TY - JOUR AB - Although much is known about how single neurons in the hippocampus represent an animal's position, how circuit interactions contribute to spatial coding is less well understood. Using a novel statistical estimator and theoretical modeling, both developed in the framework of maximum entropy models, we reveal highly structured CA1 cell-cell interactions in male rats during open field exploration. The statistics of these interactions depend on whether the animal is in a familiar or novel environment. In both conditions the circuit interactions optimize the encoding of spatial information, but for regimes that differ in the informativeness of their spatial inputs. This structure facilitates linear decodability, making the information easy to read out by downstream circuits. Overall, our findings suggest that the efficient coding hypothesis is not only applicable to individual neuron properties in the sensory periphery, but also to neural interactions in the central brain. AU - Nardin, Michele AU - Csicsvari, Jozsef L AU - Tkačik, Gašper AU - Savin, Cristina ID - 14656 IS - 48 JF - The Journal of Neuroscience TI - The structure of hippocampal CA1 interactions optimizes spatial coding across experience VL - 43 ER - TY - JOUR AB - Sleep plays a key role in preserving brain function, keeping the brain network in a state that ensures optimal computational capabilities. Empirical evidence indicates that such a state is consistent with criticality, where scale-free neuronal avalanches emerge. However, the relationship between sleep, emergent avalanches, and criticality remains poorly understood. Here we fully characterize the critical behavior of avalanches during sleep, and study their relationship with the sleep macro- and micro-architecture, in particular the cyclic alternating pattern (CAP). We show that avalanche size and duration distributions exhibit robust power laws with exponents approximately equal to −3/2 e −2, respectively. Importantly, we find that sizes scale as a power law of the durations, and that all critical exponents for neuronal avalanches obey robust scaling relations, which are consistent with the mean-field directed percolation universality class. Our analysis demonstrates that avalanche dynamics depends on the position within the NREM-REM cycles, with the avalanche density increasing in the descending phases and decreasing in the ascending phases of sleep cycles. Moreover, we show that, within NREM sleep, avalanche occurrence correlates with CAP activation phases, particularly A1, which are the expression of slow wave sleep propensity and have been proposed to be beneficial for cognitive processes. The results suggest that neuronal avalanches, and thus tuning to criticality, actively contribute to sleep development and play a role in preserving network function. Such findings, alongside characterization of the universality class for avalanches, open new avenues to the investigation of functional role of criticality during sleep with potential clinical application.Significance statementWe fully characterize the critical behavior of neuronal avalanches during sleep, and show that avalanches follow precise scaling laws that are consistent with the mean-field directed percolation universality class. The analysis provides first evidence of a functional relationship between avalanche occurrence, slow-wave sleep dynamics, sleep stage transitions and occurrence of CAP phase A during NREM sleep. Because CAP is considered one of the major guardians of NREM sleep that allows the brain to dynamically react to external perturbation and contributes to the cognitive consolidation processes occurring in sleep, our observations suggest that neuronal avalanches at criticality are associated with flexible response to external inputs and to cognitive processes, a key assumption of the critical brain hypothesis. AU - Scarpetta, Silvia AU - Morrisi, Niccolò AU - Mutti, Carlotta AU - Azzi, Nicoletta AU - Trippi, Irene AU - Ciliento, Rosario AU - Apicella, Ilenia AU - Messuti, Giovanni AU - Angiolelli, Marianna AU - Lombardi, Fabrizio AU - Parrino, Liborio AU - Vaudano, Anna Elisabetta ID - 12487 IS - 10 JF - iScience TI - Criticality of neuronal avalanches in human sleep and their relationship with sleep macro- and micro-architecture VL - 26 ER - TY - GEN AU - Rella, Simon AU - Kulikova, Y AU - Minnegalieva, Aygul AU - Kondrashov, Fyodor ID - 14862 IS - Supplement_2 KW - Public Health KW - Environmental and Occupational Health SN - 1101-1262 T2 - European Journal of Public Health TI - Complex vaccination strategies prevent the emergence of vaccine resistance VL - 33 ER - TY - JOUR AB - Alpha oscillations are a distinctive feature of the awake resting state of the human brain. However, their functional role in resting-state neuronal dynamics remains poorly understood. Here we show that, during resting wakefulness, alpha oscillations drive an alternation of attenuation and amplification bouts in neural activity. Our analysis indicates that inhibition is activated in pulses that last for a single alpha cycle and gradually suppress neural activity, while excitation is successively enhanced over a few alpha cycles to amplify neural activity. Furthermore, we show that long-term alpha amplitude fluctuations—the “waxing and waning” phenomenon—are an attenuation-amplification mechanism described by a power-law decay of the activity rate in the “waning” phase. Importantly, we do not observe such dynamics during non-rapid eye movement (NREM) sleep with marginal alpha oscillations. The results suggest that alpha oscillations modulate neural activity not only through pulses of inhibition (pulsed inhibition hypothesis) but also by timely enhancement of excitation (or disinhibition). AU - Lombardi, Fabrizio AU - Herrmann, Hans J. AU - Parrino, Liborio AU - Plenz, Dietmar AU - Scarpetta, Silvia AU - Vaudano, Anna Elisabetta AU - De Arcangelis, Lucilla AU - Shriki, Oren ID - 14402 IS - 10 JF - Cell Reports TI - Beyond pulsed inhibition: Alpha oscillations modulate attenuation and amplification of neural activity in the awake resting state VL - 42 ER - TY - GEN AB - Rhythmical cortical activity has long been recognized as a pillar in the architecture of brain functions. Yet, the dynamic organization of its underlying neuronal population activity remains elusive. Here we uncover a unique organizational principle regulating collective neural dynamics associated with the alpha rhythm in the awake resting-state. We demonstrate that cascades of neural activity obey attenuation-amplification dynamics (AAD), with a transition from the attenuation regime—within alpha cycles—to the amplification regime—across a few alpha cycles—that correlates with the characteristic frequency of the alpha rhythm. We find that this short-term AAD is part of a large-scale, size-dependent temporal structure of neural cascades that obeys the Omori law: Following large cascades, smaller cascades occur at a rate that decays as a power-law of the time elapsed from such events—a long-term AAD regulating brain activity over the timescale of seconds. We show that such an organization corresponds to the "waxing and waning" of the alpha rhythm. Importantly, we observe that short- and long-term AAD are unique to the awake resting-state, being absent during NREM sleep. These results provide a quantitative, dynamical description of the so-far-qualitative notion of the "waxing and waning" phenomenon, and suggest the AAD as a key principle governing resting-state dynamics across timescales. AU - Lombardi, Fabrizio AU - Herrmann, Hans J. AU - Parrino, Liborio AU - Plenz, Dietmar AU - Scarpetta, Silvia AU - Vaudano, Anna Elisabetta AU - de Arcangelis, Lucilla AU - Shriki, Oren ID - 10821 T2 - bioRxiv TI - Alpha rhythm induces attenuation-amplification dynamics in neural activity cascades ER - TY - JOUR AB - Statistical inference is central to many scientific endeavors, yet how it works remains unresolved. Answering this requires a quantitative understanding of the intrinsic interplay between statistical models, inference methods, and the structure in the data. To this end, we characterize the efficacy of direct coupling analysis (DCA)—a highly successful method for analyzing amino acid sequence data—in inferring pairwise interactions from samples of ferromagnetic Ising models on random graphs. Our approach allows for physically motivated exploration of qualitatively distinct data regimes separated by phase transitions. We show that inference quality depends strongly on the nature of data-generating distributions: optimal accuracy occurs at an intermediate temperature where the detrimental effects from macroscopic order and thermal noise are minimal. Importantly our results indicate that DCA does not always outperform its local-statistics-based predecessors; while DCA excels at low temperatures, it becomes inferior to simple correlation thresholding at virtually all temperatures when data are limited. Our findings offer insights into the regime in which DCA operates so successfully, and more broadly, how inference interacts with the structure in the data. AU - Ngampruetikorn, Vudtiwat AU - Sachdeva, Vedant AU - Torrence, Johanna AU - Humplik, Jan AU - Schwab, David J. AU - Palmer, Stephanie E. ID - 11638 IS - 2 JF - Physical Review Research SN - 2643-1564 TI - Inferring couplings in networks across order-disorder phase transitions VL - 4 ER - TY - JOUR AB - Models of transcriptional regulation that assume equilibrium binding of transcription factors have been less successful at predicting gene expression from sequence in eukaryotes than in bacteria. This could be due to the non-equilibrium nature of eukaryotic regulation. Unfortunately, the space of possible non-equilibrium mechanisms is vast and predominantly uninteresting. The key question is therefore how this space can be navigated efficiently, to focus on mechanisms and models that are biologically relevant. In this review, we advocate for the normative role of theory—theory that prescribes rather than just describes—in providing such a focus. Theory should expand its remit beyond inferring mechanistic models from data, towards identifying non-equilibrium gene regulatory schemes that may have been evolutionarily selected, despite their energy consumption, because they are precise, reliable, fast, or otherwise outperform regulation at equilibrium. We illustrate our reasoning by toy examples for which we provide simulation code. AU - Zoller, Benjamin AU - Gregor, Thomas AU - Tkačik, Gašper ID - 12156 IS - 9 JF - Current Opinion in Systems Biology KW - Applied Mathematics KW - Computer Science Applications KW - Drug Discovery KW - General Biochemistry KW - Genetics and Molecular Biology KW - Modeling and Simulation SN - 2452-3100 TI - Eukaryotic gene regulation at equilibrium, or non? VL - 31 ER - TY - JOUR AB - Cell dispersion from a confined area is fundamental in a number of biological processes, including cancer metastasis. To date, a quantitative understanding of the interplay of single cell motility, cell proliferation, and intercellular contacts remains elusive. In particular, the role of E- and N-Cadherin junctions, central components of intercellular contacts, is still controversial. Combining theoretical modeling with in vitro observations, we investigate the collective spreading behavior of colonies of human cancer cells (T24). The spreading of these colonies is driven by stochastic single-cell migration with frequent transient cell-cell contacts. We find that inhibition of E- and N-Cadherin junctions decreases colony spreading and average spreading velocities, without affecting the strength of correlations in spreading velocities of neighboring cells. Based on a biophysical simulation model for cell migration, we show that the behavioral changes upon disruption of these junctions can be explained by reduced repulsive excluded volume interactions between cells. This suggests that in cancer cell migration, cadherin-based intercellular contacts sharpen cell boundaries leading to repulsive rather than cohesive interactions between cells, thereby promoting efficient cell spreading during collective migration. AU - Zisis, Themistoklis AU - Brückner, David AU - Brandstätter, Tom AU - Siow, Wei Xiong AU - d’Alessandro, Joseph AU - Vollmar, Angelika M. AU - Broedersz, Chase P. AU - Zahler, Stefan ID - 10530 IS - 1 JF - Biophysical Journal KW - Biophysics SN - 0006-3495 TI - Disentangling cadherin-mediated cell-cell interactions in collective cancer cell migration VL - 121 ER - TY - JOUR AB - Predicting function from sequence is a central problem of biology. Currently, this is possible only locally in a narrow mutational neighborhood around a wildtype sequence rather than globally from any sequence. Using random mutant libraries, we developed a biophysical model that accounts for multiple features of σ70 binding bacterial promoters to predict constitutive gene expression levels from any sequence. We experimentally and theoretically estimated that 10–20% of random sequences lead to expression and ~80% of non-expressing sequences are one mutation away from a functional promoter. The potential for generating expression from random sequences is so pervasive that selection acts against σ70-RNA polymerase binding sites even within inter-genic, promoter-containing regions. This pervasiveness of σ70-binding sites implies that emergence of promoters is not the limiting step in gene regulatory evolution. Ultimately, the inclusion of novel features of promoter function into a mechanistic model enabled not only more accurate predictions of gene expression levels, but also identified that promoters evolve more rapidly than previously thought. AU - Lagator, Mato AU - Sarikas, Srdjan AU - Steinrueck, Magdalena AU - Toledo-Aparicio, David AU - Bollback, Jonathan P AU - Guet, Calin C AU - Tkačik, Gašper ID - 10736 JF - eLife TI - Predicting bacterial promoter function and evolution from random sequences VL - 11 ER - TY - JOUR AB - Activity of sensory neurons is driven not only by external stimuli but also by feedback signals from higher brain areas. Attention is one particularly important internal signal whose presumed role is to modulate sensory representations such that they only encode information currently relevant to the organism at minimal cost. This hypothesis has, however, not yet been expressed in a normative computational framework. Here, by building on normative principles of probabilistic inference and efficient coding, we developed a model of dynamic population coding in the visual cortex. By continuously adapting the sensory code to changing demands of the perceptual observer, an attention-like modulation emerges. This modulation can dramatically reduce the amount of neural activity without deteriorating the accuracy of task-specific inferences. Our results suggest that a range of seemingly disparate cortical phenomena such as intrinsic gain modulation, attention-related tuning modulation, and response variability could be manifestations of the same underlying principles, which combine efficient sensory coding with optimal probabilistic inference in dynamic environments. AU - Mlynarski, Wiktor F AU - Tkačik, Gašper ID - 12332 IS - 12 JF - PLoS Biology TI - Efficient coding theory of dynamic attentional modulation VL - 20 ER - TY - JOUR AB - Selection accumulates information in the genome—it guides stochastically evolving populations toward states (genotype frequencies) that would be unlikely under neutrality. This can be quantified as the Kullback–Leibler (KL) divergence between the actual distribution of genotype frequencies and the corresponding neutral distribution. First, we show that this population-level information sets an upper bound on the information at the level of genotype and phenotype, limiting how precisely they can be specified by selection. Next, we study how the accumulation and maintenance of information is limited by the cost of selection, measured as the genetic load or the relative fitness variance, both of which we connect to the control-theoretic KL cost of control. The information accumulation rate is upper bounded by the population size times the cost of selection. This bound is very general, and applies across models (Wright–Fisher, Moran, diffusion) and to arbitrary forms of selection, mutation, and recombination. Finally, the cost of maintaining information depends on how it is encoded: Specifying a single allele out of two is expensive, but one bit encoded among many weakly specified loci (as in a polygenic trait) is cheap. AU - Hledik, Michal AU - Barton, Nicholas H AU - Tkačik, Gašper ID - 12081 IS - 36 JF - Proceedings of the National Academy of Sciences SN - 0027-8424 TI - Accumulation and maintenance of information in evolution VL - 119 ER - TY - JOUR AB - Realistic models of biological processes typically involve interacting components on multiple scales, driven by changing environment and inherent stochasticity. Such models are often analytically and numerically intractable. We revisit a dynamic maximum entropy method that combines a static maximum entropy with a quasi-stationary approximation. This allows us to reduce stochastic non-equilibrium dynamics expressed by the Fokker-Planck equation to a simpler low-dimensional deterministic dynamics, without the need to track microscopic details. Although the method has been previously applied to a few (rather complicated) applications in population genetics, our main goal here is to explain and to better understand how the method works. We demonstrate the usefulness of the method for two widely studied stochastic problems, highlighting its accuracy in capturing important macroscopic quantities even in rapidly changing non-stationary conditions. For the Ornstein-Uhlenbeck process, the method recovers the exact dynamics whilst for a stochastic island model with migration from other habitats, the approximation retains high macroscopic accuracy under a wide range of scenarios in a dynamic environment. AU - Bod'ová, Katarína AU - Szep, Eniko AU - Barton, Nicholas H ID - 10535 IS - 12 JF - PLoS Computational Biology SN - 1553-734X TI - Dynamic maximum entropy provides accurate approximation of structured population dynamics VL - 17 ER - TY - GEN AB - Brain dynamics display collective phenomena as diverse as neuronal oscillations and avalanches. Oscillations are rhythmic, with fluctuations occurring at a characteristic scale, whereas avalanches are scale-free cascades of neural activity. Here we show that such antithetic features can coexist in a very generic class of adaptive neural networks. In the most simple yet fully microscopic model from this class we make direct contact with human brain resting-state activity recordings via tractable inference of the model's two essential parameters. The inferred model quantitatively captures the dynamics over a broad range of scales, from single sensor fluctuations, collective behaviors of nearly-synchronous extreme events on multiple sensors, to neuronal avalanches unfolding over multiple sensors across multiple time-bins. Importantly, the inferred parameters correlate with model-independent signatures of "closeness to criticality", suggesting that the coexistence of scale-specific (neural oscillations) and scale-free (neuronal avalanches) dynamics in brain activity occurs close to a non-equilibrium critical point at the onset of self-sustained oscillations. AU - Lombardi, Fabrizio AU - Pepic, Selver AU - Shriki, Oren AU - Tkačik, Gašper AU - De Martino, Daniele ID - 10912 TI - Quantifying the coexistence of neuronal oscillations and avalanches ER - TY - GEN AB - We consider a totally asymmetric simple exclusion process (TASEP) consisting of particles on a lattice that require binding by a "token" to move. Using a combination of theory and simulations, we address the following questions: (i) How token binding kinetics affects the current-density relation; (ii) How the current-density relation depends on the scarcity of tokens; (iii) How tokens propagate the effects of the locally-imposed disorder (such a slow site) over the entire lattice; (iv) How a shared pool of tokens couples concurrent TASEPs running on multiple lattices; (v) How our results translate to TASEPs with open boundaries that exchange particles with the reservoir. Since real particle motion (including in systems that inspired the standard TASEP model, e.g., protein synthesis or movement of molecular motors) is often catalyzed, regulated, actuated, or otherwise mediated, the token-driven TASEP dynamics analyzed in this paper should allow for a better understanding of real systems and enable a closer match between TASEP theory and experimental observations. AU - Kavcic, Bor AU - Tkačik, Gašper ID - 10579 T2 - arXiv TI - Token-driven totally asymmetric simple exclusion process ER - TY - JOUR AB - Resting-state brain activity is characterized by the presence of neuronal avalanches showing absence of characteristic size. Such evidence has been interpreted in the context of criticality and associated with the normal functioning of the brain. A distinctive attribute of systems at criticality is the presence of long-range correlations. Thus, to verify the hypothesis that the brain operates close to a critical point and consequently assess deviations from criticality for diagnostic purposes, it is of primary importance to robustly and reliably characterize correlations in resting-state brain activity. Recent works focused on the analysis of narrow-band electroencephalography (EEG) and magnetoencephalography (MEG) signal amplitude envelope, showing evidence of long-range temporal correlations (LRTC) in neural oscillations. However, brain activity is a broadband phenomenon, and a significant piece of information useful to precisely discriminate between normal (critical) and pathological behavior (non-critical), may be encoded in the broadband spatio-temporal cortical dynamics. Here we propose to characterize the temporal correlations in the broadband brain activity through the lens of neuronal avalanches. To this end, we consider resting-state EEG and long-term MEG recordings, extract the corresponding neuronal avalanche sequences, and study their temporal correlations. We demonstrate that the broadband resting-state brain activity consistently exhibits long-range power-law correlations in both EEG and MEG recordings, with similar values of the scaling exponents. Importantly, although we observe that the avalanche size distribution depends on scale parameters, scaling exponents characterizing long-range correlations are quite robust. In particular, they are independent of the temporal binning (scale of analysis), indicating that our analysis captures intrinsic characteristics of the underlying dynamics. Because neuronal avalanches constitute a fundamental feature of neural systems with universal characteristics, the proposed approach may serve as a general, systems- and experiment-independent procedure to infer the existence of underlying long-range correlations in extended neural systems, and identify pathological behaviors in the complex spatio-temporal interplay of cortical rhythms. AU - Lombardi, Fabrizio AU - Shriki, Oren AU - Herrmann, Hans J AU - de Arcangelis, Lucilla ID - 7463 JF - Neurocomputing SN - 0925-2312 TI - Long-range temporal correlations in the broadband resting state activity of the human brain revealed by neuronal avalanches VL - 461 ER - TY - JOUR AB - Half a century after Lewis Wolpert's seminal conceptual advance on how cellular fates distribute in space, we provide a brief historical perspective on how the concept of positional information emerged and influenced the field of developmental biology and beyond. We focus on a modern interpretation of this concept in terms of information theory, largely centered on its application to cell specification in the early Drosophila embryo. We argue that a true physical variable (position) is encoded in local concentrations of patterning molecules, that this mapping is stochastic, and that the processes by which positions and corresponding cell fates are determined based on these concentrations need to take such stochasticity into account. With this approach, we shift the focus from biological mechanisms, molecules, genes and pathways to quantitative systems-level questions: where does positional information reside, how it is transformed and accessed during development, and what fundamental limits it is subject to? AU - Tkačik, Gašper AU - Gregor, Thomas ID - 9226 IS - 2 JF - Development TI - The many bits of positional information VL - 148 ER - TY - JOUR AB - The ability to adapt to changes in stimulus statistics is a hallmark of sensory systems. Here, we developed a theoretical framework that can account for the dynamics of adaptation from an information processing perspective. We use this framework to optimize and analyze adaptive sensory codes, and we show that codes optimized for stationary environments can suffer from prolonged periods of poor performance when the environment changes. To mitigate the adversarial effects of these environmental changes, sensory systems must navigate tradeoffs between the ability to accurately encode incoming stimuli and the ability to rapidly detect and adapt to changes in the distribution of these stimuli. We derive families of codes that balance these objectives, and we demonstrate their close match to experimentally observed neural dynamics during mean and variance adaptation. Our results provide a unifying perspective on adaptation across a range of sensory systems, environments, and sensory tasks. AU - Mlynarski, Wiktor F AU - Hermundstad, Ann M. ID - 9439 JF - Nature Neuroscience SN - 1097-6256 TI - Efficient and adaptive sensory codes VL - 24 ER - TY - JOUR AB - Attachment of adhesive molecules on cell culture surfaces to restrict cell adhesion to defined areas and shapes has been vital for the progress of in vitro research. In currently existing patterning methods, a combination of pattern properties such as stability, precision, specificity, high-throughput outcome, and spatiotemporal control is highly desirable but challenging to achieve. Here, we introduce a versatile and high-throughput covalent photoimmobilization technique, comprising a light-dose-dependent patterning step and a subsequent functionalization of the pattern via click chemistry. This two-step process is feasible on arbitrary surfaces and allows for generation of sustainable patterns and gradients. The method is validated in different biological systems by patterning adhesive ligands on cell-repellent surfaces, thereby constraining the growth and migration of cells to the designated areas. We then implement a sequential photopatterning approach by adding a second switchable patterning step, allowing for spatiotemporal control over two distinct surface patterns. As a proof of concept, we reconstruct the dynamics of the tip/stalk cell switch during angiogenesis. Our results show that the spatiotemporal control provided by our “sequential photopatterning” system is essential for mimicking dynamic biological processes and that our innovative approach has great potential for further applications in cell science. AU - Zisis, Themistoklis AU - Schwarz, Jan AU - Balles, Miriam AU - Kretschmer, Maibritt AU - Nemethova, Maria AU - Chait, Remy P AU - Hauschild, Robert AU - Lange, Janina AU - Guet, Calin C AU - Sixt, Michael K AU - Zahler, Stefan ID - 9822 IS - 30 JF - ACS Applied Materials and Interfaces SN - 19448244 TI - Sequential and switchable patterning for studying cellular processes under spatiotemporal control VL - 13 ER - TY - JOUR AB - Amplitude demodulation is a classical operation used in signal processing. For a long time, its effective applications in practice have been limited to narrowband signals. In this work, we generalize amplitude demodulation to wideband signals. We pose demodulation as a recovery problem of an oversampled corrupted signal and introduce special iterative schemes belonging to the family of alternating projection algorithms to solve it. Sensibly chosen structural assumptions on the demodulation outputs allow us to reveal the high inferential accuracy of the method over a rich set of relevant signals. This new approach surpasses current state-of-the-art demodulation techniques apt to wideband signals in computational efficiency by up to many orders of magnitude with no sacrifice in quality. Such performance opens the door for applications of the amplitude demodulation procedure in new contexts. In particular, the new method makes online and large-scale offline data processing feasible, including the calculation of modulator-carrier pairs in higher dimensions and poor sampling conditions, independent of the signal bandwidth. We illustrate the utility and specifics of applications of the new method in practice by using natural speech and synthetic signals. AU - Gabrielaitis, Mantas ID - 9828 JF - IEEE Transactions on Signal Processing SN - 1053-587X TI - Fast and accurate amplitude demodulation of wideband signals VL - 69 ER - TY - JOUR AB - A central goal in systems neuroscience is to understand the functions performed by neural circuits. Previous top-down models addressed this question by comparing the behaviour of an ideal model circuit, optimised to perform a given function, with neural recordings. However, this requires guessing in advance what function is being performed, which may not be possible for many neural systems. To address this, we propose an inverse reinforcement learning (RL) framework for inferring the function performed by a neural network from data. We assume that the responses of each neuron in a network are optimised so as to drive the network towards ‘rewarded’ states, that are desirable for performing a given function. We then show how one can use inverse RL to infer the reward function optimised by the network from observing its responses. This inferred reward function can be used to predict how the neural network should adapt its dynamics to perform the same function when the external environment or network structure changes. This could lead to theoretical predictions about how neural network dynamics adapt to deal with cell death and/or varying sensory stimulus statistics. AU - Chalk, Matthew J AU - Tkačik, Gašper AU - Marre, Olivier ID - 9362 IS - 4 JF - PLoS ONE TI - Inferring the function performed by a recurrent neural network VL - 16 ER -