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The question about the size of nucleiof formation of protofibrils(which constitute mature amyloid fibrils) formed by different proteinsand peptides is yet open and debatable because of the absence of solidknowledge of underlying mechanisms of amyloid formation. In this work,a kinetic model of the process of formation of amyloid protofibrilsis suggested, which allows calculation of the size of the nuclei usingonly kinetic data. In addition to the stage of primary nucleation,which is believed to be present in many protein aggregation processes,the given model includes both linear growth of protofibrils (proceedingonly at the cost of attaching of monomers to the ends) and exponentialgrowth of protofibrils at the cost of growth from the surface, branching,and fragmentation with the secondary nuclei. Theoretically, only theexponential growth is compatible with the existence of a pronouncedlag-period (which can take much more time then the growth of aggregatesthemselves). The obtained analytical solution allows us to determinethe size of the primary and secondary nuclei from the experimentallyobtained concentration dependences of the time of growth and the newparameterthe ratio Lrelof thelag-time duration to the time of growth of amyloid protofibrils. [ABSTRACT FROM AUTHOR]

A detailed calculation of protein interactions with explicitlyconsidered water molecules takes enormous time. If water is consideredimplicitly (as media rather than as molecules), calculations becomefaster. These calculations are less precise, unless one uses voluminouscomputations of solvent-accessible areas. Our goal is to obtain parametersfor nonbonded atom–atom interactions in implicitly consideredwater without computation of solvent-accessible areas. Because the“in-vacuum” interactions of atoms are obtained fromexperimental structures of crystals and enthalpies of their sublimation,the “in-water” interactions must be corrected usingsolvation free energies obtained from Henry’s constants. Thus,we obtained parameters for the in-water van der Waals, electrostatic,and polarized interactions for atoms typical of protein structures.Parameters of covalent interactions were taken from the ENCAD forcefield and partial charges of atoms from quantum-mechanical calculations.The sought parameters of the in-water nonbonded interactions wereoptimized to achieve the best description of crystal structures andtheir sublimation and solvation at the room temperature. With theoptimized parameters, the correlation between the calculated and experimentalcohesion of molecules in crystals is 98.3% in the in-vacuum case (thesupplementary force field PFFSubl1.1) and 95.4% the in-water case(the sought force field PFFSol1.1). [ABSTRACT FROM AUTHOR]