Pathways in Two-State Protein Folding

Abstract

Thermodynamic measurements of proteins indicate that the folding to the native state takes place either through stable intermediates or through a two-state process without intermediates. The rather short folding times of proteins indicate that folding is guided through some sequence of contact bindings. We discuss the possibility of reconciling a two-state folding event with a sequential folding process in a schematic model of protein folding. We propose a new dynamical transition temperature that is lower than the temperature at which proteins in equilibrium unfold. This is in qualitative agreement with observations of in vivo protein folding activity quantified by chaperone concentration in Escherichia coli. Finally, we discuss our framework in connection with the unfolding of proteins at low temperatures.

Thermodynamical Implications of a Protein Model with Water Interactions

“…This is in agreement with experimental data, and opposite to the situation found in the earlier protein models of Refs. [8,9,11]. …”

“…φ i = 0 means that node i is open (unfolded), and φ i = 1 means that node i is folded. Assuming N nodes, a Hamiltonian (H 1 ) for the energies associated to the polypeptide chain is in a compact way written [8,9,10,11] …”

“…This is termed as the "hydrophobic force", and the water-protein interaction is incorporated by an energy ladder representing each individual water molecule associated to the unfolded parts of the protein (i.e. all nodes where φ i = 0) [8,9,11] …”

“…However, every step along the path, each describing an ensemble of conformations, should have some common structural features which acts like checkpoints for the folding. Further these checkpoints of increasing order is likely to follow a folding pathway [7,8,9,10,11], where one particular point on the pathway depends on the assumption that the main structures of the earlier steps are conserved.…”

Exact Partition Function Zeros of The Wako-Saitô-Muñoz-Eaton Protein Model

“…The two-state transition is characterized by a free energy barrier between the folded and unfolded states at the transition temperature. Another transition process, the barrierless downhill folding scenario, has also been examined both theoretically [5][6][7][8][9][10][11][12] and experimentally [13,14]. The absence of a barrier at the transition temperature results in the loss of cooperativity of the thermodynamic folding transition, usually corresponding to a higher order transition or no transition in the infinite-size limit.Downhill folding has never been analyzed in the framework of the partition function zeros (PFZs) method [4,[15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33], although characteristics of PFZs for two-state folders have been reported for several lattice model proteins [4].…”