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We investigate the rate-length scaling law of protein folding, a key undetermined scaling law in the analytical theory of protein folding. We demonstrate that chain length is a dominant factor determining folding times, and that the…
We solve a model that takes into account entropic barriers, frustration, and the organization of a protein-like molecule. For a chain of size $M$, there is an effective folding transition to an ordered structure. Without frustration, this…
We present a simple model of protein folding dynamics that captures key qualitative elements recently seen in all-atom simulations. The goals of this theory are to serve as a simple formalism for gaining deeper insight into the physical…
A simplified interaction potential for protein folding studies at the atomic level is discussed and tested on a set of peptides with about 20 residues each. The test set contains both alpha-helical (Trp cage, Fs) and beta-sheet (GB1p,…
The motion involved in barrier crossing for protein folding are investigated in terms of the chain dynamics of the polymer backbone, completing the microscopic description of protein folding presented in the previous paper. Local reaction…
A four states phase diagram for protein folding as a function of temperature and solvent quality is derived from an improved 2-d lattice model taking into account the temperature dependence of the hydrophobic effect. The phase diagram…
Inverse protein folding is challenging due to its inherent one-to-many mapping characteristic, where numerous possible amino acid sequences can fold into a single, identical protein backbone. This task involves not only identifying viable…
Protein folding and design are major biophysical problems, the solution of which would lead to important applications especially in medicine. Here a novel protein model capable of simultaneously provide quantitative protein design and…
A new lattice protein model with a four-helix bundle ground state is analyzed by a parameter-space Monte Carlo histogram technique to evaluate the effects of an extensive variety of model potentials on folding thermodynamics. Cooperative…
A general theoretical framework is developed using free energy functional methods to understand the effects of heterogeneity in the folding of a well-designed protein. Native energetic heterogeneity arising from non-uniformity in native…
In the course of evolution, proteins undergo important changes in their amino acid sequences, while their three-dimensional folded structure and their biological function remain remarkably conserved. Thanks to modern sequencing techniques,…
The simulation of a protein's folding process is often done via stochastic local search, which requires a procedure to apply structural changes onto a given conformation. Here, we introduce a constraint-based approach to enumerate lattice…
Folding and aggregation of proteins, the interaction between proteins and membranes, as well as the adsorption of organic soft matter to inorganic solid substrates belong to the most interesting challenges in understanding structure and…
Novel numerical techniques, validated by an analysis of barnase and chymotrypsin inhibitor, are used to elucidate the paramount role played by the geometry of the protein backbone in steering the folding to the correct native state. It is…
Understanding protein folding has been one of the great challenges in biochemistry and molecular biophysics. Over the past 50 years, many thermodynamic and kinetic studies have been performed addressing the stability of globular proteins.…
These lectures will address two questions. Is there a simple variational principle underlying the existence of secondary motifs in the native state of proteins? Is there a general approach which can qualitatively capture the salient…
We consider equilibrium folding transitions in lattice protein models with and without side chains. A dimensionless measure, $Omega_{c}$, is introduced to quantitatively assess the degree of cooperativity in lattice models and in real…
The energy for protein folding arises from multiple sources and is not large in total. In spite of the many specific successes of energy landscape and other approaches, there still seems to be some missing guiding factor that explains how…
Natural protein sequences contain a record of their history. A common constraint in a given protein family is the ability to fold to specific structures, and it has been shown possible to infer the main native ensemble by analyzing…
In the framework of a lattice-model study of protein folding, we investigate the interplay between designability, thermodynamic stability, and kinetics. To be ``protein-like'', heteropolymers must be thermodynamically stable, stable against…