Evolution-like selection of fast-folding model proteins

Collapse and cooperativity in protein folding

The folding of a polypeptide chain is associated both with compactness and cooperativity within local and global regions of the protein structure, and with the formation of the native-like molecular architecture. Recent experiments shed light on these issues and their relationships to the pathways of protein folding.

How the first biopolymers could have evolved

In this work, we discuss a possible origin of the first biopolymers with stable unique structures. We suggest that at the prebiotic stage of evolution, long organic polymers had to be compact to avoid hydrolysis and had to be soluble and thus must not be exceedingly hydrophobic. We present an algorithm that generates such sequences for model proteins. The evolved sequences turn out to have a stable unique structure, into which they quickly fold. This result illustrates the idea that the unique three-dimensional native structures of first biopolymers could have evolved as a side effect of nonspecific physicochemical factors acting at the prebiotic stage of evolution.

Conserved residues and the mechanism of protein folding

Experimental and simulation studies show that small monomeric proteins fold in one kinetic step, which entails overcoming the free-energy barrier between the unfolded and the native protein through a transition state. Two models of transition state formation have been proposed: a 'nonspecific' one in which it depends on the formation of a sufficient number of native-like contacts regardless of what amino acids are involved, and a 'specific' one, in which it depends on formation of a specific subset of the native structure (a folding nucleus). The latter requires that some amino acids form most of their contacts in the transition state, whereas others only do so on reaching the native conformation. If so, mutations affecting the stability of the transition state nucleus should have a greater effect on the folding kinetics than mutations elsewhere, and the residues involved should be evolutionarily conserved. Lattice-model simulations and experiments suggest that such mutations exist. Here we present a method for determining the folding nucleus of a protein with known structure with two-state folding kinetics. This method is based on the alignment of many sequences designed to fold into the native conformation of a protein to identify the positions where amino acids are most conserved in designed sequences. The method is applied to chymotrypsin inhibitor 2 (CI2), a protein whose transition state has been previously studied by protein engineering. The involvement of residues in folding nucleus of CI2 is clearly correlated with their conservation in design, and the residues forming the nucleus are highly conserved in 23 natural sequences homologous to CI2.

Monte Carlo simulations of protein folding using inexact potentials: how accurate must parameters be in order to preserve the essential features of the energy landscape?

BACKGROUND

Monte Carlo simulations of the cubic lattice protein model with engineered sequences were performed in order to address the issue of potential accuracy required for folding. The potential used for sequence selection played the role of the 'real' potential and different levels of inaccuracy were introduced by addition of noise.

RESULTS

The dependence of successful folding probability on potential noise was found to be sigmoidal and sequence-specific and can be described by an expression analytically derived from a simple theoretical model in which the density of states of the system contains a continuous region approximated by a Gaussian distribution separated from the unique native conformation by a large energy gap.

CONCLUSIONS

The decrease in folding probability with potential inaccuracy results from an average decrease in the energy gap. Sequences with large energy gaps support larger inaccuracies while retaining the ability to fold properly. As the energy gap is known to correlate with thermal stability, we suggest a simple criterion for specific real sequence selection in order to maximize success probability in realistic folding simulations.

Contact interactions method: a new algorithm for protein folding simulations

Computer simulations of simple exact lattice models are an aid in the study of protein folding process; they have sometimes resulted in predictions experimentally proved. The contact interactions (CI) method is here proposed as a new algorithm for the conformational search in the low-energy regions of protein chains modeled as copolymers of hydrophobic and polar monomers configured as self-avoiding walks on square or cubic lattices. It may be regarded as an extension of the standard Monte Carlo method improved by the concept of cooperativity deriving from nonlocal contact interactions. A major difference with respect to other algorithms is that criteria for the acceptance of new conformations generated during the simulations are not based on the energy of the entire molecule, but cooling factors associated with each residue define regions of the model protein with higher or lower mobility. Nine sequences of length ranging from 20 to 64 residues were used on the square lattice and 15 sequences of length ranging from 46 to 136 residues were used on the cubic lattice. The CI algorithm proved very efficient both in two and three dimensions, and allowed us to localize energy minima not localized by other searching algorithms described in the literature. Use of this algorithm is not limited to the conformational search, because it allows the exploration of thermodynamic and kinetic behavior of model protein chains.

Improved design of stable and fast-folding model proteins

BACKGROUND

A number of approaches to design stable and fast-folding sequences for model polypeptide chains have been based on the premise that optimization of the relative energy of the native conformation (or Z-score) is sufficient to yield stable and fast-folding sequences. Although this approach has been successful, for longer chains it often yielded sequences that failed to fold cooperatively, instead having multidomain folding behavior.

RESULTS

We show that one of the factors determining single-domain or multidomain folding behavior is the dispersion of energies of native contacts. So, we study folding of sequences optimized to have the same native conformation as a global energy minimum but having different dispersion of native contact energies. Our results suggest that under conditions at which native conformation is stable, the best-folding proteins are those that have smaller heterogeneity of native contact energies. For them, the folding transition is all-or-none. On the other hand, proteins with greater heterogeneity of native contact energies have more gradual multidomain folding transition and fold into stable native conformation much slower than those proteins with small dispersion of native contact energies.

Universality and diversity of the protein folding scenarios: a comprehensive analysis with the aid of a lattice model

BACKGROUND

The role of intermediates in protein folding has been a matter of great controversy. Although it was widely believed that intermediates play a key role in minimizing the search problem associated with the Levinthal paradox, experimental evidence has been accumulating that small proteins fold fast without any detectable intermediates.

RESULTS

We study the thermodynamics and kinetics of folding using a simple lattice model. Two folding sequences obtained by the design procedure exhibit different folding scenarios. The first sequence folds fast to the native state and does not exhibit any populated intermediates during folding. In contrast, the second sequence folds much slower, often being trapped in misfolded low-energy conformations. However, a small fraction of folding molecules for the second sequence fold on a fast track avoiding misfolded traps. In equilibrium at the same temperature the second sequence has a highly populated intermediate with structure similar to that of the kinetics intermediate.

CONCLUSIONS

Our analysis suggests that intermediates may often destabilize native conformations and derail the folding process leading it to traps. Less-optimized sequences fold via parallel pathways involving misfolded intermediates. A better designed sequence is more stable in the native state and folds fast without intermediates in a two-state process.