Fair attribution of functional contribution in artificial and biological networks

Downstream network transformations dissociate neural activity from causal functional contributions

Neuroscientists rely on distributed spatio-temporal patterns of neural activity to understand how neural units contribute to cognitive functions and behavior. However, the extent to which neural activity reliably indicates a unit's causal contribution to the behavior is not well understood. To address this issue, we provide a systematic multi-site perturbation framework that captures time-varying causal contributions of elements to a collectively produced outcome. Applying our framework to intuitive toy examples and artificial neural networks revealed that recorded activity patterns of neural elements may not be generally informative of their causal contribution due to activity transformations within a network. Overall, our findings emphasize the limitations of inferring causal mechanisms from neural activities and offer a rigorous lesioning framework for elucidating causal neural contributions.

When Neural Activity Fails to Reveal Causal Contributions

Neuroscientists rely on distributed spatio-temporal patterns of neural activity to understand how neural units contribute to cognitive functions and behavior. However, the extent to which neural activity reliably indicates a unit's causal contribution to the behavior is not well understood. To address this issue, we provide a systematic multi-site perturbation framework that captures time-varying causal contributions of elements to a collectively produced outcome. Applying our framework to intuitive toy examples and artificial neuronal networks revealed that recorded activity patterns of neural elements may not be generally informative of their causal contribution due to activity transformations within a network. Overall, our findings emphasize the limitations of inferring causal mechanisms from neural activities and offer a rigorous lesioning framework for elucidating causal neural contributions.

Use of multi-perturbation Shapley analysis in lesion studies of functional networks: The case of upper limb paresis

Understanding the impact of variation in lesion topography on the expression of functional impairments following stroke is important, as it may pave the way to modeling structure-function relations in statistical terms while pointing to constraints for adaptive remapping and functional recovery. Multi-perturbation Shapley-value analysis (MSA) is a relatively novel game-theoretical approach for multivariate lesion-symptom mapping. In this methodological paper, we provide a comprehensive explanation of MSA. We use synthetic data to assess the method's accuracy and perform parameter optimization. We then demonstrate its application using a cohort of 107 first-event subacute stroke patients, assessed for upper limb (UL) motor impairment (Fugl-Meyer Assessment scale). Under the conditions tested, MSA could correctly detect simulated ground-truth lesion-symptom relationships with a sensitivity of 75% and specificity of ~90%. For real behavioral data, MSA disclosed a strong hemispheric effect in the relative contribution of specific regions-of-interest (ROIs): poststroke UL motor function was mostly contributed by damage to ROIs associated with movement planning (supplementary motor cortex and superior frontal gyrus) following left-hemispheric damage (LHD) and by ROIs associated with movement execution (primary motor and somatosensory cortices and the ventral brainstem) following right-hemispheric damage (RHD). Residual UL motor ability following LHD was found to depend on a wider array of brain structures compared to the residual motor ability of RHD patients. The results demonstrate that MSA can provide a unique insight into the relative importance of different hubs in neural networks, which is difficult to obtain using standard univariate methods.

Inferring feature importance with uncertainties with application to large genotype data

Estimating feature importance, which is the contribution of a prediction or several predictions due to a feature, is an essential aspect of explaining data-based models. Besides explaining the model itself, an equally relevant question is which features are important in the underlying data generating process. We present a Shapley-value-based framework for inferring the importance of individual features, including uncertainty in the estimator. We build upon the recently published model-agnostic feature importance score of SAGE (Shapley additive global importance) and introduce Sub-SAGE. For tree-based models, it has the advantage that it can be estimated without computationally expensive resampling. We argue that for all model types the uncertainties in our Sub-SAGE estimator can be estimated using bootstrapping and demonstrate the approach for tree ensemble methods. The framework is exemplified on synthetic data as well as large genotype data for predicting feature importance with respect to obesity.

Systematic perturbation of an artificial neural network: A step towards quantifying causal contributions in the brain

Lesion inference analysis is a fundamental approach for characterizing the causal contributions of neural elements to brain function. This approach has gained new prominence through the arrival of modern perturbation techniques with unprecedented levels of spatiotemporal precision. While inferences drawn from brain perturbations are conceptually powerful, they face methodological difficulties. Particularly, they are challenged to disentangle the true causal contributions of the involved elements, since often functions arise from coalitions of distributed, interacting elements, and localized perturbations have unknown global consequences. To elucidate these limitations, we systematically and exhaustively lesioned a small artificial neural network (ANN) playing a classic arcade game. We determined the functional contributions of all nodes and links, contrasting results from sequential single-element perturbations with simultaneous perturbations of multiple elements. We found that lesioning individual elements, one at a time, produced biased results. By contrast, multi-site lesion analysis captured crucial details that were missed by single-site lesions. We conclude that even small and seemingly simple ANNs show surprising complexity that needs to be addressed by multi-lesioning for a coherent causal characterization.

The motto “No causation without manipulation” is canonical to scientific endeavors. In particular, neuroscience seeks to identify which brain elements are causally involved in cognition and behavior, by perturbing them. However, due to multi-dimensional interactions among the elements, this goal has remained challenging. Here, we used an Artificial Neural Network as a ground-truth model to compare the inferential capacities of two principal approaches, lesioning a system one element at a time versus sampling from the set of all possible combinations of lesions. We show that lesioning one element at a time provides misleading results. Hence, we argue for employing exhaustive perturbation regimes. We further advocate using simulation experiments and ground-truth models to verify the assumptions and limitations of current approaches for brain mapping by perturbation.

Phase-based causality analysis with partial mutual information from mixed embedding

Instantaneous phases extracted from multivariate time series can retain information about the relationships between the underlying mechanisms that generate the series. Although phases have been widely used in the study of nondirectional coupling and connectivity, they have not found similar appeal in the study of causality. Herein, we present a new method for phase-based causality analysis, which combines ideas from the mixed embedding technique and the information-theoretic approach to causality in coupled oscillatory systems. We then use the introduced method to investigate causality in simulated datasets of bivariate, unidirectionally paired systems from combinations of Rössler, Lorenz, van der Pol, and Mackey-Glass equations. We observe that causality analysis using the phases can capture the true causal relation for coupling strength smaller than the analysis based on the amplitudes can capture. On the other hand, the causality estimation based on the phases tends to have larger variability, which is attributed more to the phase extraction process than the actual phase-based causality method. In addition, an application on real electroencephalographic data from an experiment on elicited human emotional states reinforces the usefulness of phases in causality identification.

Batf-mediated epigenetic control of effector CD8+ T cell differentiation

The response of naive CD8⁺ T cells to their cognate antigen involves rapid and broad changes to gene expression that are coupled with extensive chromatin remodeling, but the mechanisms governing these changes are not fully understood. Here, we investigated how these changes depend on the basic leucine zipper ATF-like transcription factor Batf, which is essential for the early phases of the process. Through genome scale profiling, we characterized the role of Batf in chromatin organization at several levels, including the accessibility of key regulatory regions, the expression of their nearby genes, and the interactions that these regions form with each other and with key transcription factors. We identified a core network of transcription factors that cooperated with Batf, including Irf4, Runx3, and T-bet, as indicated by their colocalization with Batf and their binding in regions whose accessibility, interactions, and expression of nearby genes depend on Batf. We demonstrated the synergistic activity of this network by overexpressing the different combinations of these genes in fibroblasts. Batf and Irf4, but not Batf alone, were sufficient to increase accessibility and transcription of key loci, normally associated with T cell function. Addition of Runx3 and T-bet further contributed to fine-tuning of these changes and was essential for establishing chromatin loops characteristic of T cells. These data provide a resource for studying the epigenomic and transcriptomic landscape of effector differentiation of cytotoxic T cells and for investigating the interdependency between transcription factors and its effects on the epigenome and transcriptome of primary cells.

Mathematical indices for the influence of risk factors on the lethality of a disease

We develop a theoretical model to measure the relative relevance of different pathologies of the lethality of a disease in society. This approach allows a ranking of diseases to be determined, which can assist in establishing priorities for vaccination campaigns or prevention strategies. Among all possible measurements, we identify three families of rules that satisfy a combination of relevant properties: neutrality, irrelevance, and one of three composition concepts. One of these families includes, for instance, the Shapley value of the associated cooperative game. The other two families also include simple and intuitive indices. As an illustration, we measure the relative relevance of several pathologies in lethality due to COVID-19.

Game-theoretical mapping of fundamental brain functions based on lesion deficits in acute stroke

Lesion analysis is a fundamental and classical approach for inferring the causal contributions of brain regions to brain function. However, many studies have been limited by the shortcomings of methodology or clinical data. Aiming to overcome these limitations, we here use an objective multivariate approach based on game theory, Multi-perturbation Shapley value Analysis, in conjunction with data from a large cohort of 394 acute stroke patients, to derive causal contributions of brain regions to four principal functional components of the widely used National Institutes of Health Stroke Score measure. The analysis was based on a high-resolution parcellation of the brain into 294 grey and white matter regions. Through initial lesion symptom mapping for identifying all potential candidate regions and repeated iterations of the game-theoretical approach to remove non-significant contributions, the analysis derived the smallest sets of regions contributing to each of the four principal functional components as well as functional interactions among the regions. Specifically, the factor 'language and consciousness' was related to contributions of cortical regions in the left hemisphere, including the prefrontal gyrus, the middle frontal gyrus, the ventromedial putamen and the inferior frontal gyrus. Right and left motor functions were associated with contributions of the left and right dorsolateral putamen and the posterior limb of the internal capsule, correspondingly. Moreover, the superior corona radiata and the paracentral lobe of the right hemisphere as well as the right caudal area 23 of the cingulate gyrus were mainly related to left motor function, while the prefrontal gyrus, the external capsule and the sagittal stratum fasciculi of the left hemisphere contributed to right motor function. Our approach demonstrates a practically feasible strategy for applying an objective lesion inference method to a high-resolution map of the human brain and distilling a small, characteristic set of grey and white matter structures contributing to fundamental brain functions. In addition, we present novel findings of synergistic interactions between brain regions that provide insight into the functional organization of brain networks.

Revisiting 'brain modes' in a new computational era: approaches for the characterization of brain-behavioural associations

The study of brain-function relationships is undergoing a conceptual and methodological transformation due to the emergence of network neuroscience and the development of multivariate methods for lesion-deficit inferences. Anticipating this process, in 1998 Godefroy and co-workers conceptualized the potential of four elementary typologies of brain-behaviour relationships named 'brain modes' (unicity, equivalence, association, summation) as building blocks able to describe the association between intact or lesioned brain regions and cognitive processes or neurological deficits. In the light of new multivariate lesion inference and network approaches, we critically revisit and update the original theoretical notion of brain modes, and provide real-life clinical examples that support their existence. To improve the characterization of elementary units of brain-behavioural relationships further, we extend such conceptualization with a fifth brain mode (mutual inhibition/masking summation). We critically assess the ability of these five brain modes to account for any type of brain-function relationship, and discuss past versus future contributions in redefining the anatomical basis of human cognition. We also address the potential of brain modes for predicting the behavioural consequences of lesions and their future role in the design of cognitive neurorehabilitation therapies.

A biologically constrained spiking neural network model of the primate basal ganglia with overlapping pathways exhibits action selection

Action selection has been hypothesized to be a key function of the basal ganglia, yet the nuclei involved, their interactions and the importance of the direct/indirect pathway segregation in such process remain debated. Here, we design a spiking computational model of the monkey basal ganglia derived from a previously published population model, initially parameterized to reproduce electrophysiological activity at rest and to embody as much quantitative anatomical data as possible. As a particular feature, both models exhibit the strong overlap between the direct and indirect pathways that has been documented in non-human primates. Here, we first show how the translation from a population to an individual neuron model was achieved, with the addition of a minimal number of parameters. We then show that our model performs action selection, even though it was built without any assumption on the activity carried out during behaviour. We investigate the mechanisms of this selection through circuit disruptions and found an instrumental role of the off-centre/on-surround structure of the MSN-STN-GPi circuit, as well as of the MSN-MSN and FSI-MSN projections. This validates their potency in enabling selection. We finally study the pervasive centromedian and parafascicular thalamic inputs that reach all basal ganglia nuclei and whose influence is therefore difficult to anticipate. Our model predicts that these inputs modulate the responsiveness of action selection, making them a candidate for the regulation of the speed-accuracy trade-off during decision-making.

Game theoretical mapping of white matter contributions to visuospatial attention in stroke patients with hemineglect

White matter bundles linking gray matter nodes are key anatomical players to fully characterize associations between brain systems and cognitive functions. Here we used a multivariate lesion inference approach grounded in coalitional game theory (multiperturbation Shapley value analysis, MSA) to infer causal contributions of white matter bundles to visuospatial orienting of attention. Our work is based on the characterization of the lesion patterns of 25 right hemisphere stroke patients and the causal analysis of their impact on three neuropsychological tasks: line bisection, letter cancellation, and bells cancellation. We report that, out of the 11 white matter bundles included in our MSA coalitions, the optic radiations, the inferior fronto-occipital fasciculus and the anterior cingulum were the only tracts to display task-invariant contributions (positive, positive, and negative, respectively) to the tasks. We also report task-dependent influences for the branches of the superior longitudinal fasciculus and the posterior cingulum. By extending prior findings to white matter tracts linking key gray matter nodes, we further characterize from a network perspective the anatomical basis of visual and attentional orienting processes. The knowledge about interactions patterns mediated by white matter tracts linking cortical nodes of attention orienting networks, consolidated by further studies, may help develop and customize brain stimulation approaches for the rehabilitation of visuospatial neglect.

Perturbation-driven paradoxical facilitation of visuo-spatial function: Revisiting the 'Sprague effect'

The 'Sprague Effect' described in the seminal paper of James Sprague (Science 153:1544-1547, 1966a) is an unexpected paradoxical effect in which a second brain lesion reversed functional deficits induced by an earlier lesion. It was observed initially in the cat where severe and permanent contralateral visually guided attentional deficits generated by the ablation of large areas of the visual cortex were reversed by the subsequent removal of the superior colliculus (SC) opposite to the cortical lesion or by the splitting of the collicular commissure. Physiologically, this effect has been explained in several ways-most notably by the reduction of the functional inhibition of the ipsilateral SC by the contralateral SC, and the restoration of normal interactions between cortical and midbrain structures after ablation. In the present review, we aim at reappraising the 'Sprague Effect' by critically analyzing studies that have been conducted in the feline and human brain. Moreover, we assess applications of the 'Sprague Effect' in the rehabilitation of visually guided attentional impairments by using non-invasive therapeutic approaches such as transcranial magnetic stimulation (TMS) and transcranial direct-current stimulation (tDCS). We also review theoretical models of the effect that emphasize the inhibition and balancing between the two hemispheres and show implications for lesion inference approaches. Last, we critically review whether the resulting inter-hemispheric rivalry theories lead toward an efficient rehabilitation of stroke in humans. We conclude by emphasizing key challenges in the field of 'Sprague Effect' applications in order to design better therapies for brain-damaged patients.

An application of the Shapley value to the analysis of co-expression networks

We study the problem of identifying relevant genes in a co-expression network using a (cooperative) game theoretic approach. The Shapley value of a cooperative game is used to asses the relevance of each gene in interaction with the others, and to stress the role of nodes in the periphery of a co-expression network for the regulation of complex biological pathways of interest. An application of the method to the analysis of gene expression data from microarrays is presented, as well as a comparison with classical centrality indices. Finally, making further assumptions about the a priori importance of genes, we combine the game theoretic model with other techniques from cluster analysis.

Game theoretical mapping of causal interactions underlying visuo-spatial attention in the human brain based on stroke lesions

Anatomical studies conducted in neurological conditions have developed our understanding of the causal relationships between brain lesions and their clinical consequences. The analysis of lesion patterns extended across brain networks has been particularly useful in offering new insights on brain-behavior relationships. Here we applied multiperturbation Shapley value Analysis (MSA), a multivariate method based on coalitional game theory inferring causal regional contributions to specific behavioral outcomes from the characteristic functional deficits after stroke lesions. We established the causal patterns of contributions and interactions of nodes of the attentional orienting network on the basis of lesion and behavioral data from 25 right hemisphere stroke patients tested in visuo-spatial attention tasks. We calculated the percentage of damaged voxels for five right hemisphere cortical regions contributing to attentional orienting, involving seven specific Brodmann Areas (BA): Frontal Eye Fields, (FEF-BA6), Intraparietal Sulcus (IPS-BA7), Inferior Frontal Gyrus (IFG-BA44/BA45), Temporo-Parietal Junction (TPJ-BA39/BA40), and Inferior Occipital Gyrus (IOG-BA19). We computed the MSA contributions of these seven BAs to three behavioral clinical tests (line bisection, bells cancellation, and letter cancelation). Our analyses indicated IPS as the main contributor to the attentional orienting and also revealed synergistic influences among IPS, TPJ, and IOG (for bells cancellation and line bisection) and between TPJ and IFG (for bells and letter cancellation tasks). The findings demonstrate the ability of the MSA approach to infer plausible causal contributions of relevant right hemisphere sites in poststroke visuo-spatial attention and awareness disorders. Hum Brain Mapp 38:3454-3471, 2017. © 2017 Wiley Periodicals, Inc.

Systematic Characterization and Analysis of the Taxonomic Drivers of Functional Shifts in the Human Microbiome

Comparative analyses of the human microbiome have identified both taxonomic and functional shifts that are associated with numerous diseases. To date, however, microbiome taxonomy and function have mostly been studied independently and the taxonomic drivers of functional imbalances have not been systematically identified. Here, we present FishTaco, an analytical and computational framework that integrates taxonomic and functional comparative analyses to accurately quantify taxon-level contributions to disease-associated functional shifts. Applying FishTaco to several large-scale metagenomic cohorts, we show that shifts in the microbiome's functional capacity can be traced back to specific taxa. Furthermore, the set of taxa driving functional shifts and their contribution levels vary markedly between functions. We additionally find that similar functional imbalances in different diseases are driven by both disease-specific and shared taxa. Such integrated analysis of microbiome ecological and functional dynamics can inform future microbiome-based therapy, pinpointing putative intervention targets for manipulating the microbiome's functional capacity.

Technical considerations of a game-theoretical approach for lesion symptom mapping

Background

Various strategies have been used for inferring brain functions from stroke lesions. We explored a new mathematical approach based on game theory, the so-called multi-perturbation Shapley value analysis (MSA), to assess causal function localizations and interactions from multiple perturbation data. We applied MSA to a dataset composed of lesion patterns of 148 acute stroke patients and their National Institutes of Health Stroke Scale (NIHSS) scores, to systematically investigate the influence of different parameter settings on the outcomes of the approach. Specifically, we investigated aspects of MSA methodology including the choice of the predictor algorithm (typology and kernel functions), training dataset (original versus binary), as well as the influence of lesion thresholds. We assessed the suitability of MSA for processing real clinical lesion data and established the central parameters for this analysis.

Results

We derived general recommendations for the analysis of clinical datasets by MSA and showed that, for the studied dataset, the best approach was to use a linear-kernel support vector machine predictor, trained with a binary training dataset, where the binarization was implemented through a median threshold of lesion size for each region. We demonstrated that the results obtained with different MSA variants lead to almost identical results as the basic MSA.

Conclusions

MSA is a feasible approach for the multivariate lesion analysis of clinical stroke data. Informed choices need to be made to set parameters that may affect the analysis outcome.

Mapping causal functional contributions derived from the clinical assessment of brain damage after stroke

Lesion analysis reveals causal contributions of brain regions to mental functions, aiding the understanding of normal brain function as well as rehabilitation of brain-damaged patients. We applied a novel lesion inference technique based on game theory, Multi-perturbation Shapley value Analysis (MSA), to a large clinical lesion dataset. We used MSA to analyze the lesion patterns of 148 acute stroke patients together with their neurological deficits, as assessed by the National Institutes of Health Stroke Scale (NIHSS). The results revealed regional functional contributions to essential behavioral and cognitive functions as reflected in the NIHSS, particularly by subcortical structures. There were also side specific differences of functional contributions between the right and left hemispheric brain regions which may reflect the dominance of the left hemispheric syndrome aphasia in the NIHSS. Comparison of MSA to established lesion inference methods demonstrated the feasibility of the approach for analyzing clinical data and indicated its capability for objectively inferring functional contributions from multiple injured, potentially interacting sites, at the cost of having to predict the outcome of unknown lesion configurations. The analysis of regional functional contributions to neurological symptoms measured by the NIHSS contributes to the interpretation of this widely used standardized stroke scale in clinical practice as well as clinical trials and provides a first approximation of a 'map of stroke'.

Causal functional contributions and interactions in the attention network of the brain: an objective multi-perturbation analysis

Spatial attention is a prime example for the distributed network functions of the brain. Lesion studies in animal models have been used to investigate intact attentional mechanisms as well as perspectives for rehabilitation in the injured brain. Here, we systematically analyzed behavioral data from cooling deactivation and permanent lesion experiments in the cat, where unilateral deactivation of the posterior parietal cortex (in the vicinity of the posterior middle suprasylvian cortex, pMS) or the superior colliculus (SC) cause a severe neglect in the contralateral hemifield. Counterintuitively, additional deactivation of structures in the opposite hemisphere reverses the deficit. Using such lesion data, we employed a game-theoretical approach, multi-perturbation Shapley value analysis (MSA), for inferring functional contributions and network interactions of bilateral pMS and SC from behavioral performance in visual attention studies. The approach provides an objective theoretical strategy for lesion inferences and allows a unique quantitative characterization of regional functional contributions and interactions on the basis of multi-perturbations. The quantitative analysis demonstrated that right posterior parietal cortex and superior colliculus made the strongest positive contributions to left-field orienting, while left brain regions had negative contributions, implying that their perturbation may reverse the effects of contralateral lesions or improve normal function. An analysis of functional modulations and interactions among the regions revealed redundant interactions (implying functional overlap) between regions within each hemisphere, and synergistic interactions between bilateral regions. To assess the reliability of the MSA method in the face of variable and incomplete input data, we performed a sensitivity analysis, investigating how much the contribution values of the four regions depended on the performance of specific configurations and on the prediction of unknown performances. The results suggest that the MSA approach is sensitive to categorical, but insensitive to gradual changes in the input data. Finally, we created a basic network model that was based on the known anatomical interactions among cortical-tectal regions and reproduced the experimentally observed behavior in visual orienting. We discuss the structural organization of the network model relative to the causal modulations identified by MSA, to aid a mechanistic understanding of the attention network of the brain.

Structural control of metabolic flux

Organisms have to continuously adapt to changing environmental conditions or undergo developmental transitions. To meet the accompanying change in metabolic demands, the molecular mechanisms of adaptation involve concerted interactions which ultimately induce a modification of the metabolic state, which is characterized by reaction fluxes and metabolite concentrations. These state transitions are the effect of simultaneously manipulating fluxes through several reactions. While metabolic control analysis has provided a powerful framework for elucidating the principles governing this orchestrated action to understand metabolic control, its applications are restricted by the limited availability of kinetic information. Here, we introduce structural metabolic control as a framework to examine individual reactions' potential to control metabolic functions, such as biomass production, based on structural modeling. The capability to carry out a metabolic function is determined using flux balance analysis (FBA). We examine structural metabolic control on the example of the central carbon metabolism of Escherichia coli by the recently introduced framework of functional centrality (FC). This framework is based on the Shapley value from cooperative game theory and FBA, and we demonstrate its superior ability to assign “share of control” to individual reactions with respect to metabolic functions and environmental conditions. A comparative analysis of various scenarios illustrates the usefulness of FC and its relations to other structural approaches pertaining to metabolic control. We propose a Monte Carlo algorithm to estimate FCs for large networks, based on the enumeration of elementary flux modes. We further give detailed biological interpretation of FCs for production of lactate and ATP under various respiratory conditions.

Insight into the functioning of metabolic control to meet changing demands is a first step in rational engineering of biological systems towards a desired behavior. Metabolic control analysis provides the means to examine the impact of change of reaction fluxes on a specific target flux based on kinetic modeling, but suffers from limitations of the kinetic approach. Here, we introduce and analyze structural metabolic control as a framework to overcome these limitations. We utilize functional centrality, a framework based on the Shapley value from cooperative game theory and flux balance analysis, to determine the contribution of individual reactions to the functions accomplished by a metabolic network. These contributions, in turn, depend on the control exerted on the remaining network. Functional centrality provides the mathematical means to gain further understanding of metabolic control. The potential applications range from facilitating strategies of rational strain design to drug target identification.

Restricted cooperative games on metabolic networks reveal functionally important reactions

Understanding the emerging properties of complex biological systems is in the crux of systems biology studies. Computational methods for elucidating the role of each component in the synergetic interplay can be used to identify targets for genetic and metabolic engineering. In particular, we aim at determining the importance of reactions in a metabolic network with respect to a specific biological function. Therefore, we propose a novel game-theoretic framework which integrates restricted cooperative games with the outcome of flux balance analysis. We define productivity games on metabolic networks and present an analysis of their unrestricted and restricted variants based on the game-theoretic solution concept of the Shapley value. Correspondingly, this concept provides a characterization of the robustness and functional centrality for each enzyme involved in a given metabolic network. Furthermore, the comparison of two different environments - feast and famine - demonstrates the dependence of the results on the imposed flux capacities.

Multiperturbation analysis of distributed neural networks: the case of spatial neglect

This study assesses the feasibility of using a multiperturbation analysis (MPA) approach for lesion-symptom mapping. We analyze the relative contribution of damage in different brain regions to the expression of spatial neglect, as revealed in line-bisection performance. The data set comprised of normalized lesion information and bisection test results from 23 first-event right-hemisphere stroke patients. Obtaining quantitative measures of task relevance for different regions of interest (ROIs), the following ROIs were found to be the most contributing: the supramarginal and angular gyri of the inferior parietal lobule, the superior parietal lobule, the anterior part of the temporo-parietal junction connecting the superior temporal and supramarginal gyri, and the thalamus. MPA is likely to play an important role in elucidating the anatomical substrate of complex functions.

Through neural stimulation to behavior manipulation: a novel method for analyzing dynamical cognitive models

The dynamical systems' approach to cognition (Dynamicism) promises computational models that effectively embed cognitive processing within its more natural behavioral context. Dynamical cognitive models also pose difficult, analytical challenges, which motivate the development of new analytical methodology. We start by illustrating the challenge by applying two conventional analytical methods to a well-known Dynamicist model of categorical perception. We then introduce our own analysis, which works by analogy with neural stimulation methods, and which yields some novel insights into the way the model works. We then extend and apply the method to a second Dynamicist model, which captures the key psychophysical trends that emerge when humans and animals compare two numbers. The results of the analysis-which reveals units with tuning functions that are monotonically related to the magnitudes of the numbers that the agents must compare-offer a clear contribution to the contentious debate concerning the way number information is encoded in the brain.

Causal measures of structure and plasticity in simulated and living neural networks

A major goal of neuroscience is to understand the relationship between neural structures and their function. Recording of neural activity with arrays of electrodes is a primary tool employed toward this goal. However, the relationships among the neural activity recorded by these arrays are often highly complex making it problematic to accurately quantify a network's structural information and then relate that structure to its function. Current statistical methods including cross correlation and coherence have achieved only modest success in characterizing the structural connectivity. Over the last decade an alternative technique known as Granger causality is emerging within neuroscience. This technique, borrowed from the field of economics, provides a strong mathematical foundation based on linear auto-regression to detect and quantify “causal” relationships among different time series. This paper presents a combination of three Granger based analytical methods that can quickly provide a relatively complete representation of the causal structure within a neural network. These are a simple pairwise Granger causality metric, a conditional metric, and a little known computationally inexpensive subtractive conditional method. Each causal metric is first described and evaluated in a series of biologically plausible neural simulations. We then demonstrate how Granger causality can detect and quantify changes in the strength of those relationships during plasticity using 60 channel spike train data from an in vitro cortical network measured on a microelectrode array. We show that these metrics can not only detect the presence of causal relationships, they also provide crucial information about the strength and direction of that relationship, particularly when that relationship maybe changing during plasticity. Although we focus on the analysis of multichannel spike train data the metrics we describe are applicable to any stationary time series in which causal relationships among multiple measures is desired. These techniques can be especially useful when the interactions among those measures are highly complex, difficult to untangle, and maybe changing over time.

Combining Shapley value and statistics to the analysis of gene expression data in children exposed to air pollution

Background

In gene expression analysis, statistical tests for differential gene expression provide lists of candidate genes having, individually, a sufficiently low p-value. However, the interpretation of each single p-value within complex systems involving several interacting genes is problematic. In parallel, in the last sixty years, game theory has been applied to political and social problems to assess the power of interacting agents in forcing a decision and, more recently, to represent the relevance of genes in response to certain conditions.

Results

In this paper we introduce a Bootstrap procedure to test the null hypothesis that each gene has the same relevance between two conditions, where the relevance is represented by the Shapley value of a particular coalitional game defined on a microarray data-set. This method, which is called Comparative Analysis of Shapley value (shortly, CASh), is applied to data concerning the gene expression in children differentially exposed to air pollution. The results provided by CASh are compared with the results from a parametric statistical test for testing differential gene expression. Both lists of genes provided by CASh and t-test are informative enough to discriminate exposed subjects on the basis of their gene expression profiles. While many genes are selected in common by CASh and the parametric test, it turns out that the biological interpretation of the differences between these two selections is more interesting, suggesting a different interpretation of the main biological pathways in gene expression regulation for exposed individuals. A simulation study suggests that CASh offers more power than t-test for the detection of differential gene expression variability.

Conclusion

CASh is successfully applied to gene expression analysis of a data-set where the joint expression behavior of genes may be critical to characterize the expression response to air pollution. We demonstrate a synergistic effect between coalitional games and statistics that resulted in a selection of genes with a potential impact in the regulation of complex pathways.

Can single knockouts accurately single out gene functions?

Background

When analyzing complex biological systems, a major objective is localization of function – assessing how much each element contributes to the execution of specific tasks. To establish causal relationships, knockout and perturbation studies are commonly executed. The vast majority of studies perturb a single element at a time, yet one may hypothesize that in non-trivial biological systems single-perturbations will fail to reveal the functional organization of the system, owing to interactions and redundancies.

Results

We address this fundamental gap between theory and practice by quantifying how misleading the picture arising from classical single-perturbation analysis is, compared with the full multiple-perturbations picture. To this end we use a combination of a novel approach for quantitative, rigorous multiple-knockouts analysis based on the Shapley value from game theory, with an established in-silico model of Saccharomyces cerevisiae metabolism. We find that single-perturbations analysis misses at least 33% of the genes that contribute significantly to the growth potential of this organism, though the essential genes it does find are responsible for most of the growth potential. But when assigning gene contributions for individual metabolic functions, the picture arising from single-perturbations is severely lacking and a multiple-perturbations approach turns out to be essential.

Conclusion

The multiple-perturbations investigation yields a significantly richer and more biologically plausible functional annotation of the genes comprising the metabolic network of the yeast.

Highlights of the 15th Conference on Retroviruses and Opportunistic Infections. Basic science summary

The scientific advances made in the year leading up to the 15th Conference on Retroviruses and Opportunistic Infections were overshadowed, to some extent, by setbacks in the AIDS vaccine research arena and in particular, the failure of the Merck STEP trial. Arguably, these disappointments were offset by strong advances that were being made in basic science and pathogenesis. In particular, recent discoveries into cellular factors that influence virus-host cell interplay and new insights into the mechanisms of viral pathogenesis were highlighted at the meeting. These research discoveries paint an optimistic picture regarding the development of new strategies to combat HIV and AIDS.

Shapley ratings in brain networks

Recent applications of network theory to brain networks as well as the expanding empirical databases of brain architecture spawn an interest in novel techniques for analyzing connectivity patterns in the brain. Treating individual brain structures as nodes in a directed graph model permits the application of graph theoretical concepts to the analysis of these structures within their large-scale connectivity networks. In this paper, we explore the application of concepts from graph and game theory toward this end. Specifically, we utilize the Shapley value principle, which assigns a rank to players in a coalition based upon their individual contributions to the collective profit of that coalition, to assess the contributions of individual brain structures to the graph derived from the global connectivity network. We report Shapley values for variations of a prefrontal network, as well as for a visual cortical network, which had both been extensively investigated previously. This analysis highlights particular nodes as strong or weak contributors to global connectivity. To understand the nature of their contribution, we compare the Shapley values obtained from these networks and appropriate controls to other previously described nodal measures of structural connectivity. We find a strong correlation between Shapley values and both betweenness centrality and connection density. Moreover, a stepwise multiple linear regression analysis indicates that approximately 79% of the variance in Shapley values obtained from random networks can be explained by betweenness centrality alone. Finally, we investigate the effects of local lesions on the Shapley ratings, showing that the present networks have an immense structural resistance to degradation. We discuss our results highlighting the use of such measures for characterizing the organization and functional role of brain networks.

Causal networks in simulated neural systems

Neurons engage in causal interactions with one another and with the surrounding body and environment. Neural systems can therefore be analyzed in terms of causal networks, without assumptions about information processing, neural coding, and the like. Here, we review a series of studies analyzing causal networks in simulated neural systems using a combination of Granger causality analysis and graph theory. Analysis of a simple target-fixation model shows that causal networks provide intuitive representations of neural dynamics during behavior which can be validated by lesion experiments. Extension of the approach to a neurorobotic model of the hippocampus and surrounding areas identifies shifting causal pathways during learning of a spatial navigation task. Analysis of causal interactions at the population level in the model shows that behavioral learning is accompanied by selection of specific causal pathways-"causal cores"-from among large and variable repertoires of neuronal interactions. Finally, we argue that a causal network perspective may be useful for characterizing the complex neural dynamics underlying consciousness.

Feature Selection via Coalitional Game Theory

We present and study the contribution-selection algorithm (CSA), a novel algorithm for feature selection. The algorithm is based on the multiperturbation shapley analysis (MSA), a framework that relies on game theory to estimate usefulness. The algorithm iteratively estimates the usefulness of features and selects them accordingly, using either forward selection or backward elimination. It can optimize various performance measures over unseen data such as accuracy, balanced error rate, and area under receiver-operator-characteristic curve. Empirical comparison with several other existing feature selection methods shows that the backward elimination variant of CSA leads to the most accurate classification results on an array of data sets.

Distinguishing causal interactions in neural populations

We describe a theoretical network analysis that can distinguish statistically causal interactions in population neural activity leading to a specific output. We introduce the concept of a causal core to refer to the set of neuronal interactions that are causally significant for the output, as assessed by Granger causality. Because our approach requires extensive knowledge of neuronal connectivity and dynamics, an illustrative example is provided by analysis of Darwin X, a brain-based device that allows precise recording of the activity of neuronal units during behavior. In Darwin X, a simulated neuronal model of the hippocampus and surrounding cortical areas supports learning of a spatial navigation task in a real environment. Analysis of Darwin X reveals that large repertoires of neuronal interactions contain comparatively small causal cores and that these causal cores become smaller during learning, a finding that may reflect the selection of specific causal pathways from diverse neuronal repertoires.

Neurocontroller analysis via evolutionary network minimization

This study presents a new evolutionary network minimization (ENM) algorithm. Neurocontroller minimization is beneficial for finding small parsimonious networks that permit a better understanding of their workings. The ENM algorithm is specifically geared to an evolutionary agents setup, as it does not require any explicit supervised training error, and is very easily incorporated in current evolutionary algorithms. ENM is based on a standard genetic algorithm with an additional step during reproduction in which synaptic connections are irreversibly eliminated. It receives as input a successfully evolved neurocontroller and aims to output a pruned neurocontroller, while maintaining the original fitness level. The small neurocontrollers produced by ENM provide upper bounds on the neurocontroller size needed to perform a given task successfully, and can provide for more effcient hardware implementations.

Neural processing of counting in evolved spiking and McCulloch-Pitts agents

This article investigates the evolution of autonomous agents that perform a memory-dependent counting task. Two types of neurocontrollers are evolved: networks of McCulloch-Pitts neurons, and spiking integrate-and-fire networks. The results demonstrate the superiority of the spiky model in evolutionary success and network simplicity. The combination of spiking dynamics with incremental evolution leads to the successful evolution of agents counting over very long periods. Analysis of the evolved networks unravels the counting mechanism and demonstrates how the spiking dynamics are utilized. Using new measures of spikiness we find that even in agents with spiking dynamics, these are usually truly utilized only when they are really needed, that is, in the evolved subnetwork responsible for counting.

Axiomatic scalable neurocontroller analysis via the Shapley value

One of the major challenges in the field of neurally driven evolved autonomous agents is deciphering the neural mechanisms underlying their behavior. Aiming at this goal, we have developed the multi-perturbation Shapley value analysis (MSA)--the first axiomatic and rigorous method for deducing causal function localization from multiple-perturbation data, substantially improving on earlier approaches. Based on fundamental concepts from game theory, the MSA provides a formal way of defining and quantifying the contributions of network elements, as well as the functional interactions between them. The previously presented versions of the MSA require full knowledge (or at least an approximation) of the network's performance under all possible multiple perturbations, limiting their applicability to systems with a small number of elements. This article focuses on presenting new scalable MSA variants, allowing for the analysis of large complex networks in an efficient manner, including large-scale neurocontrollers. The successful operation of the MSA along with the new variants is demonstrated in the analysis of several neurocontrollers solving a food foraging task, consisting of up to 100 neural elements.

Quantitative analysis of genetic and neuronal multi-perturbation experiments

Perturbation studies, in which functional performance is measured after deletion, mutation, or lesion of elements of a biological system, have been traditionally employed in many fields in biology. The vast majority of these studies have been qualitative and have employed single perturbations, often resulting in little phenotypic effect. Recently, newly emerging experimental techniques have allowed researchers to carry out concomitant multi-perturbations and to uncover the causal functional contributions of system elements. This study presents a rigorous and quantitative multi-perturbation analysis of gene knockout and neuronal ablation experiments. In both cases, a quantification of the elements' contributions, and new insights and predictions, are provided. Multi-perturbation analysis has a potentially wide range of applications and is gradually becoming an essential tool in biology.

Which are the important elements of a system? What are their relative contributions to the performance of the various tasks the system is involved in? These simple and basic questions typically arise when analyzing the workings of any system, and of biological systems in particular. In the latter, the elements may be genes, proteins, cells, or tissues, depending on the level and scope of the analysis. To address these questions in a causal manner, perturbations are required, where the elements are perturbed and the resulting performance function is recorded. This approach has been one of the cornerstones of biological research. However, it has usually been confined to the perturbation of a single element at a time, which may lead to misleading results if the elements of the system functionally interact with each other. This paper addresses these questions by providing a quantitative and rigorous method for the analysis of multi-perturbation experiments, where more than one element may be concomitantly perturbed. The workings of the new method are demonstrated in the analysis of genetic multi-knockout experiments of DNA repair in the yeast Saccharomyces cerevisiae and a neural circuit in the nematode Caenorhabditis elegans accounting for chemotaxis. However, the method is general and can be applied to study many other systems in numerous pertinent biological domains.

Degenerate neuronal systems sustaining cognitive functions

The remarkable resilience of cognitive functions to focal brain damage suggests that multiple degenerate neuronal systems can sustain the same function either via similar mechanisms or by implementing different cognitive strategies. In degenerate functional neuroanatomy, multiple degenerate neuronal systems might be present in a single brain where they are either co-activated or remain latent during task performance. In degeneracy over subjects, a particular function may be sustained by only one neuronal system within a subject, but by different systems over subjects. Degeneracy over subjects might have arisen from (ab)normal variation in neurodevelopmental trajectories or long-term plastic changes following structural lesions. We discuss how degenerate neuronal systems can be revealed using (1) intersubject variability, (2) multiple lesion studies and (3) an iterative approach integrating information from lesion and functional imaging studies.

Causal connectivity of evolved neural networks during behavior

To show how causal interactions in neural dynamics are modulated by behavior, it is valuable to analyze these interactions without perturbing or lesioning the neural mechanism. This paper proposes a method, based on a graph-theoretic extension of vector autoregressive modeling and 'Granger causality,' for characterizing causal interactions generated within intact neural mechanisms. This method, called 'causal connectivity analysis' is illustrated via model neural networks optimized for controlling target fixation in a simulated head-eye system, in which the structure of the environment can be experimentally varied. Causal connectivity analysis of this model yields novel insights into neural mechanisms underlying sensorimotor coordination. In contrast to networks supporting comparatively simple behavior, networks supporting rich adaptive behavior show a higher density of causal interactions, as well as a stronger causal flow from sensory inputs to motor outputs. They also show different arrangements of 'causal sources' and 'causal sinks': nodes that differentially affect, or are affected by, the remainder of the network. Finally, analysis of causal connectivity can predict the functional consequences of network lesions. These results suggest that causal connectivity analysis may have useful applications in the analysis of neural dynamics.