The programming of biological cells by genetic circuit engineering is enabling the development of man-made devices and systems in the biochemical environment, with applications in the areas of biomedicine, security, and environmental sensing and control, amongst others. The exchange of information through biochemical reactions and molecule transport, i.e., Molecular Communication (MC), stands as one of the foundational paradigms for the design and characterization of these systems. In a previous work, the same authors developed an analog soft decoder design for MC based on biological circuits inspired by the analog information processing in biochemical reactions. While such a design was optimized for an MC channel affected by Gaussian noise, realistic noise models in molecule transport processes and biochemical reactions tend to deviate from this assumption. In this paper, these models are discussed, together with the validity of their Gaussian approximations, in light of the performance of the log-likelihood ratio calculation of the aforementioned design, numerically evaluated through biochemical simulation. These models, which are directly derived from the theory of molecular diffusion and stochastic chemical reaction analysis, are formulated with a general validity with respect to any future MC system design based on biological circuits.