Signal Amplification in Highly Ordered Networks Is Driven by Geometry.

Gábor Lippner,Éva S. Vanamee,Denise L. Faustman

doi:10.3390/cells11020272

Gábor Lippner, Éva S. Vanamee + Show 1 more

Open Access

https://doi.org/10.3390/cells11020272

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Abstract

Here, we hypothesize that, in biological systems such as cell surface receptors that relay external signals, clustering leads to substantial improvements in signaling efficiency. Representing cooperative signaling networks as planar graphs and applying Euler’s polyhedron formula, we can show that clustering may result in an up to a 200% boost in signaling amplitude dictated solely by the size and geometry of the network. This is a fundamental relationship that applies to all clustered systems regardless of its components. Nature has figured out a way to maximize the signaling amplitude in receptors that relay weak external signals. In addition, in cell-to-cell interactions, clustering both receptors and ligands may result in maximum efficiency and synchronization. The importance of clustering geometry in signaling efficiency goes beyond biological systems and can inform the design of amplifiers in nonbiological systems.

Highlights

Membrane receptors allow cells to respond to external stimuli, and earlier models have predicted the homogeneous arrangement of receptors on the cell surface for optimal ligand binding and activation
Ligands arranged in a hexagon with the right geometry doubled the rate of apoptosis compared to ligands arranged in pairs [25]
Signaling efficiency can be greatly improved in cooperative signaling networks by clustering receptors on the cell surface. We can simplify such cooperative networks as planar graphs, where the input signal is represented by the vertices or nodes, the output signal is represented by the edges, and the relationship between them is determined by Euler’s polyhedron formula

Summary

Introduction

Membrane receptors allow cells to respond to external stimuli, and earlier models have predicted the homogeneous arrangement of receptors on the cell surface for optimal ligand binding and activation. This is in contrast to a growing body of experimental evidence suggesting that signaling efficiency can be greatly improved by the clustering of receptors [1,2]. Other examples of hexagonal clustering include chemo- or phototaxis receptors [2,13,14] These represent examples of receptors that are able to self-assemble on the cell surface on the basis of their inherent symmetry, this does not rule out the participation of other proteins in the process. We hypothesize that clustering may result in signal amplification that depends on cluster size and geometry and illustrate how ordered nanoclustering can provide an optimal solution to the biological information-processing problem

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Results and Discussion

Conclusions