Anatomical connectivity defines the organization of clusters of cortical areas in the macaque monkey and the cat

The number of different cortical structures in mammalian brains and the number of extrinsic fibres linking these regions are both large. As with any complex system, systematic analysis is required to draw reliable conclusions about the organization of the complex neural networks comprising these numerous elements. One aspect of organization that has long been suspected is that cortical networks are organized into 'streams' or 'systems'. Here we report computational analyses capable of showing whether clusters of strongly interconnected areas are aspects of the global organization of cortical systems in macaque and cat. We used two different approaches to analyse compilations of corticocortical connection data from the macaque and the cat. The first approach, optimal set analysis, employed an explicit definition of a neural 'system' or 'stream', which was based on differential connectivity. We defined a two-component cost function that described the cost of the global cluster arrangement of areas in terms of the areas' connectivity within and between candidate clusters. Optimal cluster arrangements of cortical areas were then selected computationally from the very many possible arrangements, using an evolutionary optimization algorithm. The second approach, non-parametric cluster analysis (NPCA), grouped cortical areas on the basis of their proximity in multidimensional scaling representations. We used non-metric multidimensional scaling to represent the cortical connectivity structures metrically in two and five dimensions. NPCA then analysed these representations to determine the nature of the clusters for a wide range of different cluster shape parameters. The results from both approaches largely agreed. They showed that macaque and cat cortices are organized into densely intra-connected clusters of areas, and identified the constituent members of the clusters. These clusters reflected functionally specialized sets of cortical areas, suggesting that structure and function are closely linked at this gross, systems level.     

Motivation and Benefits of Complex Systems Approaches in Ecology

Studies of complex systems in other disciplines provide models and analytical strategies for understanding ecosystems and landscapes. The emphasis is on invariant properties, particularly processes that create scaling relations over wide ranges of scale, both in time and space. Translations between levels of ecological organization may be accomplished by succinct characterizations of processes that operate at fine scales, followed by renormalization group analysis to reveal patterns at broad scales. The self-organized patterns found in simple ecosystem, landscape, and forest-fire models may be explained as feedback between the system state and control parameters. Critical phenomena and phase transitions are expected in open, dissipative systems where long-range correlations defy predictions based on average population densities, a concept that becomes irrelevant as nonstationary conditions prevail. Thus, complexity theory for open systems relates to the ecology of self-entailing ecosystems that function as their own environments and thereby create constraints through emergence. Received: 14 April 1998; accepted 26 May 1998     

Incorporating anatomically realistic cellular-level connectivity in neural network models of the rat hippocampus

The specific connectivity patterns among neuronal classes can play an important role in the regulation of firing dynamics in many brain regions. Yet most neural network models are built based on vastly simplified connectivity schemes that do not accurately reflect the biological complexity. Taking the rat hippocampus as an example, we show here that enough quantitative information is available in the neuroanatomical literature to construct neural networks derived from accurate models of cellular connectivity. Computational simulations based on this approach lend themselves to a direct investigation of the potential relationship between cellular connectivity and network activity. We define a set of fundamental parameters to characterize cellular connectivity, and are collecting the related values for the rat hippocampus from published reports. Preliminary simulations based on these data uncovered a novel putative role for feedforward inhibitory neurons. In particular, "mopp" cells in the dentate gyrus are suitable to help maintain the firing rate of granule cells within physiological levels in response to a plausibly noisy input from the entorhinal cortex. The stabilizing effect of feedforward inhibition is further shown to depend on the particular ratio between the relative threshold values of the principal cells and the interneurons. We are freely distributing the connectivity data on which this study is based through a publicly accessible web archive (http://www.krasnow.gmu.edu/L-Neuron).     

Quantifying loopy network architectures

Biology presents many examples of planar distribution and structural networks having dense sets of closed loops. An archetype of this form of network organization is the vasculature of dicotyledonous leaves, which showcases a hierarchically-nested architecture containing closed loops at many different levels. Although a number of approaches have been proposed to measure aspects of the structure of such networks, a robust metric to quantify their hierarchical organization is still lacking. We present an algorithmic framework, the hierarchical loop decomposition, that allows mapping loopy networks to binary trees, preserving in the connectivity of the trees the architecture of the original graph. We apply this framework to investigate computer generated graphs, such as artificial models and optimal distribution networks, as well as natural graphs extracted from digitized images of dicotyledonous leaves and vasculature of rat cerebral neocortex. We calculate various metrics based on the asymmetry, the cumulative size distribution and the Strahler bifurcation ratios of the corresponding trees and discuss the relationship of these quantities to the architectural organization of the original graphs. This algorithmic framework decouples the geometric information (exact location of edges and nodes) from the metric topology (connectivity and edge weight) and it ultimately allows us to perform a quantitative statistical comparison between predictions of theoretical models and naturally occurring loopy graphs.     

Action-related properties shape object representations in the ventral stream

The principles driving the organization of the ventral object-processing stream remain unknown. Here, we show that stimulus-specific repetition suppression (RS) in one region of the ventral stream is biased according to motor-relevant properties of objects. Quantitative analysis confirmed that this result was not confounded with similarity in visual shape. A similar pattern of biases in RS according to motor-relevant properties of objects was observed in dorsal stream regions in the left hemisphere. These findings suggest that neural specificity for "tools" in the ventral stream is driven by similarity metrics computed over motor-relevant information represented in dorsal structures. Support for this view is provided by converging results from functional connectivity analyses of the fMRI data and a separate neuropsychological study. More generally, these data suggest that a basic organizing principle giving rise to "category specificity" in the ventral stream may involve similarity metrics computed over information represented elsewhere in the brain.     

Combining structural connectivity and response latencies to model the structure of the visual system

Several approaches exist to ascertain the connectivity of the brain, and these approaches lead to markedly different topologies, often incompatible with each other. Specifically, recent single-cell recording results seem incompatible with current structural connectivity models. We present a novel method that combines anatomical and temporal constraints to generate biologically plausible connectivity patterns of the visual system of the macaque monkey. Our method takes structural connectivity data from the CoCoMac database and recent single-cell recording data as input and employs an optimization technique to arrive at a new connectivity pattern of the visual system that is in agreement with both types of experimental data. The new connectivity pattern yields a revised model that has fewer levels than current models. In addition, it introduces subcortical-cortical connections. We show that these connections are essential for explaining latency data, are consistent with our current knowledge of the structural connectivity of the visual system, and might explain recent functional imaging results in humans. Furthermore we show that the revised model is not underconstrained like previous models and can be extended to include newer data and other kinds of data. We conclude that the revised model of the connectivity of the visual system reflects current knowledge on the structure and function of the visual system and addresses some of the limitations of previous models.     

Receptor-mediated cell attachment and detachment kinetics. II. Experimental model studies with the radial-flow detachment assay.

Quantitative information regarding the kinetics of receptor-mediated cell adhesion to a ligand-coated surface are crucial for understanding the role of certain key parameters in many physiological and biotechnology-related processes. Here, we use the probabilistic attachment and detachment models developed in the preceding paper to interpret transient data from well-defined experiments. These data are obtained with a simple model cell system that consists of receptor-coated latex beads (prototype cells) and a Radial-Flow Detachment Assay (RFDA) using a ligand-coated glass disc. The receptors and ligands used in this work are complementary antibodies. The beads enable us to examine transient behavior with particles that possess fairly uniform properties that can be varied systematically, and the RFDA is designed for direct observation of adhesion to the ligand-coated glass surface over a range of shear stresses. Our experiments focus on the effects of surface shear stress, receptor density, and ligand density. These data provide a crucial test of the probabilistic framework. We show that these data can be explained with the probabilistic analyses, whereas they cannot be readily interpreted on the basis of a deterministic analysis. In addition, we examine transient data on cell adhesion reported from other assays, demonstrating the consistency of these data with the predictions of the probabilistic models.     

Information-Theoretic Analysis of the Dynamics of an Executable Biological Model

To facilitate analysis and understanding of biological systems, large-scale data are often integrated into models using a variety of mathematical and computational approaches. Such models describe the dynamics of the biological system and can be used to study the changes in the state of the system over time. For many model classes, such as discrete or continuous dynamical systems, there exist appropriate frameworks and tools for analyzing system dynamics. However, the heterogeneous information that encodes and bridges molecular and cellular dynamics, inherent to fine-grained molecular simulation models, presents significant challenges to the study of system dynamics. In this paper, we present an algorithmic information theory based approach for the analysis and interpretation of the dynamics of such executable models of biological systems. We apply a normalized compression distance (NCD) analysis to the state representations of a model that simulates the immune decision making and immune cell behavior. We show that this analysis successfully captures the essential information in the dynamics of the system, which results from a variety of events including proliferation, differentiation, or perturbations such as gene knock-outs. We demonstrate that this approach can be used for the analysis of executable models, regardless of the modeling framework, and for making experimentally quantifiable predictions.     

Relating Structure and Function in the Human Brain: Relative Contributions of Anatomy,Stationary Dynamics,and Non-stationarities

Investigating the relationship between brain structure and function is a central endeavor for neuroscience research. Yet, the mechanisms shaping this relationship largely remain to be elucidated and are highly debated. In particular, the existence and relative contributions of anatomical constraints and dynamical physiological mechanisms of different types remain to be established. We addressed this issue by systematically comparing functional connectivity (FC) from resting-state functional magnetic resonance imaging data with simulations from increasingly complex computational models, and by manipulating anatomical connectivity obtained from fiber tractography based on diffusion-weighted imaging. We hypothesized that FC reflects the interplay of at least three types of components: (i) a backbone of anatomical connectivity, (ii) a stationary dynamical regime directly driven by the underlying anatomy, and (iii) other stationary and non-stationary dynamics not directly related to the anatomy. We showed that anatomical connectivity alone accounts for up to 15% of FC variance; that there is a stationary regime accounting for up to an additional 20% of variance and that this regime can be associated to a stationary FC; that a simple stationary model of FC better explains FC than more complex models; and that there is a large remaining variance (around 65%), which must contain the non-stationarities of FC evidenced in the literature. We also show that homotopic connections across cerebral hemispheres, which are typically improperly estimated, play a strong role in shaping all aspects of FC, notably indirect connections and the topographic organization of brain networks.     

Modeling the Spontaneous Activity of the Auditory Cortex

We present a rate model of the spontaneous activity in the auditory cortex, based on synaptic depression. A Stochastic integro-differential system of equations is derived and the analysis reveals two main regimes. The first regime corresponds to a normal activity. The second regime corresponds to epileptic spiking. A detailed analysis of each regime is presented and we prove in particular that synaptic depression stabilizes the global cortical dynamics. The transition between the two regimes is induced by a change in synaptic connectivity: when the overall connectivity is strong enough, an epileptic activity is spontaneously generated. Numerical simulations confirm the predictions of the theoretical analysis. In particular, our results explain the transition from normal to epileptic regime which can be induced in rats auditory cortex, following a specific pairing protocol. A change in the cortical maps reorganizes the synaptic connectivity and this transition between regimes is accounted for by our model. We have used data from recording experiments to fit synaptic weight distributions. Simulations with the fitted distributions are qualitatively similar to the real EEG recorded in vivo during the experiments. We conclude that changes in the synaptic weight function in our model, which affects excitatory synapses organization and reproduces the changes in cortical map connectivity can be understood as the main mechanism to explain the transitions of the EEG from the normal to the epileptic regime in the auditory cortex. D.H is incumbent to the Hass Russell Career Chair Development.     

The Disulfide Bonds in Glycoprotein E2 of Hepatitis C Virus Reveal the Tertiary Organization of the Molecule

Hepatitis C virus (HCV), a major cause of chronic liver disease in humans, is the focus of intense research efforts worldwide. Yet structural data on the viral envelope glycoproteins E1 and E2 are scarce, in spite of their essential role in the viral life cycle. To obtain more information, we developed an efficient production system of recombinant E2 ectodomain (E2e), truncated immediately upstream its trans-membrane (TM) region, using Drosophila melanogaster cells. This system yields a majority of monomeric protein, which can be readily separated chromatographically from contaminating disulfide-linked aggregates. The isolated monomeric E2e reacts with a number of conformation-sensitive monoclonal antibodies, binds the soluble CD81 large external loop and efficiently inhibits infection of Huh7.5 cells by infectious HCV particles (HCVcc) in a dose-dependent manner, suggesting that it adopts a native conformation. These properties of E2e led us to experimentally determine the connectivity of its 9 disulfide bonds, which are strictly conserved across HCV genotypes. Furthermore, circular dichroism combined with infrared spectroscopy analyses revealed the secondary structure contents of E2e, indicating in particular about 28% β-sheet, in agreement with the consensus secondary structure predictions. The disulfide connectivity pattern, together with data on the CD81 binding site and reported E2 deletion mutants, enabled the threading of the E2e polypeptide chain onto the structural template of class II fusion proteins of related flavi- and alphaviruses. The resulting model of the tertiary organization of E2 gives key information on the antigenicity determinants of the virus, maps the receptor binding site to the interface of domains I and III, and provides insight into the nature of a putative fusogenic conformational change.     

Mathematical properties of pump-leak models of cell volume control and electrolyte balance

Homeostatic control of cell volume and intracellular electrolyte content is a fundamental problem in physiology and is central to the functioning of epithelial systems. These physiological processes are modeled using pump-leak models, a system of differential algebraic equations that describes the balance of ions and water flowing across the cell membrane. Despite their widespread use, very little is known about their mathematical properties. Here, we establish analytical results on the existence and stability of steady states for a general class of pump-leak models. We treat two cases. When the ion channel currents have a linear current-voltage relationship, we show that there is at most one steady state, and that the steady state is globally asymptotically stable. If there are no steady states, the cell volume tends to infinity with time. When minimal assumptions are placed on the properties of ion channel currents, we show that there is an asymptotically stable steady state so long as the pump current is not too large. The key analytical tool is a free energy relation satisfied by a general class of pump-leak models, which can be used as a Lyapunov function to study stability.     

A method for the estimation of functional brain connectivity from time-series data

A central issue in cognitive neuroscience is which cortical areas are involved in managing information processing in a cognitive task and to understand their temporal interactions. Since the transfer of information in the form of electrical activity from one cortical region will in turn evoke electrical activity in other regions, the analysis of temporal synchronization provides a tool to understand neuronal information processing between cortical regions. We adopt a method for revealing time-dependent functional connectivity. We apply statistical analyses of phases to recover the information flow and the functional connectivity between cortical regions for high temporal resolution data. We further develop an evaluation method for these techniques based on two kinds of model networks. These networks consist of coupled Rössler attractors or of coupled stochastic Ornstein–Uhlenbeck systems. The implemented time-dependent coupling includes uni- and bi-directional connectivities as well as time delayed feedback. The synchronization dynamics of these networks are analyzed using the mean phase coherence, based on averaging over phase-differences, and the general synchronization index. The latter is based on the Shannon entropy. The combination of these with a parametric time delay forms the basis of a connectivity pattern, which includes the temporal and time lagged dynamics of the synchronization between two sources. We model and discuss potential artifacts. We find that the general phase measures are remarkably stable. They produce highly comparable results for stochastic and periodic systems. Moreover, the methods proves useful for identifying brief periods of phase coupling and delays. Therefore, we propose that the method is useful as a basis for generating potential functional connective models.     

The mechanistic basis for higher‐order interactions and non‐additivity in competitive communities

Motivated by both analytical tractability and empirical practicality, community ecologists have long treated the species pair as the fundamental unit of study. This notwithstanding, the challenge of understanding more complex systems has repeatedly generated interest in the role of so‐called higher‐order interactions (HOIs) imposed by species beyond the focal pair. Here we argue that HOIs – defined as non‐additive effects of density on per capita growth – are best interpreted as emergent properties of phenomenological models (e.g. Lotka–Volterra competition) rather than as distinct ‘ecological processes’ in their own right. Using simulations of consumer‐resource models, we explore the mechanisms and system properties that give rise to HOIs in observational data. We demonstrate that HOIs emerge under all but the most restrictive of assumptions, and that incorporating non‐additivity into phenomenological models improves the quantitative and qualitative accuracy of model predictions. Notably, we also observe that HOIs derive primarily from mechanisms and system properties that apply equally to single‐species or pairwise systems as they do to more diverse communities. Consequently, there exists a strong mandate for further recognition of non‐additive effects in both theoretical and empirical research.     

Erratum to: Mathematical properties of pump-leak models of cell volume control and electrolyte balance

Homeostatic control of cell volume and intracellular electrolyte content is a fundamental problem in physiology and is central to the functioning of epithelial systems. These physiological processes are modeled using pump-leak models, a system of differential algebraic equations that describes the balance of ions and water flowing across the cell membrane. Despite their widespread use, very little is known about their mathematical properties. Here, we establish analytical results on the existence and stability of steady states for a general class of pump-leak models. We treat two cases. When the ion channel currents have a linear current-voltage relationship, we show that there is at most one steady state, and that the steady state is globally asymptotically stable. If there are no steady states, the cell volume tends to infinity with time. When minimal assumptions are placed on the properties of ion channel currents, we show that there is an asymptotically stable steady state so long as the pump current is not too large. The key analytical tool is a free energy relation satisfied by a general class of pump-leak models, which can be used as a Lyapunov function to study stability.     

Predictive ADMET studies, the challenges and the opportunities

Predictive ADMET is the new 'hip' area in drug discovery. The aim is to use large databases of ADMET data associated with structures to build computational models that link structural changes with changes in response, from which compounds with improved properties can be designed and predicted. These databases also provide the means to enable predictions of human ADMET properties to be made from human in vitro and animal in vivo ADMET measurements. Both methods are limited by the amount of data available to build such predictive models, the limitations of modelling methods and our understanding of the systems we wish to model. The current failures, successes and opportunities are reviewed.     

On parsing the neural code in the prefrontal cortex of primates using principal dynamic modes

Nonlinear modeling of multi-input multi-output (MIMO) neuronal systems using Principal Dynamic Modes (PDMs) provides a novel method for analyzing the functional connectivity between neuronal groups. This paper presents the PDM-based modeling methodology and initial results from actual multi-unit recordings in the prefrontal cortex of non-human primates. We used the PDMs to analyze the dynamic transformations of spike train activity from Layer 2 (input) to Layer 5 (output) of the prefrontal cortex in primates performing a Delayed-Match-to-Sample task. The PDM-based models reduce the complexity of representing large-scale neural MIMO systems that involve large numbers of neurons, and also offer the prospect of improved biological/physiological interpretation of the obtained models. PDM analysis of neuronal connectivity in this system revealed “input–output channels of communication” corresponding to specific bands of neural rhythms that quantify the relative importance of these frequency-specific PDMs across a variety of different tasks. We found that behavioral performance during the Delayed-Match-to-Sample task (correct vs. incorrect outcome) was associated with differential activation of frequency-specific PDMs in the prefrontal cortex.