Homopolymer adsorption on periodically structured surfaces in systems with incommensurable lengths.

Surface-induced selective adsorption of homopolymers on a generic level is numerically analyzed for freely jointed chains (with a fixed bond length) whose monomers are attracted by the sites of regular periodic patterns. In particular, the behavior of the specific heat, the gyration tensor, and the bond order tensor are investigated as functions of the temperature. The properties of the transition are related to the interplay of the characteristic lengths. The adsorption proceeds in two steps for certain incommensurabilities of the bond length and the lattice constant. The corresponding adsorption mechanisms are elucidated by looking at the evolution of the inter bond angle distribution upon adsorption. Moreover, the origin of two steps in contrast to adsorption in one step is traced back to entropic restrictions caused by a strongly reduced phase space of the polymer for certain values of the incommensurability.

Selective homopolymer adsorption on structured surfaces as a model for pattern recognition.

Homopolymer adsorption onto chemically structured periodic surfaces and its potential for pattern recognition is investigated using Monte Carlo simulations. To analyze the surface-induced selective adsorption on a fundamental geometric level polymer chains are represented by freely jointed chains with a fixed bond length whose monomers are attracted by the sites of regular lattice patterns. The structural properties of the adsorbed low-temperature state are comprehensively discussed for different lattices by looking at the radius of gyration and the inter bond angle distributions. These observables show a non-trivial dependence on the commensurability of characteristic lengths given by the lattice constant and by the bond length. Reasons for this behavior are given by exploiting geometric and entropic arguments. The findings are examined in the context of pattern recognition by polymer adsorption. Furthermore, the adsorption transition is discussed briefly. For certain incommensurable situations the adsorption occurs in two steps due to entropic restrictions.

Brownian dynamics simulations with hard-body interactions: spherical particles.

A novel approach to account for hard-body interactions in (overdamped) Brownian dynamics simulations is proposed for systems with non-vanishing force fields. The scheme exploits the analytically known transition probability for a Brownian particle on a one-dimensional half-line. The motion of a Brownian particle is decomposed into a component that is affected by hard-body interactions and into components that are unaffected. The hard-body interactions are incorporated by replacing the "affected" component of motion by the evolution on a half-line. It is discussed under which circumstances this approach is justified. In particular, the algorithm is developed and formulated for systems with space-fixed obstacles and for systems comprising spherical particles. The validity and justification of the algorithm is investigated numerically by looking at exemplary model systems of soft matter, namely at colloids in flow fields and at protein interactions. Furthermore, a thorough discussion of properties of other heuristic algorithms is carried out.

Hard-wall interactions in soft matter systems: exact numerical treatment.

An algorithm for handling hard-wall interactions in simulations of driven diffusive particle motion is proposed. It exploits an exact expression for the one-dimensional transition probability in the presence of a hard (reflecting) wall and therefore is numerically exact in the sense that it does not introduce any additional approximation beyond the usual discretization procedures. Studying two standard situations from soft matter systems, its performance is compared to the heuristic approaches used in the literature.

Dry and wet interfaces: influence of solvent particles on molecular recognition.

We present a coarse-grained lattice model to study the influence of water on the recognition process of two rigid proteins. The basic model is formulated in terms of the hydrophobic effect. We then investigate several modifications of our basic model showing that the selectivity of the recognition process can be enhanced by considering the explicit influence of single solvent particles. When the number of cavities at the interface of a protein-protein complex is fixed as an intrinsic geometric constraint, there typically exists a characteristic fraction that should be filled with water molecules such that the selectivity exhibits a maximum. In addition, the optimum fraction depends on the hydrophobicity of the interface so that one has to distinguish between dry and wet interfaces.

Influence of correlations on molecular recognition.

The influence of the patchiness and correlations in the distribution of hydrophobic and polar residues at the interface between two rigid biomolecules on their recognition ability is investigated in idealized coarse-grained lattice models. A general two-stage approach is utilized where an ensemble of probe molecules is designed first and the recognition ability of the probe ensemble is related to the free energy of association with both the target molecule and a different rival molecule in a second step. The influence of correlation effects are investigated using numerical Monte Carlo techniques and mean field methods. Correlations lead to different optimum characteristic lengths of the hydrophobic and polar patches for the mutual design of the two biomolecules on the one hand and their recognition ability in the presence of other molecules on the other hand.

Coarse-grained lattice model for investigating the role of cooperativity in molecular recognition.

Equilibrium aspects of the molecular recognition of rigid biomolecules are investigated using coarse-grained lattice models. The analysis is carried out in two stages. First, an ensemble of probe molecules is designed with respect to the target biomolecule. The recognition ability of the probe ensemble is then investigated by calculating the free energy of association. The influence of cooperative and anticooperative effects accompanying the association of the target and probe molecules is studied. Numerical findings are presented and compared to analytical results which can be obtained in the limit of dominating cooperativity and in the mean-field formulation of the models.

Developing and analyzing idealized models for molecular recognition.

We study equilibrium aspects of molecular recognition of two biomolecules using idealized model systems and methods from statistical physics. Starting from the basic experimental findings we demonstrate exemplarily how an idealized coarse-grained model for the investigation of molecular recognition of two biomolecules can be developed. In addition we provide details regarding two model systems for the recognition of a flexible and a rigid biomolecule respectively, the latter taking into account conformational changes. We focus particularly on the interplay and influence of the correlations of the residue distributions of the biomolecules on the recognition process.

Coarse-grained lattice model for molecular recognition.

We present a simple model which allows us to investigate the equilibrium aspects of molecular recognition between rigid biomolecules on a generic level. Using a two-stage approach, which consists of a design and a testing step, the role of cooperativity and of varying bond strength in molecular recognition is investigated. Cooperativity is found to enhance selectivity. In complexes which require a high binding flexibility, a small number of strong bonds seems to be favored compared to a situation with many but weak bonds.

Continuous phase transitions with a convex dip in the microcanonical entropy.

The appearance of a convex dip in the microcanonical entropy of finite systems usually signals a first order transition. However, a convex dip also shows up in some systems with a continuous transition as, for example, in the Baxter-Wu model and in the four-state Potts model in two dimensions. We demonstrate that the appearance of a convex dip in those cases can be traced back to a finite-size effect. The properties of the dip are markedly different from those associated with a first order transition and can be understood within a microcanonical finite-size scaling theory for continuous phase transitions. Results obtained from numerical simulations corroborate the predictions of the scaling theory.