SearcharxivSearch

arXiv · 2209.03033

Design of universal chemical relaxation oscillator to control molecular computation

Abstract

Embedding efficient command operation into biochemical system has always been a research focus in synthetic biology. One of the key problems is how to sequence the chemical reactions that act as units of computation. The answer is to design chemical oscillator, a component that acts as a clock signal to turn corresponding reaction on or off. Some previous work mentioned the use of chemical oscillations. However, the models used either lack a systematic analysis of the mechanism and properties of oscillation, or are too complex to be tackled with in practice. Our work summarizes the universal process for designing chemical oscillators, including generating robust oscillatory species, constructing clock signals from these species, and setting up termination component to eventually end the loop of whole reaction modules. We analyze the dynamic properties of the proposed oscillator model in the context of ordinary differential equations, and discuss how to determine parameters for the effect we want in detail. Our model corresponds to abstract chemical reactions based on mass-action kinetics which are expected to be implemented into chemistry with the help of DNA strand displacement cascades. Our consideration of ordering chemical reaction modules helps advance the embedding of more complex calculations into biochemical environments.

Explore related subjects

Keep this discovery

BibTeXRIS

Xiaopeng Shi, Chuanhou Gao. 2022-09-07. Design of universal chemical relaxation oscillator to control molecular computation. https://arxiv.org/abs/2209.03033

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Admissible Fourier Lengths, KAM Reducibility, and Spectral Applications

We develop a perturbative KAM reducibility theory for one-frequency $\mathrm{SL}(2,\mathbb{R})$ cocycles based on an admissible Fourier length $\ell$. The regularity relevant to the iteration is measured by positive adapted Fourier width rather than ordinary smoothness in the Euclidean length $|n|$. The same length governs Fourier decay, truncation and resonance scales, and the arithmetic condition controlling the small divisors. This framework contains the classical analytic and Gevrey settings, while non-monotone choices of $\ell$ allow classical nowhere differentiable Weierstrass-type perturbations and continuous perturbations outside every positive H\"older class. As spectral applications, we obtain purely absolutely continuous spectrum for every phase and $1/2$-H\"older continuity of the integrated density of states for the associated quasiperiodic Schr\"odinger operators. The Aubry dual has pure point spectrum for Lebesgue almost every dual phase, with eigenfunctions exponentially localized in the metric induced by $\ell$. We also construct nowhere differentiable quasiperiodic potentials with purely absolutely continuous Cantor spectrum.

math.DS

Dynamics inside the attracting basins of some skew products

Polynomial skew products in $\mathbb{C}^2$ are maps of the form $F(z,w)=(P(z),Q(z,w))$, where $P$ and $Q$ are polynomials. Their local dynamics have been widely investigated. In this paper, we study the global dynamics inside Fatou components of some skew products. We consider all the inverse images in a Fatou component of a given point and use the Kobayashi metric to measure the distance between points. In the cases we consider, there are always arbitrarily large Kobayashi balls in the complement of these inverse sets.

math.DS

Ergodicity of dynamical systems without uniqueness of orbits

Recently, there has been considerable interest in the study of non-deterministic dynamical systems. To analyze the chaotic behavior of such systems from a measure-theoretic viewpoint, it is desirable to consider ergodicity. However, the classical definition of ergodicity involves invariant sets, whose definition is not unique for non-deterministic dynamical systems. Thus, we are led to the question of which invariance yields an interesting definition of ergodicity. Here, we propose a definition based on the strong backward invariance and show that analogs of classical results hold. We also consider implications of the Birkhoff ergodic theorem for systems without uniqueness of orbits.

math.DS