Minimal models of multidimensional computations

The multidimensional computations performed by many biological systems are often characterized with limited information about the correlations between inputs and outputs. Given this limitation, our approach is to construct the maximum noise entropy response function of the system, leading to a closed-form and minimally biased model consistent with a given set of constraints on the input/output moments; the result is equivalent to conditional random field models from machine learning. For systems with binary outputs, such as neurons encoding sensory stimuli, the maximum noise entropy models are logistic functions whose arguments depend on the constraints. A constraint on the average output turns the binary maximum noise entropy models into minimum mutual information models, allowing for the calculation of the information content of the constraints and an information theoretic characterization of the system's computations. We use this approach to analyze the nonlinear input/output functions in macaque retina and thalamus; although these systems have been previously shown to be responsive to two input dimensions, the functional form of the response function in this reduced space had not been unambiguously identified. A second order model based on the logistic function is found to be both necessary and sufficient to accurately describe the neural responses to naturalistic stimuli, accounting for an average of 93% of the mutual information with a small number of parameters. Thus, despite the fact that the stimulus is highly non-Gaussian, the vast majority of the information in the neural responses is related to first and second order correlations. Our results suggest a principled and unbiased way to model multidimensional computations and determine the statistics of the inputs that are being encoded in the outputs.     

Consistent Implementation of Decisions in the Brain

Despite the complexity and variability of decision processes, motor responses are generally stereotypical and independent of decision difficulty. How is this consistency achieved? Through an engineering analogy we consider how and why a system should be designed to realise not only flexible decision-making, but also consistent decision implementation. We specifically consider neurobiologically-plausible accumulator models of decision-making, in which decisions are made when a decision threshold is reached. To trade-off between the speed and accuracy of the decision in these models, one can either adjust the thresholds themselves or, equivalently, fix the thresholds and adjust baseline activation. Here we review how this equivalence can be implemented in such models. We then argue that manipulating baseline activation is preferable as it realises consistent decision implementation by ensuring consistency of motor inputs, summarise empirical evidence in support of this hypothesis, and suggest that it could be a general principle of decision making and implementation. Our goal is therefore to review how neurobiologically-plausible models of decision-making can manipulate speed-accuracy trade-offs using different mechanisms, to consider which of these mechanisms has more desirable decision-implementation properties, and then review the relevant neuroscientific data on which mechanism brains actually use.     

Analysis of multidimensional neural activity via CNN-UM

In this paper we show that the Cellular Nonlinear Network Universal Machine (CNN-UM) is an excellent tool for analyzing time series of multidimensional binary signals. The developed algorithm is dedicated to process electrophysiological multi-neuron recordings: our aim is to find specific multidimensional activity patterns, which may reflect higher order functional cell-assemblies. The analysis consists of two parts: first, the occurrences of different patterns are counted, then the statistical significance of each occurrence frequency is calculated separately.     

Task-Driven Activity Reduces the Cortical Activity Space of the Brain: Experiment and Whole-Brain Modeling

How a stimulus or a task alters the spontaneous dynamics of the brain remains a fundamental open question in neuroscience. One of the most robust hallmarks of task/stimulus-driven brain dynamics is the decrease of variability with respect to the spontaneous level, an effect seen across multiple experimental conditions and in brain signals observed at different spatiotemporal scales. Recently, it was observed that the trial-to-trial variability and temporal variance of functional magnetic resonance imaging (fMRI) signals decrease in the task-driven activity. Here we examined the dynamics of a large-scale model of the human cortex to provide a mechanistic understanding of these observations. The model allows computing the statistics of synaptic activity in the spontaneous condition and in putative tasks determined by external inputs to a given subset of brain regions. We demonstrated that external inputs decrease the variance, increase the covariances, and decrease the autocovariance of synaptic activity as a consequence of single node and large-scale network dynamics. Altogether, these changes in network statistics imply a reduction of entropy, meaning that the spontaneous synaptic activity outlines a larger multidimensional activity space than does the task-driven activity. We tested this model’s prediction on fMRI signals from healthy humans acquired during rest and task conditions and found a significant decrease of entropy in the stimulus-driven activity. Altogether, our study proposes a mechanism for increasing the information capacity of brain networks by enlarging the volume of possible activity configurations at rest and reliably settling into a confined stimulus-driven state to allow better transmission of stimulus-related information.     

Adaptive combinatorial design to explore large experimental spaces: approach and validation

Systems biology requires mathematical tools not only to analyse large genomic datasets, but also to explore large experimental spaces in a systematic yet economical way. We demonstrate that two-factor combinatorial design (CD), shown to be useful in software testing, can be used to design a small set of experiments that would allow biologists to explore larger experimental spaces. Further, the results of an initial set of experiments can be used to seed further 'Adaptive' CD experimental designs. As a proof of principle, we demonstrate the usefulness of this Adaptive CD approach by analysing data from the effects of six binary inputs on the regulation of genes in the N-assimilation pathway of Arabidopsis. This CD approach identified the more important regulatory signals previously discovered by traditional experiments using far fewer experiments, and also identified examples of input interactions previously unknown. Tests using simulated data show that Adaptive CD suffers from fewer false positives than traditional experimental designs in determining decisive inputs, and succeeds far more often than traditional or random experimental designs in determining when genes are regulated by input interactions. We conclude that Adaptive CD offers an economical framework for discovering dominant inputs and interactions that affect different aspects of genomic outputs and organismal responses.     

Persistent thermal input controls steering behavior in Caenorhabditis elegans

Motile organisms actively detect environmental signals and migrate to a preferable environment. Especially, small animals convert subtle spatial difference in sensory input into orientation behavioral output for directly steering toward a destination, but the neural mechanisms underlying steering behavior remain elusive. Here, we analyze a C. elegans thermotactic behavior in which a small number of neurons are shown to mediate steering toward a destination temperature. We construct a neuroanatomical model and use an evolutionary algorithm to find configurations of the model that reproduce empirical thermotactic behavior. We find that, in all the evolved models, steering curvature are modulated by temporally persistent thermal signals sensed beyond the time scale of sinusoidal locomotion of C. elegans. Persistent rise in temperature decreases steering curvature resulting in straight movement of model worms, whereas fall in temperature increases curvature resulting in crooked movement. This relation between temperature change and steering curvature reproduces the empirical thermotactic migration up thermal gradients and steering bias toward higher temperature. Further, spectrum decomposition of neural activities in model worms show that thermal signals are transmitted from a sensory neuron to motor neurons on the longer time scale than sinusoidal locomotion of C. elegans. Our results suggest that employments of temporally persistent sensory signals enable small animals to steer toward a destination in natural environment with variable, noisy, and subtle cues.     

Formal modeling with multistate neurones and multidimensional synapses

Multistate neurones, a generalization of the popular McCulloch-Pitts binary neurones, are described; they are intended to model the fact that neurones may be in several different states of activity, while McCulloch-Pitts neurones model two states only: active or inactive. We show that as a consequence, multidimensional synapses are necessary to describe the dynamics of the model. As an illustration, we show how to derive the parameters of formal multistate neurones and their associated multidimensional synapses from simulations involving Hodgkin-Huxley neurones. Our approach opens the way to solve in a more biologically plausible way, two problems that were addressed previously: (1) the resolution of 'inverse problems', i.e. the construction of formal networks, whose dynamics follows a pre-defined spatio-temporal binary sequence, (2) the generation of spatio-temporal patterns that reproduce exactly the 'code' extracted from experimental recordings (olfactory codes at the glomerular level).     

Combining several screening tests: optimality of the risk score

The development of biomarkers for cancer screening is an active area of research. While several biomarkers exist, none is sufficiently sensitive and specific on its own for population screening. It is likely that successful screening programs will require combinations of multiple markers. We consider how to combine multiple disease markers for optimal performance of a screening program. We show that the risk score, defined as the probability of disease given data on multiple markers, is the optimal function in the sense that the receiver operating characteristic (ROC) curve is maximized at every point. Arguments draw on the Neyman-Pearson lemma. This contrasts with the corresponding optimality result of classic decision theory, which is set in a Bayesian framework and is based on minimizing an expected loss function associated with decision errors. Ours is an optimality result defined from a strictly frequentist point of view and does not rely on the notion of associating costs with misclassifications. The implication for data analysis is that binary regression methods can be used to yield appropriate relative weightings of different biomarkers, at least in large samples. We propose some modifications to standard binary regression methods for application to the disease screening problem. A flexible biologically motivated simulation model for cancer biomarkers is presented and we evaluate our methods by application to it. An application to real data concerning two ovarian cancer biomarkers is also presented. Our results are equally relevant to the more general medical diagnostic testing problem, where results of multiple tests or predictors are combined to yield a composite diagnostic test. Moreover, our methods justify the development of clinical prediction scores based on binary regression.     

Exploring the costs and benefits of social information use: an appraisal of current experimental evidence

Research on social learning has focused traditionally on whether animals possess the cognitive ability to learn novel motor patterns from tutors. More recently, social learning has included the use of others as sources of inadvertent social information. This type of social learning seems more taxonomically widespread and its use can more readily be approached as an economic decision. Social sampling information, however, can be tricky to use and calls for a more lucid appraisal of its costs. In this four-part review, we address these costs. Firstly, we address the possibility that only a fraction of group members are actually providing social information at any one time. Secondly, we review experimental research which shows that animals are circumspect about social information use. Thirdly, we consider the cases where social information can lead to incorrect decisions and finally, we review studies investigating the effect of social information quality. We address the possibility that using social information or not is not a binary decision and present results of a study showing that nutmeg mannikins combine both sources of information, a condition that can lead to the establishment of informational cascades. We discuss the importance of empirically investigating the economics of social information use.     

A coupled oscillator model of disordered interlimb coordination in patients with Parkinson's disease

Coordination between the left and right limbs during cyclic movements, which can be characterized by the amplitude of each limb's oscillatory movement and relative phase, is impaired in patients with Parkinson's disease (PD). A pedaling exercise on an ergometer in a recent clinical study revealed several types of coordination disorder in PD patients. These include an irregular and burst-like amplitude modulation with intermittent changes in its relative phase, a typical sign of chaotic behavior in nonlinear dynamical systems. This clinical observation leads us to hypothesize that emergence of the rhythmic motor behaviors might be concerned with nonlinearity of an underlying dynamical system. In order to gain insight into this hypothesis, we consider a simple hard-wired central pattern generator model consisting of two identical oscillators connected by reciprocal inhibition. In the model, each oscillator acts as a neural half-center controlling movement of a single limb, either left or right, and receives a control input modeling a flow of descending signals from higher motor centers. When these two control inputs are tonic-constant and identical, the model has left-right symmetry and basically exhibits ordered coordination with an alternating periodic oscillation. We show that, depending on the intensities of these two control inputs and on the difference between them that introduces asymmetry into the model, the model can reproduce several behaviors observed in the clinical study. Bifurcation analysis of the model clarifies two possible mechanisms for the generation of disordered coordination in the model: one is the spontaneous symmetry-breaking bifurcation in the model with the left-right symmetry. The other is related to the degree of asymmetry reflecting the difference between the two control inputs. Finally, clinical implications by the model's dynamics are briefly discussed.     

Storage of correlated patterns in standard and bistable Purkinje cell models

The cerebellum has long been considered to undergo supervised learning, with climbing fibers acting as a 'teaching' or 'error' signal. Purkinje cells (PCs), the sole output of the cerebellar cortex, have been considered as analogs of perceptrons storing input/output associations. In support of this hypothesis, a recent study found that the distribution of synaptic weights of a perceptron at maximal capacity is in striking agreement with experimental data in adult rats. However, the calculation was performed using random uncorrelated inputs and outputs. This is a clearly unrealistic assumption since sensory inputs and motor outputs carry a substantial degree of temporal correlations. In this paper, we consider a binary output neuron with a large number of inputs, which is required to store associations between temporally correlated sequences of binary inputs and outputs, modelled as Markov chains. Storage capacity is found to increase with both input and output correlations, and diverges in the limit where both go to unity. We also investigate the capacity of a bistable output unit, since PCs have been shown to be bistable in some experimental conditions. Bistability is shown to enhance storage capacity whenever the output correlation is stronger than the input correlation. Distribution of synaptic weights at maximal capacity is shown to be independent on correlations, and is also unaffected by the presence of bistability.     

Coupling between lipid shape and membrane curvature

Using molecular dynamics simulations, we examine the behavior of lipids whose preferred curvature can be systematically varied. This curvature is imposed by controlling the headgroup size of a coarse-grained lipid model recently developed by us. To validate this approach, we examine self-assembly of each individual lipid type and observe the complete range of expected bilayer and micelle phases. We then examine binary systems consisting of lipids with positive and negative preferred curvature and find a definite sorting effect. Lipids with positive preferred curvature are found in greater proportions in outer monolayers with the opposite observed for lipids with negative preferred curvature. We also observe a similar, but slightly stronger effect for lipids in a developing spherical bud formed by adhesion to a colloid (e.g., a viral capsid). Importantly, the magnitude of this effect in both cases was large only for regions with strong mean curvature (radii of curvature <10 nm). Our results suggest that lipid shape must act in concert with other physico-chemical effects such as phase transitions or interactions with proteins to produce strong sorting in cellular pathways.     

Modeling the insect feeding decision system: A new approach utilizing fuzzy system theory

Conclusions Preliminary tests of this model have been successful using as inputs responses to pure chemicals. When the trained model is presented with computer-synthesized spike trains as inputs, it predicts behavioral results that are plausible. Future tests will employ more complex stimuli, such as binary and trinary mixtures of compounds and natural stimuli from host and non-host plants.The use of this operational computer model represents a powerful new approach to the currently intractable problem of deciphering complex, acrossfiber sensory codes. This approach provides a more comprehensive and objective assessment of the data than do the current alternatives, such as analysis of individual records by trained experts. In addition, the model can assimilate data from any number of inputs, which is well beyond the abilities of individual investigators compiling data manually. Finally, the model is dynamic and can be updated with new data, and is sufficiently general to be used for any species or comparison across species.A model trained with responses to plants ranging from highly acceptable host plants to highly deterrent non-host plants would be capable of simulating the insect's entire repertoire of feeding decisions. Because the model can divulge the rules by which it made a decision, inspection of these rules will permit identification of which sensory inputs and input patterns were the most important for that decision, thereby providing a crucial insight into complex across-fiber sensory coding. In addition, probing the model with synthesized spike trains as inputs will permit understanding of input/output relationships over wider ranges or in more combinations than would be possible to test experimentally, and thus would be helpful in predicting behavioral responses to multi-component mixtures. Modeling acceptance or rejection, and thereby determining the operative rules associated with these behaviors, may supply a rational basis for the development of baits and antifeedants and provide direction for genetic engineering of semiochemical in plants.     

Two constructive methods for designing compact feedforward networks of threshold units

We propose two algorithms for constructing and training compact feedforward networks of linear threshold units. The SHIFT procedure constructs networks with a single hidden layer while the PTI constructs multilayered networks. The resulting networks are guaranteed to perform any given task with binary or real-valued inputs. The various experimental results reported for tasks with binary and real-valued inputs indicate that our methods compare favorably with alternative procedures deriving from similar strategies, both in terms of size of the resulting networks and of their generalization properties.     

Coelom formation: binary decision of the lateral plate mesoderm is controlled by the ectoderm.

Most triploblastic animals including vertebrates have a coelomic cavity that separates the outer and inner components of the body. The coelom is lined by two different tissue components, somatopleure and splanchnopleure, which are derived from the lateral plate region. Thus, the coelom is constructed as a result of a binary decision during early specification of the lateral plate. In this report we studied the molecular mechanisms of this binary decision. We first demonstrate that the splitting of the lateral plate into the two cell sheets progresses in an anteroposterior order and this progression is not coordinated with that of the somitic segmentation. By a series of embryological manipulations we found that young splanchnic mesoderm is still competent to be respecified as somatic mesoderm, and the ectoderm overlying the lateral plate is sufficient for this redirection. The lateral ectoderm is also required for maintenance of the somatic character of the mesoderm. Thus, the ectoderm plays at least two roles in the early subdivision of the lateral plate: specification and maintenance of the somatic mesoderm. We also show that the latter interactions are mediated by BMP molecules that are localized in the lateral ectoderm. Evolutionary aspects of the coelom formation are also considered.     

Algorithmic approaches to selecting control clones in DNA array hybridization experiments

We study the problem of selecting control clones in DNA array hybridization experiments. The problem arises in the OFRG method for analyzing microbial communities. The OFRG method performs classification of rRNA gene clones using binary fingerprints created from a series of hybridization experiments, where each experiment consists of hybridizing a collection of arrayed clones with a single oligonucleotide probe. This experiment produces analog signals, one for each clone, which then need to be classified, that is, converted into binary values 1 and 0 that represent hybridization and non-hybridization events. In addition to the sample rRNA gene clones, the array contains a number of control clones needed to calibrate the classification procedure of the hybridization signals. These control clones must be selected with care to optimize the classification process. We formulate this as a combinatorial optimization problem called Balanced Covering. We prove that the problem is NP-hard, and we show some results on hardness of approximation. We propose approximation algorithms based on randomized rounding, and we show that, with high probability, our algorithms approximate well the optimum solution. The experimental results confirm that the algorithms find high quality control clones. The algorithms have been implemented and are publicly available as part of the software package called CloneTools.     

Uncovering the spatio-temporal dynamics of value-based decision-making in the human brain: a combined fMRI–EEG study

While there is a growing body of functional magnetic resonance imaging (fMRI) evidence implicating a corpus of brain regions in value-based decision-making in humans, the limited temporal resolution of fMRI cannot address the relative temporal precedence of different brain regions in decision-making. To address this question, we adopted a computational model-based approach to electroencephalography (EEG) data acquired during a simple binary choice task. fMRI data were also acquired from the same participants for source localization. Post-decision value signals emerged 200 ms post-stimulus in a predominantly posterior source in the vicinity of the intraparietal sulcus and posterior temporal lobe cortex, alongside a weaker anterior locus. The signal then shifted to a predominantly anterior locus 850 ms following the trial onset, localized to the ventromedial prefrontal cortex and lateral prefrontal cortex. Comparison signals between unchosen and chosen options emerged late in the trial at 1050 ms in dorsomedial prefrontal cortex, suggesting that such comparison signals may not be directly associated with the decision itself but rather may play a role in post-decision action selection. Taken together, these results provide us new insights into the temporal dynamics of decision-making in the brain, suggesting that for a simple binary choice task, decisions may be encoded predominantly in posterior areas such as intraparietal sulcus, before shifting anteriorly.