V Srinivasa Chakravarthy

A crucial insight into handwriting dynamics is embodied in the idea that stable, robust handwriting movements correspond to attractors of an oscillatory dynamical system. We present a phase dynamic model of visuomotor performance involved in copying simple oriented lines. Our studies on human performance in copying oriented lines revealed a systematic error pattern in orientation of drawn lines, i.e., lines at certain orientation are drawn more accurately than at other values. Furthermore, human subjects exhibit "flips" in direction at certain characteristic orientations. It is argued that this flipping behavior has its roots in the fact that copying process is inherently ambiguous-a line of given orientation may be drawn in two different (mutually opposite) directions producing the same end result. The systematic error patterns seen in human copying performance is probably a result of the attempt of our visuomotor system to cope with this ambiguity and still be able to produce accurate copying movements. The proposed nonlinear phase-dynamic model explains the experimentally observed copying error pattern and also the flipping behavior with remarkable accuracy. © 2009 Springer-Verlag.

Three-dimensional (3D) spatial cells in the mammalian hippocampal formation are believed to support the existence of 3D cognitive maps. Modeling studies are crucial to comprehend the neural principles governing the formation of these maps, yet to date very few have addressed this topic in 3D space. Here we present a hierarchical network model for the formation of 3D spatial cells using anti-Hebbian network. Built on empirical data, the model accounts for the natural emergence of 3D place, border, and grid cells, as well as a new type of previously undescribed spatial cell type which we call plane cells. It further explains the plausible reason behind the place and grid-cell anisotropic coding that has been observed in rodents and the potential discrepancy with the predicted periodic coding during 3D volumetric navigation. Lastly, it provides evidence for the importance of unsupervised learning rules in guiding the formation of higher-dimensional cognitive maps.

In an earlier study, we suggested that adaptive gap junctions (GJs) might be a basis of cardiac memory, a phenomenon which refers to persistent electrophysiological response of the heart to external pacing. Later, it was also shown that the proposed mechanism of adaptation of GJs is consistent with known electrophysiology of GJs. In the present article, we show that a pair of cardiac cell models coupled by dynamic, voltage-sensitive GJs exhibits bistable behavior under certain conditions. Three kinds of cell pairs are considered: (1) a Noble-Noble cell pair that represents adjacent cells in Purkinje network, (2) a pair of DiFranceso-Noble cells that represents adjacent SA nodal cells, and (3) a model of Noble cell coupled to Luo-Rudy cell model, which represents an interacting pair of a Purkinje fiber and a ventricular myocyte. Bistability is demonstrated in all the three cases. We suggest that this bistability might be an underlying factor behind cardiac memory. Focused analysis of a pair of Noble cell models showed that bistability is obtained only when the properties of GJs "match" with the properties of the pair of cells that is coupled by the GJs. This novel notion of match between GJs and cardiac cell types might give an insight into specialized distributions of various connexin proteins in cardiac tissue. © 2009 Springer-Verlag.

Parkinson's disease (PD) is characterized by a range of motor symptoms. Besides the cardinal symptoms (akinesia and bradykinesia, tremor and rigidity), PD patients show additional motor deficits, including: gait disturbance, impaired handwriting, grip force and speech deficits, among others. Some of these motor symptoms (e.g., deficits of gait, speech, and handwriting) have similar clinical profiles, neural substrates, and respond similarly to dopaminergic medication and deep brain stimulation (DBS). Here, we provide an extensive review of the clinical characteristics and neural substrates of each of these motor symptoms, to highlight precisely how PD and its medical and surgical treatments impact motor symptoms. In conclusion, we offer a unified framework for understanding the range of motor symptoms in PD. We argue that various motor symptoms in PD reflect dysfunction of neural structures responsible for action selection, motor sequencing, and coordination and execution of movement.

We present a computational, biophysical model of neuron-astrocyte-vessel interaction. Unlike other cells, neurons convey "hunger" signals to the vascular network via an intervening layer of glial cells (astrocytes); vessels dilate and release glucose which fuels neuronal firing. Existing computational models focus on only parts of this loop (neuron→astrocyte→vessel→neuron), whereas the proposed model describes the entire loop. Neuronal firing causes release of a neurotransmitter like glutamate which triggers release of vasodilator by astrocytes via a cascade of biochemical events. Vasodilators released from astrocytic endfeet cause blood vessels to dilate and release glucose into the interstitium, part of which is taken up by the astrocyticendfeet. Glucose is converted into lactate in the astrocyte and transported into the neuron. Glucose from the interstitium and lactate (produced from glucose) influx from astrocyte are converted into ATP in the neuron. Neuronal ATP is used to drive the Na+/K+ATPase pumps, which maintain ionic gradients necessary for neuronal firing. When placed in the metabolic loop, the neuron exhibits sustained firing only when the stimulation current is more than a minimum threshold. For various combinations of initial neuronal [ATP] and external current, the neuron exhibits a variety of firing patterns including sustained firing, firing after an initial pause, burst firing etc. Neurovascular interactions under conditions of constricted vessels are also studied. Most models of cerebral circulation describe neurovascular interactions exclusively in the "forward" neuron→vessel direction. The proposed model indicates possibility of "reverse" influence also, with vasomotion rhythms influencing neural firing patterns. Another idea that emerges out of the proposed work is that brain's computations may be more comprehensively understood in terms of neuro-glial-vascular dynamics and not in terms of neural firing alone. © 2012 Chander, Chakravarthy.

Background: Systems biological approach of molecular connectivity map has reached to a great interest to understand the gene functional similarities between the diseases. In this study, we developed a computational framework to build molecular connectivity maps by integrating mutated and differentially expressed genes of neurological and psychiatric diseases to determine its relationship with aging.Results: The systematic large-scale analyses of 124 human diseases create three classes of molecular connectivity maps. First, molecular interaction of disease protein network generates 3632 proteins with 6172 interactions, which determines the common genes/proteins between diseases. Second, Disease-disease network includes 4845 positively scored disease-disease relationships. The comparison of these disease-disease pairs with Medical Subject Headings (MeSH) classification tree suggests 25% of the disease-disease pairs were in same disease area. The remaining can be a novel disease-disease relationship based on gene/protein similarity. Inclusion of aging genes set showed 79 neurological and 20 psychiatric diseases have the strong association with aging. Third and lastly, a curated disease biomarker network was created by relating the proteins/genes in specific disease contexts, such analysis showed 73 markers for 24 diseases. Further, the overall quality of the results was achieved by a series of statistical methods, to avoid insignificant data in biological networks.Conclusions: This study improves the understanding of the complex interactions that occur between neurological and psychiatric diseases with aging, which lead to determine the diagnostic markers. Also, the disease-disease association results could be helpful to determine the symptom relationships between neurological and psychiatric diseases. Together, our study presents many research opportunities in post-genomic biomarkers development. © 2011 Ahmed et al; licensee BioMed Central Ltd.

Regeneration of complex anatomical structures is an emergent phenomenon arising from complex interplay between various underlying cellular components and processes. It is still largely unclear how coordination among cells leads to accurate regeneration of the organism, preserving the location, shape, and composition of the parts with respect to the whole. Here, we examine at the global interaction of cells in a computational model of planarian regeneration. A key feature of our model is the integration of multiple organizational levels of an organism–from cells, to network, to global shape. The computational model is able to replicate most of the experimental observations thereby facilitating study of the putative mechanisms. We observe that a hierarchical interplay between local and long range signaling acts as a positional map that guides the cellular fate at any position. Furthermore, we have quantified the quality of regeneration using a metric that provides a sense of how well the regenerated organism resembles its original shape.

Grid cells are a special class of spatial cells found in the medial entorhinal cortex (MEC) characterized by their strikingly regular hexagonal firing fields. This spatially periodic firing pattern is originally considered to be independent of the geometric properties of the environment. However, this notion was contested by examining the grid cell periodicity in environments with different polarity (Krupic et al., 2015) and in connected environments (Carpenter et al., 2015). Aforementioned experimental results demonstrated the dependence of grid cell activity on environmental geometry. Analysis of grid cell periodicity on practically infinite variations of environmental geometry imposes a limitation on the experimental study. Hence we analyze the dependence of grid cell periodicity on the environmental geometry purely from a computational point of view. We use a hierarchical oscillatory network model where velocity inputs are presented to a layer of Head Direction cells, outputs of which are projected to a Path Integration layer. The Lateral Anti-Hebbian Network (LAHN) is used to perform feature extraction from the Path Integration neurons thereby producing a spectrum of spatial cell responses. We simulated the model in five types of environmental geometries such as: (1) connected environments, (2) convex shapes, (3) concave shapes, (4) regular polygons with varying number of sides, and (5) transforming environment. Simulation results point to a greater function for grid cells than what was believed hitherto. Grid cells in the model encode not just the local position but also more global information like the shape of the environment. Furthermore, the model is able to capture the invariant attributes of the physical space ingrained in its LAHN layer, thereby revealing its ability to classify an environment using this information. The proposed model is interesting not only because it is able to capture the experimental results but, more importantly, it is able to make many important predictions on the effect of the environmental geometry on the grid cell periodicity and suggesting the possibility of grid cells encoding the invariant properties of an environment.

Spatial cells in the hippocampal complex play a pivotal role in the navigation of an animal. Exact neural principles behind these spatial cell responses have not been completely unraveled yet. Here we present two models for spatial cells, namely the Velocity Driven Oscillatory Network (VDON) and Locomotor Driven Oscillatory Network. Both models have basically three stages in common such as direction encoding stage, path integration (PI) stage, and a stage of unsupervised learning of PI values. In the first model, the following three stages are implemented: head direction layer, frequency modulation by a layer of oscillatory neurons, and an unsupervised stage that extracts the principal components from the oscillator outputs. In the second model, a refined version of the first model, the stages are extraction of velocity representation from the locomotor input, frequency modulation by a layer of oscillators, and two cascaded unsupervised stages consisting of the lateral anti-hebbian network. The principal component stage of VDON exhibits grid cell-like spatially periodic responses including hexagonal firing fields. Locomotor Driven Oscillatory Network shows the emergence of spatially periodic grid cells and periodically active border-like cells in its lower layer; place cell responses are found in its higher layer. This model shows the inheritance of phase precession from grid cell to place cell in both one- and two-dimensional spaces. It also shows a novel result on the influence of locomotion rhythms on the grid cell activity. The study thus presents a comprehensive, unifying hierarchical model for hippocampal spatial cells.

Primate vision research has shown that in the retinotopic map of the primary visual cortex, eccentricity and meridional angle are mapped onto two orthogonal axes: whereas the eccentricity is mapped onto the nasotemporal axis, the meridional angle is mapped onto the dorsoventral axis. Theoretically such a map has been approximated by a complex log map. Neural models with correlational learning have explained the development of other visual maps like orientation maps and ocular-dominance maps. In this paper it is demonstrated that activity based mechanisms can drive a self-organizing map (SOM) into such a configuration that dilations and rotations of a particular image (in this case a rectangular bar) are mapped onto orthogonal axes. We further demonstrate using the Laterally Interconnected Synergetically Self Organizing Map (LISSOM) model, with an appropriate boundary and realistic initial conditions, that a retinotopic map which maps eccentricity and meridional angle to the horizontal and vertical axes respectively can be developed. This developed map bears a strong resemblance to the complex log map. We also simulated lesion studies which indicate that the lateral excitatory connections play a crucial role in development of the retinotopic map.