Andrea Antonio Gamba

Modeling the early stages of vascular network assembly

In vertebrates, networks of capillary vessels supply tissues with nutrients. Capillary patterns are closely mimicked by endothelial cells cultured on basement membrane proteins that allow single randomly dispersed cells to self‐organize into vascular networks. Here we provide a model including chemoattraction as the fundamental mechanism for cell‐to‐cell communication in order to identify key parameters in the complexity of the formation of vascular patterns. By flanking biological experiments, theoretical insights and numerical simulations, we provide strong evidence that endothelial cell number and the range of activity of a chemoattractant factor regulate vascular network formation and size. We propose a mechanism linking the scale of formed endothelial structures to the range of cell‐to‐cell interaction mediated by the release of chemoattractants.

Percolation, Morphogenesis, and Burgers Dynamics in Blood Vessels Formation

Experiments of in vitro formation of blood vessels show that cells randomly spread on a gel matrix autonomously organize to form a connected vascular network. We propose a simple model which reproduces many features of the biological system. We show that both the model and the real system exhibit a fractal behavior at small scales, due to the process of migration and dynamical aggregation, followed at large scale by a random percolation behavior due to the coalescence of aggregates. The results are in good agreement with the analysis performed on the experimental data.

Large scale inhomogeneity of inertial particles in turbulent flows

Preferential concentration of inertial particles in turbulent flow is studied by high resolution direct numerical simulations of two-dimensional turbulence. The formation of network-like regions of high particle density, characterized by a length scale which depends on the Stokes number of inertial particles, is observed. At smaller scales, the size of empty regions appears to be distributed according to a universal scaling law.

A bistable model of cell polarity

Ultrasensitivity, as described by Goldbeter and Koshland, has been considered for a long time as a way to realize bistable switches in biological systems. It is not as well recognized that when ultrasensitivity and reinforcing feedback loops are present in a spatially distributed system such as the cell plasmamembrane, they may induce bistability and spatial separation of the system into distinct signaling phases. Here we suggest that bistability of ultrasensitive signaling pathways in a diffusive environment provides a basic mechanism to realize cell membrane polarity. Cell membrane polarization is a fundamental process implicated in several basic biological phenomena, such as differentiation, proliferation, migration and morphogenesis of unicellular and multicellular organisms. We describe a simple, solvable model of cell membrane polarization based on the coupling of membrane diffusion with bistable enzymatic dynamics. The model can reproduce a broad range of symmetry-breaking events, such as those observed in eukaryotic directional sensing, the apico-basal polarization of epithelium cells, the polarization of budding and mating yeast, and the formation of Ras nanoclusters in several cell types.

Polarity, cell division, and out-of-equilibrium dynamics control the growth of epithelial structures

The growth of a well-formed epithelial structure is governed by mechanical constraints, cellular apico-basal polarity, and spatially controlled cell division. Here we compared the predictions of a mathematical model of epithelial growth with the morphological analysis of 3D epithelial structures. In both in vitro cyst models and in developing epithelial structures in vivo, epithelial growth could take place close to or far from mechanical equilibrium, and was determined by the hierarchy of time-scales of cell division, cell-cell rearrangements, and lumen dynamics. Equilibrium properties could be inferred by the analysis of cell-cell contact topologies, and the nonequilibrium phenotype was altered by inhibiting ROCK activity. The occurrence of an aberrant multilumen phenotype was linked to fast nonequilibrium growth, even when geometric control of cell division was correctly enforced. We predicted and verified experimentally that slowing down cell division partially rescued a multilumen phenotype induced by altered polarity. These results improve our understanding of the development of epithelial organs and, ultimately, of carcinogenesis

Unraveling the influence of endothelial cell density on VEGF-A signaling

Vascular endothelial growth factor-A (VEGF) is the master determinant for the activation of the angiogenic program leading to the formation of new blood vessels to sustain solid tumor growth and metastasis. VEGF specific binding to VEGF receptor-2 (VEGFR-2) triggers different signaling pathways, including phospholipase C-γ (PLC-γ) and Akt cascades, crucial for endothelial proliferation, permeability, and survival. By combining biologic experiments, theoretical insights, and mathematical modeling, we found that: (1) cell density influences VEGFR-2 protein level, as receptor number is 2-fold higher in long-confluent than in sparse cells; (2) cell density affects VEGFR-2 activation by reducing its affinity for VEGF in long-confluent cells; (3) despite reduced ligand-receptor affinity, high VEGF concentrations provide long-confluent cells with a larger amount of active receptors; (4) PLC-γ and Akt are not directly sensitive to cell density but simply transduce downstream the upstream difference in VEGFR-2 protein level and activation; and (5) the mathematical model correctly predicts the existence of at least one protein tyrosine phosphatase directly targeting PLC-γ and counteracting the receptor-mediated signal. Our data-based mathematical model quantitatively describes VEGF signaling in quiescent and angiogenic endothelium and is suitable to identify new molecular determinants and therapeutic targets.

Exact field-theoretical description of passive scalar convection in an N-dimensional long-range velocity field

We describe a new functional integral method for the computation of averages containing chronological exponentials of random matrices of arbitrary dimension. We apply these results to the rigorous study of the statistics of a passive scalar advected by a large-scale N-dimensional flow. In the delta-correlated case the statistics of the rate of line stretching appears to be exactly Gaussian at all times and we explicitly compute the dependence of the mean value and variance of the stretching rate on the space dimension N. The probability distribution function of the passive scalar is also exactly computed. Further applications of our functional integral method are suggested.

Universal features of cell polarization processes.

Cell polarization plays a central role in the development of complex organisms. It has been recently shown that cell polarization may follow from the proximity to a phase separation instability in a bistable network of chemical reactions. An example which has been thoroughly studied is the formation of signaling domains during eukaryotic chemotaxis. In this case, the process of domain growth may be described by the use of a constrained time-dependent Landau–Ginzburg equation, admitting scale-invariant solutions a la Lifshitz and Slyozov. The constraint results here from a mechanism of fast cycling of molecules between a cytosolic, inactive state and a membrane-bound, active state, which dynamically tunes the chemical potential for membrane binding to a value corresponding to the coexistence of different phases on the cell membrane. We provide here a universal description of this process both in the presence and in the absence of a gradient in the external activation field. Universal power laws are derived for the time needed for the cell to polarize in a chemotactic gradient, and for the value of the smallest detectable gradient. We also describe a concrete realization of our scheme based on the analysis of available biochemical and biophysical data.

Donaldson-Witten invariants and pure 4D QCD with order and disorder 't Hooft-like operators

We study the first-order formalism of pure four-dimensional SU(2) Yang–Mills theory with theta-term. We describe the Green functions associated to electric and magnetic flux operators à la ’t Hooft by means of gauge-invariant non-local operators. These Green functions are related to Witten’s invariants of four-manifolds. E-mail: cattaneo@vaxmi.mi.infn.it 2 E-mail: cotta@vaxmi.mi.infn.it E-mail: gamba@pol88a.polito.it 4 Partially supported by EEC Science Project n. CHRX-CT93-0362. E-mail: martellini@vaxmi.mi.infn.it

Dissipation Statistics of a Passive Scalar in a Multidimensional Smooth Flow

AbstractWe compute analytically the probability distribution function