arXiv subjects

Jan Karbowski

Publications and source records attributed to Jan Karbowski.

At least 19 recordsLinked to original sources

arXiv2024

Information thermodynamics: from physics to neuroscience

This paper provides a perspective on applying the concepts of information thermodynamics, developed recently in non-equilibrium statistical physics, to problems in theoretical neuroscience. Historically, information and energy in neuroscience have been treated separately, in contrast to physics approaches, where the relationship of entropy production with heat is a central idea. It is argued here that also in neural systems information and energy can be considered within the same theoretical framework. Starting from basic ideas of thermodynamics and information theory on a classic Brownian particle, it is shown how noisy neural networks can infer its probabilistic motion. The decoding of the particle motion by neurons is performed with some accuracy and it has some energy cost, and both can be determined using information thermodynamics. In a similar fashion, we also discuss how neural networks in the brain can learn the particle velocity, and maintain that information in the weights of plastic synapses from a physical point of view. Generally, it is shown how the framework of stochastic and information thermodynamics can be used practically to study neural inference, learning, and information storing.

q-bio.NC↗

arXiv2024

Cooperativity, information gain, and energy cost during early LTP in dendritic spines

We investigate a mutual relationship between information and energy during early phase of LTP induction and maintenance in a large-scale system of mutually coupled dendritic spines, with discrete internal states and probabilistic dynamics, within the framework of nonequilibrium stochastic thermodynamics. In order to analyze this computationally intractable stochastic multidimensional system, we introduce a pair approximation, which allows us to reduce the spine dynamics into a lower dimensional manageable system of closed equations. It is found that the rates of information gain and energy attain their maximal values during an initial period of LTP (i.e. during stimulation), and after that they recover to their baseline low values, as opposed to a memory trace that lasts much longer. This suggests that learning phase is much more energy demanding than the memory phase. We show that positive correlations between neighboring spines increase both a duration of memory trace and energy cost during LTP, but the memory time per invested energy increases dramatically for very strong positive synaptic cooperativity, suggesting a beneficial role of synaptic clustering on memory duration. In contrast, information gain after LTP is the largest for negative correlations, and energy efficiency of that information generally declines with increasing synaptic cooperativity. We also find that dendritic spines can use sparse representations for encoding of long-term information, as both energetic and structural efficiencies of retained information and its lifetime exhibit maxima for low fractions of stimulated synapses during LTP. In general, our stochastic thermodynamics approach provides a unifying framework for studying, from first principles, information encoding and its energy cost during learning and memory in stochastic systems of interacting synapses.

q-bio.NC↗

arXiv2023

Bounds on the rates of statistical divergences and mutual information via stochastic thermodynamics

Statistical divergences are important tools in data analysis, information theory, and statistical physics, and there exist well known inequalities on their bounds. However, in many circumstances involving temporal evolution, one needs limitations on the rates of such quantities, instead. Here, several general upper bounds on the rates of some f-divergences are derived, valid for any type of stochastic dynamics (both Markovian and non-Markovian), in terms of information-like and/or thermodynamic observables. As special cases, the analytical bounds on the rate of mutual information are obtained. The major role in all those limitations is played by temporal Fisher information, characterizing the speed of global system dynamics, and some of them contain entropy production, suggesting a link with stochastic thermodynamics. Indeed, the derived inequalities can be used for estimation of minimal dissipation and global speed in thermodynamic stochastic systems. Specific applications of these inequalities in physics and neuroscience are given, which include the bounds on the rates of free energy and work in nonequilibrium systems, limits on the speed of information gain in learning synapses, as well as the bounds on the speed of predictive inference and learning rate. Overall, the derived bounds can be applied to any complex network of interacting elements, where predictability and thermodynamics of network dynamics are of prime concern.

physics.data-an↗

arXiv2023

Explicit mutual information for simple networks and neurons with lognormal activities

Networks with stochastic variables described by heavy tailed lognormal distribution are ubiquitous in nature, and hence they deserve an exact information-theoretic characterization. We derive analytical formulas for mutual information between elements of different networks with correlated lognormally distributed activities. In a special case, we find an explicit expression for mutual information between neurons when neural activities and synaptic weights are lognormally distributed, as suggested by experimental data. Comparison of this expression with the case when these two variables have short tails, reveals that mutual information with heavy tails for neurons and synapses is generally larger and can diverge for some finite variances in presynaptic firing rates and synaptic weights. This result suggests that evolution might prefer brains with heterogeneous dynamics to optimize information processing.

cond-mat.dis-nn↗

arXiv2019

Deciphering neural circuits for Caenorhabditis elegans behavior by computations and perturbations to genome and connectome

{\it Caenorhabditis elegans} nematode worms are the only animals with the known detailed neural connectivity diagram, well characterized genomics, and relatively simple quantifiable behavioral output. With this in mind, many researchers view this animal as the best candidate for a systems biology approach, where one can integrate molecular and cellular knowledge to gain global understanding of worm's behavior. This work reviews some research in this direction, emphasizing computational perspective, and points out some successes and challenges to meet this lofty goal.

q-bio.NC↗

arXiv2019

Metabolic constraints on synaptic learning and memory

Dendritic spines, the carriers of long-term memory, occupy a small fraction of cortical space, and yet they are the major consumers of brain metabolic energy. What fraction of this energy goes for synaptic plasticity, correlated with learning and memory? It is estimated here based on neurophysiological and proteomic data for rat brain that, depending on the level of protein phosphorylation, the energy cost of synaptic plasticity constitutes a small fraction of the energy used for fast excitatory synaptic transmission, typically $4.0-11.2 \%$. Next, this study analyzes a metabolic cost of a new learning and its memory trace in relation to the cost of prior memories, using a class of cascade models of synaptic plasticity. It is argued that these models must contain bidirectional cyclic motifs, related to protein phosphorylation, to be compatible with basic thermodynamic principles. For most investigated parameters longer memories generally require proportionally more energy to store. The exception are the parameters controlling the speed of molecular transitions (e.g. ATP driven phosphorylation rate), for which memory lifetime per invested energy can increase progressively for longer memories. Furthermore, in general, a memory trace decouples dynamically from a corresponding synaptic metabolic rate such that the energy expended on a new learning and its memory trace constitutes in most cases only a small fraction of the baseline energy associated with prior memories. Taken together, these empirical and theoretical results suggest a metabolic efficiency of synaptically stored information.

q-bio.NC↗

arXiv2015

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. In sum, these results suggest that the new spine economy principle may be important for brain evolutionary design in a broader context.

q-bio.NC↗

arXiv2014

What can a mathematician do in neuroscience?

Mammalian brain is one of the most complex objects in the known universe, as it governs every aspect of animal's and human behavior. It is fair to say that we have a very limited knowledge of how the brain operates and functions. Computational Neuroscience is a scientific discipline that attempts to understand and describe the brain in terms of mathematical modeling. This user-friendly review tries to introduce this relatively new field to mathematicians and physicists by showing examples of recent trends. It also discusses briefly future prospects for constructing an integrated theory of brain function.

q-bio.NC↗

arXiv2014

Synaptic polarity of the interneuron circuit controlling C. elegans locomotion

C. 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 7 pre-motor neurons implicated in the control of worm's 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.

q-bio.NC↗

arXiv2014

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

Mammalian brains span about 4 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.

q-bio.NC↗

arXiv2012

Approximate invariance of metabolic energy per synapse during development in mammalian brains

During mammalian development the cerebral metabolic rate correlates qualitatively with synaptogenesis, and both often exhibit bimodal temporal profiles. Despite these non-monotonic dependencies, it is found based on empirical data for different mammals that regional metabolic rate per synapse is approximately conserved from birth to adulthood for a given species (with a slight deviation from this constancy for human visual and temporal cortices during adolescence). A typical synapse uses about $(7\pm 2)\cdot 10^{3}$ glucose molecules per second in primate cerebral cortex, and about 5 times of that amount in cat and rat visual cortices. A theoretical model for brain metabolic expenditure is used to estimate synaptic signaling and neural spiking activity during development. It is found that synaptic efficacy is generally inversely correlated with average firing rate, and additionally, synapses consume a bulk of metabolic energy, roughly $50-90 %$ during most of the developmental process (except human temporal cortex $ < 50%$). Overall, these results suggest a tight regulation of brain electrical and chemical activities during the formation and consolidation of neural connections. This presumably reflects strong energetic constraints on brain development.

q-bio.NC↗

arXiv2011

Scaling of brain metabolism and blood flow in relation to capillary and neural scaling

Brain is one of the most energy demanding organs in mammals, and its total metabolic rate scales with brain volume raised to a power of around 5/6. This value is significantly higher than the more common exponent 3/4 relating whole body resting metabolism with body mass and several other physiological variables in animals and plants. This article investigates the reasons for brain allometric distinction on a level of its microvessels. Based on collected empirical data it is found that regional cerebral blood flow CBF across gray matter scales with cortical volume $V$ as $CBF \sim V^{-1/6}$, brain capillary diameter increases as $V^{1/12}$, and density of capillary length decreases as $V^{-1/6}$. It is predicted that velocity of capillary blood is almost invariant ($\sim V^ε$), capillary transit time scales as $V^{1/6}$, capillary length increases as $V^{1/6+ε}$, and capillary number as $V^{2/3-ε}$, where $ε$ is typically a small correction for medium and large brains, due to blood viscosity dependence on capillary radius. It is shown that the amount of capillary length and blood flow per cortical neuron are essentially conserved across mammals. These results indicate that geometry and dynamics of global neuro-vascular coupling have a proportionate character. Moreover, cerebral metabolic, hemodynamic, and microvascular variables scale with allometric exponents that are simple multiples of 1/6, rather than 1/4, which suggests that brain metabolism is more similar to the metabolism of aerobic than resting body. Relation of these findings to brain functional imaging studies involving the link between cerebral metabolism and blood flow is also discussed.

q-bio.NC↗

arXiv2009

Thermodynamic constraints on neural dimensions, firing rates, brain temperature and size

There have been suggestions that heat caused by cerebral metabolic activity may constrain mammalian brain evolution, architecture, and function. This article investigates physical limits on brain wiring and corresponding changes in brain temperature that are imposed by thermodynamics of heat balance determined mainly by Na$^{+}$/K$^{+}$-ATPase, cerebral blood flow, and heat conduction. It is found that even moderate firing rates cause significant intracellular Na$^{+}$ build-up, and the ATP consumption rate associated with pumping out these ions grows nonlinearly with frequency. Surprisingly, the power dissipated by the Na$^{+}$/K$^{+}$ pump depends biphasically on frequency, which can lead to the biphasic dependence of brain temperature on frequency as well. Both the total power of sodium pumps and brain temperature diverge for very small fiber diameters, indicating that too thin fibers are not beneficial for thermal balance. For very small brains blood flow is not a sufficient cooling mechanism deep in the brain. The theoretical lower bound on fiber diameter above which brain temperature is in the operational regime is strongly frequency dependent but finite due to synaptic depression. For normal neurophysiological conditions this bound is at least an order of magnitude smaller than average values of empirical fiber diameters, suggesting that neuroanatomy of the mammalian brains operates in the thermodynamically safe regime. Analytical formulas presented can be used to estimate average firing rates in mammals, and relate their changes to changes in brain temperature, which can have important practical applications. In general, activity in larger brains is found to be slower than in smaller brains.

q-bio.NC↗

arXiv2007

Systems level circuit model of C. elegans undulatory locomotion: mathematical modeling and molecular genetics

To establish the relationship between locomotory behavior and dynamics of neural circuits in the nematode C. elegans we combined molecular and theoretical approaches. In particular, we quantitatively analyzed the motion of C. elegans with defective synaptic GABA and acetylcholine transmission, defective muscle calcium signaling, and defective muscles and cuticle structures, and compared the data with our systems level circuit model. The major experimental findings are: (i) anterior-to-posterior gradients of body bending flex for almost all strains both for forward and backward motion, and for neuronal mutants, also analogous weak gradients of undulatory frequency, (ii) existence of some form of neuromuscular (stretch receptor) feedback, (iii) invariance of neuromuscular wavelength, (iv) biphasic dependence of frequency on synaptic signaling, and (v) decrease of frequency with increase of the muscle time constant. Based on (i) we hypothesize that the Central Pattern Generator (CPG) is located in the head both for forward and backward motion. Points (i) and (ii) are the starting assumptions for our theoretical model, whose dynamical patterns are qualitatively insensitive to the details of the CPG design if stretch receptor feedback is sufficiently strong and slow. The model reveals that stretch receptor coupling in the body wall is critical for generation of the neuromuscular wave. Our model agrees with our behavioral data(iii), (iv), and (v), and with other pertinent published data, e.g., that frequency is an increasing function of muscle gap-junction coupling.

q-bio.NC↗

arXiv2007

Global and regional brain metabolic scaling and its functional consequences

Background: Information processing in the brain requires large amounts of metabolic energy, the spatial distribution of which is highly heterogeneous reflecting complex activity patterns in the mammalian brain. Results: Here, it is found based on empirical data that, despite this heterogeneity, the volume-specific cerebral glucose metabolic rate of many different brain structures scales with brain volume with almost the same exponent around -0.15. The exception is white matter, the metabolism of which seems to scale with a standard specific exponent -1/4. The scaling exponents for the total oxygen and glucose consumptions in the brain in relation to its volume are identical and equal to $0.86\pm 0.03$, which is significantly larger than the exponents 3/4 and 2/3 suggested for whole body basal metabolism on body mass. Conclusions: These findings show explicitly that in mammals (i) volume-specific scaling exponents of the cerebral energy expenditure in different brain parts are approximately constant (except brain stem structures), and (ii) the total cerebral metabolic exponent against brain volume is greater than the much-cited Kleiber's 3/4 exponent. The neurophysiological factors that might account for the regional uniformity of the exponents and for the excessive scaling of the total brain metabolism are discussed, along with the relationship between brain metabolic scaling and computation.

q-bio.NC↗

arXiv2006

Conservation rules, their breakdown, and optimality in Caenorhabditis sinusoidal locomotion

Undulatory locomotion is common to nematodes as well as to limbless vertebrates, but its control is not understood in spite of the identification of hundred of genes involved in Caenorhabditis elegans locomotion. To reveal the mechanisms of nematode undulatory locomotion, we quantitatively analyzed the movement of C. elegans with genetic perturbations to neurons, muscles, and skeleton (cuticle). We also compared locomotion of different Caenorhabditis species. We constructed a theoretical model that combines mechanics and biophysics, and that is constrained by the observations of propulsion and muscular velocities, as well as wavelength and amplitude of undulations. We find that normalized wavelength is a conserved quantity among wild-type C. elegans individuals, across mutants, and across different species. The velocity of forward propulsion scales linearly with the velocity of the muscular wave and the corresponding slope is also a conserved quantity and almost optimal; the exceptions are in some mutants affecting cuticle structure. In theoretical terms, the optimality of the slope is equivalent to the exact balance between muscular and visco-elastic body reaction bending moments. We find that the amplitude and frequency of undulations are inversely correlated and provide a theoretical explanation for this fact. These experimental results are valid both for young adults and for all larval stages of wild type C. elegans. In particular, during development, the amplitude scales linearly with the wavelength, consistent with our theory. We also investigated the influence of substrate firmness on motion parameters, and found that it does not affect the above invariants. In general, our biomechanical model can explain the observed robustness of the mechanisms controlling nematode undulatory locomotion.

q-bio.NC↗

arXiv2004

Model of the early development of thalamo-cortical connections and area patterning via signaling molecules

The mammalian cortex is divided into architectonic and functionally distinct areas. There is growing experimental evidence that their emergence and development is controlled by both epigenetic and genetic factors. The latter were recently implicated as dominating the early cortical area specification. In this paper, we present a theoretical model that explicitly considers the genetic factors and that is able to explain several sets of experiments on cortical area regulation involving transcription factors Emx2 and Pax6, and fibroblast growth factor FGF8. The model consists of the dynamics of thalamo- cortical connections modulated by signaling molecules that are regulated genetically, and by axonal competition for neocortical space. The model can make predictions and provides a basic mathematical framework for the early development of the thalamo-cortical connections and area patterning that can be further refined as more experimental facts become known.

q-bio.NC↗

arXiv2004

Towards comparative theoretical neuroanatomy of the cerebral cortex

Despite differences in brain sizes and cognitive niches among mammals, their cerebral cortices posses many common features and regularities. These regularities have been a subject of experimental investigation in neuroanatomy for the last 100 years. It is believed that such studies may provide clues about cortical design principles and perhaps function. However, on a theoretical side there has been little interest, until recently, in studying quantitatively these regularities. This article reviews some attempts in this direction with an emphasis on neuronal connectivity. It is suggested that the brain development is influenced by different, conflicting in outcome, functional/biochemical constraints. Because of these conflicting constraints, it is hypothesized that the architecture of the cerebral cortex is shaped by some global optimization plan.

q-bio.NC↗