Web page of: Jan Karbowski

"Physics of the brain"

Hello, my name is Jan Karbowski. Currently, I am an Associate Professor in the Math Dept. of the University of Warsaw.

Email: jkarbowski@mimuw.edu.pl

I am a neuroscientist, although I was formally educated in theoretical physics, but curiously I work in the Mathematics Department. (Interesting combination, isn't it? Some might say that it is even contradictory...).

I am interested and work profesionally in neuroscience (computational/theoretical) and related "biological physics" (neurophysics). Previously I was a theoretical physicist (Ph.D in condensed matter/statistical mechanics at Warsaw University in 1996). I use the methods of theoretical physics (stochastic thermodynamics, information theory, scaling laws) and applied mathematics (dynamical systems, optimization, statistics) to neuroscience problems. Broadly speaking, I try to understand how the real brains work and are designed from a physical or engineering point of view (how can we describe them using mathematical models and physical principles?). A main theme in my research is neural and synaptic information processing and storing in terms of energy efficiency, and brain scaling rules. Specific topics I am interested in are described below.
I had worked in various institutions (in Poland and USA) in different departments (physics, mathematics, engineering, and biology), and therefore I can say that I had gained diverse skills and unique experience (mostly good, but sometimes also bad...). For example, I was working in Boston University (Physics and Math Depts.), University of Pittsburgh (Math Dept.), California Institute of Technology (Biology Dept.), and Polish Academy of Sciences (in Physics Institute and Biocybernetics Institute).

Major interests:

Evolutionary scaling laws and principles for brain neuroanatomy and metabolism.
Biophysics of synaptic plasticity and information encoding in the context of learning and memory.
Neural circuit controling locomotion in the nematode C. elegans.
Statistical mechanics in the contex of neural networks.

Fellowships, scholarships, awards:

Marie Curie Fellow (IBIB Polish Academy of Sciences), 2009-2012.
The Sloan-Swartz Fellowship (Caltech, USA), 2003-2008.
The Fulbright Fellowship (Boston University, USA), 1997-1998.
The Scholarship/Award of the Foundation for Polish Science (Fundacja na Rzecz Nauki Polskiej) for young scientists of all disciplines, 1995.
Laureate of the Polish National Physics Olympics for High School Students, 1987.

Main scientific achievements:

Showing, based on data, that the total brain energy cost and its blood flow scale with brain size with the exponent close to 5/6, which is different than the so-called Kleiber law (power 3/4).

BMC Biology 5: 18 (2007).

PLoS ONE 6: e26709 (2011).

Front. Neural Circuits 8: 9 (2014).

Estimating, based on data, that the energy cost of synaptic plasticity is relatively small under standard conditions (about 10% of much more demanding fast synaptic transmission), and deriving the formula for energy rate of neurons. The former means that synaptic learning is relatively cheap ...

J. Neurophysiol. 122: 1473-1490 (2019).

J. Comput. Neurosci. 49, 71-106 (2021).

PLoS ONE 7, e33425 (2012).

J. Comput. Neurosci. 27, 415-436 (2009).

Showing that the sizes of cortical and hippocampal dendritic spines (synapses) nearly maximize their information capacity across mammalian brains.

Scientific Reports 13: 22207 (2023).

Other significant results:

Showing that cerebral cortex in the brain of mammals has a "small world network" architecture.

Phys. Rev. Lett. 86, 3674 (2001).

Derivation of the inequalities for generalized information rates (KL, Renyi, Tsallis, mutual info) in terms of stochastic thermodynamics, which may have implications in physics, neuroscience, machine learning, etc.

Phys. Rev. E 109, 054126 (2024).

Proposing, based on data, a new principle of neuroanatomical organization of neural circuits in the cerebral cortex called "(dendritic) spine economy maximization".

PLoS Comput. Biol. 11: e1004532 (2015).

Showing that the so-called spike-timing-dependent-plasticity (STDP) can lead to neural network synchronization when synaptic potentiation and depression are (even approximately) balanced.

Phys. Rev. E 65, 031902 (2002).

Showing that the neural switch controling forward and backward locomotory transitions in C. elegans has an inhibitory character.

PLoS Comput. Biol. 13: e1005834 (2017).

Front. Comput. Neurosci. 7: 128 (2013).

Curr. Opin. in Systems Biol. 13, 44-51 (2019).

Proposing a mathematical model of neuron's dynamics that can be called "absolute integrate-and-fire neuron", which is an alternative to the classic IF model with slightly more realistic dynamics.

Neural Computation 12, 1573-1606 (2000).

Publications:

J. Karbowski. "Information thermodynamics: from physics to neuroscience", Entropy 26, 779 (2024).

J. Karbowski. "Bounds on the rates of statistical divergences and mutual information via stochastic thermodynamics", Physical Review E 109, 054126 (2024).

J. Karbowski, P. Urban. "Cooperativity, information gain, and energy cost during early LTP in dendritic spines", Neural Computation 36, 271-311 (2024).

M. Chwilka, J. Karbowski. "Explicit mutual information for simple networks and neurons with lognormal activities", Physical Review E 109, 014117 (2024).

J. Karbowski, P. Urban. "Information encoded in volumes and areas of dendritic spines is nearly maximal across mammalian brains", Scientific Reports 13: 22207 (2023).

J. Karbowski. "Energetics of stochastic BCM type synaptic plasticity and storing of accurate information", Journal of Computational Neuroscience 49: 71-106 (2021).

J. Karbowski. "Metabolic constraints on synaptic learning and memory", Journal of Neurophysiology 122: 1473-1490 (2019).

J. Karbowski. "Deciphering neural circuits for Caenorhabditis elegans behavior by computations and perturbations to genome and connectome", Current Opinion in Systems Biology 13: 44-51 (2019).

F. Rakowski, J. Karbowski. "Optimal synaptic signaling connectome for locomotory behavior in Caenorhabditis elegans: Design minimizing energy cost", PLoS Computational Biology 13: e1005834 (2017).

J. Karbowski. "Cortical composition hierarchy driven by spine proportion economical maximization or wire volume minimization", PLoS Computational Biology 11: e1004532 (2015).

Y. Yu, J. Karbowski, RNS Sachdev, J Feng. "Effect of temperature and glia in brain size enlargement and origin of allometric body-brain size scaling in vertebrates", BMC Evolutionary Biology 14: 178 (2014).

J. Karbowski. "Constancy and trade-offs in the neuroanatomical and metabolic design of the cerebral cortex", Front. Neural Circuits 8: 9 (2014).

F. Rakowski, J. Srinivasan, PW Sternberg, J. Karbowski. "Synaptic polarity of the interneuron circuit controling C. elegans locomotion", Front. Comput. Neurosci. 7: 128 (2013).

J. Karbowski. "What can a mathematician do in neuroscience", Mathematica Applicanda 40(1), 37-48 (2012).

J. Karbowski. "Approximate invariance of metabolic energy per synapse during development in mammalian brains", PLoS ONE 7, e33425 (2012).

J. Karbowski. "Scaling of brain metabolism and blood flow in relation to capillary and neural scaling", PLoS ONE 6, e26709 (2011).

J. Karbowski. "Thermodynamic constraints on neural dimensions, firing rates, brain temperature and size", Journal of Computational Neuroscience 27, 415-436 (2009).

J. Karbowski, G. Schindelman, C.J. Cronin, A. Seah, P.W. Sternberg. "Systems level circuit model of C. elegans undulatory locomotion: mathematical modeling and molecular genetics", Journal of Computational Neuroscience 24, 253-276 (2008).

J. Karbowski. "Global and regional brain metabolic scaling and its functional consequences", BMC Biology 5: 18 (2007).

J. Karbowski, C.J. Cronin, A. Seah, J.E. Mendel, D. Cleary, P.W. Sternberg. "Conservation rules, their breakdown, and optimality in Caenorhabditis sinusoidal locomotion", Journal of Theoretical Biology 242, 652-669 (2006).

J. Karbowski and G.B. Ermentrout. "Model of the early development of thalamo-cortical connections and area patterning via signaling molecules", Journal of Computational Neuroscience 17, 347-363 (2004).

J. Karbowski. "How does connectivity between cortical areas depend on brain size? Implications for efficient computation", Journal of Computational Neuroscience 15, 347-356 (2003).

J. Karbowski and G.B. Ermentrout. "Synchrony arising from a balanced synaptic plasticity in a network of heterogeneous neural oscillators", Physical Review E 65, 031902 (2002).

J. Karbowski. "Optimal wiring principle and plateaus in the degree of separation for cortical neurons", Physical Review Letters 86, 3674-3677 (2001).
Shorter version of this article appeared in Neurocomputing 44, 875-879 (2002), as proceedings of the "Computational Neuroscience Meeting CNS'01", San Francisco-Monterey, Jul 2001.

J. Karbowski and N. Kopell. ``Multispikes and synchronization in a large neural network with temporal delays'', Neural Computation 12, 1573-1606 (2000).

J. Karbowski. "Fisher information and temporal correlations for spiking neurons with stochastic dynamics", Physical Review E 61, 4235-4252 (2000).

J. Karbowski and L.A. Turski. "The Bose-Einstein condensation in random box", Physica A 276, 489-494 (2000).

M. Cieplak, M. Henkel, J. Karbowski and J.R. Banavar. "Master equation approach to protein folding and kinetic traps", Physical Review Letters 80, 3654-3657 (1998).

J. Karbowski. "Quantum fluctuations in the Kondo insulators: Slave boson approach", Physical Review B 54, R728-R731 (1996).

J. Karbowski and J. Spalek. "Superconducting instabilities in the finite U Anderson lattice model", Physica B 206-207, 716 (1995).

J. Karbowski and J. Spalek. "Interorbital pairing for heavy fermions and universal scaling of their basic characteristics", Physical Review B 49, 1454-1457 (1994).

J. Karbowski and J. Spalek. "Universal scaling of basic properties of the heavy fermion superconductors", Acta Physica Polonica A 85, 341-345 (1994).

J. Spalek, K. Byczuk, J. Karbowski, and W. Wojcik. "Strongly correlated fermions at low temperatures", Physica Scripta T. 49A, 206-214 (1993).