Interplay between ATP and hydrolysis free energy in promoting and restraining biochemical switches

In living cells, the bistable switches involving phosphorylation-dephosphorylation (PdP) cycles, operate far from thermodynamic equilibrium and consume hydrolysis free energy to perform ultrasensitive response and exhibit strong robustness against noise. Here, we focus on the distinct roles of cellular ATP levels ([ATP]) and hydrolysis free energy (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi mathvariant="normal">Δ</a:mi><a:mi>μ</a:mi></a:mrow></a:math>) in bistable switches with different structures of reaction network. Specifically, we herein propose thermodynamically consistent models of single- and double-PdP-cycle bistable switches to study the relationship between network structures and the interplay between [ATP] and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi mathvariant="normal">Δ</c:mi><c:mi>μ</c:mi></c:mrow></c:math>. We demonstrate that [ATP] and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mi mathvariant="normal">Δ</e:mi><e:mi>μ</e:mi></e:mrow></e:math> act cooperatively to promote the activation of switches in identical networks wherein all phosphorylations promote target production, irrespective of different feedback mechanisms. On the other hand, the competition between [ATP] and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mi mathvariant="normal">Δ</g:mi><g:mi>μ</g:mi></g:mrow></g:math> found in the nonidentical, or reversed, networks can enhance the robustness of bistability. We also discuss special network structures inducing multistability or nonmonotonic functions of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mrow><i:mi mathvariant="normal">Δ</i:mi><i:mi>μ</i:mi></i:mrow></i:math>. Our results gain insight into the relationship between network structures and the roles of [ATP] and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:mrow><k:mi mathvariant="normal">Δ</k:mi><k:mi>μ</k:mi></k:mrow></k:math> in bistable switches, potentially guiding the future design of synthetic biochemical switches. Published by the American Physical Society 2024