Research

# My research focuses on statistical mechanics and its application to biology.

**Statistical mechanics of spin glasses** - Understanding the nature of complex systems like glasses constitutes one of the deepest unsolved problems in condensed-matter theory. While in the last decades there has been significant progress in capturing the physics of glasses on a mean-field level, a complete understanding of the physics of realistic glassy systems is still out of reach. My research focuses on studying the simplest non-mean-field models of spin glasses (for example dilute solutions of Mn in Cu), and structural glasses (glycerol, o-terphenyl). My work introduced a novel renormalization-group method for spin glasses to study their phase diagram, and it established for the first time the existence of a finite-temperature phase transition for a non-mean-field structural glass.

*Collaborators*: Giorgio Parisi, Silvio Franz, Adriano Barra, Francesco Guerra.

Recently, the statistical mechanics of disordered systems has been shown to have many applications to biological systems. In particular, I am interested in the application of statistical mechanics to neural networks, animal behavior, and cell biology.

**Neural networks** - Recent studies have shown that statistical mechanics is a useful tool to model the behavior of networks of neurons. In the maximum-entropy framework, neural networks can be described in terms of statistical-mechanics models of spin glasses, whose parameters can be inferred from experimental data. With my collaborators, I developed a novel formulation of the maximum-entropy method, through which the inference problem above can be solved in an analytical way by exploiting the duality between the direct and the inverse problem in statistical mechanics. As a result, this method allows for drawing the phase diagram of the model inferred from the data, and to predict the location of the system in such a phase diagram.

*Collaborators*: William Bialek.

**Bird flocking** - The collective behavior of flocks of birds is another example of a biological system that can be described with tools inspired from statistical mechanics. In the maximum-entropy framework, bird flocks are modeled as Heisenberg spin models, where each bird's vector velocity is treated as a Heisenberg spin, and the maximum-entropy method allows for deriving the distribution of velocities of the flock. My collaborators and I focus on the possibility that this distribution of velocities can induce a distribution of positions. While in most animal-behavior studies the interactions between individuals are metric, our analysis of the positional distribution suggests that bird-to-bird interactions in flocks are topological.

*Collaborators*: Andrea Cavagna, Irene Giardina, William Bialek.

*Flock of starlings (Sturnus Vulgaris).** *

**Enzyme clustering** - The aggregation of multiple enzyme molecules into compact agglomerates is a striking phenomenon observed in yeast, mammalian cells, and some bacteria. A long-standing idea is that cells naturally form such clusters to maximize the metabolic efficiency of enzymes. Inspired by statistical-mechanics, it is natural to expect that such many-enzyme systems can be properly studied and understood when the number of proteins involved is large. This idea allowed us to model the large number of molecules involved in enzyme clustering in a computationally tractable way. Our work provides the first quantitative demonstration that enzyme configurations made of multiple compact clusters yield the highest metabolic efficiency for realistic, multiple-step metabolic pathways, and this prediction has been tested and confirmed in *Escherichia coli* bacterium by our experimental collaborators. Finally, the model predictions for the cluster radius and inter-cluster spacing are in agreement with those observed in mammalian cells and yeast.

*Collaborators*: Ned S. Wingreen, Zemer Gitai.

*Purine-biosynthesis enzymes form multiple clusters in HeLa cells (from Zhao et al. (2013) PLoS ONE 8(2): e56203). ** *

**Non-equilibrium mechanisms in bacterial transcription and translation** - In bacteria such as *Escherichia coli*, DNA is densely compacted into a nucleoid near the cell center, while ribosomes—the molecular complexes that translate messenger RNAs (mRNAs) into proteins—are localized near the cell endcaps. We study the impact of this intracellular spatial localization using a minimal reaction-diffusion model for the cellular transcriptional-translational machinery. Our model predicts that ∼90% of mRNAs are localized near the cell endcaps—a prediction which may be directly tested in future experimental studies. In addition, our model reveals a “circulation” of ribosomes driven by the non-equilibrium mRNA flux, from synthesis in the nucleoid to degradation in the endcap region, showing that these circular fluxes increase ribosome efficiency, and thus the rate at which proteins are synthesized in the cell.

*Collaborators*: Ned S. Wingreen.

*Ribosome localization (from Bakshi et al. (2012) Mol. Microbiol. 85(1): 21). Top: superresolution image of ribosomes (yellow dots) in a single cell of** Escherichia coli bacterium*. Middle: spherocylindrical model of the cell. Bottom: relative number of ribosomes along the position on the long cell axis, where the gray background shows the theoretical profile for a uniform distribution.