Frozen states of a disordered globular heteropolymer

The statistics of unique native states for random peptides

Given a probability distribution from which the energy spectrum of a random peptide is to be sampled, we derive a general expression for the probability that such a peptide will fold to a unique native state and for the probability distribution of the native energy. This latter result allows us to localize the energy of folding based on model parameters and is one advantage of our formulation. Evidence from both the lattice theory of proteins and protein threading experiments suggest that the energy spectrum for the compact states of a peptide chain is Gaussian in form. For this reason we have derived from the more general framework the specific formulas that apply in the Gaussian case, where one requires only the number of states and the variance of the Gaussian distribution in order to apply the theory. This simplicity allows us to perform calculations that we compare with calculations previously made by others based on statistical thermodynamics. We find qualitative agreement, but a significant correction to prior estimates of folding probability derived from the Gaussian assumption is necessary.

The nature of folded states of globular proteins

We suggest, using dynamical simulations of a simple heteropolymer modelling the alpha-carbon sequence in a protein, that generically the folded states of globular proteins correspond to statistically well-defined metastable states. This hypothesis, called the metastability hypothesis, states that there are several free energy minima separated by barriers of various heights such that the folded conformations of a polypeptide chain in each of the minima have similar structural characteristics but have different energies from one another. The calculated structural characteristics, such as bond angle and dihedral angle distribution functions, are assumed to arise from only those configurations belonging to a given minimum. The validity of this hypothesis is illustrated by simulations of a continuum model of a heteropolymer whose low temperature state is a well-defined beta-barrel structure. The simulations were done using a molecular dynamics algorithm (referred to as the "noisy" molecular dynamics method) containing both friction and noise terms. It is shown that for this model there are several distinct metastable minima in which the structural features are similar. Several new methods of analyzing fluctuations in structures belonging to two distinct minima are introduced. The most notable one is a dynamic measure of compactness that can in principle provide the time required for maximal compactness to be achieved. The analysis shows that for a given metastable state in which the protein has a well-defined folded structure the transition to a state of higher compactness occurs very slowly, lending credence to the notion that the system encounters a late barrier in the process of folding to the most compact structure. The examination of the fluctuations in the structures near the unfolding----folding transition temperature indicates that the transition state for the unfolding to folding process occurs closer to the folded state.

Generalized protein tertiary structure recognition using associative memory Hamiltonians

In previous papers, a method of protein tertiary structure recognition was described based on the construction of an associative memory Hamiltonian, which encoded the amino acid sequence and the C alpha co-ordinates of a set of database proteins. Using molecular dynamics with simulated annealing, the ability of the Hamiltonian to successfully recall the structure of a protein in the memory database was successfully demonstrated, as long as the total number of database proteins did not exceed a characteristic value, called the capacity of the Hamiltonian, equal to 0.5N to 0.7N, where N is the number of amino acid residues in the protein to be recalled. In this paper, we describe the development of additional methods to increase the capacity of the Hamiltonian, including use of a more complete representation of the protein backbone and the incorporation of contextual information into the Hamiltonian through the use of secondary structure prediction. In addition, we further extend the ability of associative memory models to predict the tertiary structures of proteins not present in the protein data set, by making the Hamiltonian invariant with respect to biological symmetries that represent site mutations and insertions and deletions. The ability of the Hamiltonian to generalize from homologous proteins to an unknown protein in the presence of other unrelated proteins in the data set is demonstrated.

Theory of molecular machines. I. Channel capacity of molecular machines

Like macroscopic machines, molecular-sized machines are limited by their material components, their design, and their use of power. One of these limits is the maximum number of states that a machine can choose from. The logarithm to the base 2 of the number of states is defined to be the number of bits of information that the machine could "gain" during its operation. The maximum possible information gain is a function of the energy that a molecular machine dissipates into the surrounding medium (Py), the thermal noise energy which disturbs the machine (Ny) and the number of independently moving parts involved in the operation (dspace): Cy = dspace log2 [( Py + Ny)/Ny] bits per operation. This "machine capacity" is closely related to Shannon's channel capacity for communications systems. An important theorem that Shannon proved for communication channels also applies to molecular machines. With regard to molecular machines, the theorem states that if the amount of information which a machine gains is less than or equal to Cy, then the error rate (frequency of failure) can be made arbitrarily small by using a sufficiently complex coding of the molecular machine's operation. Thus, the capacity of a molecular machine is sharply limited by the dissipation and the thermal noise, but the machine failure rate can be reduced to whatever low level may be required for the organism to survive.

Formation of unique structure in polypeptide chains. Theoretical investigation with the aid of a replica approach

A replica approach analogous to that used in spin glass systems is implemented to study the configurational space of a heteropolymeric model of protein with a quenched, disordered sequence of links in the limit of a large number of link types. It is shown that there exists a threshold value of chain heterogeneity which separates two qualitatively different types of behavior. For a low degree of heterogeneity the protein globule is like a homopolymer in a collapsed state without definite chain folds: an exponentially large number of folds make a significant contribution to the partition function in this regime. After the threshold heterogeneity has been overcome, the chain freezes drastically but without latent heat; few (approx. 1) frozen states with definite chain folds are thermodynamically dominant in this state. The relation of these results to thermodynamic aspects of protein folding is discussed.

Toward Protein Tertiary Structure Recognition by Means of Associative Memory Hamiltonians

The statistical mechanics of associative memories and spin glasses suggests ways to design Hamiltonians for protein folding. An associative memory Hamiltonian based on hydrophobicity patterns is shown to have a large capacity for recall and to be capable of recognizing tertiary structure for moderately variant sequences.