Design of Universal Chemical Relaxation Oscillator to Control Molecular Computation

Accurate control to run and stop chemical reactions via relaxation oscillators

“…Based on these considerations, we adjust the structure of the 2-dimension relaxation oscillation model and couple it with a symmetric truncated subtraction operation system. Model presented in this paper is similar to the one we constructed in (Shi and Gao (2022)) as follows:…”

“…uv is a truncated subtraction module adjusted from the one in (Vasić et al (2020)). We use this subsystem to set the value of x close to zero at low amplitudes via a large enough parameter c. The structure of the subsystem uv shows a certain degree of symmetry, so as to ensure that u and v can act as a pair of symmetric clock signals while they are affected by the oscillatory element x and oscillate along with it(See (Shi and Gao (2022))). Parameters η 2 and p determine the response and amplitudes of u and v. What needs to be emphasized is that we only restrict the value of the parameters to a certain extent, and each parameter is chosen to be explained accordingly.…”

“…However, selection of initial points is free for that as long as point E is avoided (see Fig. 1), the initial points in the first quadrant will cause the trajectory to converge to the periodic orbit of relaxation oscillation (Shi and Gao (2022)). This ensures the feasibility of our oscillator model in practical applications.…”

“…We need to prepare a strategy for the system to terminate oscillations on its own while introducing chemical oscillators for module regulation. In our previous work, we proposed a chemical oscillator structure based on relaxation oscillation, and obtained satisfactory results in the oscillation mechanism and parameter selection (Shi and Gao (2022)). However, that work only focused on the adjustment task of two modules and failed to solve the problem of automatic cycle termination well.…”

“…A naive idea is to set up physical compartments to separate the modules (Blount et al (2017)), but this does not always work in a biochemical context, especially when applied to cellular programming and synthetic gene circles (Qian et al (2018)). Another design that is more suitable for biochemical environment is to build chemical oscillators in order to generate periodic intervention clock signals (Jiang et al (2011); Vasić et al (2020); Arredondo and Lakin (2022); Shi and Gao (2022)). These intervention signals serve in the biochemical system as catalysts and regulate the switch of the module according to the periodic fluctuations of their concentrations.…”