High affinity extremes in combinatorial libraries and repertoires

Hierarchy and extremes in selections from pools of randomized proteins

Variation and selection are the core principles of Darwinian evolution, but quantitatively relating the diversity of a population to its capacity to respond to selection is challenging. Here, we examine this problem at a molecular level in the context of populations of partially randomized proteins selected for binding to well-defined targets. We built several minimal protein libraries, screened them in vitro by phage display, and analyzed their response to selection by high-throughput sequencing. A statistical analysis of the results reveals two main findings. First, libraries with the same sequence diversity but built around different "frameworks" typically have vastly different responses; second, the distribution of responses of the best binders in a library follows a simple scaling law. We show how an elementary probabilistic model based on extreme value theory rationalizes the latter finding. Our results have implications for designing synthetic protein libraries, estimating the density of functional biomolecules in sequence space, characterizing diversity in natural populations, and experimentally investigating evolvability (i.e., the potential for future evolution).

The universal statistical distributions of the affinity, equilibrium constants, kinetics and specificity in biomolecular recognition

We uncovered the universal statistical laws for the biomolecular recognition/binding process. We quantified the statistical energy landscapes for binding, from which we can characterize the distributions of the binding free energy (affinity), the equilibrium constants, the kinetics and the specificity by exploring the different ligands binding with a particular receptor. The results of the analytical studies are confirmed by the microscopic flexible docking simulations. The distribution of binding affinity is Gaussian around the mean and becomes exponential near the tail. The equilibrium constants of the binding follow a log-normal distribution around the mean and a power law distribution in the tail. The intrinsic specificity for biomolecular recognition measures the degree of discrimination of native versus non-native binding and the optimization of which becomes the maximization of the ratio of the free energy gap between the native state and the average of non-native states versus the roughness measured by the variance of the free energy landscape around its mean. The intrinsic specificity obeys a Gaussian distribution near the mean and an exponential distribution near the tail. Furthermore, the kinetics of binding follows a log-normal distribution near the mean and a power law distribution at the tail. Our study provides new insights into the statistical nature of thermodynamics, kinetics and function from different ligands binding with a specific receptor or equivalently specific ligand binding with different receptors. The elucidation of distributions of the kinetics and free energy has guiding roles in studying biomolecular recognition and function through small-molecule evolution and chemical genetics.

Uncovering the principles and underlying mechanisms of biomolecular recognition and molecular binding process is crucial for understanding the function and evolution, yet challenging. We meet the challenge by quantifying the statistical natures of the relevant physical variables of biomolecular recognition using the analytical model combined with microscopic flexible docking simulation methods. We uncovered the universal statistical laws obeyed by the affinity, equilibrium constant, intrinsic specificity and kinetics for biomolecular recognition. The general statistical laws based on energy landscape theory can serve as a conceptual framework for molecular recognition in biological repertoires. They can be applied to molecular selection, in vitro evolution process, high throughput screening and virtual screening for drug discovery. The statistical laws in combinations with experiments provide quantitative signatures of a specific ligand binding to a specific receptor, these resultant laws as a guideline will contribute to drug design against a specific target. Our developed statistical methodology is general and applicable for all other biomolecular recognitions.