Statistical models for experimental model membranes.

Biological membranes are constituted from lipid bilayers and proteins. Investigation of protein-membrane interaction, essential for biological function of cells, must rest upon solid knowledge of lipid bilayer behavior. Thus, extensive studies of an experimental model for membranes, lipid bilayers in water solution, have been undertaken in the last decades. These systems present structural, thermal and electrical properties which depend on temperature, ionic strength or concentration. In this talk, we shall discuss statistical models for lipid bilayers, as well as the relation between their properties and results for properties of lipid dispersions investigated by the laboratories supervised by Teresa Lamy (IF-USP) and Amando Ito (FFCL-USP)

Rotational diffusion membrane and fluorescence anisotropy.

Structural properties of model membranes, such as lipid vesicles, may be investigated through the addition of fluorescent probes. After incorporation, the fluorescent molecules are excited with linearly polarized light and the fluorescence emission is depolarized due to translational as well as rotational diffusion during the lifetime of the excited state. The monitoring of emitted light is undertaken through the technique of time-resolved fluorescence: the intensity of the emitted light informs on fluorescence decay times, and the decay of the components of the emitted light yield rotational correlation times which inform on the fluidity of the medium. The fluorescent molecule DPH, of uniaxial symmetry, is rather hydrophobic and has collinear transition and emission moments. It has been used frequently as a probe for the monitoring of the fluidity of the lipid bilayer along the phase transition of the chains. The interpretation of experimental data requires models for localization of fluorescent molecules as well as for possible restrictions on their movement. In this study, we develop calculations for two models for uniaxial diffusion of fluorescent molecules, such as DPH, suggested in several articles in the literature. A zeroth order test model consists of a free randomly rotating dipole in a homogeneous solution, and serves as the basis for the study of the diffusion of models in anisotropic media. In the second model, we consider random rotations of emitting dipoles distributed within cones with their axes perpendicular to the vesicle spherical geometry. In the third model, the dipole rotates in the plane of the of bilayer spherical geometry, within a movement that might occur between the monolayers forming the bilayer. For each of the models analysed, two methods are used by us in order to analyse the rotational diffusion: (I) solution of the corresponding rotational diffusion equation for a single molecule, taking into account the boundary conditions imposed by the models, for the probability of the fluorescent molecule to be found with a given configuration at time t. Considering the distribution of molecules in the geometry proposed, we obtain the analytical expression for the fluorescence anisotropy, except for the cone geometry, for which the solution is obtained numerically; (II) numerical simulations of a restricted rotational random walk in the two geometries corresponding to the two models. The latter method may be very useful in the cases of low-symmetry geometries or of composed geometries

Compressible Ising model - elastic fluctuations and magnetic transition order

Neste trabalho, estuda-se o comportamento crítico de spins de Ising colocados em três tipos de rede elástica: uma rede rígida de volume variável (Ll): uma rede cujas posições dos íons podem variar, sem tensão de cisalhamento (L2); uma rede do tipo \"colchão de molas\", com acoplamento elástico entre primeiros e segundos vizinhos (L3). Verificamos que o acoplamento spin-rede pode ser simulado por uma interação efetiva de longo alcance entre pares de spins, em vários casos. Nas hamiltonianas correspondentes, a integral de troca dos spins é considerada linearmente dependente da distância inter-iônica e a interação elástica é considerada apenas na aproximação harmônica. Mostramos que o coeficiente do termo de quatro spins, que representa a interação magneto-elástica na hamiltoniana efetiva de spins, tem sinal diferente para as flutuações elásticas microscópicas (na posição dos íons) e macroscópicas (de volume). O efeito dessa interação efetiva é alterar os expoentes críticos da transição magnética no primeiro caso, renormalizando-os, e transformar a transição contínua em uma transição de primeira ordem, no segundo caso. Em um sistema real, ambos os tipos de flutuação estão presentes e os dois efeitos competem entre si para determinar a ordem da transição. No modelo (L3), o mais \"realista\" entre os três estudados, os efeitos de volume predominam. Entretanto, não é possível fazer previsões para outros modelos específicos, pois os dois efeitos são da mesma ordem de grandeza. Estudamos, ainda, o efeito sobre a hamiltoniana efetiva de spins de se alterar as condições de contorno, assim como de se alterar o valor do spin, no caso do segundo modelo (L2 ). Para prever a ordem da transição, as hamiltonianas efetivas de spin são analisadas no contexto de campo médio, de grupo de renormalização e de uma solução exata em duas dimensões.We study the critical behavior of Ising S=1/2 spins on three compressible lattices: a compressible but rigid lattice (Ll): an elastic lattice without shearing forces (L2) and a \"spring mattress\", with elastic couplings between nearest and next-nearest neighbors (L3). The corresponding hamiltonians contain an exchange interaction linearly dependent on the interionic distance and an elastic interaction considered in the harmonic approximation. We show that both pure macroscopic (volume) and pure microscopic (ion position) fluctuations lead to a pair-pair interaction term in the effective spin hamiltonian. However, the coefficient of this additional term is negative in the first case, which turns the transition first order, and positive in the second case, which renormalizes the critical exponents. In a real system, both kinds of fluctuation are present and the two effects will compete. Model (L3), the closest to the above condition, has the volume effect as predominant. The delicate balance between the competing effects of the same order of magnitude forbid a prediction for other models. We also show that different effective spin Hamiltonians may be arrived at according to the choice of boundary condition of or ensemble. In one case (L2), we also consider spin S =1. We use mean-field, an exact solution for dimensionalty two and momentum space renormalization group to predict the order of the transitions

Compressible Ising model - elastic fluctuations and magnetic transition order

Neste trabalho, estuda-se o comportamento crítico de spins de Ising colocados em três tipos de rede elástica: uma rede rígida de volume variável (Ll): uma rede cujas posições dos íons podem variar, sem tensão de cisalhamento (L2); uma rede do tipo \"colchão de molas\", com acoplamento elástico entre primeiros e segundos vizinhos (L3). Verificamos que o acoplamento spin-rede pode ser simulado por uma interação efetiva de longo alcance entre pares de spins, em vários casos. Nas hamiltonianas correspondentes, a integral de troca dos spins é considerada linearmente dependente da distância inter-iônica e a interação elástica é considerada apenas na aproximação harmônica. Mostramos que o coeficiente do termo de quatro spins, que representa a interação magneto-elástica na hamiltoniana efetiva de spins, tem sinal diferente para as flutuações elásticas microscópicas (na posição dos íons) e macroscópicas (de volume). O efeito dessa interação efetiva é alterar os expoentes críticos da transição magnética no primeiro caso, renormalizando-os, e transformar a transição contínua em uma transição de primeira ordem, no segundo caso. Em um sistema real, ambos os tipos de flutuação estão presentes e os dois efeitos competem entre si para determinar a ordem da transição. No modelo (L3), o mais \"realista\" entre os três estudados, os efeitos de volume predominam. Entretanto, não é possível fazer previsões para outros modelos específicos, pois os dois efeitos são da mesma ordem de grandeza. Estudamos, ainda, o efeito sobre a hamiltoniana efetiva de spins de se alterar as condições de contorno, assim como de se alterar o valor do spin, no caso do segundo modelo (L2 ). Para prever a ordem da transição, as hamiltonianas efetivas de spin são analisadas no contexto de campo médio, de grupo de renormalização e de uma solução exata em duas dimensões.We study the critical behavior of Ising S=1/2 spins on three compressible lattices: a compressible but rigid lattice (Ll): an elastic lattice without shearing forces (L2) and a \"spring mattress\", with elastic couplings between nearest and next-nearest neighbors (L3). The corresponding hamiltonians contain an exchange interaction linearly dependent on the interionic distance and an elastic interaction considered in the harmonic approximation. We show that both pure macroscopic (volume) and pure microscopic (ion position) fluctuations lead to a pair-pair interaction term in the effective spin hamiltonian. However, the coefficient of this additional term is negative in the first case, which turns the transition first order, and positive in the second case, which renormalizes the critical exponents. In a real system, both kinds of fluctuation are present and the two effects will compete. Model (L3), the closest to the above condition, has the volume effect as predominant. The delicate balance between the competing effects of the same order of magnitude forbid a prediction for other models. We also show that different effective spin Hamiltonians may be arrived at according to the choice of boundary condition of or ensemble. In one case (L2), we also consider spin S =1. We use mean-field, an exact solution for dimensionalty two and momentum space renormalization group to predict the order of the transitions

The degree of polydispersity in micellar dispersions: A sum rule approach

Statistical properties of a two-dimensional ideal dispersion of polydisperse micelles are derived by analyzing the convergence properties of a sum rule set by mass conservation. Internal micellar degrees of freedom are accounted for by a microscopic model describing small displacements of the constituting amphiphiles with respect to their equilibrium positions. The transfer matrix (TM) method is employed to compute internal micelle partition function. We show that the conditions under which the sum rule is saturated by the largest eigenvalue of the TM determine the value of amphiphile concentration above which the dispersion becomes highly polydisperse and micelle sizes approach a Schultz distribution. (C) 2011 Elsevier B.V. All rights reserved.Brazilian agency CNPqConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Brazilian agency FAPESPFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP

Liquid polymorphism and density anomaly in a lattice gas model

We present a simple model for an associating liquid in which polymorphism and density anomaly are connected. Our model combines a two dimensional lattice gas with particles interacting through a soft core potential and orientational degrees of freedom represented through thermal “ice variables.” The competition between the directional attractive forces and the soft core potential leads to a phase diagram in which two liquid phases and a density anomaly are present. The coexistence line between the low density liquid and the high density liquid has a positive slope contradicting the surmise that the presence of a density anomaly implies that the high density liquid is more entropic than the low density liquid

Liquid polymorphism and density anomaly in a lattice gas model

We present a simple model for an associating liquid in which polymorphism and density anomaly are connected. Our model combines a two dimensional lattice gas with particles interacting through a soft core potential and orientational degrees of freedom represented through thermal “ice variables.” The competition between the directional attractive forces and the soft core potential leads to a phase diagram in which two liquid phases and a density anomaly are present. The coexistence line between the low density liquid and the high density liquid has a positive slope contradicting the surmise that the presence of a density anomaly implies that the high density liquid is more entropic than the low density liquid