Derangement model of ligand-receptor binding
We introduce a derangement model of ligand-receptor binding that allows us to quantitatively frame the question "How can ligands seek out and bind to their optimal receptor sites in a sea of other competing ligands and suboptimal receptor sites?" To answer the question, we first derive a formula to count the number of partial generalized derangements in a list, thus extending the derangement result of Gillis and Even. We then compute the general partition function for the ligand-receptor system and derive the equilibrium expressions for the average number of bound ligands and the average number of optimally bound ligands. A visual model of squares assembling onto a grid allows us to easily identify fully optimal bound states. Equilibrium simulations of the system reveal its extremes to be one of two types, qualitatively distinguished by whether optimal ligand-receptor binding is the dominant form of binding at all temperatures and quantitatively distinguished by the relative values of two critical temperatures. One of those system types (termed "search-limited," as it was in previous work) does not exhibit kinetic traps and we thus infer that biomolecular systems where optimal ligand-receptor binding is functionally important are likely to be search-limited.
Code (1)
Tasks
modelSimilar Papers 제목 키워드 기반
The most probable dynamics of receptor-ligand binding on cell membrane
We devise a method for predicting certain receptor-ligand binding behaviors, based on stochastic dynamical modelling. We consider the dynamics of a receptor binding to a ligand on the cell membrane, where the receptor an…
Binding kinetics of membrane-anchored receptors and ligands: molecular dynamics simulations and theory
The adhesion of biological membranes is mediated by the binding of membrane-anchored receptor and ligand proteins. Central questions are how the binding kinetics of these proteins is affected by the membranes and by the …
Accurate sensing of multiple ligands with a single receptor
Cells use surface receptors to estimate the concentration of external ligands. Limits on the accuracy of such estimations have been well studied for pairs of ligand and receptor species. However, the environment typicall…
Binding equilibrium and kinetics of membrane-anchored receptors and ligands in cell adhesion: insights from computational model systems and theory
The adhesion of cell membranes is mediated by the binding of membrane-anchored receptor and ligand proteins. In this article, we review recent results from simulations and theory that lead to novel insights on how the bi…
Physical limit to concentration sensing amid spurious ligands
To adapt their behaviour in changing environments, cells sense concentrations by binding external ligands to their receptors. However, incorrect ligands may bind nonspecifically to receptors, and when their concentration…