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Our current understanding of ion permeation through the selectivity filter of the KcsA potassium channel is based on the concept of a multi-ion transport mechanism. The details of this concerted movement, however, are not well understood. In the present paper we report on molecular dynamics simulations which provides new insights. It is shown that ion translocation is based on the collective hopping of ions and water molecules which is mediated by the flexible charged carbonyl groups lining the backbone of the pore. In particular, there is strong evidence for pairwise translocations where one ion and one water molecule form a bound state. We suggest a physical explanation of the observed phenomena employing a simple lattice model. It is argued that the water molecules can act as rectifiers during the hopping of ion-water pairs.

Analysis of the geometric properties of a mean-field HP model on a square lattice for protein structure shows that structures with large number of switch backs between surface and core sites are chosen favorably by peptides as unique ground states. Global comparison of model (binary) peptide sequences with concatenated (binary) protein sequences listed in the Protein Data Bank and the Dali Domain Dictionary indicates that the highest correlation occurs between model peptides choosing the favored structures and those portions of protein sequences containing alpha-helices.PACS number: 87.10.+e, 87.15.By The three-dimensional structure of proteins is a complex physical and mathematical problem of prime importance in molecular biology, medicine and pharmacology [1]. It is believed that the folding instruction of a protein is encoded in its amino acid sequence [2] and from model studies much has been learned about protein structure and folding kinetics [3][4][5][6]. Yet much still remains to be understood. This simple fact is already intriguing: the number of possible globular structures for a peptide of typical length -about 300 amino acids -is practically infinite; the number of proteins whose structures are known empirically or hypothetically is more than a hundred thousand and is growing rapidly with time; the number of classes of native protein structures is about five hundred and is believed unlikely to exceed a thousand in the long run [1,7]. Numerical simulations based on lattice models have shown that structures of exceptionally high designability -those that attract a large number of protein sequences to conform to it -do exist [5,6,8]. Why such structures would emerge is however not well understood. Protein folding also has an outstanding temporal feature: the initial collapse to globular shape and the formation of α-helices are completed in less than 10 −7 seconds [10], while the rest of the folding takes up to ten seconds to complete.In this report, based on results from a mean-field lattice model we observe that structures with high designability are preponderant in a type of substructure that suggests α-helices in real proteins and we explain the reason for this phenomenon. This notion is supported by global comparisons of model structural sequences with (binary) sequences constructed from sets of proteins of known structure: the Protein Data Bank (PDB) [9] and the Dali Domain Dictionary (DDD) [7]. Since the meanfield in the model represents the hydrophobic potential that is known to cause the initial collapse of a peptide to a globular shape, the results may explain why the initial collapse and the formation of α-helices occur essentially simultaneously and rapidly, and are temporally separated from other slower folding processes that are driven by far-neighbor inter-residual interactions.In the minimal model for protein folding, the HP model of Dill et al. [3], the 20 kinds of amino acids are divided into two types, hydrophobic and polar. This reduces a peptide chain of length N to a binary "pepti...

Lattice models, for their coarse-grained nature, are best suited for the study of the "designability problem", the phenomenon in which most of the about 16,000 proteins of known structure have their native conformations concentrated in a relatively small number of about 500 topological classes of conformations. Here it is shown that on a lattice the most highly designable simulated protein structures are those that have the largest number of surface-core switchbacks. A combination of physical, mathematical and biological reasons that causes the phenomenon is given. By comparing the most foldable model peptides with protein sequences in the Protein Data Bank, it is shown that whereas different models may yield similar designabilities, predicted foldable peptides will simulate natural proteins only when the model incorporates the correct physics and biology, in this case if the main folding force arises from the differing hydrophobicity of the residues, but does not originate, say, from the steric hindrance effect caused by the differing sizes of the residues.

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