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In this paper we investigate charge transport in the a-helix proteins. It is considered that charge carriers are partially dressed small polarons, that are formed by electron self-trapping in the weak coupling limit. Polaron properties are considered by applying mean-field theory based upon the modified Lang-Firsov transformation and the Bogolyubov theorem. The transport properties have been calculated on the basis of the Holstein MC model. The obtained results are compared with the results of previous models.