Andrew Kuznetsov
If biological objects are created by natural selection, why are they composed of discrete modules? What has been the nature of mutations since the Darwinian epoch? This paper presents examples of genetic circuits in terms of stochastic -calculus; a new mathematical language for nanosystems. The author used a constructor of five elements such as decay, null gate, gene product, and negative and positive gates. These primitives were applied to design genetic switches, oscillators, feedforward and feedback loops, pulse generators, memory elements, and combinatorial logics. The behaviors of those circuits were investigated – functions, such as oscillations or a spontaneous pulse generation were performed simply, flip-flops between stable states occurred in the noisy environment. The modular essence of -calculus and the following up features of Stochastic Pi Machine (SPiM) programming language allowed us to change the topology of networks that resembled a gene exchange in nature. Other types of mutations were considered as variations in parameters. Perturbations modified system behavior in unpredictable ways that generated diversity for a possible future design by selection of appropriative variants.
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