Control of nonspecific protein adsorption is very important for the design of biocompatible and biomimetic materials as well as drug carriers. Grafted polymer layers can be used to prevent protein adsorption. We have studied the molecular factors that determine the equilibrium and kinetic control of protein adsorption by grafted polymer layers. We find that polymers that are not attracted to the surface are very effective for kinetic control but not very good for equilibrium reduction of protein adsorption. Polymers with attractions to the surface show exactly the opposite behavior. The implications for molecular design of biocompatible materials also are discussed in this paper. P rotein adsorption plays a major role in a variety of important biological-related processes. Biocompatible materials are required to eliminate, or largely reduce, the adsorption of blood proteins, for example, to avoid surface-induced thrombosis (1, 2). In recent years special attention has been given to the modification of protein-surface interactions using grafted polymers (3, 4, 5, 6). The idea, borrowed from many years of research in colloidal stabilization (7) and mimicking one of the roles of polysaccharides in cell membranes (8), is to build a steric barrier to the proteins by the presence of the polymer layer (9, 10). In practice, however, there is still no systematic way of modifying surfaces that are successful in preventing protein adsorption. This is because of the complexity involved in the process caused by the interplay between changing average structure of the polymer-protein layer, strong protein-surface attractions, and polymer-surface interactions (11). For example, liposomes † formed by mixtures of lipid and lipid-polymer have shown increased longevity in the bloodstream and are now being used as drug delivery systems (12, 13). It is believed that the role of the polymers tethered to the liposome interface is to present a steric barrier to approaching proteins from the blood. However, the amount of polymer on the surface is rather small, and experimental observations of the same polymer grafted on hydrophobic surfaces, at the same surface coverage, show that although the amount of protein adsorbed is lower than in the absence of polymer, there is still a significant amount of protein adsorption (14).In this paper we demonstrate that the molecular factors that determine the ability of the polymer layer to prevent protein adsorption are different for the kinetic control as compared with the equilibrium case. We will demonstrate that our theoretical predictions can quantitatively reproduce experimental observations of protein adsorption isotherms. We will show that surface-polymer interactions play a central role in the ability of the polymer layer to prevent protein adsorption. However, the role of those interactions is different for kinetic as compared with equilibrium control. Our findings enable us to rationalize why the surface-modified liposomes have an increased longevity but polymers on hydrophobic surfaces ar...

We propose a stochastic lattice gas model to describe the dynamics of two animal species population, one being a predator and the other a prey. This model comprehends the mechanisms of the Lotka-Volterra model. Our analysis was performed by using a dynamical mean-field approximation and computer simulations. Our results show that the system exhibits an oscillatory behavior of the population densities of prey and predators. For the sets of parameters used in our computer simulations, these oscillations occur at a local level. Mean-field results predict synchronized collective oscillations. 02.50.Ga,05.70.Ln Typeset using REVT E X

The kinetics of protein adsorption are studied using a generalized diffusion approach which shows that the time-determining step in the adsorption is the crossing of the kinetic barrier presented by the polymers and already adsorbed proteins. The potential of mean-force between the adsorbing protein and the polymer-protein surface changes as a function of time due to the deformation of the polymer layers as the proteins adsorb. Furthermore, the range and strength of the repulsive interaction felt by the approaching proteins increases with grafted polymer molecular weight and surface coverage. The effect of molecular weight on the kinetics is very complex and different than its role on the equilibrium adsorption isotherms. The very large kinetic barriers make the timescale for the adsorption process very long and the computational effort increases with time, thus, an approximate kinetic approach is developed. The kinetic theory is based on the knowledge that the time-determining step is crossing the potential-of-mean-force barrier. Kinetic equations for two states (adsorbed and bulk) are written where the kinetic coefficients are the product of the Boltzmann factor for the free energy of adsorption (desorption) multiplied by a preexponential factor determined from a Kramers-like theory. The predictions from the kinetic approach are in excellent quantitative agreement with the full diffusion equation solutions demonstrating that the two most important physical processes are the crossing of the barrier and the changes in the barrier with time due to the deformation of the polymer layer as the proteins adsorb/desorb. The kinetic coefficients can be calculated a priori allowing for systematic calculations over very long timescales. It is found that, in many cases where the equilibrium adsorption shows a finite value, the kinetics of the process is so slow that the experimental system will show no adsorption. This effect is particularly important at high grafted polymer surface coverage. The construction of guidelines for molecular weight/surface coverage necessary for kinetic prevention of protein adsorption in a desired timescale is shown. The time-dependent desorption is also studied by modeling how adsorbed proteins leave the surface when in contact with a pure water solution. It is found that the kinetics of desorption are very slow and depend in a nonmonotonic way in the polymer chain length. When the polymer layer thickness is shorter than the size of the protein, increasing polymer chain length, at fixed surface coverage, makes the desorption process faster. For polymer layers with thickness larger than the protein size, increases in molecular weight results in a longer time for desorption. This is due to the grafted polymers trapping the adsorbed proteins and slowing down the desorption process. These results offer a possible explanation to some experimental data on adsorption. Limitations and extension of the developed approaches for practical applications are discussed.

We have developed a top-down, rule-based mathematical model to explore the basic principles that coordinate mechanochemical events during animal cell migration, particularly the local-stimulation-global-inhibition model suggested originally for chemotaxis. Cells were modeled as a shape machine that protrudes or retracts in response to a combination of local protrusion and global retraction signals. Using an optimization algorithm to identify parameters that generate specific shapes and migration patterns, we show that the mechanism of local stimulation global inhibition can readily account for the behavior of Dictyostelium under a large collection of conditions. Within this collection, some parameters showed strong correlation, indicating that a normal phenotype may be maintained by complementation among functional modules. In addition, comparison of parameters for control and nocodazole-treated Dictyostelium identified the most prominent effect of microtubules as regulating the rates of retraction and protrusion signal decay, and the extent of global inhibition. Other changes in parameters can lead to profound transformations from amoeboid cells into cells mimicking keratocytes, neurons, or fibroblasts. Thus, a simple circuit of local stimulation-global inhibition can account for a wide range of cell behaviors. A similar top-down approach may be applied to other complex problems and combined with molecular manipulations to define specific protein functions.

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