Jan Karbowski

Synaptic polarity of the interneuron circuit controlling C. elegans locomotion

Caenorhabditis elegans is the only animal for which a detailed neural connectivity diagram has been constructed. However, synaptic polarities in this diagram, and thus, circuit functions are largely unknown. Here, we deciphered the likely polarities of seven pre-motor neurons implicated in the control of worms locomotion, using a combination of experimental and computational tools. We performed single and multiple laser ablations in the locomotor interneuron circuit and recorded times the worms spent in forward and backward locomotion. We constructed a theoretical model of the locomotor circuit and searched its all possible synaptic polarity combinations and sensory input patterns in order to find the best match to the timing data. The optimal solution is when either all or most of the interneurons are inhibitory and forward interneurons receive the strongest input, which suggests that inhibition governs the dynamics of the locomotor interneuron circuit. From the five pre-motor interneurons, only AVB and AVD are equally likely to be excitatory, i.e., they have probably similar number of inhibitory and excitatory connections to distant targets. The method used here has a general character and thus can be also applied to other neural systems consisting of small functional networks.

Constancy and trade-offs in the neuroanatomical and metabolic design of the cerebral cortex

Mammalian brains span about four orders of magnitude in cortical volume and have to operate in different environments that require diverse behavioral skills. Despite these geometric and behavioral diversities, the examination of cerebral cortex across species reveals that it contains a substantial number of conserved characteristics that are associated with neuroanatomy and metabolism, i.e., with neuronal connectivity and function. Some of these cortical constants or invariants have been known for a long time but not sufficiently appreciated, and others were only recently discovered. The focus of this review is to present the cortical invariants and discuss their role in the efficient information processing. Global conservation in neuroanatomy and metabolism, as well as their correlated regional and developmental variability suggest that these two parallel systems are mutually coupled. It is argued that energetic constraint on cortical organization can be strong if cerebral blood supplied is either below or above a certain level, and it is rather soft otherwise. Moreover, because maximization or minimization of parameters associated with cortical connectivity, function and cost often leads to conflicts in design, it is argued that the architecture of the cerebral cortex is a result of structural and functional compromises.

Effect of temperature and glia in brain size enlargement and origin of allometric body-brain size scaling in vertebrates

BackgroundBrain signaling requires energy. The cost of maintaining and supporting energetically demanding neurons is the key constraint on brain size. The dramatic increase in brain size among mammals and birds cannot be understood without solving this conundrum: larger brains, with more neurons, consume more energy.ResultsHere we examined the intrinsic relationships between metabolism, body-brain size ratios and neuronal densities of both endothermic and ectothermic animals. We formulated a general model to elucidate the key factors that correlate with brain enlargement, and the origin of allometric body-brain size scaling. This framework identified temperature as a critical factor in brain enlargement via temperature-regulated changes in metabolism. Our framework predicts that ectothermic animals living in tropical climates should have brain sizes that are several times larger than those of ectothermic animals living in cold climates. This prediction was confirmed by data from experiments in fish brains. Our framework also suggests that a rapid increase in the number of less energy-demanding glial cells may be another important factor contributing to the ten-fold increase in the brain sizes of endotherms compared with ectotherms.ConclusionsThis study thus provides a quantitative theory that predicts the brain sizes of all the major types of animals and quantifies the contributions of temperature-dependent metabolism, body size and neuronal density.

Cortical Composition Hierarchy Driven by Spine Proportion Economical Maximization or Wire Volume Minimization

The structure and quantitative composition of the cerebral cortex are interrelated with its computational capacity. Empirical data analyzed here indicate a certain hierarchy in local cortical composition. Specifically, neural wire, i.e., axons and dendrites take each about 1/3 of cortical space, spines and glia/astrocytes occupy each about (1/3)2, and capillaries around (1/3)4. Moreover, data analysis across species reveals that these fractions are roughly brain size independent, which suggests that they could be in some sense optimal and thus important for brain function. Is there any principle that sets them in this invariant way? This study first builds a model of local circuit in which neural wire, spines, astrocytes, and capillaries are mutually coupled elements and are treated within a single mathematical framework. Next, various forms of wire minimization rule (wire length, surface area, volume, or conduction delays) are analyzed, of which, only minimization of wire volume provides realistic results that are very close to the empirical cortical fractions. As an alternative, a new principle called “spine economy maximization” is proposed and investigated, which is associated with maximization of spine proportion in the cortex per spine size that yields equally good but more robust results. Additionally, a combination of wire cost and spine economy notions is considered as a meta-principle, and it is found that this proposition gives only marginally better results than either pure wire volume minimization or pure spine economy maximization, but only if spine economy component dominates. However, such a combined meta-principle yields much better results than the constraints related solely to minimization of wire length, wire surface area, and conduction delays. Interestingly, the type of spine size distribution also plays a role, and better agreement with the data is achieved for distributions with long tails. In sum, these results suggest that for the efficiency of local circuits wire volume may be more primary variable than wire length or temporal delays, and moreover, the new spine economy principle may be important for brain evolutionary design in a broader context.

Strongly correlated fermions at low temperatures

We summarize recent theoretical results concerning strongly correlated fermion system at nonzero temperature within a mean-field picture. In case of narrow-band systems (Part 1) we describe the Mott-Hubbard (localization) boundary, the presence of the T3 ln T term in the specific heat in almost localized systems, as well as the metamagnetism and spin-split heavy masses. We also mention the concept of a statistical spin liquid state and the stability of an extended s-wave superconducting state in two dimensions for this case. In Part 2 (hybridized systems) we introduce an interobital pairing mediated by a Kondo-type interaction and propose an universal scaling of superconducting properties for heavy fermion systems.

Optimal synaptic signaling connectome for locomotory behavior in Caenorhabditis elegans: Design minimizing energy cost

The detailed knowledge of C. elegans connectome for 3 decades has not contributed dramatically to our understanding of worm’s behavior. One of main reasons for this situation has been the lack of data on the type of synaptic signaling between particular neurons in the worm’s connectome. The aim of this study was to determine synaptic polarities for each connection in a small pre-motor circuit controlling locomotion. Even in this compact network of just 7 neurons the space of all possible patterns of connection types (excitation vs. inhibition) is huge. To deal effectively with this combinatorial problem we devised a novel and relatively fast technique based on genetic algorithms and large-scale parallel computations, which we combined with detailed neurophysiological modeling of interneuron dynamics and compared the theory to the available behavioral data. As a result of these massive computations, we found that the optimal connectivity pattern that matches the best locomotory data is the one in which all interneuron connections are inhibitory, even those terminating on motor neurons. This finding is consistent with recent experimental data on cholinergic signaling in C. elegans, and it suggests that the system controlling locomotion is designed to save metabolic energy. Moreover, this result provides a solid basis for a more realistic modeling of neural control in these worms, and our novel powerful computational technique can in principle be applied (possibly with some modifications) to other small-scale functional circuits in C. elegans.

The metabolic cost of maintaining a synapse during development

Background Experimental data indicate that cerebral energy consumption and synaptic density qualitatively correlate during development [1,2], presumably indicating that energy plays a key role during the process. The purpose of this study is two-fold. First, to collect empirical data on cortical metabolism and synaptic density during development (from birth to adulthood for different mammals), and to quantify their dependence. Second, to provide atheoretical link between neural metabolism and electrical activities of neurons and synapses [3]. A theoretical model allows us to estimate synaptic contribution to the overall energy used by neurons.

Superconducting instabilities in the finite U Anderson lattice model

Abstract We have investigated superconducting instabilities in the finite U Anderson lattice model within the Zou-Anderson slave boson representation in the Kondo lattice limit appropriate for heavy fermion systems. We found Cooper instability in the p channel and a repulsion in both the s and d channels. Based on the above mechanism of pairing, we have derived a ratio of the Gruneisen parameters Γ ( T c )/ Γ ( T K ) which can be negative or positive, consistent with the experimental data. This result cannot be achieved in the U = ∞ limit, which gives only positive values for this ratio.