What happens to facilitated diffusion when the protein carriers become saturated?

Facilitated Diffusion Requires Membrane Carrier Proteins

Facilitated diffusion is also calledcarrier-mediated diffusion because a substance transported in this manner diffuses through the membrane with the help of a specific carrier protein. That is, the carrierfacilitates diffusion of the substance to the other side.

Facilitated diffusion differs from simple diffusion in the following important way. Although the rate of simple diffusion through an open channel increases proportionately with the concentration of the diffusing substance, in facilitated diffusion the rate of diffusion approaches a maximum, called Vmax, as the concentration of the diffusing substance increases. This difference between simple diffusion and facilitated diffusion is demonstrated inFigure 4-7. The figure shows that as the concentration of the diffusing substance increases, the rate of simple diffusion continues to increase proportionately but, in the case of facilitated diffusion, the rate of diffusion cannot rise higher than the Vmax level.

What is it that limits the rate of facilitated diffusion? A probable answer is the mechanism illustrated inFigure 4-8. This Figure shows a carrier protein with a pore large enough to transport a specific molecule partway through. It also shows a binding receptor on the inside of the protein carrier. The molecule to be transported enters the pore and becomes bound. Then, in a fraction of a second, a conformational or chemical change occurs in the carrier protein, so that the pore now opens to the opposite side of the membrane. Because the binding force of the receptor is weak, the thermal motion of the attached molecule causes it to break away and be released on the opposite side of the membrane. The rate at which molecules can be transported by this mechanism can never be greater than the rate at which the carrier protein molecule can undergo change back and forth between its two states. Note specifically, though, that this mechanism allows the transported molecule to move—that is, diffuse—in either direction through the membrane.

Among the many substances that cross cell membranes by facilitated diffusion areglucose and most of theamino acids. In the case of glucose, at least 14 members of a family of membrane proteins (calledGLUT) that transport glucose molecules have been discovered in various tissues. Some of these GLUT proteins transport other monosaccharides that have structures similar to that of glucose, including galactose and fructose. One of these, glucose transporter 4 (GLUT4), is activated by insulin, which can increase the rate of facilitated diffusion of glucose as much as 10- to 20-fold in insulin-sensitive tissues. This is the principal mechanism whereby insulin controls glucose use in the body, as discussed inChapter 79.

6.6.1 Diffusion in Inhomogeneous and Anisotropic Media

Macroscopic diffusion model is based on underlying microscopic dynamics and should reflect the microscopic properties of the diffusion process. A single diffusion equation with a constant diffusion coefficient may not represent inhomogeneous and anisotropic diffusion in macro and micro scales. The diffusion equation from the continuity equation yields

(6.302)∂P∂t=−∇⋅J

where P and J are the density (probability or number) and diffusion flow of the particles. Following Christensen and Pedersen (2003), a definition for the diffusion flow J is

(6.303)J=−( Pμˆ∇V+Dˆ∇P)

where V is an external potential, μˆ is the mobility, and Dˆ is the diffusion tensor given by the Einstein relation

(6.304)μˆkT=Dˆ

In Eq. (6.303), the first term represents the drift in the potential force field V and the second is the diffusional drift given by Fick's law. Combining Eq. (6.302) with Eq. (6.303), we have

(6.305)∂P∂t=∇⋅(Pμˆ∇V+Dˆ∇P)

Since Eq. (6.305) cannot represent systems with inhomogeneous temperatures, we may have the following alternative equation

(6.306)∂P∂t=∇⋅(Pμˆ∇V+ ∇⋅DˆP)=∇⋅(P(μˆ∇V+∇⋅ Dˆ)+Dˆ∇P)

Equations (6.305) and (6.306) are different because of the drift term ∇ ⋅(P∇⋅Dˆ), which is sometimes called a “spurious” drift term. These diffusion equations have different equilibrium distributions and are two special cases of a more general diffusion equation.

Some carriers facilitate the passive diffusion of small solutes such as glucose

Carrier-mediated transport systems transfer a broad range of ions and organic solutes across the plasma membrane. Each carrier protein has a specific affinity for binding one or a small number of solutes and transporting them across the bilayer. The simplest passive carrier-mediated transporter is one that mediatesfacilitated diffusion. Below, we will introducecotransporters (which carry two or more solutes in the same direction) andexchangers (which move them in opposite directions).

All carriers that do not either hydrolyze ATP or couple to an electron transport chain are members of thesolute carrier (SLC) superfamily,

N5-8

The SLC Superfamily of Solute Carriers

The SLC superfamily was the subject of a series of reviews—one per family member—in 2013. The reference below is the introduction to the series.

Summary

Solutes move by diffusion from regions of high concentration to regions of low concentration. Fick’s First Law of Diffusion states that the flux is proportional to the negative of the gradient of C:

Js=−D∂C∂x

where Js is the solute flux, D is the diffusion coefficient, and ∂C/∂x is the one-dimensional gradient. The continuity equation states that changes in concentration with time must be due to changes in flux with distance:

∂C∂t=−∂Js∂x

Fick’s Second Law of Diffusion derives from his First Law and the Continuity Equation:

∂C∂t=D∂2C∂x2

Fick’s Second Law can be derived from a random walk model of diffusion in which molecules take large numbers of small steps. Using Stirling’s approximation, the discrete binomial probability distribution can be converted to a continuous one, resulting in a Gaussian probability distribution. For a narrow starting distribution at time t=0, the distribution of solute at time t is given as

C(x,t) =C01/4πDte−x2/4Dt

From the random walk, D is identified as λ2/2tc, where λ is the distance between collisions and tc is the time between collisions. The time of diffusion is typically estimated as the variance of the Gaussian distribution, which gives

t=x22D

Although diffusion is a statistical result, it is equivalent to a force in that it produces a flow of material. Other forces can also make solutes move. These forces include electrical forces on charged solutes, solvent drag (convection), and gravitational forces. An external force applied to solute particles causes a flux given by

J=DkTfC

where f is the force per molecule, k is Boltzmann’s constant (k=R/N0), T is the absolute temperature, and C is the concentration. In the presence of a concentration gradient, the total diffusive flux in the presence of an external force is

J=−D∂C∂x+Df CkT

Stokes derived an equation for the drag force on a spherical object. Einstein combined this with his expression for the drag force in terms of the diffusion constant and gave us the Stokes–Einstein equation:

D=kT6πηas

where η is the viscosity of the medium in which diffusion occurs and as is the radius of a spherical solute.

Facilitated Diffusion

Like simple diffusion, facilitated diffusion occurs down an electrochemical potential gradient; thus it requires no input of metabolic energy. Unlike simple diffusion, however, facilitated diffusion uses a membrane carrier and exhibits all the characteristics of carrier-mediated transport: saturation, stereospecificity, and competition. At low solute concentration, facilitated diffusion typically proceeds faster than simple diffusion (i.e., is facilitated) because of the function of the carrier. However, at higher concentrations, the carriers will become saturated and facilitated diffusion will level off. (In contrast, simple diffusion will proceed as long as there is a concentration gradient for the solute.)

An excellent example of facilitated diffusion is the transport ofd-glucose into skeletal muscle and adipose cells by theGLUT4 transporter. Glucose transport can proceed as long as the blood concentration of glucose is higher than the intracellular concentration of glucose and as long as the carriers are not saturated. Other monosaccharides such asd-galactose, 3-O-methyl glucose, and phlorizin competitively inhibit the transport of glucose because they bind to transport sites on the carrier. The competitive solute may itself be transported (e.g.,d-galactose), or it may simply occupy the binding sites and prevent the attachment of glucose (e.g., phlorizin). As noted previously, the nonphysiologic stereoisomer,l-glucose, is not recognized by the carrier for facilitated diffusion and therefore is not bound or transported.

Publisher Summary

This chapter describes the phenomenon of diffusion in the body box. Diffusion is the process of transfer of gas from alveolus to blood. A variety of methods can be used to measure the transfer factor: the steady state method, the single-breath method, and the rebreathing method. The steady state method can be used in even severely disabled subjects, and it can be used during exercise. A major disadvantage of the method is that the pattern of breathing may affect the results. The steady breathing method involves inspiring a gas mixture containing approximately 0.3 percent carbon monoxide and 14 percent helium in air. The breath is held for approximately ten seconds, and an alveolar sample is then collected after a washout of dead space. The consequent analysis of the volume inspired and the breath holding time makes it possible to calculate the transfer factor. This method is readily repeatable, independent of breathing pattern, and standardized. A separate measurement of residual volume is required for patients with respiratory disabilities.

13.2 DIFFUSION

Diffusion is the spreading-out of a material into its surroundings. The two major types encountered are molecular diffusion and eddy diffusion. Molecular diffusion can be denned as the transport of matter on a molecular scale through a stagnant fluid or, if the fluid is in laminar flow, in a direction perpendicular to the main flow (see section 3.5).

In contrast, eddy diffusivity is concerned with mass transfer processes involving bulk fluid motion.

In practice the two types of diffusion processes are found together but it is the molecular diffusion processes that has a major influence in many processes because it is concerned with mass transfer over the boundary layer which exists in all flow situations and within the food matrix, where it is not usually possible to induce turbulence. Much of the following discussion will be concerned with molecular diffusion and diffusivity measurement in gases, liquids and solids.

Abstract

Diffusion is a major transport mechanism in living organisms. In the cerebellum, diffusion is responsible for the propagation of molecular signaling involved in synaptic plasticity and metabolism, both intracellularly and extracellularly. In this chapter, we present an overview of the cerebellar structure and function. We then discuss the types of diffusion processes present in the cerebellum and their biological importance. We particularly emphasize the differences between extracellular and intracellular diffusion and the presence of tortuosity and anomalous diffusion in different parts of the cerebellar cortex. We provide a mathematical introduction to diffusion and a conceptual overview of various computational modeling techniques. We discuss their scope and their limit of application. Although our focus is the cerebellum, we have aimed at presenting the biological and mathematical foundations as general as possible to be applicable to any other area in biology in which diffusion is of importance.

How MR can Measure Diffusion

Diffusion MR observes Brownian motion by tagging populations of water molecules and observing their movements (Tanner and Stejskal, 1968). The diffusion MR experiment is analogous to a simple diffusion experiment where a drop of dye is placed in a bowl of water. Using the equations for diffusion, the observed change in the dye’s concentration can be used to calculate the diffusion coefficient of the liquid. MR diffusion techniques are sensitive to the magnitude of the diffusion coefficient and work in much the same way. Instead of visible dye, a known concentration gradient of spin-labeled water molecules is established with the MR scanner and then changes in concentration are measured over time. The MR signal in a diffusion-weighted image is related to the diffusion coefficient as follows:

(3.2.2)SS0=e−bD

In this relationship, S refers to the intensity of the MR signal when the diffusion gradient is applied. As the diffusion coefficient increases, the value of S decreases. The term S0 refers to the baseline MR signal level without diffusion weighting. The ratio of S to S0 is related to the b-value and the (apparent) diffusion coefficient, D, of the water. The b-value is related to the level of diffusion weighting applied. The b-value must be sufficiently high to observe anisotropic diffusion. A typical clinical diffusion tensor scan uses a b-value of approximately 1,000 s/mm2. Since each scan encodes diffusion in a single specific direction, multiple diffusion-weighted scans are required to represent the directional differences in diffusion (note at least six directions are required to be encoded for simple DTI; more are required for advanced modeling).

Abstract

Diffusion is the basic mode of transport for molecules in living cells. Diffusion leads to dispersion of individual molecules, but it is also the driving force behind biochemical reactions and pattern formation as diffusional motion mediates reactant encounters. Owing to macromolecular crowding in all cellular fluids and biomembranes, diffusion of molecules in cells is quite different from the motion observed in dilute solutions in a test tube. Hindered and anomalous diffusion are seen in cells, and biochemical reactions are affected by these. This review is intended to give an introduction and a brief overview about causes and consequences of crowding-induced diffusion anomalies and their impact on biochemical reactions.