Spatial partitioning improves the reliability of biochemical signaling

Abstract

Spatial heterogeneity is a hallmark of living systems, even at the molecular scale in individual cells. A key example is the partitioning of membrane-bound proteins via lipid domain formation or cytoskeleton-induced corralling. However, the impact of this spatial heterogeneity on biochemical signaling processes is poorly understood. Here, we demonstrate that partitioning improves the reliability of biochemical signaling. We exactly solve a stochastic model describing a ubiquitous motif in membrane signaling. The solution reveals that partitioning improves signaling reliability via two effects: it moderates the nonlinearity of the switching response, and it reduces noise in the response by suppressing correlations between molecules. An optimal partition size arises from a trade-off between minimizing the number of proteins per partition to improve signaling reliability and ensuring sufficient proteins per partition to maintain signal propagation. The predicted optimal partition size agrees quantitatively with experimentally observed systems. These results persist in spatial simulations with explicit diffusion barriers. Our findings suggest that molecular partitioning is not merely a consequence of the complexity of cellular substructures, but also plays an important functional role in cell signaling.

Fig. 1.

Schematic depiction of the model system. (A) We consider a model representative of signal detection by receptors and signal transmission at the cell membrane. (B) The model consists of two molecular species ( and ), which can each exist in active (X∗, Y∗) or inactive (X, Y) states. Molecules in the X state are activated by the external signal of strength α, and active X∗ molecules subsequently activate Y molecules. (C) We consider these reactions taking place in a single domain with all components well mixed, or in a domain consisting of smaller compartments, which are each individually well mixed but between which no interaction is possible. The total system volumes in the two scenarios are equal and assumed to scale with the number of molecules.

Fig. 2.

Spatial partitioning improves signaling performance. (A) The mean response 〈n〉/N as a function of the mean X∗ activity q = 〈m〉/M = α/(α + 1), and (B) the output variance as a function of the mean response, plotted for a well-mixed system with M = N = 2 (thick solid) and a partitioned system of π = 2 compartments, each containing one and one molecule (thick dashed). Partitioning linearizes the output response and reduces noise across the full range of responses, leading to a higher transmitted information. The thin solid curves show the mean field response 〈n〉/N = βq/(βq + 1) in A and the binomial noise limit (3) in B. Allowing exchange of molecules between compartments (thick dot-dashed) compresses the output response and increases the noise compared with the perfectly partitioned system, dramatically reducing information transmission. Here, β = 20 and γ = 1.

Fig. 3.

Partitioning reduces correlations between output modules. (A) In the partitioned system, each molecule receives an independent signal m_i(t). The variance is simply that of independent two-state switches. (B) In the well-mixed system, each molecule reacts to the same m(t), which leads to correlations between in the states of different molecules and an increase in the variance . Sample trajectories are generated using parameters as in Fig. 2, with α = 1.

Fig. 4.

Exchange between partitions leads to different configurations of the system with a range of signaling performance. Multiplicities listed above each configuration are due to symmetry. Parameters are as in Fig. 2.

Fig. 5.

An optimal partition size. (A) For M = N > 3 molecules, a system with π > 1 partitions achieves higher information transmission that a well-mixed system (π = 1). (B) As M = N is increased, the optimal partition number also increases such that the optimal number of proteins per partition M/π∗ = N/π∗ ∼ 3 is roughly constant. Parameters are as in Fig. 2.

Fig. 6.

The effects of partitioning persist in simulations with explicit diffusion. As the probability of crossing a diffusion barrier p_hop is decreased, (A) the mean response becomes more graded, and (B) the output noise decreases. (C) The information transmission has a maximum as a function of the partition size. Here M = N = 49, β = 20, γ = 1, the system is λ = 70 lattice spacings squared, and the ratio of diffusion to reaction propensities is p_D/p_r = 1. In A and B, π = 49; in C, p_hop = 0.001, and the partition size is varied by taking from 25 to 1.