TY - GEN AU - Tugrul, Murat AU - Paixao, Tiago AU - Barton, Nicholas H AU - Tkačik, Gašper ID - 9712 TI - Other fitness models for comparison & for interacting TFBSs ER - TY - JOUR AB - Evolution of gene regulation is crucial for our understanding of the phenotypic differences between species, populations and individuals. Sequence-specific binding of transcription factors to the regulatory regions on the DNA is a key regulatory mechanism that determines gene expression and hence heritable phenotypic variation. We use a biophysical model for directional selection on gene expression to estimate the rates of gain and loss of transcription factor binding sites (TFBS) in finite populations under both point and insertion/deletion mutations. Our results show that these rates are typically slow for a single TFBS in an isolated DNA region, unless the selection is extremely strong. These rates decrease drastically with increasing TFBS length or increasingly specific protein-DNA interactions, making the evolution of sites longer than ∼ 10 bp unlikely on typical eukaryotic speciation timescales. Similarly, evolution converges to the stationary distribution of binding sequences very slowly, making the equilibrium assumption questionable. The availability of longer regulatory sequences in which multiple binding sites can evolve simultaneously, the presence of “pre-sites” or partially decayed old sites in the initial sequence, and biophysical cooperativity between transcription factors, can all facilitate gain of TFBS and reconcile theoretical calculations with timescales inferred from comparative genomics. AU - Tugrul, Murat AU - Paixao, Tiago AU - Barton, Nicholas H AU - Tkacik, Gasper ID - 1666 IS - 11 JF - PLoS Genetics TI - Dynamics of transcription factor binding site evolution VL - 11 ER - TY - JOUR AB - Gene expression is controlled primarily by interactions between transcription factor proteins (TFs) and the regulatory DNA sequence, a process that can be captured well by thermodynamic models of regulation. These models, however, neglect regulatory crosstalk: the possibility that noncognate TFs could initiate transcription, with potentially disastrous effects for the cell. Here, we estimate the importance of crosstalk, suggest that its avoidance strongly constrains equilibrium models of TF binding, and propose an alternative nonequilibrium scheme that implements kinetic proofreading to suppress erroneous initiation. This proposal is consistent with the observed covalent modifications of the transcriptional apparatus and predicts increased noise in gene expression as a trade-off for improved specificity. Using information theory, we quantify this trade-off to find when optimal proofreading architectures are favored over their equilibrium counterparts. Such architectures exhibit significant super-Poisson noise at low expression in steady state. AU - Cepeda Humerez, Sarah A AU - Rieckh, Georg AU - Tkacik, Gasper ID - 1576 IS - 24 JF - Physical Review Letters TI - Stochastic proofreading mechanism alleviates crosstalk in transcriptional regulation VL - 115 ER - TY - JOUR AB - Quantifying behaviors of robots which were generated autonomously from task-independent objective functions is an important prerequisite for objective comparisons of algorithms and movements of animals. The temporal sequence of such a behavior can be considered as a time series and hence complexity measures developed for time series are natural candidates for its quantification. The predictive information and the excess entropy are such complexity measures. They measure the amount of information the past contains about the future and thus quantify the nonrandom structure in the temporal sequence. However, when using these measures for systems with continuous states one has to deal with the fact that their values will depend on the resolution with which the systems states are observed. For deterministic systems both measures will diverge with increasing resolution. We therefore propose a new decomposition of the excess entropy in resolution dependent and resolution independent parts and discuss how they depend on the dimensionality of the dynamics, correlations and the noise level. For the practical estimation we propose to use estimates based on the correlation integral instead of the direct estimation of the mutual information based on next neighbor statistics because the latter allows less control of the scale dependencies. Using our algorithm we are able to show how autonomous learning generates behavior of increasing complexity with increasing learning duration. AU - Martius, Georg S AU - Olbrich, Eckehard ID - 1655 IS - 10 JF - Entropy TI - Quantifying emergent behavior of autonomous robots VL - 17 ER - TY - CONF AB - It has been long argued that, because of inherent ambiguity and noise, the brain needs to represent uncertainty in the form of probability distributions. The neural encoding of such distributions remains however highly controversial. Here we present a novel circuit model for representing multidimensional real-valued distributions using a spike based spatio-temporal code. Our model combines the computational advantages of the currently competing models for probabilistic codes and exhibits realistic neural responses along a variety of classic measures. Furthermore, the model highlights the challenges associated with interpreting neural activity in relation to behavioral uncertainty and points to alternative population-level approaches for the experimental validation of distributed representations. AU - Savin, Cristina AU - Denève, Sophie ID - 1708 IS - January TI - Spatio-temporal representations of uncertainty in spiking neural networks VL - 3 ER - TY - JOUR AB - Information processing in the sensory periphery is shaped by natural stimulus statistics. In the periphery, a transmission bottleneck constrains performance; thus efficient coding implies that natural signal components with a predictably wider range should be compressed. In a different regime—when sampling limitations constrain performance—efficient coding implies that more resources should be allocated to informative features that are more variable. We propose that this regime is relevant for sensory cortex when it extracts complex features from limited numbers of sensory samples. To test this prediction, we use central visual processing as a model: we show that visual sensitivity for local multi-point spatial correlations, described by dozens of independently-measured parameters, can be quantitatively predicted from the structure of natural images. This suggests that efficient coding applies centrally, where it extends to higher-order sensory features and operates in a regime in which sensitivity increases with feature variability. AU - Hermundstad, Ann AU - Briguglio, John AU - Conte, Mary AU - Victor, Jonathan AU - Balasubramanian, Vijay AU - Tkacik, Gasper ID - 1886 IS - November JF - eLife TI - Variance predicts salience in central sensory processing ER - TY - JOUR AB - Biopolymer length regulation is a complex process that involves a large number of biological, chemical, and physical subprocesses acting simultaneously across multiple spatial and temporal scales. An illustrative example important for genomic stability is the length regulation of telomeres - nucleoprotein structures at the ends of linear chromosomes consisting of tandemly repeated DNA sequences and a specialized set of proteins. Maintenance of telomeres is often facilitated by the enzyme telomerase but, particularly in telomerase-free systems, the maintenance of chromosomal termini depends on alternative lengthening of telomeres (ALT) mechanisms mediated by recombination. Various linear and circular DNA structures were identified to participate in ALT, however, dynamics of the whole process is still poorly understood. We propose a chemical kinetics model of ALT with kinetic rates systematically derived from the biophysics of DNA diffusion and looping. The reaction system is reduced to a coagulation-fragmentation system by quasi-steady-state approximation. The detailed treatment of kinetic rates yields explicit formulas for expected size distributions of telomeres that demonstrate the key role played by the J factor, a quantitative measure of bending of polymers. The results are in agreement with experimental data and point out interesting phenomena: an appearance of very long telomeric circles if the total telomere density exceeds a critical value (excess mass) and a nonlinear response of the telomere size distributions to the amount of telomeric DNA in the system. The results can be of general importance for understanding dynamics of telomeres in telomerase-independent systems as this mode of telomere maintenance is similar to the situation in tumor cells lacking telomerase activity. Furthermore, due to its universality, the model may also serve as a prototype of an interaction between linear and circular DNA structures in various settings. AU - Kollár, Richard AU - Bod'ová, Katarína AU - Nosek, Jozef AU - Tomáška, Ľubomír ID - 1896 IS - 3 JF - Physical Review E Statistical Nonlinear and Soft Matter Physics TI - Mathematical model of alternative mechanism of telomere length maintenance VL - 89 ER - TY - JOUR AB - Summary: Phenotypes are often environmentally dependent, which requires organisms to track environmental change. The challenge for organisms is to construct phenotypes using the most accurate environmental cue. Here, we use a quantitative genetic model of adaptation by additive genetic variance, within- and transgenerational plasticity via linear reaction norms and indirect genetic effects respectively. We show how the relative influence on the eventual phenotype of these components depends on the predictability of environmental change (fast or slow, sinusoidal or stochastic) and the developmental lag τ between when the environment is perceived and when selection acts. We then decompose expected mean fitness into three components (variance load, adaptation and fluctuation load) to study the fitness costs of within- and transgenerational plasticity. A strongly negative maternal effect coefficient m minimizes the variance load, but a strongly positive m minimises the fluctuation load. The adaptation term is maximized closer to zero, with positive or negative m preferred under different environmental scenarios. Phenotypic plasticity is higher when τ is shorter and when the environment changes frequently between seasonal extremes. Expected mean population fitness is highest away from highest observed levels of phenotypic plasticity. Within- and transgenerational plasticity act in concert to deliver well-adapted phenotypes, which emphasizes the need to study both simultaneously when investigating phenotypic evolution. AU - Ezard, Thomas AU - Prizak, Roshan AU - Hoyle, Rebecca ID - 1909 IS - 3 JF - Functional Ecology TI - The fitness costs of adaptation via phenotypic plasticity and maternal effects VL - 28 ER - TY - JOUR AB - In infectious disease epidemiology the basic reproductive ratio, R0, is defined as the average number of new infections caused by a single infected individual in a fully susceptible population. Many models describing competition for hosts between non-interacting pathogen strains in an infinite population lead to the conclusion that selection favors invasion of new strains if and only if they have higher R0 values than the resident. Here we demonstrate that this picture fails in finite populations. Using a simple stochastic SIS model, we show that in general there is no analogous optimization principle. We find that successive invasions may in some cases lead to strains that infect a smaller fraction of the host population, and that mutually invasible pathogen strains exist. In the limit of weak selection we demonstrate that an optimization principle does exist, although it differs from R0 maximization. For strains with very large R0, we derive an expression for this local fitness function and use it to establish a lower bound for the error caused by neglecting stochastic effects. Furthermore, we apply this weak selection limit to investigate the selection dynamics in the presence of a trade-off between the virulence and the transmission rate of a pathogen. AU - Humplik, Jan AU - Hill, Alison AU - Nowak, Martin ID - 1928 JF - Journal of Theoretical Biology TI - Evolutionary dynamics of infectious diseases in finite populations VL - 360 ER - TY - JOUR AB - A wealth of experimental evidence suggests that working memory circuits preferentially represent information that is behaviorally relevant. Still, we are missing a mechanistic account of how these representations come about. Here we provide a simple explanation for a range of experimental findings, in light of prefrontal circuits adapting to task constraints by reward-dependent learning. In particular, we model a neural network shaped by reward-modulated spike-timing dependent plasticity (r-STDP) and homeostatic plasticity (intrinsic excitability and synaptic scaling). We show that the experimentally-observed neural representations naturally emerge in an initially unstructured circuit as it learns to solve several working memory tasks. These results point to a critical, and previously unappreciated, role for reward-dependent learning in shaping prefrontal cortex activity. AU - Savin, Cristina AU - Triesch, Jochen ID - 1931 IS - MAY JF - Frontiers in Computational Neuroscience TI - Emergence of task-dependent representations in working memory circuits VL - 8 ER - TY - JOUR AB - Understanding the dynamics of noisy neurons remains an important challenge in neuroscience. Here, we describe a simple probabilistic model that accurately describes the firing behavior in a large class (type II) of neurons. To demonstrate the usefulness of this model, we show how it accurately predicts the interspike interval (ISI) distributions, bursting patterns and mean firing rates found by: (1) simulations of the classic Hodgkin-Huxley model with channel noise, (2) experimental data from squid giant axon with a noisy input current and (3) experimental data on noisy firing from a neuron within the suprachiasmatic nucleus (SCN). This simple model has 6 parameters, however, in some cases, two of these parameters are coupled and only 5 parameters account for much of the known behavior. From these parameters, many properties of spiking can be found through simple calculation. Thus, we show how the complex effects of noise can be understood through a simple and general probabilistic model. AU - Bodova, Katarina AU - Paydarfar, David AU - Forger, Daniel ID - 2028 JF - Journal of Theoretical Biology TI - Characterizing spiking in noisy type II neurons VL - 365 ER - TY - JOUR AB - We describe a simple adaptive network of coupled chaotic maps. The network reaches a stationary state (frozen topology) for all values of the coupling parameter, although the dynamics of the maps at the nodes of the network can be nontrivial. The structure of the network shows interesting hierarchical properties and in certain parameter regions the dynamics is polysynchronous: Nodes can be divided in differently synchronized classes but, contrary to cluster synchronization, nodes in the same class need not be connected to each other. These complicated synchrony patterns have been conjectured to play roles in systems biology and circuits. The adaptive system we study describes ways whereby this behavior can evolve from undifferentiated nodes. AU - Botella Soler, Vicente AU - Glendinning, Paul ID - 2183 IS - 6 JF - Physical Review E Statistical Nonlinear and Soft Matter Physics TI - Hierarchy and polysynchrony in an adaptive network VL - 89 ER - TY - JOUR AB - Based on the measurements of noise in gene expression performed during the past decade, it has become customary to think of gene regulation in terms of a two-state model, where the promoter of a gene can stochastically switch between an ON and an OFF state. As experiments are becoming increasingly precise and the deviations from the two-state model start to be observable, we ask about the experimental signatures of complex multistate promoters, as well as the functional consequences of this additional complexity. In detail, we i), extend the calculations for noise in gene expression to promoters described by state transition diagrams with multiple states, ii), systematically compute the experimentally accessible noise characteristics for these complex promoters, and iii), use information theory to evaluate the channel capacities of complex promoter architectures and compare them with the baseline provided by the two-state model. We find that adding internal states to the promoter generically decreases channel capacity, except in certain cases, three of which (cooperativity, dual-role regulation, promoter cycling) we analyze in detail. AU - Rieckh, Georg AU - Tkacik, Gasper ID - 2231 IS - 5 JF - Biophysical Journal SN - 00063495 TI - Noise and information transmission in promoters with multiple internal states VL - 106 ER - TY - JOUR AB - Adaptation in the retina is thought to optimize the encoding of natural light signals into sequences of spikes sent to the brain. While adaptive changes in retinal processing to the variations of the mean luminance level and second-order stimulus statistics have been documented before, no such measurements have been performed when higher-order moments of the light distribution change. We therefore measured the ganglion cell responses in the tiger salamander retina to controlled changes in the second (contrast), third (skew) and fourth (kurtosis) moments of the light intensity distribution of spatially uniform temporally independent stimuli. The skew and kurtosis of the stimuli were chosen to cover the range observed in natural scenes. We quantified adaptation in ganglion cells by studying linear-nonlinear models that capture well the retinal encoding properties across all stimuli. We found that the encoding properties of retinal ganglion cells change only marginally when higher-order statistics change, compared to the changes observed in response to the variation in contrast. By analyzing optimal coding in LN-type models, we showed that neurons can maintain a high information rate without large dynamic adaptation to changes in skew or kurtosis. This is because, for uncorrelated stimuli, spatio-temporal summation within the receptive field averages away non-gaussian aspects of the light intensity distribution. AU - Tkacik, Gasper AU - Ghosh, Anandamohan AU - Schneidman, Elad AU - Segev, Ronen ID - 3263 IS - 1 JF - PLoS One TI - Adaptation to changes in higher-order stimulus statistics in the salamander retina VL - 9 ER - TY - JOUR AB - Transgenerational effects are broader than only parental relationships. Despite mounting evidence that multigenerational effects alter phenotypic and life-history traits, our understanding of how they combine to determine fitness is not well developed because of the added complexity necessary to study them. Here, we derive a quantitative genetic model of adaptation to an extraordinary new environment by an additive genetic component, phenotypic plasticity, maternal and grandmaternal effects. We show how, at equilibrium, negative maternal and negative grandmaternal effects maximize expected population mean fitness. We define negative transgenerational effects as those that have a negative effect on trait expression in the subsequent generation, that is, they slow, or potentially reverse, the expected evolutionary dynamic. When maternal effects are positive, negative grandmaternal effects are preferred. As expected under Mendelian inheritance, the grandmaternal effects have a lower impact on fitness than the maternal effects, but this dual inheritance model predicts a more complex relationship between maternal and grandmaternal effects to constrain phenotypic variance and so maximize expected population mean fitness in the offspring. AU - Prizak, Roshan AU - Ezard, Thomas AU - Hoyle, Rebecca ID - 537 IS - 15 JF - Ecology and Evolution TI - Fitness consequences of maternal and grandmaternal effects VL - 4 ER - TY - GEN AB - Redundancies and correlations in the responses of sensory neurons may seem to waste neural resources, but they can also carry cues about structured stimuli and may help the brain to correct for response errors. To investigate the effect of stimulus structure on redundancy in retina, we measured simultaneous responses from populations of retinal ganglion cells presented with natural and artificial stimuli that varied greatly in correlation structure; these stimuli and recordings are publicly available online. Responding to spatio-temporally structured stimuli such as natural movies, pairs of ganglion cells were modestly more correlated than in response to white noise checkerboards, but they were much less correlated than predicted by a non-adapting functional model of retinal response. Meanwhile, responding to stimuli with purely spatial correlations, pairs of ganglion cells showed increased correlations consistent with a static, non-adapting receptive field and nonlinearity. We found that in response to spatio-temporally correlated stimuli, ganglion cells had faster temporal kernels and tended to have stronger surrounds. These properties of individual cells, along with gain changes that opposed changes in effective contrast at the ganglion cell input, largely explained the pattern of pairwise correlations across stimuli where receptive field measurements were possible. AU - Simmons, Kristina AU - Prentice, Jason AU - Tkačik, Gašper AU - Homann, Jan AU - Yee, Heather AU - Palmer, Stephanie AU - Nelson, Philip AU - Balasubramanian, Vijay ID - 9752 TI - Data from: Transformation of stimulus correlations by the retina ER - TY - JOUR AB - Maximum entropy models are the least structured probability distributions that exactly reproduce a chosen set of statistics measured in an interacting network. Here we use this principle to construct probabilistic models which describe the correlated spiking activity of populations of up to 120 neurons in the salamander retina as it responds to natural movies. Already in groups as small as 10 neurons, interactions between spikes can no longer be regarded as small perturbations in an otherwise independent system; for 40 or more neurons pairwise interactions need to be supplemented by a global interaction that controls the distribution of synchrony in the population. Here we show that such “K-pairwise” models—being systematic extensions of the previously used pairwise Ising models—provide an excellent account of the data. We explore the properties of the neural vocabulary by: 1) estimating its entropy, which constrains the population's capacity to represent visual information; 2) classifying activity patterns into a small set of metastable collective modes; 3) showing that the neural codeword ensembles are extremely inhomogenous; 4) demonstrating that the state of individual neurons is highly predictable from the rest of the population, allowing the capacity for error correction. AU - Tkacik, Gasper AU - Marre, Olivier AU - Amodei, Dario AU - Schneidman, Elad AU - Bialek, William AU - Berry, Michael ID - 2257 IS - 1 JF - PLoS Computational Biology SN - 1553734X TI - Searching for collective behavior in a large network of sensory neurons VL - 10 ER - TY - CHAP AB - Progress in understanding the global brain dynamics has remained slow to date in large part because of the highly multiscale nature of brain activity. Indeed, normal brain dynamics is characterized by complex interactions between multiple levels: from the microscopic scale of single neurons to the mesoscopic level of local groups of neurons, and finally to the macroscopic level of the whole brain. Among the most difficult tasks are those of identifying which scales are significant for a given particular function and describing how the scales affect each other. It is important to realize that the scales of time and space are linked together, or even intertwined, and that causal inference is far more ambiguous between than within levels. We approach this problem from the perspective of our recent work on simultaneous recording from micro- and macroelectrodes in the human brain. We propose a physiological description of these multilevel interactions, based on phase–amplitude coupling of neuronal oscillations that operate at multiple frequencies and on different spatial scales. Specifically, the amplitude of the oscillations on a particular spatial scale is modulated by phasic variations in neuronal excitability induced by lower frequency oscillations that emerge on a larger spatial scale. Following this general principle, it is possible to scale up or scale down the multiscale brain dynamics. It is expected that large-scale network oscillations in the low-frequency range, mediating downward effects, may play an important role in attention and consciousness. AU - Valderrama, Mario AU - Botella Soler, Vicente AU - Le Van Quyen, Michel ED - Meyer, Misha ED - Pesenson, Z. ID - 2413 SN - 9783527411986 T2 - Multiscale Analysis and Nonlinear Dynamics: From Genes to the Brain TI - Neuronal oscillations scale up and scale down the brain dynamics ER - TY - JOUR AB - Models of neural responses to stimuli with complex spatiotemporal correlation structure often assume that neurons are selective for only a small number of linear projections of a potentially high-dimensional input. In this review, we explore recent modeling approaches where the neural response depends on the quadratic form of the input rather than on its linear projection, that is, the neuron is sensitive to the local covariance structure of the signal preceding the spike. To infer this quadratic dependence in the presence of arbitrary (e.g., naturalistic) stimulus distribution, we review several inference methods, focusing in particular on two information theory–based approaches (maximization of stimulus energy and of noise entropy) and two likelihood-based approaches (Bayesian spike-triggered covariance and extensions of generalized linear models). We analyze the formal relationship between the likelihood-based and information-based approaches to demonstrate how they lead to consistent inference. We demonstrate the practical feasibility of these procedures by using model neurons responding to a flickering variance stimulus. AU - Rajan, Kanaka AU - Marre, Olivier AU - Tkacik, Gasper ID - 2818 IS - 7 JF - Neural Computation TI - Learning quadratic receptive fields from neural responses to natural stimuli VL - 25 ER - TY - JOUR AB - Recent work emphasizes that the maximum entropy principle provides a bridge between statistical mechanics models for collective behavior in neural networks and experiments on networks of real neurons. Most of this work has focused on capturing the measured correlations among pairs of neurons. Here we suggest an alternative, constructing models that are consistent with the distribution of global network activity, i.e. the probability that K out of N cells in the network generate action potentials in the same small time bin. The inverse problem that we need to solve in constructing the model is analytically tractable, and provides a natural 'thermodynamics' for the network in the limit of large N. We analyze the responses of neurons in a small patch of the retina to naturalistic stimuli, and find that the implied thermodynamics is very close to an unusual critical point, in which the entropy (in proper units) is exactly equal to the energy. © 2013 IOP Publishing Ltd and SISSA Medialab srl. AU - Tkacik, Gasper AU - Marre, Olivier AU - Mora, Thierry AU - Amodei, Dario AU - Berry, Michael AU - Bialek, William ID - 2850 IS - 3 JF - Journal of Statistical Mechanics Theory and Experiment TI - The simplest maximum entropy model for collective behavior in a neural network VL - 2013 ER - TY - JOUR AB - The number of possible activity patterns in a population of neurons grows exponentially with the size of the population. Typical experiments explore only a tiny fraction of the large space of possible activity patterns in the case of populations with more than 10 or 20 neurons. It is thus impossible, in this undersampled regime, to estimate the probabilities with which most of the activity patterns occur. As a result, the corresponding entropy - which is a measure of the computational power of the neural population - cannot be estimated directly. We propose a simple scheme for estimating the entropy in the undersampled regime, which bounds its value from both below and above. The lower bound is the usual 'naive' entropy of the experimental frequencies. The upper bound results from a hybrid approximation of the entropy which makes use of the naive estimate, a maximum entropy fit, and a coverage adjustment. We apply our simple scheme to artificial data, in order to check their accuracy; we also compare its performance to those of several previously defined entropy estimators. We then apply it to actual measurements of neural activity in populations with up to 100 cells. Finally, we discuss the similarities and differences between the proposed simple estimation scheme and various earlier methods. © 2013 IOP Publishing Ltd and SISSA Medialab srl. AU - Berry, Michael AU - Tkacik, Gasper AU - Dubuis, Julien AU - Marre, Olivier AU - Da Silveira, Ravá ID - 2851 IS - 3 JF - Journal of Statistical Mechanics Theory and Experiment TI - A simple method for estimating the entropy of neural activity VL - 2013 ER - TY - JOUR AB - Neural populations encode information about their stimulus in a collective fashion, by joint activity patterns of spiking and silence. A full account of this mapping from stimulus to neural activity is given by the conditional probability distribution over neural codewords given the sensory input. For large populations, direct sampling of these distributions is impossible, and so we must rely on constructing appropriate models. We show here that in a population of 100 retinal ganglion cells in the salamander retina responding to temporal white-noise stimuli, dependencies between cells play an important encoding role. We introduce the stimulus-dependent maximum entropy (SDME) model—a minimal extension of the canonical linear-nonlinear model of a single neuron, to a pairwise-coupled neural population. We find that the SDME model gives a more accurate account of single cell responses and in particular significantly outperforms uncoupled models in reproducing the distributions of population codewords emitted in response to a stimulus. We show how the SDME model, in conjunction with static maximum entropy models of population vocabulary, can be used to estimate information-theoretic quantities like average surprise and information transmission in a neural population. AU - Granot Atedgi, Einat AU - Tkacik, Gasper AU - Segev, Ronen AU - Schneidman, Elad ID - 2863 IS - 3 JF - PLoS Computational Biology TI - Stimulus-dependent maximum entropy models of neural population codes VL - 9 ER - TY - JOUR AB - We consider a two-parameter family of piecewise linear maps in which the moduli of the two slopes take different values. We provide numerical evidence of the existence of some parameter regions in which the Lyapunov exponent and the topological entropy remain constant. Analytical proof of this phenomenon is also given for certain cases. Surprisingly however, the systems with that property are not conjugate as we prove by using kneading theory. AU - Botella Soler, Vicente AU - Oteo, José AU - Ros, Javier AU - Glendinning, Paul ID - 2861 IS - 12 JF - Journal of Physics A: Mathematical and Theoretical TI - Lyapunov exponent and topological entropy plateaus in piecewise linear maps VL - 46 ER - TY - JOUR AB - The ability of an organism to distinguish between various stimuli is limited by the structure and noise in the population code of its sensory neurons. Here we infer a distance measure on the stimulus space directly from the recorded activity of 100 neurons in the salamander retina. In contrast to previously used measures of stimulus similarity, this "neural metric" tells us how distinguishable a pair of stimulus clips is to the retina, based on the similarity between the induced distributions of population responses. We show that the retinal distance strongly deviates from Euclidean, or any static metric, yet has a simple structure: we identify the stimulus features that the neural population is jointly sensitive to, and show the support-vector-machine- like kernel function relating the stimulus and neural response spaces. We show that the non-Euclidean nature of the retinal distance has important consequences for neural decoding. AU - Tkacik, Gasper AU - Granot Atedgi, Einat AU - Segev, Ronen AU - Schneidman, Elad ID - 2913 IS - 5 JF - Physical Review Letters TI - Retinal metric: a stimulus distance measure derived from population neural responses VL - 110 ER - TY - JOUR AB - 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. AU - Dubuis, Julien AU - Tkacik, Gasper AU - Wieschaus, Eric AU - Gregor, Thomas AU - Bialek, William ID - 3261 IS - 41 JF - PNAS TI - Positional information, in bits VL - 110 ER - TY - JOUR AB - Exposure of an isogenic bacterial population to a cidal antibiotic typically fails to eliminate a small fraction of refractory cells. Historically, fractional killing has been attributed to infrequently dividing or nondividing "persisters." Using microfluidic cultures and time-lapse microscopy, we found that Mycobacterium smegmatis persists by dividing in the presence of the drug isoniazid (INH). Although persistence in these studies was characterized by stable numbers of cells, this apparent stability was actually a dynamic state of balanced division and death. Single cells expressed catalase-peroxidase (KatG), which activates INH, in stochastic pulses that were negatively correlated with cell survival. These behaviors may reflect epigenetic effects, because KatG pulsing and death were correlated between sibling cells. Selection of lineages characterized by infrequent KatG pulsing could allow nonresponsive adaptation during prolonged drug exposure. AU - Wakamoto, Yurichi AU - Dhar, Neraaj AU - Chait, Remy P AU - Schneider, Katrin AU - Signorino Gelo, François AU - Leibler, Stanislas AU - Mckinney, John ID - 499 IS - 6115 JF - Science TI - Dynamic persistence of antibiotic-stressed mycobacteria VL - 339 ER - TY - JOUR AB - Redundancies and correlations in the responses of sensory neurons may seem to waste neural resources, but they can also carry cues about structured stimuli and may help the brain to correct for response errors. To investigate the effect of stimulus structure on redundancy in retina, we measured simultaneous responses from populations of retinal ganglion cells presented with natural and artificial stimuli that varied greatly in correlation structure; these stimuli and recordings are publicly available online. Responding to spatio-temporally structured stimuli such as natural movies, pairs of ganglion cells were modestly more correlated than in response to white noise checkerboards, but they were much less correlated than predicted by a non-adapting functional model of retinal response. Meanwhile, responding to stimuli with purely spatial correlations, pairs of ganglion cells showed increased correlations consistent with a static, non-adapting receptive field and nonlinearity. We found that in response to spatio-temporally correlated stimuli, ganglion cells had faster temporal kernels and tended to have stronger surrounds. These properties of individual cells, along with gain changes that opposed changes in effective contrast at the ganglion cell input, largely explained the pattern of pairwise correlations across stimuli where receptive field measurements were possible. AU - Simmons, Kristina AU - Prentice, Jason AU - Tkacik, Gasper AU - Homann, Jan AU - Yee, Heather AU - Palmer, Stephanie AU - Nelson, Philip AU - Balasubramanian, Vijay ID - 2277 IS - 12 JF - PLoS Computational Biology TI - Transformation of stimulus correlations by the retina VL - 9 ER - TY - JOUR AB - The scale invariance of natural images suggests an analogy to the statistical mechanics of physical systems at a critical point. Here we examine the distribution of pixels in small image patches and show how to construct the corresponding thermodynamics. We find evidence for criticality in a diverging specific heat, which corresponds to large fluctuations in how "surprising" we find individual images, and in the quantitative form of the entropy vs energy. We identify special image configurations as local energy minima and show that average patches within each basin are interpretable as lines and edges in all orientations. AU - Stephens, Greg AU - Mora, Thierry AU - Tkacik, Gasper AU - Bialek, William ID - 2914 IS - 1 JF - Physical Review Letters TI - Statistical thermodynamics of natural images VL - 110 ER - TY - JOUR AB - Living cells must control the reading out or "expression" of information encoded in their genomes, and this regulation often is mediated by transcription factors--proteins that bind to DNA and either enhance or repress the expression of nearby genes. But the expression of transcription factor proteins is itself regulated, and many transcription factors regulate their own expression in addition to responding to other input signals. Here we analyze the simplest of such self-regulatory circuits, asking how parameters can be chosen to optimize information transmission from inputs to outputs in the steady state. Some nonzero level of self-regulation is almost always optimal, with self-activation dominant when transcription factor concentrations are low and self-repression dominant when concentrations are high. In steady state the optimal self-activation is never strong enough to induce bistability, although there is a limit in which the optimal parameters are very close to the critical point. AU - Tkacik, Gasper AU - Walczak, Aleksandra AU - Bialek, William ID - 3262 IS - 4 JF - Physical Review E statistical nonlinear and soft matter physics TI - Optimizing information flow in small genetic networks. III. A self-interacting gene VL - 85 ER - TY - JOUR AB - A boundary element model of a tunnel running through horizontally layered soil with anisotropic material properties is presented. Since there is no analytical fundamental solution for wave propagation inside a layered orthotropic medium in 3D, the fundamental displacements and stresses have to be calculated numerically. In our model this is done in the Fourier domain with respect to space and time. The assumption of a straight tunnel with infinite extension in the x direction makes it possible to decouple the system for every wave number kx, leading to a 2.5D-problem, which is suited for parallel computation. The special form of the fundamental solution, resulting from our Fourier ansatz, and the fact, that the calculation of the boundary integral equation is performed in the Fourier domain, enhances the stability and efficiency of the numerical calculations. AU - Rieckh, Georg AU - Kreuzer, Wolfgang AU - Waubke, Holger AU - Balazs, Peter ID - 3274 IS - 6 JF - Engineering Analysis with Boundary Elements TI - A 2.5D-Fourier-BEM model for vibrations in a tunnel running through layered anisotropic soil VL - 36 ER - TY - JOUR AB - Genetic regulatory networks enable cells to respond to changes in internal and external conditions by dynamically coordinating their gene expression profiles. Our ability to make quantitative measurements in these biochemical circuits has deepened our understanding of what kinds of computations genetic regulatory networks can perform, and with what reliability. These advances have motivated researchers to look for connections between the architecture and function of genetic regulatory networks. Transmitting information between a network's inputs and outputs has been proposed as one such possible measure of function, relevant in certain biological contexts. Here we summarize recent developments in the application of information theory to gene regulatory networks. We first review basic concepts in information theory necessary for understanding recent work. We then discuss the functional complexity of gene regulation, which arises from the molecular nature of the regulatory interactions. We end by reviewing some experiments that support the view that genetic networks responsible for early development of multicellular organisms might be maximizing transmitted 'positional information'. AU - Tkacik, Gasper AU - Walczak, Aleksandra ID - 3374 IS - 15 JF - Journal of Physics: Condensed Matter TI - Information transmission in genetic regulatory networks a review VL - 23 ER - TY - JOUR AB - Here we introduce a database of calibrated natural images publicly available through an easy-to-use web interface. Using a Nikon D70 digital SLR camera, we acquired about six-megapixel images of Okavango Delta of Botswana, a tropical savanna habitat similar to where the human eye is thought to have evolved. Some sequences of images were captured unsystematically while following a baboon troop, while others were designed to vary a single parameter such as aperture, object distance, time of day or position on the horizon. Images are available in the raw RGB format and in grayscale. Images are also available in units relevant to the physiology of human cone photoreceptors, where pixel values represent the expected number of photoisomerizations per second for cones sensitive to long (L), medium (M) and short (S) wavelengths. This database is distributed under a Creative Commons Attribution-Noncommercial Unported license to facilitate research in computer vision, psychophysics of perception, and visual neuroscience. AU - Tkacik, Gasper AU - Garrigan, Patrick AU - Ratliff, Charles AU - Milcinski, Grega AU - Klein, Jennifer AU - Seyfarth, Lucia AU - Sterling, Peter AU - Brainard, David AU - Balasubramanian, Vijay ID - 3384 IS - 6 JF - PLoS One TI - Natural images from the birthplace of the human eye VL - 6 ER -