## Exploratory adaptation in cellular networks

Cells have multiple gene-regulation “programs” to answer to specific challenges; still, they are sometimes required to address unforeseen challenges for which no response is readily available. Here, exploratory dynamics can provide an in-principle unlimited repertoire of new responses and cell states; this process is, in some respects, similar to learning. We study exploratory adaptation in theoretical models of random networks, with particular focus on properties of biological networks that allow such exploration in high dimensional space to converge.

The experimental roots of this theory come from a joint work with Erez Braun from the Physics Dept. at Technion. Yeast cells were rewired synthetically and conditions are set such that the genetic regulatory system faces unforeseen severely challenging conditions. We have found that rewired cells can adapt over short (~10 generation) timescales to these challenging conditions. This adaptation is not induced by random mutation but is nevertheless stable over hundreds of generations. We studied the roles of population phenotypic variability, global gene expression and other cellular mechanisms on this plastic behavior, which we believe are representative of the physiological plasticity exhibited in evolution following gene co-option events.

__E. Stolovicki, T. Dror, N. Brenner and E. Braun, “Synthetic gene-recruitment reveals adaptive reprogramming of gene regulation in yeast”, Genetics 173, 75-85 (2006).____S. Stern, T. Dror, E. Stolovicki, N. Brenner and E. Braun, “Genome-wide transcriptional plasticity underlies cellular adaptation to novel challenge”, Mol. Sys. Biol. 3, article #106 (2007) . (LINK TO: Stern_MSB2007.PDF). See also commentary by E.V. Koonin, Mol. Sys. Biol.__**3**, article # 107 (2007).

## Statistical Mechanics of Protein Variation in Cell Populations

Variation is a fundamental property of biological populations at all levels. In particular highly expressed proteins are usually relevant phenotypes that nevertheless exhibits large variation among cells in a clonal population under uniform conditions. We study protein distributions in microorganism populations using Statistical Mechanics approaches and concepts, via an experiment-theory collaboration (with Erez Braun, Technion; Hanna Salman, Pittsburgh Universaity). We have characterized the quantitative features of protein distributions in dividing cell populations: these are highly non-Gaussian and skewed. We have found that these protein distrbutions from two microorganisms, yeast and bacteria, and under a broad range of conditions, collapse to a universal curve under scaling. Moreover the protein temporal fluctuations in the same scaled units obey an ergodic property and display the same distribution shape as the population snapshots. On the other hand, some statistical properties (long-term averages and autocorrelation functions) are distinct among individual cells over many generations. A theoretical model including exponential accumulation and division with cellular homeostasis explains both the universal and the individual statistical properties.

__N. Brenner, C.M. Newman, D. Osmanovic, Y. Rabin, H. Salman and D.L Stein, Universal protein distributions in a model of cell growth and division. Phys. Rev. E__**92**, 042713 (2015).__H. Salman, N. Brenner, Ch-K. Tung, N. Elyahu, E. Stolovicki, L. Moore, A. Libchaber and E. Braun, “Universal protein fluctuations in microorganism populations. Phys. Rev. Lett. 108, 238105 (2012).____T. Friedlander and N. Brenner, “Cellular properties and asymptotics in the population balance equation”,__*Phys. Rev. Lett.***101**, 018104 (2008).__N. Brenner and Y. Shokef, “Non-equilibrium statistical mechanics of dividing cell populations”,__*Phys. Rev. Lett*.**99**, 138102-1 – 138102-4 (2007).__N. Brenner, K. Farkash and E. Braun, “Dynamics of protein distributions in cell populations”,__*Phys. Biol*.**3**, 172-182 (2006).

## Cooperative interactions between microorganisms

Cells (and microorganisms in particular) interact with one another by direct signaling as well as indirectly through their common environment. These interactions are mediated by products of cell metabolism and gene expression. We are interested in the relation between these two levels of organization; namely in the effects of cellular processes, through interactions, on the population-level dynamics and back on the cells. Game theory and nonlinear dynamics systems are the main tools we use in this research. Our recent work focuses on the dramatic effects of fluctuations on these systems, showing that coexistence can be induced purely by such fluctuations

__H. Behar, N. Brenner, G. Ariel and Y. Luzoun, “Fluctuations-induced coexistence in public goods dynamics”. under review 2016.____H. Behar, N. Brenner and Y. Louzoun,”Coexistence by Spatiotemporal patterns in a cooperation problem”.Theoret. Pop. Biol.__**96**, 20-29 (2014).__Y. Elhanati, S. Schuster and N. Brenner, “Dynamic modeling of cooperative protein secretion in microorganism populations”. Theor. Pop. Biol.__**80**, 49-63 (2011).__S. Schuster, A. Schroeter, N. Brenner, F. Wessely, G. Theissen, E. Ruppin and J.U. Kreft. “Cooperation and cheating in exoenzyme production by microorganisms – theoretical analysis in view of biotechnological applications”. Biotech. J.__**5**, 751-758 (2010).

**Variability and dynamics of synapse populations**

Populations of synapses have long been thought to be important in learning and memory. However only recently have quantitative measurements of large populations of synapses become directly accessible. In collaboration with the lab of Noam Ziv at the Technion, we study and model both statistical and dynamical properties of such synaptic populations. We have found that many properties of these populations can be captured by a mesoscopic-scale effective model known as the Kesten Process. At the biophysical level we have found that cooperative binding and unbinding are sufficient and necessary conditions to recover the statistical properties of synaptic populations (work in progress).

## Adaptive cellular response to signals

Cells sense their environment and respond to it adaptively. These adaptive responses address the challenge of environments changing over an extremely broad range of time and signal scales. We study adaptive cellular response in a general theoretic framework which can distinguish universal features common to many cellular systems, from system-specific ones. In particular we address kinetic mechanisms underlying dynamic-range enlargement (background compensation) and multiple-time-scale behavior.

__T. Friedlander and N. Brenner, “Adaptive response and enlargement of dynamic range”. Mathematical Biosciences and Engineering__**8**, 515 – 528 (2011).__T. Friedlander and N. Brenner, “Adaptive response by state-dependent inactivation”. PNAS__**106,**22558-22563 (2009).__G. Gilboa, R. Chen and N. Brenner, “History dependent multiple time scale dynamics in a single neuron model”, J. Neurosci.__**25**, 6479-6489 (2005).