Factors Governing the Foldability of Proteins

We use a three dimensional cubic lattice model of proteins to study their properties that determine folding to the native state. The protein chain is modeled as a sequence of $N$ beads. The interactions between beads are taken from a Gaussian distribution of energies. We studied 56 sequences with unique ground states for $N = 15$ and $27$. Thermodynamic and kinetic properties were determined using Monte Carlo simulations and exhaustive enumeration. For all sequences we find collapse temperature, $T_{\theta}$, at which the protein collapses into compact structure, and folding temperature, $T_{f}$, at which the protein acquires the native state. We show that parameter $\sigma = (T_{\theta} - T_{f})/T_{\theta}$ correlates extremely well with folding times. Fast folders reach the native state via a nucleation collapse mechanism without forming any intermediates, whereas for moderate and slow folders only a fraction of molecules $\Phi $ reaches the native state by this process. The remaining fraction folds via three stage multipathway process. The simultaneous requirement of native state stability and kinetic accessibility can be achieved for the sequences with small values of $\sigma $.