Different dimensions of robustness - noise, topology and rates - are nearly independent in chemical switches

Life prospers despite adverse conditions in many unpredictable dimensions. This requires that cellular processes work reliably, that is they are robust against many kinds of perturbations. For example, a cellular decision to differentiate should be stable despite changes in metabolic conditions and stochasticity due to thermal noise. For evolutionary stability, the same differentiation switch should function despite mutations or the evolution of further regulatory inputs. We asked how cellular decision making responds to these three forms of perturbation, expressed in chemical terms as rate parameters, stochasticity, and reaction topology. Remarkably, we found that there was no correlation between noise robustness and either of the others and only a weak correlation between robustness to parameters and topology. Thus, a given chemical switch could be robust to noise yet sensitive to parametric or topological changes. However, we found families of reaction topologies derived from a common core bistable with symmetric feedback loops, which retained bistability despite the removal of reactions or substantially changing parameters. We propose that evolution involving chemical switches must navigate a complex landscape involving multiple forms of robustness, and the only way for a given switch to have a systematic advantage in robustness is to come from a ‘good family’ of mirrorsymmetric topologies.Significance StatementLife endures despite metabolic fluctuations and environmental assaults. For the thousands of cellular decisions to continue to work, they must be robust to these perturbations. Many cellular decisions are made and stored by chemical switches, which like light switches retain their state – on or off – even after the trigger is gone. We computationally explored what makes chemical switches robust. It turns out that some are robust to thermal noise, others to mutations that disable part of the switch, or to changes in chemical conditions. Surprisingly, these different forms of robustness are mostly independent. However, chemical switches come in families built around core reactions, and these families tend to score high or low on several measures of robustness.

Reaction topology of excited state potential energy hypersurfaces

Topology ("rubber geometry") is an exceptionally suitable mathematical framework for a global quantum chemical description of the fundamental relations between nonrigid molecular systems, chemical reactions, and many photochemical processes. In Reaction Topology the concept of nuclear geometry is replaced by open subsets of an abstract nuclear configuration space nR. The ground and various excited state energy expectation value functionals induce a sequence of topologies in the nuclear configuration space nR, leading to a consistent topological description of molecular structure, excimers, exciplexes, and reaction mechanisms. Utilizing earlier results on topological properties of the abstract nuclear charge space wZ, a theorem is proven on the ordering of excited state potential energy hypersurfaces for sequences of isoelectronic molecules.