Cell polarity and directional sensing
A sophisticated chemical compass is used by eukaryotic cells to orient and move in the direction of chemical extracellular gradients. This orientational mechanism is necessary for instance for the development of multicellular organisms. In recent years, studies have shown that eukaryotic cells exposed to slight differences in the concentration of a chemical attractant from side to side respond with the formation of clusters of signaling molecules localized in complementary regions of the cell membrane and oriented in the gradient direction. This early symmetry breaking leads subsequently to changes in the cell morphology and movement towards the attractant source.
We have performed direct simulations of the relevant reaction-diffusion kinetics, showing that receptor activation acts as an external field which renders the signaling network unstable with respect to the separation in two phases, respectively rich in one of the two species of signaling molecules, that phase separation times may be dramatically accelerated by the presence of slight gradients in the external chemotactic field, and that clusters of signaling molecules become aligned with the direction of extracellular gradients, thus allowing the cell membrane to work as a chemical compass [1].
We have then shown that the process of directional sensing may be described as a universal "coarsening" process, whereby large signaling patches grow at the expense of small ones. This observation leads to the prediction of simple laws relating the steepness of the stimulation gradient to the polarization time, and the existence of a threshold in detectable gradients. This theory of cell polarization is mostly independent of microscopic details of the interactions, such as the precise values of physical and chemical reaction parameters and the specific nature of the molecules involved [2,4]. The coarsening dynamics may be conveniently investigated using a lattice-gas model of the signaling network [3].
[1] Diffusion limited phase separation in eukaryotic chemotaxis
A. Gamba, A. de Candia, S. Di Talia, A. Coniglio, F. Bussolino, G. Serini
Proc. Nat. Acad. Sci. U.S.A. 102, 16927-16932 (2005)
[2] Patch coalescence as a mechanism for eukaryotic directional sensing
A. Gamba, I. Kolokolov, V. Lebedev, G. Ortenzi
Phys. Rev. Lett. 99 158101 (2007)
[3] Spatial signal amplification in cell biology: a lattice-gas model for self-tuned phase ordering
T. Ferraro, A. de Candia, A. Gamba, A. Coniglio
EPL 83 50009 (2008)
[4] Universal features of cell polarization processes
A. Gamba, I. Kolokolov, V. Lebedev, G. Ortenzi
J. Stat. Mech. P02019 (2009)
Chemotaxis: Phase transitions as a gradient amplifier (Editor's Choice, Science STKE)
Phase separation in eukaryotic chemotaxis (slides)
Vascular morphogenesis
The formation of a functioning vascular architecture during organism development results from a complex growth dynamic, regulated by cells communicating through the exchange of soluble chemical factors. The balance between attractive and repulsive chemical factors results in an appropriate vascular architecture, while its deregulation leads to the appearance of altered capillaries characterizing pathological angiogenesis.
We have proposed a model of blood vessels growth based on free migration and the exchange of a chemical attractant, which allows to reproduce with high precision the phenomenology of in vitro blood vessel formation [1,2]. The model correctly predicts a percolative transition below a critical cell density and reproduces the power-law exponents observed in experimental blood vessel networks.
[1] Percolation, morphogenesis, and Burgers dynamics in blood vessels formation
A. Gamba, D. Ambrosi, A. Coniglio, A. de Candia, S. Di Talia,
E. Giraudo, G. Serini, L. Preziosi, F. Bussolino.
Phys. Rev. Lett. 90, 118101 (2003)
[2] Modeling the early stages of vascular network assembly
G. Serini, D. Ambrosi, E. Giraudo, A. Gamba, L. Preziosi, F. Bussolino
EMBO J. 22, 1771-1779 (2003)
Blood vessel networks (Physics News Update)
Blood vessel networks (Physics News Graphics)
Math connects vascular network to the universe (JCB research roundup)
Statistical mechanics of nonequilibrium systems
Rare fluctuations away from equilibrium are responsible for many physical processes, such as phase transitions, nucleation, activation of chemical reactions, etc. Such fluctuations are related to the emergence of irreversible behaviors out of the reversible dynamics of microscopic agents. In this respect, it is interesting to investigate the relation between fluctuation and relaxation paths around an equilibrium or nonequilibrium steady state. Recent results by Bertini, De Sole, Gabrielli, Jona-Lasinio e Landim, show that temporal asymmetries between fluctuation and dissipation paths should be observable in mesoscopic systems. We have tested their theory in the context of a simple particle system, the Lorentz gas with constant external forcing [1].
[1] Current fluctuations in the nonequilibrium Lorentz gas
A. Gamba, L. Rondoni
Physica A 340, 274 (2004).
Statistical hydrodynamics
During the last decade, the application of statistical physics methods to the study of the Lagrangian dynamics of fluid particles allowed to obtain a quantitative theory of intermittency in the turbulent transport of scalar fields, such as dyes, thin dispersed particles, or heat. From the point of view of theoretical physics, turbulence is the field theory of an out-of-equilibrium system with many interacting degrees of freedom.
The statistics of transport in a turbulent flow may be studied theoretically using synthetic, gaussian velocity fields, since an important part of turbulent phenomenology, such as Kolmogorov scaling exponents with anomalous corrections, dissipative anomaly, intermittency, are still present in this simpler problem. In the case of a Batchelor-Kraichnan (smooth, delta-correlated) velocity field, analytic computations may be performed, which allow to better explain the phenomenology of passive transport and of turbulence itself.
We have obtained analytic results showing the emergence of intermittency in the scalar concentration field and in the corresponding dissipation field, and in deriving explicit expressions for the statistics of Lyapunov exponents of the system [1,2,3].
The statistical properties of passively advected scalar and tensor fields are encoded in the statistics of the corresponding Lyapunov exponents. Using functional integral and group theoretic methods we have given a complete description of the statistics of finite-time Lyapunov exponents in the general case of a continous product of stochastic transformations forming a representation of a semisimple Lie group; this general case includes the cases of the transport of passive tensor fields [4].
The analytic study of simplified models of turbulent transport must be accompanied by the study of simulations of more realistic models. We have shown with direct simulations the existence of universal scaling laws in the distribution of inertial (non passive) particles transported by a turbulent velocity field [5].
[1] Exact field-theoretical description of passive scalar convection in an n-dimensional long range velocity field
M. Chertkov, A. Gamba, I. Kolokolov
Phys. Lett. A 192 435 (1994)
[2] The Lyapunov spectrum of a continuous product of random matrices
A. Gamba, I. Kolokolov
J. Stat. Phys. 85, 489 (1996)
[3] Dissipation statistics of a passive scalar in a multidimensional smooth flow
A. Gamba, I. Kolokolov
J. Stat. Phys. 94, 759 (1999)
[4] Finite-time Lyapunov exponents for products of random transformations
A. Gamba
J. Stat. Phys. 112, 193-218 (2003)
[5] Large scale inhomogeneity of inertial particles in turbulent flow
G. Boffetta, F. De Lillo, A. Gamba
Phys., Fluids 16, L20 (2004)
Updated: Jul. 5, 2009