The differences between refolding mechanisms of sperm whale apomyoglobin subsequent to three different unfolding conditions have been examined by atomistic level computer simulations. The three unfolding conditions used in this work are high-temperature, low temperature and low pH. The folding of this protein has been extensively studied experimentally, providing a large data base of folding parameters which can be probed using simulations. The crystal structure of sperm whale myoglobin was taken from Protein Data Bank, followed by the removal of the heme unit and a subsequent energy minimization was performed in order to generate the native apomyoblogin form. Thus, the native conformation of apomyoglobin utilized is the same in all the three different refolding simulations done in the present work. The differences are the way the initial unfolded conformations were obtained. The refolding trajectories were obtained at room temperature using the Stochastic Difference Equation in Length algorithm. The results reveal differences between the three refolding routes. In contrast to previous molecular simulations that modeled low pH denaturation, an extended intermediate with large helical content was not observed in the refolding simulations from the high-temperature unfolded state. Otherwise, a structural collapse occurs without formation of helices or native contacts. Once the protein structure is more compact (radius of gyration less than 18 angstroms) secondary and tertiary structures appear. The low pH simulations show some agreement with the low pH experimental data and previous molecular dynamics simulations, like formation of a conformation having radius of gyration around 20 angstroms and large helical content. And the refolding simulations after the low temperature unfolding present differences in the properties of apomyoglobin folding route, comparing to the other two previous conditions. The collapse of the protein during folding occurs later in the simulation when compared with high-temperature denaturing state, but earlier when compared to low pH simulations. These differences strongly suggest that a protein can follow different folding routes, depending on the nature and the structure of the unfolded state.

Indiana University-Purdue University Indianapolis (IUPUI) / We derive the differential identities for isomonodromic tau functions, describing their monodromy dependence. For Painlev´e equations we obtain them from the relation of tau function to classical action which is a consequence of quasihomogeneity of corresponding Hamiltonians. We use these identities to solve the connection problem for generic solution of Painlev´e-III(D8) equation, and homogeneous Painlev´e-II equation. We formulate conjectures on Hamiltonian and symplectic structure of general isomonodromic deformations we obtained during our studies and check them for Painlev´e equations.