Self-regulation in a minimal model of chemical self-replication

Abstract

In biological systems, regulation plays an important role in keeping metabolite concentrations within physiological ranges. To study the dynamical implications of selfregulation, we consider a functional form used in genetic networks and couple it to a mechanism associated with chemical self-replication. For the two-variable minimal model, we find that activation can yield chemical toggles similar to those reported for gene repression in E. coli as well as more complex dynamics.

From Cascaded Catalytic Nucleic Acids to Enzyme–DNA Nanostructures: Controlling Reactivity, Sensing, Logic Operations, and Assembly of Complex Structures

“…Thus, the template-assisted linkage between A and B generates a second template molecule, thus providing exponential growth of the product (template) units in the system. The kinetics of the isothermal autonomous replication of a template structure using molecular ligation has been theoretically − and experimentally modeled. − While the isothermal replication path seems simple, it suffers from some basic limitations. As the ligated product reveals enhanced binding affinity to the template molecule, as compared to the binding affinity of the substrate subunits, effective displacement of the product molecule by the substrate subunits occurs only in early stages of the reaction (where the concentrations of the substrate subunits are high), and the self-inhibition process by the product is enhanced, as the isothermal autonomous replication reaction proceeds.…”

Complex Dynamics of Competitive First Order Chemical Self-Replication

“…In previous work [41][42][43][44][45][46][47][48][49][50][51], we have considered Rebek's and Joyce's self-replicating systems and modeled ideal self-replication using a self-complementary template mechanism. For this experimental design, we used a reasonable chemical model consistent with the laboratory work on self-replication.…”

“…In previous work, we have analyzed at length the case of no-limiting reagent, Yt ðÞ¼Y 0 ðÞ ¼ 0, where At ðÞ¼Bt ðÞ [41][42][43][44][45][46][47][48][49][50][51]. But here we relax the no-limiting reagent condition and notice, since Y o ¼ 0, that the variable Y has a simple solution, Yt ðÞ¼Y 0 ðÞ .…”

“…Under these so-called batch conditions, researchers have found exponential growth and, therefore, self-replication. Using Joyce's experiments, we have proposed a minimal Templator Mode [41] and determined parameter values for our model, and we have extended our analyses to open conditions to characterize probable dynamic behaviors [41][42][43][44][45][46][47][48][49][50][51].…”

Self‐regulation in a stochastic model of chemical self‐replication

“…By virtue of ( 16), we can compute the dynamics of the moments of the proposed self-replication model. In particular, taking into account (11), (12), and the ODE ( 13)-( 15), we can write the equations of the first-order moment*…”