@article{1701,
abstract = {The activity of a neural network is defined by patterns of spiking and silence from the individual neurons. Because spikes are (relatively) sparse, patterns of activity with increasing numbers of spikes are less probable, but, with more spikes, the number of possible patterns increases. This tradeoff between probability and numerosity is mathematically equivalent to the relationship between entropy and energy in statistical physics. We construct this relationship for populations of up to N = 160 neurons in a small patch of the vertebrate retina, using a combination of direct and model-based analyses of experiments on the response of this network to naturalistic movies. We see signs of a thermodynamic limit, where the entropy per neuron approaches a smooth function of the energy per neuron as N increases. The form of this function corresponds to the distribution of activity being poised near an unusual kind of critical point. We suggest further tests of criticality, and give a brief discussion of its functional significance. },
author = {Tkacik, Gasper and Mora, Thierry and Marre, Olivier and Amodei, Dario and Palmer, Stephanie and Berry Ii, Michael and Bialek, William},
journal = {PNAS},
number = {37},
pages = {11508 -- 11513},
publisher = {National Academy of Sciences},
title = {{Thermodynamics and signatures of criticality in a network of neurons}},
doi = {10.1073/pnas.1514188112},
volume = {112},
year = {2015},
}
@article{1827,
abstract = {Bow-tie or hourglass structure is a common architectural feature found in many biological systems. A bow-tie in a multi-layered structure occurs when intermediate layers have much fewer components than the input and output layers. Examples include metabolism where a handful of building blocks mediate between multiple input nutrients and multiple output biomass components, and signaling networks where information from numerous receptor types passes through a small set of signaling pathways to regulate multiple output genes. Little is known, however, about how bow-tie architectures evolve. Here, we address the evolution of bow-tie architectures using simulations of multi-layered systems evolving to fulfill a given input-output goal. We find that bow-ties spontaneously evolve when the information in the evolutionary goal can be compressed. Mathematically speaking, bow-ties evolve when the rank of the input-output matrix describing the evolutionary goal is deficient. The maximal compression possible (the rank of the goal) determines the size of the narrowest part of the network—that is the bow-tie. A further requirement is that a process is active to reduce the number of links in the network, such as product-rule mutations, otherwise a non-bow-tie solution is found in the evolutionary simulations. This offers a mechanism to understand a common architectural principle of biological systems, and a way to quantitate the effective rank of the goals under which they evolved.},
author = {Friedlander, Tamar and Mayo, Avraham and Tlusty, Tsvi and Alon, Uri},
journal = {PLoS Computational Biology},
number = {3},
publisher = {Public Library of Science},
title = {{Evolution of bow-tie architectures in biology}},
doi = {10.1371/journal.pcbi.1004055},
volume = {11},
year = {2015},
}
@article{1861,
abstract = {Continuous-time Markov chains are commonly used in practice for modeling biochemical reaction networks in which the inherent randomness of themolecular interactions cannot be ignored. This has motivated recent research effort into methods for parameter inference and experiment design for such models. The major difficulty is that such methods usually require one to iteratively solve the chemical master equation that governs the time evolution of the probability distribution of the system. This, however, is rarely possible, and even approximation techniques remain limited to relatively small and simple systems. An alternative explored in this article is to base methods on only some low-order moments of the entire probability distribution. We summarize the theory behind such moment-based methods for parameter inference and experiment design and provide new case studies where we investigate their performance.},
author = {Ruess, Jakob and Lygeros, John},
journal = {ACM Transactions on Modeling and Computer Simulation},
number = {2},
publisher = {ACM},
title = {{Moment-based methods for parameter inference and experiment design for stochastic biochemical reaction networks}},
doi = {10.1145/2688906},
volume = {25},
year = {2015},
}
@article{1885,
abstract = {The concept of positional information is central to our understanding of how cells determine their location in a multicellular structure and thereby their developmental fates. Nevertheless, positional information has neither been defined mathematically nor quantified in a principled way. Here we provide an information-theoretic definition in the context of developmental gene expression patterns and examine the features of expression patterns that affect positional information quantitatively. We connect positional information with the concept of positional error and develop tools to directly measure information and error from experimental data. We illustrate our framework for the case of gap gene expression patterns in the early Drosophila embryo and show how information that is distributed among only four genes is sufficient to determine developmental fates with nearly single-cell resolution. Our approach can be generalized to a variety of different model systems; procedures and examples are discussed in detail. },
author = {Tkacik, Gasper and Dubuis, Julien and Petkova, Mariela and Gregor, Thomas},
journal = {Genetics},
number = {1},
pages = {39 -- 59},
publisher = {Genetics Society of America},
title = {{Positional information, positional error, and readout precision in morphogenesis: A mathematical framework}},
doi = {10.1534/genetics.114.171850},
volume = {199},
year = {2015},
}
@article{1940,
abstract = {We typically think of cells as responding to external signals independently by regulating their gene expression levels, yet they often locally exchange information and coordinate. Can such spatial coupling be of benefit for conveying signals subject to gene regulatory noise? Here we extend our information-theoretic framework for gene regulation to spatially extended systems. As an example, we consider a lattice of nuclei responding to a concentration field of a transcriptional regulator (the "input") by expressing a single diffusible target gene. When input concentrations are low, diffusive coupling markedly improves information transmission; optimal gene activation functions also systematically change. A qualitatively new regulatory strategy emerges where individual cells respond to the input in a nearly step-like fashion that is subsequently averaged out by strong diffusion. While motivated by early patterning events in the Drosophila embryo, our framework is generically applicable to spatially coupled stochastic gene expression models.},
author = {Sokolowski, Thomas R and Tkacik, Gasper},
journal = {Physical Review E Statistical Nonlinear and Soft Matter Physics},
number = {6},
publisher = {American Institute of Physics},
title = {{Optimizing information flow in small genetic networks. IV. Spatial coupling}},
doi = {10.1103/PhysRevE.91.062710},
volume = {91},
year = {2015},
}
@article{1538,
abstract = {Systems biology rests on the idea that biological complexity can be better unraveled through the interplay of modeling and experimentation. However, the success of this approach depends critically on the informativeness of the chosen experiments, which is usually unknown a priori. Here, we propose a systematic scheme based on iterations of optimal experiment design, flow cytometry experiments, and Bayesian parameter inference to guide the discovery process in the case of stochastic biochemical reaction networks. To illustrate the benefit of our methodology, we apply it to the characterization of an engineered light-inducible gene expression circuit in yeast and compare the performance of the resulting model with models identified from nonoptimal experiments. In particular, we compare the parameter posterior distributions and the precision to which the outcome of future experiments can be predicted. Moreover, we illustrate how the identified stochastic model can be used to determine light induction patterns that make either the average amount of protein or the variability in a population of cells follow a desired profile. Our results show that optimal experiment design allows one to derive models that are accurate enough to precisely predict and regulate the protein expression in heterogeneous cell populations over extended periods of time.},
author = {Ruess, Jakob and Parise, Francesca and Milias Argeitis, Andreas and Khammash, Mustafa and Lygeros, John},
journal = {PNAS},
number = {26},
pages = {8148 -- 8153},
publisher = {National Academy of Sciences},
title = {{Iterative experiment design guides the characterization of a light-inducible gene expression circuit}},
doi = {10.1073/pnas.1423947112},
volume = {112},
year = {2015},
}
@article{1539,
abstract = {Many stochastic models of biochemical reaction networks contain some chemical species for which the number of molecules that are present in the system can only be finite (for instance due to conservation laws), but also other species that can be present in arbitrarily large amounts. The prime example of such networks are models of gene expression, which typically contain a small and finite number of possible states for the promoter but an infinite number of possible states for the amount of mRNA and protein. One of the main approaches to analyze such models is through the use of equations for the time evolution of moments of the chemical species. Recently, a new approach based on conditional moments of the species with infinite state space given all the different possible states of the finite species has been proposed. It was argued that this approach allows one to capture more details about the full underlying probability distribution with a smaller number of equations. Here, I show that the result that less moments provide more information can only stem from an unnecessarily complicated description of the system in the classical formulation. The foundation of this argument will be the derivation of moment equations that describe the complete probability distribution over the finite state space but only low-order moments over the infinite state space. I will show that the number of equations that is needed is always less than what was previously claimed and always less than the number of conditional moment equations up to the same order. To support these arguments, a symbolic algorithm is provided that can be used to derive minimal systems of unconditional moment equations for models with partially finite state space. },
author = {Ruess, Jakob},
journal = {Journal of Chemical Physics},
number = {24},
publisher = {American Institute of Physics},
title = {{Minimal moment equations for stochastic models of biochemical reaction networks with partially finite state space}},
doi = {10.1063/1.4937937},
volume = {143},
year = {2015},
}
@article{1564,
author = {Gilson, Matthieu and Savin, Cristina and Zenke, Friedemann},
journal = {Frontiers in Computational Neuroscience},
number = {11},
publisher = {Frontiers Research Foundation},
title = {{Editorial: Emergent neural computation from the interaction of different forms of plasticity}},
doi = {10.3389/fncom.2015.00145},
volume = {9},
year = {2015},
}
@article{1570,
abstract = {Grounding autonomous behavior in the nervous system is a fundamental challenge for neuroscience. In particular, self-organized behavioral development provides more questions than answers. Are there special functional units for curiosity, motivation, and creativity? This paper argues that these features can be grounded in synaptic plasticity itself, without requiring any higher-level constructs. We propose differential extrinsic plasticity (DEP) as a new synaptic rule for self-learning systems and apply it to a number of complex robotic systems as a test case. Without specifying any purpose or goal, seemingly purposeful and adaptive rhythmic behavior is developed, displaying a certain level of sensorimotor intelligence. These surprising results require no systemspecific modifications of the DEP rule. They rather arise from the underlying mechanism of spontaneous symmetry breaking,which is due to the tight brain body environment coupling. The new synaptic rule is biologically plausible and would be an interesting target for neurobiological investigation. We also argue that this neuronal mechanism may have been a catalyst in natural evolution.},
author = {Der, Ralf and Martius, Georg S},
journal = {PNAS},
number = {45},
pages = {E6224 -- E6232},
publisher = {National Academy of Sciences},
title = {{Novel plasticity rule can explain the development of sensorimotor intelligence}},
doi = {10.1073/pnas.1508400112},
volume = {112},
year = {2015},
}
@article{1576,
abstract = {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.},
author = {Cepeda Humerez, Sarah A and Rieckh, Georg and Tkacik, Gasper},
journal = {Physical Review Letters},
number = {24},
publisher = {American Physical Society},
title = {{Stochastic proofreading mechanism alleviates crosstalk in transcriptional regulation}},
doi = {10.1103/PhysRevLett.115.248101},
volume = {115},
year = {2015},
}
@article{1655,
abstract = {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.},
author = {Martius, Georg S and Olbrich, Eckehard},
journal = {Entropy},
number = {10},
pages = {7266 -- 7297},
publisher = {Multidisciplinary Digital Publishing Institute},
title = {{Quantifying emergent behavior of autonomous robots}},
doi = {10.3390/e17107266},
volume = {17},
year = {2015},
}
@inproceedings{1658,
abstract = {Continuous-time Markov chain (CTMC) models have become a central tool for understanding the dynamics of complex reaction networks and the importance of stochasticity in the underlying biochemical processes. When such models are employed to answer questions in applications, in order to ensure that the model provides a sufficiently accurate representation of the real system, it is of vital importance that the model parameters are inferred from real measured data. This, however, is often a formidable task and all of the existing methods fail in one case or the other, usually because the underlying CTMC model is high-dimensional and computationally difficult to analyze. The parameter inference methods that tend to scale best in the dimension of the CTMC are based on so-called moment closure approximations. However, there exists a large number of different moment closure approximations and it is typically hard to say a priori which of the approximations is the most suitable for the inference procedure. Here, we propose a moment-based parameter inference method that automatically chooses the most appropriate moment closure method. Accordingly, contrary to existing methods, the user is not required to be experienced in moment closure techniques. In addition to that, our method adaptively changes the approximation during the parameter inference to ensure that always the best approximation is used, even in cases where different approximations are best in different regions of the parameter space.},
author = {Bogomolov, Sergiy and Henzinger, Thomas A and Podelski, Andreas and Ruess, Jakob and Schilling, Christian},
location = {Nantes, France},
pages = {77 -- 89},
publisher = {Springer},
title = {{Adaptive moment closure for parameter inference of biochemical reaction networks}},
doi = {10.1007/978-3-319-23401-4_8},
volume = {9308},
year = {2015},
}
@article{1666,
abstract = {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.},
author = {Tugrul, Murat and Paixao, Tiago and Barton, Nicholas H and Tkacik, Gasper},
journal = {PLoS Genetics},
number = {11},
publisher = {Public Library of Science},
title = {{Dynamics of transcription factor binding site evolution}},
doi = {10.1371/journal.pgen.1005639},
volume = {11},
year = {2015},
}
@inproceedings{1708,
abstract = {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.},
author = {Savin, Cristina and Denève, Sophie},
location = {Montreal, Canada},
number = {January},
pages = {2024 -- 2032},
publisher = {Neural Information Processing Systems},
title = {{Spatio-temporal representations of uncertainty in spiking neural networks}},
volume = {3},
year = {2014},
}
@article{1886,
abstract = {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.},
author = {Hermundstad, Ann and Briguglio, John and Conte, Mary and Victor, Jonathan and Balasubramanian, Vijay and Tkacik, Gasper},
journal = {eLife},
number = {November},
publisher = {eLife Sciences Publications},
title = {{Variance predicts salience in central sensory processing}},
doi = {10.7554/eLife.03722},
year = {2014},
}
@article{1896,
abstract = {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.},
author = {Kollár, Richard and Bod'ová, Katarína and Nosek, Jozef and Tomáška, Ľubomír},
journal = {Physical Review E Statistical Nonlinear and Soft Matter Physics},
number = {3},
publisher = {American Institute of Physics},
title = {{Mathematical model of alternative mechanism of telomere length maintenance}},
doi = {10.1103/PhysRevE.89.032701},
volume = {89},
year = {2014},
}
@article{1909,
abstract = {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.},
author = {Ezard, Thomas and Prizak, Roshan and Hoyle, Rebecca},
journal = {Functional Ecology},
number = {3},
pages = {693 -- 701},
publisher = {Wiley-Blackwell},
title = {{The fitness costs of adaptation via phenotypic plasticity and maternal effects}},
doi = {10.1111/1365-2435.12207},
volume = {28},
year = {2014},
}
@article{1928,
abstract = {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.},
author = {Humplik, Jan and Hill, Alison and Nowak, Martin},
journal = {Journal of Theoretical Biology},
pages = {149 -- 162},
publisher = {Elsevier},
title = {{Evolutionary dynamics of infectious diseases in finite populations}},
doi = {10.1016/j.jtbi.2014.06.039},
volume = {360},
year = {2014},
}
@article{1931,
abstract = {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.},
author = {Savin, Cristina and Triesch, Jochen},
journal = {Frontiers in Computational Neuroscience},
number = {MAY},
publisher = {Frontiers Research Foundation},
title = {{Emergence of task-dependent representations in working memory circuits}},
doi = {10.3389/fncom.2014.00057},
volume = {8},
year = {2014},
}
@article{2231,
abstract = {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.},
author = {Rieckh, Georg and Tkacik, Gasper},
issn = {00063495},
journal = {Biophysical Journal},
number = {5},
pages = {1194 -- 1204},
publisher = {Biophysical Society},
title = {{Noise and information transmission in promoters with multiple internal states}},
doi = {10.1016/j.bpj.2014.01.014},
volume = {106},
year = {2014},
}