NNB conceived and designed the experiments. NNB, LAS, and DOS performed the experiments. NNB, LAS, and DOS analyzed the data. ML edited the paper and provided a nurturing environment. NNB wrote the paper.
¤ Current address: Samuel Lunenfeld Research Institute, Toronto, Ontario, Canada
The authors have declared that no competing interests exist.
Of the many important signaling events that take place on the surface of a mammalian cell, activation of signal transduction pathways via interactions of cell surface receptors is one of the most important. Evidence suggests that cell surface proteins are not as freely diffusible as implied by the classic fluid mosaic model and that their confinement to membrane domains is regulated. It is unknown whether these dynamic localization mechanisms function to enhance signal transduction activation rate or to minimize cross talk among pathways that share common intermediates. To determine which of these two possibilities is more likely, we derive an explicit equation for the rate at which cell surface membrane proteins interact based on a Brownian motion model in the presence of endocytosis and exocytosis. We find that in the absence of any diffusion constraints, cell surface protein interaction rate is extremely high relative to cytoplasmic protein interaction rate even in a large mammalian cell with a receptor abundance of a mere two hundred molecules. Since a larger number of downstream signaling events needs to take place, each occurring at a much slower rate than the initial activation via association of cell surface proteins, we conclude that the role of co-localization is most likely that of cross-talk reduction rather than coupling efficiency enhancement.
Cells coordinate activities with their neighboring cells by releasing and responding to chemical signals, such as hormones and growth factors. These extracellular signals often are transmitted to the intracellular regulatory machinery through associations of freely diffusing cell surface receptors whose random movement (Brownian motion) results from collisions with thermally agitated lipid molecules. Receptors on the cell surface signaling proteins are co-localized transiently on membrane patches, but how such spatial restriction contributes to signal transduction is unclear. Batada and colleagues set out to determine which is more likely to be the biophysical function of co-localization: increasing coupling efficiency of slowly diffusing membrane proteins or reducing cross talk along pathways with common intermediates. Using a mathematical model to describe Brownian motion–based association of receptors on a 2-D spherical surface, the authors show that the rate of signal transduction initiation is extremely fast compared with the cytoplasmic signal relay events, even when the number of receptors is low. Because enhancement of a process that is already fast is not beneficial to the cell, minimization of detrimental cross talk among pathways is the most likely reason why cells need to co-localize plasma membrane signaling proteins.
The surface of a eukaryotic cell is embedded with a diversity of receptors that serve as the primary conduits for transmission of environmental information into the cell's signaling network. Binding of extracellular chemical signals to receptors and the subsequent interaction of these ligand occupied receptors constitute primary and necessary events in the activation of many signal transduction pathways[
Why has a dimerization mechanism evolved when a single monomer could do just as well? Dimerization may aid signaling via presentation of more exposed intracellular signaling domains, creating larger and more diverse interfaces for recognition of cytosolic transducer and linker molecules [
How does the cell ensure reliable and fast response for the dimerization triggered signal transduction initiation? The picture of a cell surface membrane as a sea of lipids in which transmembrane proteins diffuse freely as suggested by the fluid mosaic model [
How does co-localization of cell surface proteins affect signal transduction? In the context of signal transduction, there are potentially two biophysical reasons for limiting the range of membrane proteins: first, to insulate pathways that share common intermediates (i.e., to increase the specificity of response), and second, to enhance the activation rate by increasing coupling efficiency of the membrane embedded components of these pathways. The enhancement of interactions may be important because the diffusion coefficient of receptors and proteins on the cell surface membrane are generally more than two orders of magnitude smaller than in the cytoplasm [
How do proteins diffuse on the cell surface? Erratic motions of macromolecules are caused by collision with thermally powered molecules in the medium; in the case of cell surface receptors, movement is driven by incessant collisions with the lipid molecules of the membrane bilayer. Evidence for the existence of obstacles to protein movement has been obtained for several cell types by imaging experiments [
Suppose (
Figure 1 verifies that the SDE constructed in
(A)
We use the term dimerization to describe the physical association event between freely diffusing cell surface proteins and receptors, and limit the scope of our model to dynamic hetero-dimerization—those situations where protein–protein interaction event itself is part of a decision point in the signaling process. We make the following two assumptions: 1) signal transduction activation via interaction of membrane proteins is diffusion controlled; 2) exocytosis (the process that inserts proteins into the cell surface) and endocytosis (the process that removes proteins from the cell surface) activities are constitutive (i.e., occurring continuously and independently of the presence of ligand) and uniform throughout the cell surface [
The term
As soon as receptors are introduced onto the cell surface, they undergo isotropic Brownian motion. At any given time, there is a small constant probability that a protein may be removed from the cell surface via endocytosis. If at any time two receptors of different type come within close proximity, they may form an active dimeric complex with probability
Using the receptor dimerization model described in the previous section, we would like to derive the mean rate at which different types of receptors interact at steady state upon uniform activation by some extracellular chemical signal. Simulation studies [
For a pair of Brownian motions (
If
Let
After accounting for steady state levels of proteins of each type, rescaling to general radius
For certain combinations of physiologically relevant parameters,
Since the number of proteins of type
For a mammalian cell,
Is the activation of a signal transduction pathway via dimerization of receptors on the cell membrane the rate-limiting step in the overall signaling process? The standard chemical kinetics measure of association, given in units of
A typical signal transduction involves multiple distributive interactions, such as recruitment of signaling proteins to activated receptor complexes and the subsequent protein–protein interactions and post-translational modifications before the activated transcription factors diffuses into the nucleus and bind to an appropriate gene promoter. As the latter step is relatively quick [
Inspired by the recent experimental findings that maintenance of dynamic spatial inhomogeneity of membrane proteins is achieved by transient confinement in high viscosity membrane patches such as lipid rafts [
How sensitive is our conclusion to variations in parameters? A key parameter in
We note some limitations of our model. First, we have assumed constitutive endocytosis. But in some cases endocytosis is regulated such that activated receptor complexes are preferentially internalized [
Although high viscosity patches such as lipid rafts and caveolins are shown to play a key part in membrane trafficking and signal transduction, their functional role is unclear. Our finding that dimerization-based signal transduction activation is not the rate-limiting event in the overall signal transduction in response to extracellular signals, provides theoretical support against the view that membrane domains function to enhance coupling efficiency of receptors. We propose that the more likely function of plasma membrane co-localization mechanisms such as receptor clustering is to minimize nonspecific cross talk between disparate pathways that share membrane components.
In this section, we give a detailed derivation of the interaction rate given in
First note that if (
Let
To express
Using the formula 15.3.10 in Abramowitz and Stegun [
Finally, the rate at which particles of different types with birth rates
In this section, we derive the mean interaction time of two cell surface proteins starting
If the distance between two proteins on a sphere is uniformly distributed, then the expected value of the meeting time (after rescaling with
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A matlab program to compute the rate at which receptors/proteins interact (on a spherical cell surface).
(38 KB DOC)
We thank Joseph Schlessinger, Anirvan Sengupta, and the anonymous reviewers for helpful comments on the manuscript.
stochastic differential equation