An exactly solvable model based on the topology of a protein native state is applied to identify bottlenecks and key sites for the folding of human immunodeficiency virus type 1 (HIV-1) protease. the deterministic procedure proposed in this study. The high statistical significance of the observed correlations suggests that the approach may be promisingly used in conjunction with traditional techniques to identify candidate locations for drug attacks. that two sites and in a long harmonic chain (the peptide) are in contact (Flory 1956). The approximation introduced by Flory was to neglect correlations between residues which amounts to considering the chain embedded in a highly dimensional space. As a result the is the strength of the peptide bonds assumed to be harmonic and is the absolute temperature in units of the Boltzmann constant. The relative position between amino-acid centroids is denoted by r= rand the corresponding native positions are indicated with the superscript 0. Δ is the contact matrix whose element Δis 1 if residues and are in contact in the native GS-1101 state (i.e. their Cα separation is below the cutoff = 6.5 ?) and 0 otherwise. The matrix Δij along with the set r0encodes the topology of the protein. The factor θhas the form (2) where θ(?) is the unitary step function and is a distance cutoff defining the range of the interaction between non-consecutive amino acids. In standard off-lattice approaches the interaction between non-bonded amino acids at a distance = 3 ? in the present study) to penalize conformations where the separation of two residues differs significantly from the native one. In the native state each θis close to 1 while in the denaturated state cases usually are negligible. While the present form of the model does not accurately describe the effects of self-avoidance this does not lead to a qualitatively wrong behavior in the highly denatured ensemble (large ). The treatment of steric effects becomes more accurate as temperature is lowered progressively. In fact the model guarantees that the native state is the true ground state and therefore protein conformations found at low temperature inherit the native self-avoidance. The connectedness of the chain as well as its entropy are captured in a simple but non-trivial manner. The most significant advantage of the model is that it can be GS-1101 used to explore the equilibrium thermodynamics without being hampered by inaccurate or sluggish dynamics. Two limit cases of the model described by equation 1 are worthy of notice. In the absence of any bias towards the target structure (i.e. when both Δand GS-1101 the {(when all native contacts are established and the bonded-energy term fluctuations are negligible) the model reduces to the Gaussian network model that has been introduced and used to study the near-native vibrational properties of several proteins GS-1101 (Bahar et al. 1997 1999 Keskin et al. 2000; Atilgan et al. 2001). The thermodynamics of the model are fully determined by the partition function (3) In the integral of equation 3 and in the following it is always meant that translational invariance is explicitly broken by fixing for example the center of mass of the system (see Appendix). The integral (3) is still hard to treat analytically because of the presence of nonquadratic interactions in the last term of Hamiltonian (1). We thus perform a further but non-trivial simplification by replacing with the variational Hamiltonian are now substituted by parameters independent of the coordinates. Because of its quadratic form the model described by equation 4 can be solved with the standard techniques for Gaussian integrals. Such parameters have to be optimally determined so as to ensure self-consistency: (5) The symbol ?. . .?0 indicates that the thermal averages are performed through the Rabbit polyclonal to HNRNPM. Hamiltonian has the following explicit expression: (6) where the matrix is defined as (7) and the prime in equation 6 denotes that the zero eigenvalue of has to be omitted (see Appendix). The quantities in equation 5 represent precisely the occurrence probability of a contact between residues and and indicate the frequency with which that native contact is established. At thermal equilibrium their dependence on temperature reflects the.