Closed-form information capacity of canonical signaling models

Mathematical methods of information theory provide a useful framework for describing how stimuli are encoded by signaling effectors in biological systems. Yet applying this perspective remains conceptually and computationally challenging, often due to the lack of analytical formulations that connect directly to biophysical models. Here, by deriving closed-form or easily computable information capacity formulas, we quantify how well different signaling models, including binomial, multinomial, Poisson, Gaussian, and Gamma distributions, discriminate among input signals. These expressions clarify how key features such as signal or response range, noise scaling, pathway length, and receiver diversity shape the theoretical limits of sensing. Our results provide intuitive, analytically grounded tools to benchmark and guide the analysis of real signaling systems without requiring computationally expensive mutual information estimation. While motivated by cellular communication, the framework generalizes to any system where noisy input-output relationships constrain transmission fidelity, including synthetic biology, sensor networks, and engineered communication channels. Biological signaling systems face challenges in accurately resolving inputs due to complex noise and signal interactions. This study employs a unified framework using Fisher Information to derive a framework that reveal how signal characteristics and noise affect sensing limits, offering analytically grounded tools for analyzing and optimizing signaling systems in the context of synthetic biology, sensor networks, and engineered communication channels.