Protein-protein interaction networks can be highly sensitive to the membrane phase transition

TL;DR

A model and a Monte Carlo simulation framework are presented to investigate how changes in the domain size that arise from perturbations to membrane criticality can lead to changes in the rate of interactions among components, leading to altered outcomes.

Abstract

Many protein-protein interaction (PPI) networks take place in the fluid yet structured plasma membrane. Lipid domains, sometimes termed rafts, have been implicated in the functioning of various membrane-bound signaling processes. Here, we present a model and a Monte Carlo simulation framework to investigate how changes in the domain size that arise from perturbations to membrane criticality can lead to changes in the rate of interactions among components, leading to altered outcomes. For simple PPI networks, we show that the activity can be highly sensitive to thermodynamic parameters near the critical point of the membrane phase transition. When protein-protein interactions change the partitioning of some components, our system sometimes forms out of equilibrium domains we term pockets, driven by a mixture of thermodynamic interactions and kinetic sorting. More generally, we predict that near the critical point many different PPI networks will have their outcomes depend sensitively on perturbations that influence critical behavior.

Figures (6)

• Figure 1: Effective reaction rates between components depend on solvent's distance to the critical point.A: Signal components are disks of spins that diffuse in the 2D Ising Model. At time $t_0$, an activator (black) comes in contact with an inactive target (pink). In the same time step, the target is activated (blue) at some fixed rate. During the next sweep, the activated target diffuses away. Because of coupling to Ising degrees of freedom, the effective rate of these reactions depends on the state of the surrounding membrane through their rate of coming into contact. B: Cascade diagram with component partitioning. Sign above reaction arrow (purple +/-) indicates that the pathway increases/decreases target activity. Sign below reaction arrow (orange +/-) indicates whether interaction rate increases or decreases with rescaled temperature. The product of these two signs (here positive in both cases) predicts how increasing temperature changes the target's activity. C: In this PPI the product of the upper and lower signs is positive for all reactions, indicating target activity should increase monotonically with respect to temperature, as sketched. While the explicit reaction rates do not change with temperature, the effective rate of the activating reaction increases while the deactivating reaction decreases as unlike components interact more at higher temperature and like components interact less.
• Figure 2: Interaction networks are highly sensitive to solvent properties near criticality. Results are from the interaction network depicted in figure \ref{['fig:model']}B when carried out with Monte Carlo simulation. A: Configurations of the simulation at a range of rescaled temperatures. As temperature increases domains become smaller and the target is more likely to be found near its activator which prefers a different domain, thus increasing the activity. B: Radially-averaged cross-correlation functions between the activators and targets (solid lines) and between the inactivators and targets (dashed lines) for the three temperature values in part A. As temperature is increased, the activator is found closer to the target while the inactivator is found more distant. C: The target's activity grows with rescaled temperature, most steeply near the critical point. D: Taking a closer look at the near-critical region of part C, the greatest increase in target activity occurs between $\tau=1$ and $\tau=1.1$. Binning the various simulation runs by activity clearly demonstrates the increased variance near the critical point.
• Figure 3: Larger components are more sensitive to critical solvent properties.A: Visual schematic of lattice shape for each disk radii discussed here. A network containing radii zero components has spatial configurations equivalent to the standard 2D Ising model. The solid boundary of each disk denotes the spins which interact with the solvent while the spins they bound have no impact. B: Activity data (diamond markers) for various disk radii along with the result of fitting each data set with a logistic function (solid lines). C: The growth width $\Delta \tau$ of the logistic curve fits from A. Increasing disk size results in a stronger sensor of $T_c$. The error bars here denote the 95% confidence interval for each $\Delta\tau$ value. All fit values are tabled in the supplement.
• Figure 4: PPIs with large components are also sensitive to the composition parameter parallel to the tie-lines. In the Ising model, this is parameterized by magnetization, $m$, which previous figures take to be zero (equal area of bright and dark phases below $T_c$). Here we explore varying $m$ for systems with small components ($r=0$, A-C) and larger components ($r=3$D-F), for the interaction network depicted in figure \ref{['fig:model']}B. A,B: Activity as a function of $m$ for three values of temperature and activity as a function of temperature for three values of $m$. When components are small results do not depend strongly on $m$, though they do depend on temperature. C: configurations at two values of $m$ and $\tau$. At negative $m$, $\tau<1$ the system has less dark phase. Above the critical temperature, there are still fewer dark domains. D,E: Activity as a function of $m$ and $\tau$ for the same network with larger components, $r=3$. With these larger components the system is sensitive to both $m$ and $\tau$ near the critical temperature. F: At negative $m$, there is less dark phase similar to C, but the larger inclusions form higher contrast domains even above the critical temperature of the bare Ising model.
• Figure 5: Dynamics that modify component partitioning produce non-equilibrium domains.A: Diagram of an interaction network in which the target's partitioning is modified alongside its state. The target’s inactive state (pink) prefers disorder while its active state (blue) prefers order indicated by the respective membrane legs. Qualitative analysis suggest the target’s activity should increase with $\tau$. B: Mean activity measurements follow these predictions, but below the critical temperature a small number of simulations produce outliers with very high activity. We term this phenomenon pocketing and trace it to the formation of non-equilibrium domains. C: Three example configurations from simulations in which pockets form with their activity vs time traces below. We understand pocket formation kinetically. First, a pocket originates when an activator (dark preferring) and an inactive target (white preferring) meet in a disordered (white) domain, leading to target activation. Now each prefer the dark (ordered) domain and with some probability such a dark domain will form around them before they diffuse to a larger dark domain. We term this domain a pocket. Once this pocket is formed, inactive targets (white preferring) can diffuse through the surrounding white phase. But when they make contact with the pocket, they can be activated, preventing them from leaving. Dark lipids are small enough to diffuse through the white phase to join the pocket as well but inactivators are excluded kinetically. D,E: The same interaction network in a system with composition adjusted to $m=-0.4$ demonstrates an enhanced pocketing rate, including at temperatures $\tau > 1$.