Information and redundancy in the burial folding code of globular proteins within a wide range of shapes and sizes.

Recent ab initio folding simulations for a limited number of small proteins have corroborated a previous suggestion that atomic burial information obtainable from sequence could be sufficient for tertiary structure determination when combined to sequence-independent geometrical constraints. Here, we use simulations parameterized by native burials to investigate the required amount of information in a diverse set of globular proteins comprising different structural classes and a wide size range. Burial information is provided by a potential term pushing each atom towards one among a small number L of equiprobable concentric layers. An upper bound for the required information is provided by the minimal number of layers L(min) still compatible with correct folding behavior. We obtain L(min) between 3 and 5 for seven small to medium proteins with 50 ≤ Nr ≤ 110 residues while for a larger protein with Nr = 141 we find that L ≥ 6 is required to maintain native stability. We additionally estimate the usable redundancy for a given L ≥ L(min) from the burial entropy associated to the largest folding-compatible fraction of "superfluous" atoms, for which the burial term can be turned off or target layers can be chosen randomly. The estimated redundancy for small proteins with L = 4 is close to 0.8. Our results are consistent with the above-average quality of burial predictions used in previous simulations and indicate that the fraction of approachable proteins could increase significantly with even a mild, plausible, improvement on sequence-dependent burial prediction or on sequence-independent constraints that augment the detectable redundancy during simulations.

Ab initio protein folding simulations using atomic burials as informational intermediates between sequence and structure.

The three-dimensional structure of proteins is determined by their linear amino acid sequences but decipherment of the underlying protein folding code has remained elusive. Recent studies have suggested that burials, as expressed by atomic distances to the molecular center, are sufficiently informative for structural determination while potentially obtainable from sequences. Here we provide direct evidence for this distinctive role of burials in the folding code, demonstrating that burial propensities estimated from local sequence can indeed be used to fold globular proteins in ab initio simulations. We have used a statistical scheme based on a Hidden Markov Model (HMM) to classify all heavy atoms of a protein into a small number of burial atomic types depending on sequence context. Molecular dynamics simulations were then performed with a potential that forces all atoms of each type towards their predicted burial level, while simple geometric constraints were imposed on covalent structure and hydrogen bond formation. The correct folded conformation was obtained and distinguished in simulations that started from extended chains for a selection of structures comprising all three folding classes and high burial prediction quality. These results demonstrate that atomic burials can act as informational intermediates between sequence and structure, providing a new conceptual framework for improving structural prediction and understanding the fundamentals of protein folding.

Protein folding cooperativity: basic insights from minimalist models.

Basic concepts about two-state, cooperative protein folding and its relation to first-order phase transitions are reviewed. Minimalist models capable of reproducing the required free energy barrier between folded and unfolded macroscopic states are described. A significantly more restrictive "calorimetric" criterion is also discussed, which is based on direct comparison between model and experimental heat capacities with additional assumptions about conformational enthalpy variation in the unfolded state.

Relevance of structural segregation and chain compaction for the thermodynamics of folding of a hydrophobic protein model.

The relevance of inside-outside segregation and chain compaction for the thermodynamics of folding of a hydrophobic protein model is probed by complete enumeration of two-dimensional chains of up to 18 monomers in the square lattice. The exact computation of Z scores for uniquely designed sequences confirms that Z tends to decrease linearly with sigma square root of N, as previously suggested by theoretical analysis and Monte Carlo simulations, where sigma, the standard deviation of the number of contacts made by different monomers in the target structure, is a measure of structural segregation and N is the chain length. The probability that the target conformation is indeed the unique global energy minimum of the designed sequence is found to increase dramatically with sigma, approaching unity at maximal segregation. However, due to the huge number of conformations with sub-maximal values of sigma, which correspond to intermediate, only mildly discriminative, values of Z, in addition to significant oscillations of Z around its estimated value, the probability that a correctly designed sequence corresponds to a maximally segregated conformation is small. This behavior of Z also explains the observed relation between sigma and different measures of folding cooperativity of correctly designed sequences.