Nonequilibrium models of optimal enhancer function

In prokaryotes, thermodynamic models of gene regulation provide a highly quantitative mapping from promoter sequences to gene-expression levels that is compatible with in vivo and in vitro biophysical measurements. Such concordance has not been achieved for models of enhancer function in eukaryotes. In equilibrium models, it is difficult to reconcile the reported short transcription factor (TF) residence times on the DNA with the high specificity of regulation. In nonequilibrium models, progress is difficult due to an explosion in the number of parameters. Here, we navigate this complexity by looking for minimal nonequilibrium enhancer models that yield desired regulatory phenotypes: low TF residence time, high specificity, and tunable cooperativity. We find that a single extra parameter, interpretable as the “linking rate,” by which bound TFs interact with Mediator components, enables our models to escape equilibrium bounds and access optimal regulatory phenotypes, while remaining consistent with the reported phenomenology and simple enough to be inferred from upcoming experiments. We further find that high specificity in nonequilibrium models is in a trade-off with gene-expression noise, predicting bursty dynamics—an experimentally observed hallmark of eukaryotic transcription. By drastically reducing the vast parameter space of nonequilibrium enhancer models to a much smaller subspace that optimally realizes biological function, we deliver a rich class of models that could be tractably inferred from data in the near future.

Multiple steady states in a CSTR with total condenser: Comparison of equilibrium and nonequilibrium models

Comparison of equilibrium and nonequilibrium models of a CSTR with total condenser focused on the multiple steady states and dynamic behaviour was carried out. The steady-state behaviour of the model system, MTBE synthesis from methanol and isobutene in a reactive distillation column, was studied in terms of the input parameters, i. e. feed flow rate of methanol or butenes, reflux ratio, and mass of catalyst. The dynamic behaviour of the system during the start-up was investigated and perturbations of manipulated variables were found to cause transitions between the parallel steady states.