Coupled membrane transporters reduce noise

Molecular systems are inherently probabilistic and operate in a noisy environment, yet, despite all these uncertainties, molecular functions are surprisingly reliable and robust. The principles used by natural systems to deal with noise are still not well understood, especially in a nonhomogeneous environment where molecules can diffuse across different compartments. In this paper we show that membrane transport mechanisms have very effective properties of noise reduction. In particular, we show that active transport mechanisms (those that can transport against a gradient of concentration by using energy or by means of the concentration gradient of other substances), such as symporters and antiporters, have surprising efficiency in noise reduction, which outperforms passive diffusion mechanisms and are well below Poisson levels. We link our results to the coupled transport of potassium, sodium, and glucose to show that the noise in internal glucose level can be greatly reduced. Our results show that compartmentalization can be a highly effective mechanism of noise reduction and suggests that membrane transport could give this extra benefit, contributing to the emergence of complex compartmentalization in eukaryotes.

Figure 1

Transporters: Common transmembrane transporters (top) and their respective reaction schemes [(I), (II), and (III)], where circles denote species and squares denote reversible reactions. Subscripts indicate compartment numbers (inside or outside the membrane). Direct reactions have solid arrowhead, while inverse (assumed weaker) reactions have hollow arrowheads. Ambient noise (indicated by noisy graphs) is applied to the input species.

Figure 2

Plot of upper bound of Fano factor of $B_2$ and $A_2$ at steady state as a function of the flux $r$ and of $b_{AB}.$ Lower bound is identically 0.5.

Figure 3

Combination of an antiporter with a symporter. In this example we consider a sodium-potassium antiporter pump coupled with a glucose-sodium symporter [16]. We test with this how extracellular (top, molecules with subscript 1) noise in all three molecules could affect intracellular (bottom, molecules with subscript 2) signals downstream of these molecules.

Figure 4

Fano factor intracellular glucose. The figure plots the Fano factor of $C_2$ at steady state as a function of the rate of the transport $k=k_3=k_4$ and the bursts on the input process $b_A.$ The figure has been obtained numerically by solving the LNA.

Figure 5

Comparison of a model where the degradation of the species is assumed to be slower compared to all the other rates (I) and one where degradation of the species is explicitly considered (II). All plots are obtained by performing stochastic simulations of the CME [15]. In both cases it is possible to observe how $A_2$ has reduced variability.

Figure 6

We consider a reaction network where a symporter is used to transport molecules of species A and B between two compartments (I). In II we plot the time evolution of mean and variance $A_1$ and $A_2$ according to a linear noise approximation of the CME [15]. In III we plot the time evolution of the same species according to the CME. It is possible to observe that while the variance is equal in both figures, the mean is slightly different. This is due to the fact that the LNA only considers the first two moments of the distribution and neglects corrections terms of order higher than the first to estimate the mean. Note that this difference becomes less and less important the more molecules are in the system and is already negligible when $A_1$ and $B_1$ have a mean of few tens of molecules at steady state.