Oscillations and multiple steady states in active membrane transport models

Stoichiometric network analysis in reaction networks yielding spontaneous mirror symmetry breaking in a prebiotic atmosphere

The generation of amino acid homochirality under prebiotic atmosphere conditions is a relevant issue in the study of the origin of life. This research is based on the production of amino acids via Strecker synthesis and how it is adjusted to the Kondepudi-Nelson autocatalytic model. The spontaneous mirror symmetry breaking (SMSB) of the new Kondepudi-Nelson-Strecker model, subject to two modifications (with Limited Enantioselective and Cross Inhibition), and also their combination were studied using the stoichiometric network analysis (SNA). In the calculations, the values obtained from the literature for alanine were considered. A total production of alanine of 7.56 × 10⁹ mol year^-1 was determined under prebiotic atmosphere conditions and starting from that value, the reaction rates for the models studied were estimated. Only the model with cross inhibition or achiral dimer formation is driven by stochastic fluctuations during SMSB. The stochastic fluctuation was estimated for a value of 2.619 × 10^-15 mol L^-1. This perturbation was sufficient to trigger SMSB. Finally, the results of SMSB were used to calculate the entropy production for the cross inhibition model.

Spatial bistability generates hunchback expression sharpness in the Drosophila embryo

During embryonic development, the positional information provided by concentration gradients of maternal factors directs pattern formation by providing spatially dependent cues for gene expression. In the fruit fly, Drosophila melanogaster, a classic example of this is the sharp on-off activation of the hunchback (hb) gene at midembryo, in response to local concentrations of the smooth anterior-posterior Bicoid (Bcd) gradient. The regulatory region for hb contains multiple binding sites for the Bcd protein as well as multiple binding sites for the Hb protein. Some previous studies have suggested that Bcd is sufficient for properly sharpened Hb expression, yet other evidence suggests a need for additional regulation. We experimentally quantified the dynamics of hb gene expression in flies that were wild-type, were mutant for hb self-regulation or Bcd binding, or contained an artificial promoter construct consisting of six Bcd and two Hb sites. In addition to these experiments, we developed a reaction-diffusion model of hb transcription, with Bcd cooperative binding and hb self-regulation, and used Zero Eigenvalue Analysis to look for multiple stationary states in the reaction network. Our model reproduces the hb developmental dynamics and correctly predicts the mutant patterns. Analysis of our model indicates that the Hb sharpness can be produced by spatial bistability, in which hb self-regulation produces two stable levels of expression. In the absence of self-regulation, the bistable behavior vanishes and Hb sharpness is disrupted. Bcd cooperative binding affects the position where bistability occurs but is not itself sufficient for a sharp Hb pattern. Our results show that the control of Hb sharpness and positioning, by hb self-regulation and Bcd cooperativity, respectively, are separate processes that can be altered independently. Our model, which matches the changes in Hb position and sharpness observed in different experiments, provides a theoretical framework for understanding the data and in particular indicates that spatial bistability can play a central role in threshold-dependent reading mechanisms of positional information.