivial assumptions about the structure of data. Here, we reformulate the clustering problem from an information theoretic perspective that avoids many of these assumptions. In particular, our formulation obviates the need for defining a cluster "prototype," does not require an a priori similarity metric, is invariant to changes in the representation of the data, and naturally captures nonlinear relations. We apply this approach to different domains and find that it consistently produces clusters that are more coherent than those extracted by existing algorithms. Finally, our approach provides a way of clustering based on collective notions of similarity rather than the traditional pairwise measures.

Algorithms↗

PubMed2005

Diffusion and scaling during early embryonic pattern formation.

Development of spatial patterns in multicellular organisms depends on gradients in the concentration of signaling molecules that control gene expression. In the Drosophila embryo, Bicoid (Bcd) morphogen controls cell fate along 70% of the anteroposterior axis but is translated from mRNA localized at the anterior pole. Gradients of Bcd and other morphogens are thought to arise through diffusion, but this basic assumption has never been rigorously tested in living embryos. Furthermore, because diffusion sets a relationship between length and time scales, it is hard to see how patterns of gene expression established by diffusion would scale proportionately as egg size changes during evolution. Here, we show that the motion of inert molecules through the embryo is well described by the diffusion equation on the relevant length and time scales, and that effective diffusion constants are essentially the same in closely related dipteran species with embryos of very different size. Nonetheless, patterns of gene expression in these different species scale with egg length. We show that this scaling can be traced back to scaling of the Bcd gradient itself. Our results, together with constraints imposed by the time scales of development, suggest that the mechanism for scaling is a species-specific adaptation of the Bcd lifetime.

Animals↗

PubMed2005

A sensory source for motor variation.

Suppose that the variability in our movements is caused not by noise in the motor system itself, nor by fluctuations in our intentions or plans, but rather by errors in our sensory estimates of the external parameters that define the appropriate action. For tasks in which precision is at a premium, performance would be optimal if no noise were added in movement planning and execution: motor output would be as accurate as possible given the quality of sensory inputs. Here we use visually guided smooth-pursuit eye movements in primates as a testing ground for this notion of optimality. In response to repeated presentations of identical target motions, nearly 92% of the variance in eye trajectory can be accounted for as a consequence of errors in sensory estimates of the speed, direction and timing of target motion, plus a small background noise that is observed both during eye movements and during fixations. The magnitudes of the inferred sensory errors agree with the observed thresholds for sensory discrimination by perceptual systems, suggesting that the very different neural processes of perception and action are limited by the same sources of noise.

Animals↗

PubMed2005

Physical limits to biochemical signaling.

Many crucial biological processes operate with surprisingly small numbers of molecules, and there is renewed interest in analyzing the impact of noise associated with these small numbers. Twenty-five years ago, Berg and Purcell showed that bacterial chemotaxis, where a single-celled organism must respond to small changes in concentration of chemicals outside the cell, is limited directly by molecule counting noise and that aspects of the bacteria's behavioral and computational strategies must be chosen to minimize the effects of this noise. Here, we revisit and generalize their arguments to estimate the physical limits to signaling processes within the cell and argue that recent experiments are consistent with performance approaching these limits.

Bacterial Physiological Phenomena↗

PubMed2004

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.

Journal Article↗

PubMed2004

Time course of information about motion direction in visual area MT of macaque monkeys.

We used the responses of neurons in extrastriate visual area MT to determine how well neural noise can be reduced by averaging the responses of neurons across time. For individual MT neurons, we calculated the time course of Shannon information about motion direction from sustained motion at constant velocities. Stimuli were random dot patterns moving at the preferred speed of the cell for 256 msec, in a direction chosen randomly with 15 degrees increments. Information about motion direction calculated from cumulative spike count rose rapidly from the onset of the neural response and then saturated, reaching 80% of maximum information in the first 100 msec. Most of the early saturation of information could be attributed to correlated fluctuations in the spike counts of individual neurons on time scales in excess of 100 msec. Thus, temporal correlations limit the benefits of averaging across time, much as correlations among the responses of different neurons limit the benefits of averaging across large populations. Although information about direction was available quickly from MT neurons, the direction discrimination by individual MT neurons was poor, with mean thresholds above 30 degrees in most neurons. We conclude that almost all available directional information could be extracted from the first few spikes of the response of the neuron, on a time scale comparable with the initiation of smooth pursuit eye movements. However, neural responses still must be pooled across the population in MT to account for the direction discrimination of the pursuit behavior.

Action Potentials↗

PubMed2004

Introductory science and mathematics education for 21st-Century biologists.

Galileo wrote that "the book of nature is written in the language of mathematics"; his quantitative approach to understanding the natural world arguably marks the beginning of modern science. Nearly 400 years later, the fragmented teaching of science in our universities still leaves biology outside the quantitative and mathematical culture that has come to define the physical sciences and engineering. This strikes us as particularly inopportune at a time when opportunities for quantitative thinking about biological systems are exploding. We propose that a way out of this dilemma is a unified introductory science curriculum that fully incorporates mathematics and quantitative thinking.

Biological Science Disciplines↗

PubMed2004

How many clusters? An information-theoretic perspective.

Clustering provides a common means of identifying structure in complex data, and there is renewed interest in clustering as a tool for the analysis of large data sets in many fields. A natural question is how many clusters are appropriate for the description of a given system. Traditional approaches to this problem are based on either a framework in which clusters of a particular shape are assumed as a model of the system or on a two-step procedure in which a clustering criterion determines the optimal assignments for a given number of clusters and a separate criterion measures the goodness of the classification to determine the number of clusters. In a statistical mechanics approach, clustering can be seen as a trade-off between energy- and entropy-like terms, with lower temperature driving the proliferation of clusters to provide a more detailed description of the data. For finite data sets, we expect that there is a limit to the meaningful structure that can be resolved and therefore a minimum temperature beyond which we will capture sampling noise. This suggests that correcting the clustering criterion for the bias that arises due to sampling errors will allow us to find a clustering solution at a temperature that is optimal in the sense that we capture maximal meaningful structure--without having to define an external criterion for the goodness or stability of the clustering. We show that in a general information-theoretic framework, the finite size of a data set determines an optimal temperature, and we introduce a method for finding the maximal number of clusters that can be resolved from the data in the hard clustering limit.

Journal Article↗

PubMed2004

Analyzing neural responses to natural signals: maximally informative dimensions.

We propose a method that allows for a rigorous statistical analysis of neural responses to natural stimuli that are nongaussian and exhibit strong correlations. We have in mind a model in which neurons are selective for a small number of stimulus dimensions out of a high-dimensional stimulus space, but within this subspace the responses can be arbitrarily nonlinear. Existing analysis methods are based on correlation functions between stimuli and responses, but these methods are guaranteed to work only in the case of gaussian stimulus ensembles. As an alternative to correlation functions, we maximize the mutual information between the neural responses and projections of the stimulus onto low-dimensional subspaces. The procedure can be done iteratively by increasing the dimensionality of this subspace. Those dimensions that allow the recovery of all of the information between spikes and the full unprojected stimuli describe the relevant subspace. If the dimensionality of the relevant subspace indeed is small, it becomes feasible to map the neuron's input-output function even under fully natural stimulus conditions. These ideas are illustrated in simulations on model visual and auditory neurons responding to natural scenes and sounds, respectively.

Acoustic Stimulation↗

PubMed2003

Synergy, redundancy, and independence in population codes.

A key issue in understanding the neural code for an ensemble of neurons is the nature and strength of correlations between neurons and how these correlations are related to the stimulus. The issue is complicated by the fact that there is not a single notion of independence or lack of correlation. We distinguish three kinds: (1) activity independence; (2) conditional independence; and (3) information independence. Each notion is related to an information measure: the information between cells, the information between cells given the stimulus, and the synergy of cells about the stimulus, respectively. We show that these measures form an interrelated framework for evaluating contributions of signal and noise correlations to the joint information conveyed about the stimulus and that at least two of the three measures must be calculated to characterize a population code. This framework is compared with others recently proposed in the literature. In addition, we distinguish questions about how information is encoded by a population of neurons from how that information can be decoded. Although information theory is natural and powerful for questions of encoding, it is not sufficient for characterizing the process of decoding. Decoding fundamentally requires an error measure that quantifies the importance of the deviations of estimated stimuli from actual stimuli. Because there is no a priori choice of error measure, questions about decoding cannot be put on the same level of generality as for encoding.

Action Potentials↗

PubMed2003

Network information and connected correlations.

Entropy and information provide natural measures of correlation among elements in a network. We construct here the information theoretic analog of connected correlation functions: irreducible N-point correlation is measured by a decrease in entropy for the joint distribution of N variables relative to the maximum entropy allowed by all the observed N-1 variable distributions. We calculate the "connected information" terms for several examples and show that it also enables the decomposition of the information that is carried by a population of elements about an outside source.

Information Services↗

PubMed2003

The information content of receptive fields.

The nervous system must observe a complex world and produce appropriate, sometimes complex, behavioral responses. In contrast to this complexity, neural responses are often characterized through very simple descriptions such as receptive fields or tuning curves. Do these characterizations adequately reflect the true dimensionality reduction that takes place in the nervous system, or are they merely convenient oversimplifications? Here we address this question for the target-selective descending neurons (TSDNs) of the dragonfly. Using extracellular multielectrode recordings of a population of TSDNs, we quantify the completeness of the receptive field description of these cells and conclude that the information in independent instantaneous position and velocity receptive fields accounts for 70%-90% of the total information in single spikes. Thus, we demonstrate that this simple receptive field model is close to a complete description of the features in the stimulus that evoke TSDN response.

Action Potentials↗

PubMed2003

Computation in a single neuron: Hodgkin and Huxley revisited.

A spiking neuron "computes" by transforming a complex dynamical input into a train of action potentials, or spikes. The computation performed by the neuron can be formulated as dimensional reduction, or feature detection, followed by a nonlinear decision function over the low-dimensional space. Generalizations of the reverse correlation technique with white noise input provide a numerical strategy for extracting the relevant low-dimensional features from experimental data, and information theory can be used to evaluate the quality of the low-dimensional approximation. We apply these methods to analyze the simplest biophysically realistic model neuron, the Hodgkin-Huxley (HH) model, using this system to illustrate the general methodological issues. We focus on the features in the stimulus that trigger a spike, explicitly eliminating the effects of interactions between spikes. One can approximate this triggering "feature space" as a two-dimensional linear subspace in the high-dimensional space of input histories, capturing in this way a substantial fraction of the mutual information between inputs and spike time. We find that an even better approximation, however, is to describe the relevant subspace as two dimensional but curved; in this way, we can capture 90% of the mutual information even at high time resolution. Our analysis provides a new understanding of the computational properties of the HH model. While it is common to approximate neural behavior as "integrate and fire," the HH model is not an integrator nor is it well described by a single threshold.

Action Potentials↗

PubMed2002

Statistical properties of spike trains: universal and stimulus-dependent aspects.

Statistical properties of spike trains measured from a sensory neuron in vivo are studied experimentally and theoretically. Experiments are performed on an identified neuron in the visual system of the blowfly. It is shown that the spike trains exhibit universal behavior over a short time, modulated by a stimulus-dependent envelope over a long time. A model of the neuron as a nonlinear oscillator driven by noise and by an external stimulus is suggested to account for these results. In the short-time universal regime, the main biophysical effect is refractoriness, which can be described as a repulsive ( 1/x) interaction law among spikes. A universal distribution function for intervals is found, defining a point process with special symmetry properties. The long-time modulations in the spike train are related in a simple way to the properties of the input stimulus as seen through the neuronal nonlinearity. Thus our model enables a separation of the effects of internal neuronal properties from the effect of external stimulus properties. Explicit formulas are derived for different statistical properties, which are in very good agreement with the data in both the universal and the stimulus-dependent regimes.

Animals↗

PubMed2002

Occam factors and model independent Bayesian learning of continuous distributions.

Learning of a smooth but nonparametric probability density can be regularized using methods of quantum field theory. We implement a field theoretic prior numerically, test its efficacy, and show that the data and the phase space factors arising from the integration over the model space determine the free parameter of the theory ("smoothness scale") self-consistently. This persists even for distributions that are atypical in the prior and is a step towards a model independent theory for learning continuous distributions. Finally, we point out that a wrong parametrization of a model family may sometimes be advantageous for small data sets.

Journal Article↗