TY - JOUR AB - Gene regulatory networks evolve through rewiring of individual components—that is, through changes in regulatory connections. However, the mechanistic basis of regulatory rewiring is poorly understood. Using a canonical gene regulatory system, we quantify the properties of transcription factors that determine the evolutionary potential for rewiring of regulatory connections: robustness, tunability and evolvability. In vivo repression measurements of two repressors at mutated operator sites reveal their contrasting evolutionary potential: while robustness and evolvability were positively correlated, both were in trade-off with tunability. Epistatic interactions between adjacent operators alleviated this trade-off. A thermodynamic model explains how the differences in robustness, tunability and evolvability arise from biophysical characteristics of repressor–DNA binding. The model also uncovers that the energy matrix, which describes how mutations affect repressor–DNA binding, encodes crucial information about the evolutionary potential of a repressor. The biophysical determinants of evolutionary potential for regulatory rewiring constitute a mechanistic framework for understanding network evolution. AU - Igler, Claudia AU - Lagator, Mato AU - Tkacik, Gasper AU - Bollback, Jonathan P AU - Guet, Calin C ID - 67 IS - 10 JF - Nature Ecology and Evolution TI - Evolutionary potential of transcription factors for gene regulatory rewiring VL - 2 ER - TY - DATA AB - Mean repression values and standard error of the mean are given for all operator mutant libraries. AU - Igler, Claudia AU - Lagator, Mato AU - Tkacik, Gasper AU - Bollback, Jonathan P AU - Guet, Calin C ID - 5585 TI - Data for the paper Evolutionary potential of transcription factors for gene regulatory rewiring ER - TY - JOUR AB - Bacteria in groups vary individually, and interact with other bacteria and the environment to produce population-level patterns of gene expression. Investigating such behavior in detail requires measuring and controlling populations at the single-cell level alongside precisely specified interactions and environmental characteristics. Here we present an automated, programmable platform that combines image-based gene expression and growth measurements with on-line optogenetic expression control for hundreds of individual Escherichia coli cells over days, in a dynamically adjustable environment. This integrated platform broadly enables experiments that bridge individual and population behaviors. We demonstrate: (i) population structuring by independent closed-loop control of gene expression in many individual cells, (ii) cell-cell variation control during antibiotic perturbation, (iii) hybrid bio-digital circuits in single cells, and freely specifiable digital communication between individual bacteria. These examples showcase the potential for real-time integration of theoretical models with measurement and control of many individual cells to investigate and engineer microbial population behavior. AU - Chait, Remy P AU - Ruess, Jakob AU - Bergmiller, Tobias AU - Tkacik, Gasper AU - Guet, Calin C ID - 613 IS - 1 JF - Nature Communications SN - 20411723 TI - Shaping bacterial population behavior through computer interfaced control of individual cells VL - 8 ER - TY - CONF AB - We present an approach that enables robots to self-organize their sensorimotor behavior from scratch without providing specific information about neither the robot nor its environment. This is achieved by a simple neural control law that increases the consistency between external sensor dynamics and internal neural dynamics of the utterly simple controller. In this way, the embodiment and the agent-environment coupling are the only source of individual development. We show how an anthropomorphic tendon driven arm-shoulder system develops different behaviors depending on that coupling. For instance: Given a bottle half-filled with water, the arm starts to shake it, driven by the physical response of the water. When attaching a brush, the arm can be manipulated into wiping a table, and when connected to a revolvable wheel it finds out how to rotate it. Thus, the robot may be said to discover the affordances of the world. When allowing two (simulated) humanoid robots to interact physically, they engage into a joint behavior development leading to, for instance, spontaneous cooperation. More social effects are observed if the robots can visually perceive each other. Although, as an observer, it is tempting to attribute an apparent intentionality, there is nothing of the kind put in. As a conclusion, we argue that emergent behavior may be much less rooted in explicit intentions, internal motivations, or specific reward systems than is commonly believed. AU - Der, Ralf AU - Martius, Georg S ID - 652 SN - 978-150905069-7 TI - Dynamical self consistency leads to behavioral development and emergent social interactions in robots ER - TY - JOUR AB - With the accelerated development of robot technologies, control becomes one of the central themes of research. In traditional approaches, the controller, by its internal functionality, finds appropriate actions on the basis of specific objectives for the task at hand. While very successful in many applications, self-organized control schemes seem to be favored in large complex systems with unknown dynamics or which are difficult to model. Reasons are the expected scalability, robustness, and resilience of self-organizing systems. The paper presents a self-learning neurocontroller based on extrinsic differential plasticity introduced recently, applying it to an anthropomorphic musculoskeletal robot arm with attached objects of unknown physical dynamics. The central finding of the paper is the following effect: by the mere feedback through the internal dynamics of the object, the robot is learning to relate each of the objects with a very specific sensorimotor pattern. Specifically, an attached pendulum pilots the arm into a circular motion, a half-filled bottle produces axis oriented shaking behavior, a wheel is getting rotated, and wiping patterns emerge automatically in a table-plus-brush setting. By these object-specific dynamical patterns, the robot may be said to recognize the object's identity, or in other words, it discovers dynamical affordances of objects. Furthermore, when including hand coordinates obtained from a camera, a dedicated hand-eye coordination self-organizes spontaneously. These phenomena are discussed from a specific dynamical system perspective. Central is the dedicated working regime at the border to instability with its potentially infinite reservoir of (limit cycle) attractors "waiting" to be excited. Besides converging toward one of these attractors, variate behavior is also arising from a self-induced attractor morphing driven by the learning rule. We claim that experimental investigations with this anthropomorphic, self-learning robot not only generate interesting and potentially useful behaviors, but may also help to better understand what subjective human muscle feelings are, how they can be rooted in sensorimotor patterns, and how these concepts may feed back on robotics. AU - Der, Ralf AU - Martius, Georg S ID - 658 IS - MAR JF - Frontiers in Neurorobotics SN - 16625218 TI - Self organized behavior generation for musculoskeletal robots VL - 11 ER - TY - JOUR AB - Advances in multi-unit recordings pave the way for statistical modeling of activity patterns in large neural populations. Recent studies have shown that the summed activity of all neurons strongly shapes the population response. A separate recent finding has been that neural populations also exhibit criticality, an anomalously large dynamic range for the probabilities of different population activity patterns. Motivated by these two observations, we introduce a class of probabilistic models which takes into account the prior knowledge that the neural population could be globally coupled and close to critical. These models consist of an energy function which parametrizes interactions between small groups of neurons, and an arbitrary positive, strictly increasing, and twice differentiable function which maps the energy of a population pattern to its probability. We show that: 1) augmenting a pairwise Ising model with a nonlinearity yields an accurate description of the activity of retinal ganglion cells which outperforms previous models based on the summed activity of neurons; 2) prior knowledge that the population is critical translates to prior expectations about the shape of the nonlinearity; 3) the nonlinearity admits an interpretation in terms of a continuous latent variable globally coupling the system whose distribution we can infer from data. Our method is independent of the underlying system’s state space; hence, it can be applied to other systems such as natural scenes or amino acid sequences of proteins which are also known to exhibit criticality. AU - Humplik, Jan AU - Tkacik, Gasper ID - 720 IS - 9 JF - PLoS Computational Biology SN - 1553734X TI - Probabilistic models for neural populations that naturally capture global coupling and criticality VL - 13 ER - TY - JOUR AB - Individual computations and social interactions underlying collective behavior in groups of animals are of great ethological, behavioral, and theoretical interest. While complex individual behaviors have successfully been parsed into small dictionaries of stereotyped behavioral modes, studies of collective behavior largely ignored these findings; instead, their focus was on inferring single, mode-independent social interaction rules that reproduced macroscopic and often qualitative features of group behavior. Here, we bring these two approaches together to predict individual swimming patterns of adult zebrafish in a group. We show that fish alternate between an “active” mode, in which they are sensitive to the swimming patterns of conspecifics, and a “passive” mode, where they ignore them. Using a model that accounts for these two modes explicitly, we predict behaviors of individual fish with high accuracy, outperforming previous approaches that assumed a single continuous computation by individuals and simple metric or topological weighing of neighbors’ behavior. At the group level, switching between active and passive modes is uncorrelated among fish, but correlated directional swimming behavior still emerges. Our quantitative approach for studying complex, multi-modal individual behavior jointly with emergent group behavior is readily extensible to additional behavioral modes and their neural correlates as well as to other species. AU - Harpaz, Roy AU - Tkacik, Gasper AU - Schneidman, Elad ID - 725 IS - 38 JF - PNAS SN - 00278424 TI - Discrete modes of social information processing predict individual behavior of fish in a group VL - 114 ER - TY - GEN AB - Across the nervous system, certain population spiking patterns are observed far more frequently than others. A hypothesis about this structure is that these collective activity patterns function as population codewords–collective modes–carrying information distinct from that of any single cell. We investigate this phenomenon in recordings of ∼150 retinal ganglion cells, the retina’s output. We develop a novel statistical model that decomposes the population response into modes; it predicts the distribution of spiking activity in the ganglion cell population with high accuracy. We found that the modes represent localized features of the visual stimulus that are distinct from the features represented by single neurons. Modes form clusters of activity states that are readily discriminated from one another. When we repeated the same visual stimulus, we found that the same mode was robustly elicited. These results suggest that retinal ganglion cells’ collective signaling is endowed with a form of error-correcting code–a principle that may hold in brain areas beyond retina. AU - Prentice, Jason AU - Marre, Olivier AU - Ioffe, Mark AU - Loback, Adrianna AU - Tkačik, Gašper AU - Berry, Michael ID - 9709 TI - Data from: Error-robust modes of the retinal population code ER - TY - JOUR AB - In order to respond reliably to specific features of their environment, sensory neurons need to integrate multiple incoming noisy signals. Crucially, they also need to compete for the interpretation of those signals with other neurons representing similar features. The form that this competition should take depends critically on the noise corrupting these signals. In this study we show that for the type of noise commonly observed in sensory systems, whose variance scales with the mean signal, sensory neurons should selectively divide their input signals by their predictions, suppressing ambiguous cues while amplifying others. Any change in the stimulus context alters which inputs are suppressed, leading to a deep dynamic reshaping of neural receptive fields going far beyond simple surround suppression. Paradoxically, these highly variable receptive fields go alongside and are in fact required for an invariant representation of external sensory features. In addition to offering a normative account of context-dependent changes in sensory responses, perceptual inference in the presence of signal-dependent noise accounts for ubiquitous features of sensory neurons such as divisive normalization, gain control and contrast dependent temporal dynamics. AU - Chalk, Matthew J AU - Masset, Paul AU - Gutkin, Boris AU - Denève, Sophie ID - 680 IS - 6 JF - PLoS Computational Biology SN - 1553734X TI - Sensory noise predicts divisive reshaping of receptive fields VL - 13 ER - TY - GEN AB - Includes derivation of optimal estimation algorithm, generalisation to non-poisson noise statistics, correlated input noise, and implementation of in a multi-layer neural network. AU - Chalk, Matthew J AU - Masset, Paul AU - Gutkin, Boris AU - Denève, Sophie ID - 9855 TI - Supplementary appendix ER - TY - JOUR AB - Antibiotics elicit drastic changes in microbial gene expression, including the induction of stress response genes. While certain stress responses are known to “cross-protect” bacteria from other stressors, it is unclear whether cellular responses to antibiotics have a similar protective role. By measuring the genome-wide transcriptional response dynamics of Escherichia coli to four antibiotics, we found that trimethoprim induces a rapid acid stress response that protects bacteria from subsequent exposure to acid. Combining microfluidics with time-lapse imaging to monitor survival and acid stress response in single cells revealed that the noisy expression of the acid resistance operon gadBC correlates with single-cell survival. Cells with higher gadBC expression following trimethoprim maintain higher intracellular pH and survive the acid stress longer. The seemingly random single-cell survival under acid stress can therefore be predicted from gadBC expression and rationalized in terms of GadB/C molecular function. Overall, we provide a roadmap for identifying the molecular mechanisms of single-cell cross-protection between antibiotics and other stressors. AU - Mitosch, Karin AU - Rieckh, Georg AU - Bollenbach, Tobias ID - 666 IS - 4 JF - Cell Systems SN - 24054712 TI - Noisy response to antibiotic stress predicts subsequent single cell survival in an acidic environment VL - 4 ER - TY - JOUR AB - The Ising model is one of the simplest and most famous models of interacting systems. It was originally proposed to model ferromagnetic interactions in statistical physics and is now widely used to model spatial processes in many areas such as ecology, sociology, and genetics, usually without testing its goodness-of-fit. Here, we propose an exact goodness-of-fit test for the finite-lattice Ising model. The theory of Markov bases has been developed in algebraic statistics for exact goodness-of-fit testing using a Monte Carlo approach. However, this beautiful theory has fallen short of its promise for applications, because finding a Markov basis is usually computationally intractable. We develop a Monte Carlo method for exact goodness-of-fit testing for the Ising model which avoids computing a Markov basis and also leads to a better connectivity of the Markov chain and hence to a faster convergence. We show how this method can be applied to analyze the spatial organization of receptors on the cell membrane. AU - Martin Del Campo Sanchez, Abraham AU - Cepeda Humerez, Sarah A AU - Uhler, Caroline ID - 2016 IS - 2 JF - Scandinavian Journal of Statistics SN - 03036898 TI - Exact goodness-of-fit testing for the Ising model VL - 44 ER - TY - JOUR AB - In the early visual system, cells of the same type perform the same computation in different places of the visual field. How these cells code together a complex visual scene is unclear. A common assumption is that cells of a single-type extract a single-stimulus feature to form a feature map, but this has rarely been observed directly. Using large-scale recordings in the rat retina, we show that a homogeneous population of fast OFF ganglion cells simultaneously encodes two radically different features of a visual scene. Cells close to a moving object code quasilinearly for its position, while distant cells remain largely invariant to the object's position and, instead, respond nonlinearly to changes in the object's speed. We develop a quantitative model that accounts for this effect and identify a disinhibitory circuit that mediates it. Ganglion cells of a single type thus do not code for one, but two features simultaneously. This richer, flexible neural map might also be present in other sensory systems. AU - Deny, Stephane AU - Ferrari, Ulisse AU - Mace, Emilie AU - Yger, Pierre AU - Caplette, Romain AU - Picaud, Serge AU - Tkacik, Gasper AU - Marre, Olivier ID - 1104 IS - 1 JF - Nature Communications SN - 20411723 TI - Multiplexed computations in retinal ganglion cells of a single type VL - 8 ER - TY - JOUR AB - In real-world applications, observations are often constrained to a small fraction of a system. Such spatial subsampling can be caused by the inaccessibility or the sheer size of the system, and cannot be overcome by longer sampling. Spatial subsampling can strongly bias inferences about a system’s aggregated properties. To overcome the bias, we derive analytically a subsampling scaling framework that is applicable to different observables, including distributions of neuronal avalanches, of number of people infected during an epidemic outbreak, and of node degrees. We demonstrate how to infer the correct distributions of the underlying full system, how to apply it to distinguish critical from subcritical systems, and how to disentangle subsampling and finite size effects. Lastly, we apply subsampling scaling to neuronal avalanche models and to recordings from developing neural networks. We show that only mature, but not young networks follow power-law scaling, indicating self-organization to criticality during development. AU - Levina (Martius), Anna AU - Priesemann, Viola ID - 993 JF - Nature Communications SN - 20411723 TI - Subsampling scaling VL - 8 ER - TY - JOUR AB - Gene expression is controlled by networks of regulatory proteins that interact specifically with external signals and DNA regulatory sequences. These interactions force the network components to co-evolve so as to continually maintain function. Yet, existing models of evolution mostly focus on isolated genetic elements. In contrast, we study the essential process by which regulatory networks grow: the duplication and subsequent specialization of network components. We synthesize a biophysical model of molecular interactions with the evolutionary framework to find the conditions and pathways by which new regulatory functions emerge. We show that specialization of new network components is usually slow, but can be drastically accelerated in the presence of regulatory crosstalk and mutations that promote promiscuous interactions between network components. AU - Friedlander, Tamar AU - Prizak, Roshan AU - Barton, Nicholas H AU - Tkacik, Gasper ID - 955 IS - 1 JF - Nature Communications SN - 20411723 TI - Evolution of new regulatory functions on biophysically realistic fitness landscapes VL - 8 ER - TY - JOUR AB - In this work it is shown that scale-free tails in metabolic flux distributions inferred in stationary models are an artifact due to reactions involved in thermodynamically unfeasible cycles, unbounded by physical constraints and in principle able to perform work without expenditure of free energy. After implementing thermodynamic constraints by removing such loops, metabolic flux distributions scale meaningfully with the physical limiting factors, acquiring in turn a richer multimodal structure potentially leading to symmetry breaking while optimizing for objective functions. AU - De Martino, Daniele ID - 959 IS - 6 JF - Physical Review E Statistical Nonlinear and Soft Matter Physics SN - 24700045 TI - Scales and multimodal flux distributions in stationary metabolic network models via thermodynamics VL - 95 ER - TY - JOUR AB - Viewing the ways a living cell can organize its metabolism as the phase space of a physical system, regulation can be seen as the ability to reduce the entropy of that space by selecting specific cellular configurations that are, in some sense, optimal. Here we quantify the amount of regulation required to control a cell's growth rate by a maximum-entropy approach to the space of underlying metabolic phenotypes, where a configuration corresponds to a metabolic flux pattern as described by genome-scale models. We link the mean growth rate achieved by a population of cells to the minimal amount of metabolic regulation needed to achieve it through a phase diagram that highlights how growth suppression can be as costly (in regulatory terms) as growth enhancement. Moreover, we provide an interpretation of the inverse temperature β controlling maximum-entropy distributions based on the underlying growth dynamics. Specifically, we show that the asymptotic value of β for a cell population can be expected to depend on (i) the carrying capacity of the environment, (ii) the initial size of the colony, and (iii) the probability distribution from which the inoculum was sampled. Results obtained for E. coli and human cells are found to be remarkably consistent with empirical evidence. AU - De Martino, Daniele AU - Capuani, Fabrizio AU - De Martino, Andrea ID - 947 IS - 1 JF - Physical Review E Statistical Nonlinear and Soft Matter Physics SN - 24700045 TI - Quantifying the entropic cost of cellular growth control VL - 96 ER - TY - JOUR AB - Like many developing tissues, the vertebrate neural tube is patterned by antiparallel morphogen gradients. To understand how these inputs are interpreted, we measured morphogen signaling and target gene expression in mouse embryos and chick ex vivo assays. From these data, we derived and validated a characteristic decoding map that relates morphogen input to the positional identity of neural progenitors. Analysis of the observed responses indicates that the underlying interpretation strategy minimizes patterning errors in response to the joint input of noisy opposing gradients. We reverse-engineered a transcriptional network that provides a mechanistic basis for the observed cell fate decisions and accounts for the precision and dynamics of pattern formation. Together, our data link opposing gradient dynamics in a growing tissue to precise pattern formation. AU - Zagórski, Marcin P AU - Tabata, Yoji AU - Brandenberg, Nathalie AU - Lutolf, Matthias AU - Tkacik, Gasper AU - Bollenbach, Tobias AU - Briscoe, James AU - Kicheva, Anna ID - 943 IS - 6345 JF - Science SN - 00368075 TI - Decoding of position in the developing neural tube from antiparallel morphogen gradients VL - 356 ER - TY - JOUR AB - The resolution of a linear system with positive integer variables is a basic yet difficult computational problem with many applications. We consider sparse uncorrelated random systems parametrised by the density c and the ratio α=N/M between number of variables N and number of constraints M. By means of ensemble calculations we show that the space of feasible solutions endows a Van-Der-Waals phase diagram in the plane (c, α). We give numerical evidence that the associated computational problems become more difficult across the critical point and in particular in the coexistence region. AU - Colabrese, Simona AU - De Martino, Daniele AU - Leuzzi, Luca AU - Marinari, Enzo ID - 823 IS - 9 JF - Journal of Statistical Mechanics: Theory and Experiment SN - 17425468 TI - Phase transitions in integer linear problems VL - 2017 ER - TY - JOUR AB - Neural responses are highly structured, with population activity restricted to a small subset of the astronomical range of possible activity patterns. Characterizing these statistical regularities is important for understanding circuit computation, but challenging in practice. Here we review recent approaches based on the maximum entropy principle used for quantifying collective behavior in neural activity. We highlight recent models that capture population-level statistics of neural data, yielding insights into the organization of the neural code and its biological substrate. Furthermore, the MaxEnt framework provides a general recipe for constructing surrogate ensembles that preserve aspects of the data, but are otherwise maximally unstructured. This idea can be used to generate a hierarchy of controls against which rigorous statistical tests are possible. AU - Savin, Cristina AU - Tkacik, Gasper ID - 730 JF - Current Opinion in Neurobiology SN - 09594388 TI - Maximum entropy models as a tool for building precise neural controls VL - 46 ER -