The Hill function is the universal Hopfield barrier for sharpness of input-output responses.

Autor:	Martinez-Corral R; Department of Systems Biology, Harvard Medical School, Boston, MA 02115., Nam KM; Department of Systems Biology, Harvard Medical School, Boston, MA 02115., DePace AH; Department of Systems Biology, Harvard Medical School, Boston, MA 02115.; HHMI, Boston, MA 02115., Gunawardena J; Department of Systems Biology, Harvard Medical School, Boston, MA 02115.
Jazyk:	angličtina
Zdroj:	Proceedings of the National Academy of Sciences of the United States of America [Proc Natl Acad Sci U S A] 2024 May 28; Vol. 121 (22), pp. e2318329121. Date of Electronic Publication: 2024 May 24.
DOI:	10.1073/pnas.2318329121
Abstrakt:	The Hill functions, [Formula: see text], have been widely used in biology for over a century but, with the exception of [Formula: see text], they have had no justification other than as a convenient fit to empirical data. Here, we show that they are the universal limit for the sharpness of any input-output response arising from a Markov process model at thermodynamic equilibrium. Models may represent arbitrary molecular complexity, with multiple ligands, internal states, conformations, coregulators, etc, under core assumptions that are detailed in the paper. The model output may be any linear combination of steady-state probabilities, with components other than the chosen input ligand held constant. This formulation generalizes most of the responses in the literature. We use a coarse-graining method in the graph-theoretic linear framework to show that two sharpness measures for input-output responses fall within an effectively bounded region of the positive quadrant, [Formula: see text], for any equilibrium model with [Formula: see text] input binding sites. [Formula: see text] exhibits a cusp which approaches, but never exceeds, the sharpness of [Formula: see text], but the region and the cusp can be exceeded when models are taken away from thermodynamic equilibrium. Such fundamental thermodynamic limits are called Hopfield barriers, and our results provide a biophysical justification for the Hill functions as the universal Hopfield barriers for sharpness. Our results also introduce an object, [Formula: see text], whose structure may be of mathematical interest, and suggest the importance of characterizing Hopfield barriers for other forms of cellular information processing. Competing Interests: Competing interests statement:The authors declare no competing interest.
Databáze:	MEDLINE
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