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We report on charge transport and current fluctuations in a single bacteriorhodpsin protein in a wide range of applied voltages covering direct and injection tunnelling regimes. The satisfactory agreement between theory and available experiments validates the physical plausibility of the model developed here. In particular, we predict a rather abrupt increase of the variance of current fluctuations in concomitance with that of the I-V characteristic. The sharp increase, for about five orders of magnitude of current variance is associated with the opening of low resistance paths responsible for the sharp increase of the I-V characteristics. A strong non-Gaussian behavior of the associated probability distribution function is further detected by numerical calculations.