Cells receive signaling molecules by receptors and relay the information via sensory networks so that they can respond properly depending on the type of signals . Recent studies show that cells can extract multi-dimensional information from dynamical concentration patterns of signaling molecules. Here we study how cells generally and optimally process multi-dimensional information embedded in dynamical patterns through biochemical networks. Considering a deterministic limit, we model the decoding networks by linear response functions, and optimize the functions with the calculus of variations to maximize the mutual information between patterns and output. We find that optimal decoders are realized with multiple distinct non-monotonic response functionsand that such optimal decoderscan extract information much more efficiently than typical single-layer linear decoders. We also consider the decorrelation of informationembedded in the dynamical patternsand show that decorrelating decoders converge to the upper bound of the mutual information in the weak noise limit. We explore the biochemical implementations of these decoders using control theory and demonstrate that they can be implemented biochemically through  modification of cascade-type networks, which are prevalent in actual signaling pathways.
Cells receive signaling molecules by receptors and relay information via sensory networks so that they can respond properly depending on the type of signal . Recent studies have shown that cells can extract multi-dimensional information from dynamical concentration patterns of signaling molecules. We herein study how biochemical systems can process multi-dimensional information embedded in dynamical patterns . We model the decoding networks by linear response functions, and optimize the functions with the calculus of variations to maximize the mutual information between patterns and output. We find that , when the noise intensity is lower, decoders with different linear response functions, i.e., distinct decoders, can extract much information. However, when the noise intensity is higher, distinct decoders do not provide the maximum amount of information. This indicates that, when transmitting information by dynamical patterns, embedding information in multiple patterns is not optimal when the noise intensity is very large. Furthermore, we explore the biochemical implementations of these decoders using control theory and demonstrate that these decoders can be implemented biochemically through the modification of cascade-type networks, which are prevalent in actual signaling pathways.
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optimal decoders are realized with multiple distinct non-monotonic response functionsand that such optimal decoderscan extract information much more efficiently than typical single-layer linear decoders. We also consider the decorrelation of informationembedded in the dynamical patternsand show that decorrelating decoders converge to the upper bound of the mutual information in the weak noise limit. We
, when the noise intensity is lower, decoders with different linear response functions, i.e., distinct decoders, can extract much information. However, when the noise intensity is higher, distinct decoders do not provide the maximum amount of information. This indicates that, when transmitting information by dynamical patterns, embedding information in multiple patterns is not optimal when the noise intensity is very large. Furthermore, we
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