Statistical Physics of Complex and Biological Systems

Statistical Physics of Complex and Biological Systems


Marco Baiesi, Fulvio Baldovin Amos Maritan, Enzo Orlandini, Flavio Seno Attilio Stella Samir Suweis, Antonio Trovato.

Other members

Post-Docs: Anna Tovo, Daniel Maria Busiello, Stefano Lubini

Ph.D.: Ilenia Apicella, Loren Kocillari, Gianluca Teza, Davide Colì, Leonardo Pacciani.

Research Activity

The theoretical research activity of our group covers scientific areas ranging from statistical mechanics to complex systems physics. We deal with interdisciplinary topics such as biopolymer and protein physics, liquid crystal dynamics, collective motions in self-propelling particle systems, physics of ecological systems, biological and physics econophysics. Our approach to these topics includes data mining, data analysis, statistical analysis, computational and analytic modeling.

For a wider and more detailed overview of our group's research topics please see below.

Emergent Patterns in Complex Systems

(Suweis, Maritan)
Universal scaling behavior is an attractive feature in statistical physics because a wide range of models can be classified purely in terms of their collective behavior whose characteristics depend only on few details like the dimensionality of the system and symmetries of the problem (eventually on the kind of decay of the interaction strength) but not on finer details. Scaling phenomena, as epitomized by fine size scaling, have been observed in many branches of physics,chemistry, biology, ecology economics and sociology. Our research interests include ecological and biological systems, physics of interacting particle, optimal transportation network, complex networks dynamics with applications on environmental science and sustainability.

Organization of Ecosystems and Dynamics of Evolution

(Suweis, Maritan)
Understanding the origin, maintenance and loss of biodiversity in ecological systems is a goal of the highest scientific priority given the rapidity of global biodiversity loss. Ecological communities exhibit pervasive patterns and interrelationships between size, abundance, and the availability of resources. Non-equilibrium statistical mechanics is the natural candidate to develop a unified framework for understanding the distribution of organism sizes, their energy use, and spatial distribution. We have demonstrated that optimal use of resources, both at the individual and community level, leads to a consistent scaling theory in plant communities which is well supported by observational data. We believe that variational/optimization principles, which have been so successful in physics, are also able to explain other commonly observed spatio-temporal patterns in natural systems (e.g. architecture of ecological interaction networks, species area relationship) and, eventually, predict new ones not yet discovered. Our research of complex living systems incorporates theoretical inquiry, modeling, and empirical study.

Robustness, adaptability and critical transitions in living systems

(Suweis, Maritan)
Understanding of biological/social systems needs more than a mere generalization of the standard statistical mechanics approach. In the latter, it is fundamental to determine the order parameter, which characterizes the different system phases. This is a crucial step to obtain the key ingredients needed to formulate a modeling framework, so as to obtain a better understanding of the system's macroscopic behavior. However, asking for the order parameters for living systems is a difficult and not well-defined problem. Yet, there is increasing evidence that the key feature of living systems is in the architecture of their interaction networks. Our research focus on: 1) Developing a unifying theoretical framework that can provide a parsimonious and general explanation for the macroscopic behavior of these systems; 2) To investigate network responses to local or global perturbations; 3) To design new network architectures aimed at maximizing different objective functions describing different goals in terms of network adaptability or robustness.

Quorum Sensing

Quorum sensing (QS) is a system of stimuli and responses correlated to population density. For instance, quorum sensing allows bacteria to restrict the expression of specific genes to the high cell densities at which the resulting phenotypes will be most beneficial. Examples of such behavior are biofilm formation, virulence and antibiotic resistance. In similar fashion, some social insects use quorum sensing to determine where to nest. Quorum sensing can function as a decision-making process in any decentralized system, as long as individual components have: (a) a means of assessing the number of other components they interact with and (b) a standard response once a threshold number of components is detected. A deep comprehension of the QS mechanism might allow the development of next generation drugs able to overcome the problems arising from antibiotic-resistant bacterial diseases.We are developing mathematical models to predict bacterial expression patterns and in particular we are focusing our work to study the dynamical activation of the process and the trade-off between cell density and population extension from boundaries.

Proteins and Biopolymers

Biopolymers in general and proteins in particular are essential for life. The problem of determining the native ensemble of proteins is of formidable complexity, due to the high number and non trivial correlation of the involved degrees of freedom. Misfolded conformations may also be relevant, since they trigger pathological protein aggregation specifically related to a number of devastating degenerative diseases. In our approach we wish on the one hand to capture unifying emerging aspects in protein physics, typically by means of a statistical approach that employs simplified coarse-grained models. On the other hand, we focus on identifying which protein features can be understood in the context of standard polymer physics. A non exhaustive list of specific topics include the understanding of the origin of protein native folds based on geometry and symmetry, the development of statistical potentials to evaluate the quality of protein-like structures, the development of both sequence- and structure-based algorithms to predict a range of protein features, the investigation of the main mechanisms driving protein folding and aggregation.

Polymer dynamics

(Baiesi, Baldovin, Orlandini, Stella)
The translocation of a biopolymer through a membrane nanopore is an example of polymer dynamics with which living cells exchange information and energy. Other examples are the unwinding of the DNA double helix in the denaturation process and the supercoiling dynamics of the double stranded DNAs. Our research focus on developing and studying minimal models that capture the essential, universal, mechanisms underlying these dynamics and that allow a statistical characterization of these processes.

Conformational transitions in polymers

(Baiesi, Orlandini, Seno, Stella, Trovato)
Polymers in solution can undergo different relevant conformational transitions depending on the properties of the surrounding medium, such as the solvent chemical composition, the temperature, the presence of geometrical constraints and external forces. One of the most studied conformational transition is the "Theta" collapse of polymers from an extended to a globular phase that, for example, can be triggered by the progressive deterioration of the quality of the solvent. Other examples of conformational transitions are the adsorption transition on attractive substrates and the thermal or mechanical denaturation of the double stranded DNA. Here we analytically and numerically the thermodynamic properties of these transitions, relying on coarse-grained models of polymers, on simulations of stochastic processes and on analytical approaches for the exact calculation of generating functions and partition functions.

Topological properties of polymers

(Baiesi, Baldovin, Orlandini, Seno, Stella, Trovato)
The topological entanglement of polymers and proteins, described in terms of knots and links, is a timely argument of research that span several scientific disciplines, such as mathematics, chemistry, biology and physics. Of particular interest is the understanding of how and to which extent the topological properties of polymers depend on either intrinsic properties (for instance, chain bending and torsional rigidity) and extrinsic factors, such as the quality of the solvent, the degree of confinement and external stresses. Since polymers in solution are flexible fluctuating objects, a natural approach to topological entanglement is statistical mechanics. In the last years this group has produced many results on this field. Recently we have introduced and developed methods to locate and measure the size of topological entanglements within a single polymer and between polymers or polypeptidic chains. These results have opened new, still unexplored, perpsectives on these issues, which we are currently exploring.

Dynamical and rheological properties of active and passive liquid crystals

Liquid crystals (LC) are complex fluids made by anysotropic molecules that, under given conditions, give rise to orientationally ordered phases such as the nematic, cholesteric and blue phases. For these reasons they are structured fluids that respond to external stresses either as elastic or as viscous materials. They also display uncommon anisotropic optical and magnetic responses and for these reasons they are greatly implemented in optical devices. Moreover, models of LC can be properly extended to include non-equilibrium terms that mimics the physics of active fluids and gels such as the solution of actin and cystokeleton filaments in presence of molecular motors. A description of these systems in terms of Landau-de Gennes free energy and lattice Boltzmann equations have been one of the main achievment of this group and in the last years has allowed to obtain several results on the rheological, dynamical and optical properties of these systems. We now plan to extend these investigations to mixtures and emulsions of LC either passive or active.

Collective dynamics and patterning in systems of self-propelled particles

(Baldovin, Orlandini)
Bacterial suspensions, flocks of birds and swarms of insects are examples of self-propelled and interacting N-body systems that, under proper conditions, display collective motion, aggregation and patterning. If one neglects the details of these systems, each individual can be described as a particle that burns internal energy to move in the environment. Hence these systems are intrinsically out-of-equilibrium and their statistical behaviour is different from the one observed in their passive counterparts where equilibrium holds. Our research focuses on the design of simple models of self-propelled particles and the study of their statistical properties such as the aggregation phenomena and dynamical patterning that occurs as a result of spatial confinement, effective long-range interactions and mechanisms of communication between individuals. Our investigational approaches are either numerical or and analytical (Smoluchowski equations) on models in which individuals are described either as anisotropic Brownian particles with internal directional force or as point-like objects with a given position, direction of motion and constant speed. This activity has an experimental counterpart that is carried out in the laboratory of surfaces and interfaces of this Department (LaFSI:

Nonequilibrium Statistical Mechanics

(Baiesi, Maritan, Baldovin, Stella)
A general statistical mechanical theory for nonequilibrium systems is under construction. We have in mind systems that maintain fluxes, e.g. of heat, or that are relaxing, or that are not based on the usual physical laws of systems that reach the thermodynamic equilibrium. Often these are small systems (at the micrometer scale), in which fluctuations are relevant. We deal with these systems, for example by generalizing the concept of energy equipartition and the virial theorem, or by developing a theory of linear response. We can thus discuss concepts such as the specific heat or the mobility of particles in systems subject to nonequilibrium forcings. Among the phenomena we study, there are unusual regimes of "negative response", such as particles that slow down if the force that pulls them is increased.

Econophysics and Economic Complexity

(Baldovin, Stella)
The dynamics of markets shows robust stylized facts whose modelization stimulates since long time the use of statistical physics methods. Scaling and techniques inspired by the renormalization group are used as key ingredients for this modelization, for the pricing of derivative products, and for operative definitions of quantities like the time in finance. Another field of interest is that of growth processes realized in a context of global economic complexity. The networks of products and o producing countries play here a fundamental role in descriptions based on stochastic differential equations.

Statistical Physics & Machine Learning

(Maritan, Orlandini, Baiesi e Suweis)
There is a growing interest in problem solving via machine learning techniques. This is leading us to evaluate the new ideas and tools from the community studying machine learning, with the aim of applying these quite new methods in contexts such as complex systems, brain networks or polymer phases.  One goal is to understand how machine learning performs in distinguishing polymeric, epigenetic and brain phases. A general plan is to apply machine learning techniques to infer emergent patterns in complex ecological, biological, social, and geophysical systems. Finally we would like to understand if and in which sense neural networks are critical, and how their performance can be understood through information theory and statistical physics.