>> Tetsuya J. Kobayashi, University of Tokyo, Japan

An integrative view of biological adaptation from single-cell to population

Adaptability to ever-changing environment is a fundamental property of living systems. One typical mechanism of such biological adaptations is Darwinian evolutionary adaptation via natural selection, in which adapted organisms are selected from an intrinsically heterogeneous population.

The evolutionary adaptation is passive, non-anticipatory, and a posteriori in nature, because organisms are blind to whether they are doing better than others or not until they are selected by the environment eventually.

Also the evolutionary adaptation is inevitably collective, because a heterogeneous population is indispensable for the adaptation to function.

Another type of biological adaptations is predictive adaptation, in which organisms sense the environment, process the information obtained, and choose better behaviors or states for the future environmental state.

This adaptation is active, anticipatory, and a priori in nature, because organisms are aware of better behaviors and states for future before the future environmental state realizes.

In contrast to the evolutionary adaptation, the prediction adaptation can work at the single-cell-level. In real biological adaptations, however, both evolutionary and predictive adaptations are mixed up with different weights, which requires us to understand them integratively.

In this lecture, I would like to introduce a path-wise formulation of opulation dynamics with single-cell-level decision-making as a mathematical basis for integrative analysis of biological adaptations. As applications of this formulation, I am going to touch on the following topics in the lecture:

[a] Thermodynamic structure of population dynamics [1, 2]

[b] Fitness response relation to perturbations via large deviation theory [2]

[c] Natural selection as information processing [3]

[d] Fluctuation relations of fitness and information (an extension of evolutionary stable state) [3,4]

[e] Excess fitness and Clausius-like inequality under external control of fitness [5]

[f] Fitness values of information [4,6,7]

References

[1] Stanislas Leibler and Edo Kussell, “Individual histories and selection in heterogeneous populations”, PNAS, (2010), 107 (29) 13183-13188.

[2] Yuki Sughiyama, Tetsuya J. Kobayashi, Koji Tsumura, and Kazuyuki Aihara, “Pathwise thermodynamic structure in population dynamics”, Phys. Rev. E, (2015), 91, 32120.

[3] Tetsuya J. Kobayashi, and Yuki Sughiyama, “Fluctuation Relations of Fitness and Information in Population Dynamics”, Phys. Rev. Lett., (2015), 115(23), 238102.

[4] Tetsuya J. Kobayashi, and Yuki Sughiyama, “Information thermodynamic structure in population dynamics in fluctuating environment”, Phys. Rev. E, (2017), 96, 012402.

[5] Yuki Sughiyama, and Tetsuya J. Kobayashi, “Steady-state thermodynamics for population growth in fluctuating environments”, Phys. Rev. E, (2017), 95, 012131.

[6] O. Rivoire, and S. Leibler, “The value of information for populations in varying environments”, J. Stat. Phys., (2011), 142, 1124-66.

[7] Tetsuya J. Kobayashi, and Yuki Sughiyama, “Individual Sensing can Gain more Fitness than its Information”, arXiv:1712.09462, (2017).

>> Christian Maes, Katholieke Universiteit, Leuven, Belgium

Non-dissipative aspects in nonequilibrium

Studying the role of activity parameters and the nature of time-symmetric path-variables constitutes an important part of nonequilibrium physics, so we argue. As these time-symmetric aspects can vary independently from the entropy production we call them non-dissipative effects, ranking among features of nonequilibrium that have traditionally not been much included in statistical mechanics until recently. We present elementary illustrations covering population inversion, response and fluctuation theory. We believe these aspects are in fact crucial for many biological processes.

References:

* Christian Maes, Non-Dissipative Effects in Nonequilibrium Systems. SpringerBriefs in Complexity, ISBN 978-3-319-67780-4 (2018).
* Marco Baiesi and Christian Maes, Life efficiency does not always increase with the dissipation rate.



 

>> Armita Nourmohammad, Max Planck Institute for Dynamics and Self-Organisation, Goettingen, Germany



Statistical physics of molecular evolution across scales

A venerable question in evolutionary biology is: if the tape of life was replayed, would the outcome be the same? We do not know how evolutionary predictability relates to different molecular scales, ranging from genotypes (DNA and amino acids) to molecular phenotypes (functions such as protein activity). I discuss universal properties of molecular phenotypes, encoded by genotypes with large degrees of freedom, which allow for the predictive description of their evolution. Populations are often subject to time-dependent pressure from the environment. I introduce a non-equilibrium framework for adaptive evolution of molecular phenotypes in time-dependent conditions. I will discuss a number of biological examples in this context: I present strong evidence that environmental fluctuations drive the evolution of gene expression levels in Drosophila. Co-evolving populations reciprocally affect the fitness of each other, acting as time-dependent environments with feedback. I show evidence of co-adaptation between interacting cellular populations of HIV viruses and the antibody repertoire of a patient over the course of an infection.

References:

* A. Nourmohammad, J. Otwinowski and J. Plotkin (2016) Host-pathogen coevolution and the emergence of broadly neutralizing antibodies in chronic infections, PLoS Genet. 12(7): e1006171
* A. Nourmohammad, J. Rambeau, T. Held, V. Kovacova, J. Berg and M. Lässig (2017) Adaptive evolution of gene expression in Drosophila, Cell Reports 20, 1385-95
* T. Held, A. Nourmohammad and M. Lässig (2014) Adaptive evolution of molecular phenotypes, J. Stat. Mech, P09029
* A. Nourmohammad, S. Schiffles and M. Lässig (2013) Evolution of molecular phenotypes under stabilizing selection, J. Stat. Mech. P01012

>> Olivier Rivoire, College de France, Paris, France

Models of information processing in evolving populations

I will review mathematical models of evolutionary dynamics in which the adaptive value of different types of informations can be quantified. The models are inspired by information theory and, in some limits, correspond to known models of investment or stochastic control.

References:

* O. Rivoire, S. Leibler (2011). The value of information for populations in varying environments. J. Stat. Phys. 142: 1124-66.
* O. Rivoire, S. Leibler (2014). A model for the generation and transmission of variations in evolution. PNAS 111: E1940-E1949.
* O. Rivoire (2016). Informations in models of evolutionary dynamics. J. Stat. Phys. 162: 1324-1352.



 

>> Gasper Tkacik, Institute of Science and Technology, Vienna, Austria

Information processing in neural and gene regulatory networks
 

Life depends as much on the flow of information as on the flow of energy. Efforts to make this intuition precise started already in the 1950s, very soon after Shannon formulated his information theory, but progress was limited by the quality and quantity of experimental data. Recent advances allow us to measure the information transmitted by small biological networks, as well as to read it out and reconstruct the network inputs. Developing in parallel with this data-driven approach has been the theoretical idea of "efficient representation": the idea that biological systems could be optimized, through the course of evolution or learning, to transmit themaximal amount of (useful) information. In my talk I will highlight the unity of these theoretical ideas across two very different biological systems: a network of retinal ganglion cells encoding visual information, and a gene regulatory network responsible for the early development of the fruit fly. I will present examples of how biophysical constraints and stimulus statistics shape the functioning of these systems, and conclude by describing our early efforts to build a quantitative and predictive theory for biochemical regulatory networks.

>> Adam Bobrowski, Lublin University of Technology, Lublin, Poland

Fast diffusion: a bit of math, a bit more of intuition

We will cover some recent biology inspired mathematical results concerning fast diffusions in regions separated by semi-permeable membranes, and diffusions in thin domains. This is a joint work with Bogdan Kaźmierczak and Tomasz Lipniacki.



 

We give a short introduction into the framework of piecewise deterministic Markov processes (PDMPs) [1]. We illustrate the abstract mathematical setting with a gene expression model [2] described by a switching system - a kind of PDMP.Then we present some new results concerning the long-time decomposition of substochastic semigroups [3] induced by such Markov processes and their applications to the above mentioned model. We also analyse the properties of the deterministic limit of our model when jump rates between active and inactive states tend to infinity.

References

[1] R.Rudnicki, M.Tyran-Kamińska, Piecewise Deterministic Processes in Biological Models, SpringerBriefs in Applied Sciences and Technology, 2017.
[2] R. Rudnicki, A. Tomski On a stochastic gene expression with pre-mRNA, mRNA and protein contribution, J. Theor. Biol., 387 (2015), 54-67.
[3] K. Pichór, R. Rudnicki, Asymptotic decomposition of substochastic operators and semigroups, J. Math. Anal. Appl. 436 (2016), 305-32


 

 >> Marta Tyran-Kamińska, Institute of Mathematics, Polish Academy of Sciences, and University of Silesia, Katowice, Poland

Mathematics of bacterial gene regulation
	

We will describe simple deterministic and stochastic models of gene networks in bacteria with an emphasis on the dynamic behavior of inducible and repressible operons.

Reference

* M.C. Mackey, M. Santilan, M. Tyran-Kamińska, E. Zeron, Simple Mathematical Models of Gene Regulatory Dynamics, Lecture Notes on Mathematical Modelling in the Life Sciences, Springer, Cham, 2016.