Quantifying density fluctuations in volumes of all shapes and sizes using indirect umbrella sampling

Water density fluctuations are an important statistical mechanical observable that is related to many-body correlations, as well as hydrophobic hydration and interactions. Local water density fluctuations at a solid-water surface have also been proposed as a measure of its hydrophobicity. These fluctuations can be quantified by calculating the probability, $P_v(N)$, of observing $N$ waters in a probe volume of interest $v$. When $v$ is large, calculating $P_v(N)$ using molecular dynamics simulations is challenging, as the probability of observing very few waters is exponentially small, and the standard procedure for overcoming this problem (umbrella sampling in $N$) leads to undesirable impulsive forces. Patel et al. [J. Phys. Chem. B, 114, 1632 (2010)] have recently developed an indirect umbrella sampling (INDUS) method, that samples a coarse-grained particle number to obtain $P_v(N)$ in cuboidal volumes. Here, we present and demonstrate an extension of that approach to other basic shapes, like spheres and cylinders, as well as to collections of such volumes. We further describe the implementation of INDUS in the NPT ensemble and calculate $P_v(N)$ distributions over a broad range of pressures. Our method may be of particular interest in characterizing the hydrophobicity of interfaces of proteins, nanotubes and related systems.Comment: 11 pages, 6 figure

Effects of lengthscales and attractions on the collapse of hydrophobic polymers in water

We present results from extensive molecular dynamics simulations of collapse transitions of hydrophobic polymers in explicit water focused on understanding effects of lengthscale of the hydrophobic surface and of attractive interactions on folding. Hydrophobic polymers display parabolic, protein-like, temperature-dependent free energy of unfolding. Folded states of small attractive polymers are marginally stable at 300 K, and can be unfolded by heating or cooling. Increasing the lengthscale or decreasing the polymer-water attractions stabilizes folded states significantly, the former dominated by the hydration contribution. That hydration contribution can be described by the surface tension model, $\Delta G=\gamma (T)\Delta A$, where the surface tension, $\gamma$, is lengthscale dependent and decreases monotonically with temperature. The resulting variation of the hydration entropy with polymer lengthscale is consistent with theoretical predictions of Huang and Chandler (Proc. Natl. Acad. Sci.,97, 8324-8327, 2000) that explain the blurring of entropy convergence observed in protein folding thermodynamics. Analysis of water structure shows that the polymer-water hydrophobic interface is soft and weakly dewetted, and is characterized by enhanced interfacial density fluctuations. Formation of this interface, which induces polymer folding, is strongly opposed by enthalpy and favored by entropy, similar to the vapor-liquid interface.Comment: 24 pages, 5 figure

Origin of entropy convergence in hydrophobic hydration and protein folding

An information theory model is used to construct a molecular explanation why hydrophobic solvation entropies measured in calorimetry of protein unfolding converge at a common temperature. The entropy convergence follows from the weak temperature dependence of occupancy fluctuations for molecular-scale volumes in water. The macroscopic expression of the contrasting entropic behavior between water and common organic solvents is the relative temperature insensitivity of the water isothermal compressibility. The information theory model provides a quantitative description of small molecule hydration and predicts a negative entropy at convergence. Interpretations of entropic contributions to protein folding should account for this result.Comment: Phys. Rev. Letts. (in press 1996), 3 pages, 3 figure

Nature inspired antibody design and optimization

The biotech industry has seen an explosion in the development of therapeutic antibodies in the last decade. The advantages of antibodies as therapeutics – namely their high affinity, specificity, potency, stability, manufacturability and low toxicity – are compelling. Nevertheless, there are many challenges associated with antibody discovery and development that require key technical advances to improve the rational and reliable generation of potent antibody therapeutics. We have made three key discoveries that address some of these fundamental challenges related to the design and selection of antibodies with high affinity, specificity, stability and solubility. First, we find that the accumulation of affinity-enhancing mutations in the complementaritydetermining regions (CDRs) during affinity maturation is often a destabilizing process. Surprisingly, mutations that enhance antibody binding affinity are commonly destabilizing. Second, we have developed novel yeast surface display methods for co-evolving antibody affinity and stability to address the general problem of antibody destabilization during affinity maturation. Our approach simultaneously evaluates antibody binding to both antigen and a conformational ligand that acts as a folding sensor to rapidly identify sets of mutations that promote both high antibody affinity and stability. This methodology has enabled us to identify novel compensatory mutations that offset the destabilizing effects of affinity-enhancing mutations and lead to affinitymaturated antibodies with high thermodynamic stability. Interestingly, our directed evolution method appears to mimic some aspects of natural antibody evolution, as natural antibodies also accumulate similar types of compensatory mutations to maintain thermodynamic stability during in vivo affinity maturation. Third, we have developed novel antibody library design and selection methods for generating antibodies with high specificity. It is common for antibody specificity to be compromised during in vitro affinity maturation. We have developed innovative methods for designing antibody libraries based on natural antibody diversity to simultaneously sample residues at many sites in the CDRs and framework regions that are most likely to promote high specificity. By coupling these nature-inspired antibody libraries with novel positive and negative selection methods, we have isolated antibodies with specificities that rival those of natural antibodies and which are much higher than typical antibodies identified using in vitro selection methods. Interestingly, we find that antibodies with improved specificity also possess excellent biophysical properties, including high solubility and stability. We are currently using computational methods to understand how rare antibody variants are able to maintain high specificity and stability during affinity maturation. Our long-term goal is to develop systematic and robust design methods to rapidly generate and optimize antibodies for use in a range of diagnostic and therapeutic applications

Sitting at the edge: How biomolecules use hydrophobicity to tune their interactions and function

Water near hydrophobic surfaces is like that at a liquid-vapor interface, where fluctuations in water density are substantially enhanced compared to that in bulk water. Here we use molecular simulations with specialized sampling techniques to show that water density fluctuations are similarly enhanced, even near hydrophobic surfaces of complex biomolecules, situating them at the edge of a dewetting transition. Consequently, water near these surfaces is sensitive to subtle changes in surface conformation, topology, and chemistry, any of which can tip the balance towards or away from the wet state, and thus significantly alter biomolecular interactions and function. Our work also resolves the long-standing puzzle of why some biological surfaces dewet and other seemingly similar surfaces do not.Comment: 12 pages, 4 figure