10.2: Diffusion Across a Membrane - Passive and Facilitated Diffusion

 

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Learning Goals

(Learning goals written by Claude, Sonnet 4.6, Anthropic)

Thermodynamics and Kinetics of Passive Diffusion

• Apply Fick's First Law of Diffusion to predict the direction and magnitude of solute flux across a membrane as a function of the concentration gradient, diffusion coefficient, membrane thickness, and permeability coefficient, and explain why a plot of flux versus concentration difference is linear for passive diffusion.
• Explain how solute size, polarity, and charge density determine the permeability coefficient for membrane crossing, and use the electrochemical potential — combining chemical potential and electrical potential — to describe the thermodynamic driving force for the passive diffusion of charged solutes across a membrane with a transmembrane potential.
• Derive the conditions under which net ion flux across a membrane ceases, relate this to the Goldman equation, and compare it to the Nernst equation used in electrochemistry to describe equilibrium reduction potentials.

Facilitated Diffusion: Mechanism and Kinetics

• Derive the hyperbolic relationship between initial solute flux and external solute concentration for facilitated diffusion mediated by a carrier protein, identify the kinetic parameters J_max and K_D by analogy to enzyme kinetics and equilibrium binding equations, and explain the physical assumptions (k₂ >> k₃; A₀ >> R₀) that validate this treatment.
• Distinguish between carrier proteins (permeases/transporters) and channel proteins as the two classes of facilitators of passive diffusion, explaining how each mediates solute movement — conformational change driving alternating access in carriers versus ligand-gated or voltage-gated pore opening in channels — and why the mathematical treatment derived for carriers does not apply to channels.

Biological Examples of Facilitated Diffusion

• Describe the structural and functional properties of the glucose transporter GLUT1 as a model carrier protein, explain how its inward-open and outward-open conformational states mediate glucose translocation down a concentration gradient, and contrast constitutive (GLUT1) with insulin-regulated (GLUT4) glucose uptake.
• Explain why the mitochondrial ADP-ATP carrier protein can operate by facilitated diffusion without requiring ATP hydrolysis, and connect the direction of net ADP-ATP exchange across the inner mitochondrial membrane to the concentration gradients established by oxidative phosphorylation.
• Evaluate the evidence for and against passive versus facilitated diffusion of long-chain fatty acids across the plasma membrane, describe the roles of albumin, cytoplasmic fatty acid-binding proteins (FABPs), CD36, and fatty acid transport proteins (FATPs) in buffering and transferring free fatty acids, and explain why free fatty acid concentrations must be maintained well below the critical micelle concentration.

Diffusion Across a Membrane

We have studied molecular aggregates (micelles and bilayers) and macromolecular structures (mostly proteins). We also studied binding interactions, which are the first steps in a macromolecule's biological activity. For some proteins, reversible binding is their sole function (consider the binding of dioxygen to myoglobin and hemoglobin). For many others, it is not. For those, what can happen next?

You already have one possible answer. A bound reactant, which we will call a substrate, can be converted to a product in a chemical step involving the breaking and making of covalent bonds catalyzed by a protein enzyme. However, there is an even simpler process that does not involve changes to covalent bonds. If a small molecule is bound to a membrane protein, it could be transported in a purely physical step across a membrane. Just as reactions can proceed with and without an enzyme, a solute can move down a concentration gradient across a semipermeable membrane, driven by diffusion alone in a thermodynamically favorable process, either by itself, in a process called passive diffusion, or with the assistance of a membrane protein, in a process called facilitated diffusion. Large pores composed of protein assemblies can also form, allowing the passage of many solutes across the membrane.

There are many occasions when moving a molecule across a membrane from a region of low to a region of high concentration would be optimal. This process is called active transport. It is not thermodynamically favored, so it requires an external energy source. This is often the thermodynamically favored cleavage of ATP to ADP and Pi. The uphill transport can also be powered by the downhill diffusion of a "co-transport" molecule from high to low concentration. We will explore these processes in this and the remaining chapter sections. First, we should understand the simplest process, "passive diffusion", that requires no protein "help".

Let's step back and consider how difficult it is for a chemical species to cross a lipid bilayer. Chemical intuition suggests that both size and polarity are important. The bigger the size and the greater the charge, the more difficult it would be to cross the membrane. The permeability coefficient is related to the ease with which solutes traverse the membrane. Figure \(\PageIndex{1}\) shows the permeability coefficients for relevant biological molecules.

Figure \(\PageIndex{1}\): Permeability coefficients for relevant biological molecules

Smaller, higher charge density ions (like Na⁺) have a lower permeability coefficient than do larger, lower charge density ions (like K⁺) as seen in (Table \(\PageIndex{1}\)). What about natural membranes?

Table \(\PageIndex{1}\): Permeability coefficient (cm/s) of natural and synthetic membranes to D-Glucose and D-mannitol at 25 °C

Membrane Preparation	D-Glucose	D-Mannitol
Synthetic Lipid Bilayer	2.4 x 10^-10	4.4 x 10^-11
Calculated Passive Diffusion	4 x 10^-9	3 x 10^-9
Intact Human Erythrocyte (red blood cell)	2.0 x 10^-4	5 x 10^-9

It looks like D-glucose gets a little help getting across. We'll see the mechanism below.

Passive Diffusion

Let's start with the passive diffusion of uncharged solute A across a membrane, represented by the chemical equation A_out ↔ A_in. Intuitively, you probably believe that the rate of net diffusion or the flux of A across the membrane is directly proportional to the concentration gradient. If concentrations of A are identical across the membrane, the net flux J should be 0. If you double the concentration gradient, the net rate should double. We will see that the net rate is a linear function of [ΔA] across the membrane. Figure \(\PageIndex{2}\) shows the flux of A_out across a semipermeable membrane of thickness Δx (we will use dx instead when Δx is very small).

Figure \(\PageIndex{2}\): Flux of A_out across a semipermeable membrane of thickness Δx

Let's animate diffusion using a PHET simulation, as shown in Figure \(\PageIndex{3}\).

Figure \(\PageIndex{3}\): PHET animation of passive diffusion. PHET: https://phet.colorado.edu/

The flux of molecules \(A\) (\(J__A\)) is proportional to the concentration gradient across the membrane, \(ΔA/Δx\) (which we will refer to as \(dA/dx\), which is the derivative of \(A\) with respect to \(x\)). The equation below is Fick's First Law of Diffusion:

\[\mathrm{J}_{\mathrm{A}} \propto \frac{d \mathrm{~A}}{d x}=-\mathrm{D} \frac{d \mathrm{~A}}{d x} \label{Ficks1}\]

where \(D\) is the diffusion coefficient. The negative sign is necessary since concentration increases to the left in the figure above in the opposite direction of net flux, which is to the right. For these derivations, we will assume the J_A is the initial flux. That is, the flux is measured for a short enough time that the relative concentrations of A on both sides of the membrane do not change significantly. It should be clear that eventually, the net flux levels off to zero when the concentrations of A on both sides of the membrane are equal. Under these conditions, the free energy \(G_{A\, out}\) = \(G_{A\, in}\), so \(ΔG = 0\). This thermodynamic relation can also be expressed as

\begin{equation}
J_A=-L \frac{d G_A}{d x}
\end{equation}

This equation bridges the kinetic and thermodynamic aspects of diffusion.

Dimensional analysis of Fick's 1st Law (Equation \ref{Ficks1}) shows that the units of \(D\) are cm²/s, which gives the number (dimensionless) of molecules crossing a 1 cm² surface area of membrane each second.

\(J\) = moles/area/sec = mol/cm^2.s = - (cm²/s) mol/cm³/cm. Hence, the units of \(D\) are cm²/s.

Let's rearrange Fick's 1st Law and use a bit of calculus to get Equation 4.

\begin{equation}
\begin{gathered}
\mathrm{J}_{\mathrm{A}} \int_0^{\mathrm{x}} \mathrm{dx}=-D \int_{\mathrm{A}_{\text {out }}}^{A_{\mathrm{in}}} \mathrm{dA} \\
\mathrm{J}_{\mathrm{A}} \mathrm{x}=-\mathrm{D}\left(\mathrm{A}_{\mathrm{in}}-\mathrm{A}_{\mathrm{out}}\right) \\
\mathrm{J}_{\mathrm{A}}=\frac{\mathrm{D}}{\mathrm{x}}\left(\mathrm{A}_{\text {out }}-\mathrm{A}_{\mathrm{in}}\right)
\end{gathered}
\end{equation}

or

\begin{equation}
J_A=P\left(A_{\text {out }}-A_{\mathrm{in}}\right)=P \Delta A
\end{equation}

where P is the permeability coefficient, which has units of cm²/s/cm or cm/s. (We discussed permeability coefficients for different solutes traversing model bilayers when we discussed lipids.) That unit is less intuitive, but the final unit is very intuitive.

A plot of J_A vs (A_out - A_in) is linear, with a slope of P = D/x

It's important to remember that diffusion of A across the membrane continues at equilibrium, since the equilibrium is dynamic. There is no net diffusion, however. This is where animations come in handy.

The table below shows the reaction diagram (left), the progress curve (middle), and animations of reversible diffusion A_out ↔ A_in across a membrane under the conditions below. The reactant A and product are called species and are shown as green spheres. The yellow square is a reaction node indicating a reaction connects A to P. The lines connect the species that participate in the reaction. The velocities (the slope of the concentration vs. time curve at any given time) are called fluxes, J, in Vcell and many other similar programs. When we get to metabolism, we will talk about fluxes of metabolites through pathways. Also, fluxes describe the rate of solute movement through membranes.

VcellModel

Initial Conditions

Click Select Omex below to run the simulation produced in Vcell.

 

 

Animations

Now, let's look at animations of the same passive diffusion reaction of a neutral species across a semipermeable membrane. Animations are by Shraddha Nakak and Hui Liu.

Aout ↔ Ain [Ain]t=0 = 100; [Aout]t=0 = 0; P = 2	Aout ↔ Ain [Ain]t=0 = 50; [Aout]t=0 = 0; P = 2

Note the dynamic nature of the diffusion. An equilibrium is reached when the number of particles inside equals that outside. Diffusion occurs in both directions from compartments of equal volume so that the particles moving to the outside don't escape into a comparatively huge volume. (Animations by Shraddha Nayak and Hui Lui)

Passive Diffusion of ions across a membrane - Transmembrane Potentials

Before moving on to facilitated diffusion, let's alter the scenario and use a charged solute. In the example of passive diffusion above, the only thermodynamic driving force for the movement of A across the membrane was the ΔG_A, the change in free energy/mol of A across the membrane (or more strictly Δμ = change in chemical potential). Solute A moves spontaneously across the membrane from high to low concentration. But what if A was charged?

We could add a bunch of positively or negatively charged species to Figure \(\PageIndex{2}\) and ask what would happen. You can't go to a chemical stockroom and find a bottle of K⁺ ions, but you could find a bottle of neutral KCl. Let's set up our experiment system as a vesicle with an aqueous inner compartment containing 0.1 M KCl and an outer compartment containing 0.1 M NaCl. We could easily prepare such vesicles by making large unilamellar vesicles (LUVs) with entrapped 0.1M KCl in a solution of 0.1 M KCl and then separating the vesicles from the 0.1 M KCl not encapsulated on liposome formation using a size exclusion gel chromatography column equilibrated and eluted in 0.1 M NaCl. These vesicles are illustrated on the left of Figure \(\PageIndex{4}\).

Figure \(\PageIndex{4}\): Making vesicles with a transmembrane potential

In these prepared vesicles, is there a net thermodynamic driving force for K⁺ and Cl^- to move from inside to outside the vesicle? Not for Cl^- since its concentration is the same on both sides of the membrane (see Fick's 1^st Law above). However, a clear thermodynamic driving force is needed to take K⁺_in → K⁺_out. If the membrane were impermeable, net outward flux would not occur even though it is favored thermodynamically. Think of this as an example of a reaction under complete kinetic control! Note that this example also has a net driving force to move Na⁺ ions from outside to inside.

In our next step, let's make the membrane permeable to only K⁺ ions. We can do this by adding a small antibiotic, valinomycin, which binds to the membrane and, once there, carries K⁺ ions across it. It is called an ionophore. Figure \(\PageIndex{5}\) shows an interactive iCn3D model of K⁺ bound to Valinomycin.

Figure \(\PageIndex{5}\): K⁺ bound to Valinomycin (xxxx). (Copyright; author via source). Click the image for a popup or use this external link: Not available.

Valinomycin, from Streptomyces fulvissimus, is a cyclic peptide consisting of L and D-Val, L-lactate, and D-hydroxy isovalerate, connected through both ester and amide bonds. The K⁺ ion is in the center. The six valine carbonyl oxygens bind the K⁺ ion. The hydrophilic groups are pointed toward the center. In contrast, the hydrophobic groups point outward, allowing the K⁺ ion to be sequestered in a polar environment as the nonpolar exterior of the complex traverses the membrane. This ionophore is specific for K⁺ and binds Na⁺ weakly. Two factors can account for this. The smaller sodium ion binds less tightly to the chelating carbonyl oxygens. Also, the sodium ion has a higher charge density, so the Na⁺/water interactions must be more stable and difficult to break than those of K⁺. The ion must be desolvated before it binds to the complex. Other ionophores are specific for other ions.

Once the ionophore binds, the kinetic barriers to K⁺ efflux are removed, and K⁺ begins moving from inside to outside. However, as soon as it does, the charge balance across the membrane is lost, with the outside becoming net positive and the inside becoming net negative. A transmembrane electric potential develops across the membrane. This prevents K⁺ efflux to the outside and eventually stops it, even as the membrane concentration difference for K⁺ still favors efflux.

If you were a positive ion stuck in the middle of a membrane, as illustrated in Figure \(\PageIndex{6}\), which way would you move?

Figure \(\PageIndex{6}\): Which way does a positive ion move across a membrane with a transmembrane potential? (adapted from https://commons.m.wikimedia.org/wiki/File:Dib_1.jpg

There are now two thermodynamic driving forces for K⁺ movement from inside to outside:

• a ΔG_{concentration}, which favors K⁺ efflux. At time t=0, ΔG_{concentration} << 0, and it becomes a bit less negative (less favored) with efflux.
• a ΔG_{membrane pot}, which is zero to start and slowly becomes positive, increasingly disfavoring K⁺ efflux.

When these driving forces are equal and opposite, net K⁺ movement across the membrane stops, and the system is in dynamic equilibrium.

Since we use electric potential to describe electrical phenomena (electron, ion movement), we often use the word chemical potential, in this case, to describe the movement of ions across a concentration gradient. Add them together, and we call it the electrochemical potential.

\begin{equation}
\begin{array}{c}
\Delta \mathrm{G}_{\text {electrochemical }}=\Delta \mathrm{G}_{\text {chemical }}+\Delta \mathrm{G}_{\text {electrical }} \text { or } \\
\Delta \mu_{\text {electrochemical }}=\Delta \mu_{\text {chemical }}+\Delta \mu_{\text {electrical }}
\end{array}
\end{equation}

We can use this understanding to derive an equation for flux J of a charged solute across a membrane of a given potential. The equation is called the Goldman Equation and is shown below.

\begin{equation}
J=\frac{P \frac{Z F}{R T}\left(E_{1}-E_{2}\right) C_{1}\left(1-\frac{C_{2}}{C_{1}} e^{\frac{Z F}{R T}\left(E_{2}-E_{1}\right)}\right)}{1-e^{\frac{Z F}{R T}\left(E_{2}-E_{1}\right)}}
\end{equation}

where

• P is the permeability coefficient
• Z is the charge or valence on the ion
• F is the Faraday constant
• R is the ideal gas constant
• T is temperature
• E2-E1 and the reverse is the transmembrane potential
• C2-C1 are the concentrations of the ions across the membrane

Compare this to the Nernst equation you learned in introductory numerics. Solve the Goldman equation numerically

\begin{equation}
E=E^{o}-\frac{R T}{n F} \ln Q
\end{equation}

that relates the reduction potential of an electrochemical reaction to the standard electrode potential, temperature, and concentration, where E is the potential difference.

Now, let's run a Vcell simulation for the diffusion of an anion across a semipermeable membrane. To do so, we must first set the initial transmembrane potential to numerically solve the Goldman equation. At present, this type of simulation can not be embedded in this book. So instead, the concentration vs. time graphs for two simulations, one at an initial transmembrane potential (E₂-E₁) = - 0.001 (i.e., 0) and one at -60 mV (a typical cell resting potential), are presented in the Figure below. The reaction is A-in↔ A-out [A-in]t=0 = 100 for each.

A^-in↔ A^-out [A^-in]t=0 = 100; [A^-in]t=0 = 0; P = 100; Vinitial = 0 (-0.001 V)	A^-in↔ A^-out [A^-in]t=0 = 100; [A^-in]t=0 = 0; P = 100; Vinitial = -60 mV

Here are animations showing the selective reversible movement of anions (A^-, left panel, red) and cations (C⁺, right panel, cyan) across a membrane from the inside to the outside. This is a very simplified simulation as it shows no counterions on either side. Assume they exist, even though having a "container" with just anions or cations would be impossible. The initial transmembrane potential (t=0) is 0 (actually -0.001 to allow the calculations using Vcell).

A^-in ↔ A^-out [A^-in]t=0 = 100; [A^-out]t=0 = 0; P = 100; Vinitial = 0 (-0.001 V)	C^+in ↔ C^+out [C^+in]t=0 = 100; [C^+out]t=0 = 0; P = 100; Vinitial = 0 (-0.001 V)

As anions move to the outside (left animation), the inside becomes less negative with respect to the outside, so the membrane potential V becomes more positive. This is indicated by the membrane turning blue. Conversely, as cations move to the outside (right animation), the inside becomes more negative relative to the outside, so the membrane potential V becomes more negative. This is indicated by the membrane turning red. (Animations by Shraddha Nayak and Hui Lui)

Facilitated Diffusion

Now, let's return to the diffusion of a noncharged solute down a concentration gradient (i.e., favored) after binding to a membrane receptor. The answer to that question depends on the macromolecule's biological function. We can simplify this process by adding one additional step, as reflected in the equilibrium binding expression shown below:

\[\ce{M + L <=> ML <=> M + X} \nonumber \]

This expression indicates that the free ligand has changed in some fashion to x. In the next two chapters, we will consider two kinds of transformations:

• L is a ligand on the outside of a biological membrane (Lout) that binds to a membrane protein receptor, R. This undergoes a conformational change (as we studied in the binding of dioxygen to hemoglobin), which leads to the expulsion of the bound ligand to the inside of the membrane (Lin). This can be modeled with the simple equation:
  \[\ce{R + L_{out} <=> RL <=> R + L_{in}}. \nonumber \] This process is called facilitated diffusion and represents a physical as opposed to chemical process since no covalent bonds are made or broken. This process proceeds down a concentration or chemical potential gradient (Δμ < 0) and hence is spontaneous (thermodynamically favored). If the ligand concentration is higher inside the cell, net diffusion carries it out of the cell. Passive (non-facilitated) diffusion is kinetically slow in the absence of a receptor, as membranes present formidable barriers to the passage of polar molecules.
• L is a ligand (or substrate S) that binds to a protein enzyme, E. The bound substrate is chemically altered to produce a new product, P, which dissociates from the enzyme. This can be expressed most simply as:
  E + S <==> ES <==> E + P .

Consider the mechanism illustrated in Figure \(\PageIndex{7}\).

Figure \(\PageIndex{7}\): Mechanism for faciliatated diffusion

Let's assume that the initial flux will be measured for this system. We want to derive equations showing J as a function of A_out (assuming that A_in is negligible over the time of measuring the initial flux). Also, assume that the J_facilitated >> J_passive. In contrast to passive diffusion, JA is not proportional to A_out but rather to [A_bound].

Consider this example to help you understand the proportionality. Pretend that the receptor is a truck that can carry one particle across the membrane at a time (i.e., 1/1 stoichiometry). Also, assume the particle can't cross without being carried by the truck. If no trucks are in the membrane, no load can be delivered. If trucks are in the membrane without particles, no load will be delivered. As the number of particles available to be loaded into the truck increases, the truck will have an increased chance to be loaded (depending, of course, on the affinity of the particle for the truck). If the number of loaded trucks is doubled, the number of particles dumped to the other side will double. Therefore, by analogy,

JA is proportional to [RA] or

\begin{equation}
J_A=\operatorname{const}[\mathrm{RA}]=\mathrm{k}_3[\mathrm{RA}]
\end{equation}

How can we calculate RA when we know A and R? Let us assume that A_total (A₀) >> R₀, as is the likely biological case, and A_in = 0. We can calculate RA using the following equations and the same procedure we used for the derivation of the binding equation

\begin{equation}
[\mathrm{ML}]=\frac{\left[\mathrm{M}_0\right][\mathrm{L}]}{\mathrm{K}_{\mathrm{D}}+[\mathrm{L}]}
\end{equation}

The equation for the dissociation constant K_D

\begin{equation}
\mathrm{K}_{\mathrm{D}}=\frac{[\mathrm{A}]_{\mathrm{eq}}[\mathrm{R}]_{\mathrm{eq}}}{[\mathrm{RA}]_{\mathrm{eq}}}=\frac{(\mathrm{A})(\mathrm{R})}{\mathrm{RA}}
\end{equation}

The equation of mass balance of R

\begin{equation}
\mathrm{R}_0=\mathrm{R}+\mathrm{RA} \text { so } \mathrm{R}=\mathrm{R}_0-\mathrm{RA}
\end{equation}

Since we will assume that A₀ is much greater than R₀, we will not need the mass balance for A (which is Ao = A + RA).

Substitute x into x and rearrange to get:

\begin{equation}
\begin{gathered}
\mathrm{K}_{\mathrm{D}}(R A)=(A)(\mathrm{R})=(A)\left(\left(\mathrm{R}_0\right)-(A)(R A)\right. \\
\mathrm{K}_{\mathrm{D}}(R A)+(A)(R A)=(A)\left(\mathrm{R}_0\right) \\
\left(\mathrm{K}_{\mathrm{D}}+\mathrm{A}\right)(R A)=(A)\left(\left(\mathrm{R}_0\right)\right. \\
(R A)=\frac{\left(\mathrm{R}_0\right) A}{\mathrm{~K}_{\mathrm{D}}+\mathrm{A}}
\end{gathered}
\end{equation}

Substitute x into z gives the final equation,

\begin{equation}
\mathrm{J}_{\mathrm{A}}=\mathrm{k}_3[\mathrm{RA}]=\frac{\mathrm{k}_3\left(\mathrm{R}_0\right) A}{\mathrm{~K}_{\mathrm{D}}+\mathrm{A}}=\frac{\mathrm{J}_{\max } A}{\mathrm{~K}_{\mathrm{D}}+\mathrm{A}}
\end{equation}

It should be clear to you from this equation that:

• a plot of J_A vs A is hyperbolic
• J_A = 0 when A = 0.
• J_A = J_max when A is much greater than K_D
• A = K_D when J_A = J_max/2.

These are the same conditions we detailed for understanding the binding equation.

This derivation assumes that the K_D can determine the relative concentrations of A, R, and AR for the interactions, as well as the concentrations of each species during the early part of diffusion (i.e., under initial-rate conditions). Remember, under these conditions, A_out changes little over time. Is this a valid assumption? Examine the mechanism shown in the above figure. A_out binds to R with a second-order rate constant k₁. RA has two fates. It can dissociate with a first-order rate constant k₂ to A_out + R (to give the original species) or dissociate with a first-order rate constant of k₃ to give A_in + R (as A moves across the membrane). If we assume that k₂ >> k₃ (i.e., that the complex falls apart much more quickly than A is carried in), then the relative ratios of A, R, and RA can be described by K_D. Alternatively, you can think about it this way. If A binds to R, most of A will dissociate, and a small amount will be carried across the membrane. If this happened, R would be free and quickly bind A_out and reequilibrate. This occurs since the most likely fate of bound A is to dissociate, not to be carried across the membrane since k₃ << k₂.

Vcell Model:

 

Initial Condition

Click Select Omex below to run the simulation produced in Vcell.

 

 

Note that the J_M values for facilitated diffusion are 1000 times the k values for passive diffusion.

"Receptors" in Facilitated Diffusion

Two types of proteins are involved in facilitated diffusion: carriers and channels. Carrier proteins (also called permeases or transporters), such as the glucose transporter (GLUT1), facilitate the movement of solute molecules across a membrane.  Channels/pores facilitate the diffusion of ions down a concentration gradient by providing a pore through the membrane. In this section, we won't describe the more complicated processes of phagocytosis and endocytosis. These processes are illustrated in Figure \(\PageIndex{8}\).

Figure \(\PageIndex{8}\): Movement of particles across a membrane

In the case of permeases and transport proteins, ligands bind and induce a conformational change in the receptor as illustrated in the case of the glucose transport protein shown in Figure \(\PageIndex{9}\).

Figure \(\PageIndex{9}\): Model for facilitated diffusion of glucose across a membrane

A ligand can bind to the receptor (channel protein) in channels and pores, inducing a conformational change in the receptor and opening a "ligand-gated" channel through the membrane. This process would lead to the diffusion of many ions across the membrane (down a concentration gradient) until the channel closes (which can be induced by ligand dissociation or other events).

The mathematics we derived for the carrier proteins does not apply to the channel proteins. In addition, there are other ways to "gate" open a channel protein, which we will discuss later. Also, some transporters can move solute molecules across a membrane against a concentration gradient. These proteins require an external energy source (such as ATP or the favorable collapse of a second transmembrane gradient) to drive this thermodynamically unfavored process. This is called active transport and will be discussed in the next chapter section.

• ribitol diffusion through a glycerol channel using interactive molecular dynamics

Both links above are from the Theoretical and Computational Biophysics group at the Beckman Institute, University of Illinois at Urbana-Champaign. These molecular dynamic simulations were made with VMD/NAMD/BioCoRE/JMV/other software support developed by the Group with NIH support.

Carrier proteins (permeases or transporters)

Now let's look at some examples of carrier proteins:

Glucose Transport Proteins

Glucose is a key metabolic fuel, so its movement into cells is critical and highly regulated. There are multiple types of glucose transporters. GLUT 1, a plasma membrane protein found in most cells, is responsible for constitutive or basal glucose uptake.  GLUT 4 is involved in insulin-regulated glucose uptake in skeletal and heart muscles and adipose cells after meals. Its official name is solute carrier family 2, or facilitated glucose transporter member 4. No structure is yet available for GLUT4, but one is available for GLUT1, which is highly expressed in cancer cells with high energy demands.

Figure \(\PageIndex{10}\) shows an interactive iCn3D model of a glucose transporter, GLUT1 (5eqg), bound to an inhibitor, cytochalasin B (spacefill). The inhibitor binds in the inward-open state where glucose binds.

Figure \(\PageIndex{10}\): Glucose transporter, GLUT1 bound to the inhibitor, cytochalasin B (5eqg). (Copyright; author via source). Click the image for a popup or use this external link: https://structure.ncbi.nlm.nih.gov/i...zUTZEcTWQrQAX6

Mitochondrial ADP-ATP Carrier Protein

We will see in a few chapters that most of the ATP produced in cells is made in the mitochondrial matrix. It won't do cells much good if it stays there since it is needed in the cytoplasm and elsewhere to drive unfavored processes. Likewise, ADP is concomitantly high when ATP is depleted in a cell. What is needed is an inner mitochondrial membrane protein that can shuttle ATP out of the mitochondria and ADP in down concentration gradients. It would not make sense to need to power an uphill movement of ATP into the mitochondria from low to high concentration, driven by ATP cleavage. Let's look at the structure of the bovine ADP-ATP carrier protein, which resides in the inner membrane. Figure \(\PageIndex{11}\) shows an interactive iCn3D model of the bovine mitochondrial ADP-ATP carrier protein (1okc).

Figure \(\PageIndex{11}\): Bovine mitochondrial ADP-ATP carrier protein (1okc). (Copyright; author via source). Click the image for a popup or use this external link: https://structure.ncbi.nlm.nih.gov/icn3d/share.html?Zc9iLpCncYYD7gBc6

The transmembrane domain contains six alpha-helices, forming a depression leading to the inner leaflet. The cyan spacefill amino acids on the bottom of the depression are RRRMM, a motif found in nucleotide carrier protein. A conformational transition must transiently open the depression into a channel. The spacefill molecule in CPK colors represents carboxyatractyloside, a diterpene glycoside that inhibits the carrier protein.

A Special Case: Fatty acid carrier proteins

You might guess that free fatty acids, derived, for example, from lipids after the actions of lipases on triacylglycerol, would not need a carrier protein to move across the cell membrane since they are almost completely nonpolar. Hexanoic acid can indeed pass readily, but for solute diffusion across the membrane, size matters as well. A whole family of proteins, Fatty Acid Transport Proteins (FATPs) have evolved to help long-chain fatty acids across membranes. Human fatty acid transport proteins are transmembrane proteins. Its mechanism of action is unclear. No crystal structures of these are readily available. Many proteins in this class catalyze the formation of fatty acid-CoASH derivatives, an endergonic reaction powered by ATP. The mechanism for fatty acid movement across the membrane probably involves simple diffusion coupled to processes driven by ATP. However, there is still controversy over the role of passive vs. facilitated diffusion in fatty acid transport.

First, consider the cell's problems in moving fatty acids across two aqueous environments. Figure \(\PageIndex{12}\) shows a mass balance depiction of the reservoirs of fatty acids in the extracellular and intracellular environment.

Figure \(\PageIndex{12}\): Mass balance depiction of the reservoirs of fatty acid in the extracellular and intracellular environment

Free fatty acids are very insoluble in aqueous solution, so their concentrations on either side of the membrane are very low, in the low nanomolar range. Hence, no great thermodynamic drive exists to move free fatty acids across the membrane. Assuming that fatty acids can reasonably transverse the membrane without a carrier protein, there would be no huge kinetic barriers to movement except for their low concentrations.

On each side of the membrane, the free fatty acids are in an "equilibrium" with protein-bound amino acids. In blood and interstitial fluids, albumin, which can bind multiple fatty acids, is at a high concentration, so it can act as a buffer to keep free fatty acids within a useful concentration range. Likewise, in the cytoplasm, fatty acid-binding proteins (FABPs), which typically bind a single fatty acid, are also relatively abundant and buffer free fatty acids. One other note. Free fatty acids are single-chain amphiphiles, making them detergents that can easily lyse cell membranes; therefore, their free concentrations must be kept very low relative to the critical micelle concentration.

Figure \(\PageIndex{13}\) shows an interactive iCn3D model of the human brain fatty acid-binding protein bound to docosahexaenoic acid (1fdq).

Figure \(\PageIndex{13}\): Human brain fatty acid-binding protein bound to docosahexaenoic acid (1fdq). (Copyright; author via source). Click the image for a popup or use this external link: https://structure.ncbi.nlm.nih.gov/i...M2sTpEuU6hj5RA

How do long-chain fatty acids cross the membrane? We will first examine the role of proteins. Let's look at a couple of players.

Fatty acid transport proteins (FATPs): There are six members of the human FATP family, which is also known as the Solute carrier family 27. FATP 1 (SLC27A-1) is found in plasma and endoplasmic reticulum membranes, and based on sequence analysis, it is a single-pass membrane protein. Its highest expression is in muscle and adipose cells. It possesses a C-terminal AMP-binding domain and acyl-CoA synthase activity. The mouse protein has an N-terminal transmembrane domain, and predictions from the human sequence indicate that there is likely only one transmembrane helix at the N terminus (amino acids 13-35). Given this and the absence of a 3D structure, it would appear that this protein would not bind or transfer the bound lipid across the membrane via a conformational change in the transmembrane domain. FATP 4, located in the ER membrane, is predicted to have 2 transmembrane helices, which would probably be inadequate to serve as a class translocase. It is expressed in the endoplasmic reticulum cell membrane.

Platelet Glycoprotein 4 (CD36): Another candidate is platelet glycoprotein 4, which is also called CD36, Glycoprotein IIIb, fatty acid translocase, or the thrombospondin receptor. The protein has many functions and binds many types of proteins (thrombospondin, fibronectin, collagen, or amyloid-beta) and lipids (oxidized low-density lipoprotein (ox-LDL), anionic phospholipids, long-chain fatty acids, and bacterial diacylated lipopeptides). It is present in plasma and Golgi membranes. Sequence analysis shows that it traverses the membrane twice (amino acids 7-29 and 441-463) and is palmitoylated at both the N- and C-terminal ends. A PDB structure (5LGD) for most of the protein, except the putative N- and C-terminal helices, is known. In the structure, it is bound to a malarial protein (shown in grey) and two palmitic acids (spacefill) bound in the nonmembrane domains. Again, from this description, it doesn't appear that the bound fatty acids are translocated via a conformational change in the glucose and ADP/ATP receptor, as described above.

Fatty Acid Binding Proteins (FABPs): These proteins might also participate in the process. In addition to the cytoplasmic form, there is a plasma membrane-associated fatty acid-binding protein (FABP_pm), also known as FABP-1. It's the same protein as mitochondrial aspartate aminotransferase (UniProtKB - P00505 (AATM_HUMAN). It has many possible functions.

Figure \(\PageIndex{14}\) shows a possible model for how fatty acids may transfer or be handed off from albumin to membrane-bound GP36 or FATP-1, possibly through an intermediary protein like FABPpm (for GP36).

Figure \(\PageIndex{14}\): Possible model for how fatty acids may move from albumin to membrane-bound GP36 or FATP-1

Some proteins (albumin, FABP) deliver fatty acids to the membrane proteins (CD36, FATP-1), which deliver free fatty acids into the outer leaflet, where they flip to the inner leaflet, where they are picked up by membrane-associated cytoplasmic fatty acid binding proteins (FABP). Until structures are known for the transmembrane-bound proteins GP36 and FATP-1, whose full amino acid sequences don't suggest a classic carrier protein, this mechanism is a reasonable one. FATP-1 has acyl-CoA synthase activity, so the transferred fatty acid is likely converted to the acyl-CoASH before moving to the cytoplasm. Fatty acid transporters are also implicated in insulin resistance and type 2 diabetes.

The alternative model proposes that long-chain fatty acids, the preferred energy source for cardiac muscle, can cross the membrane by passive diffusion (red boxed area above) even when CD36 activity is inhibited. Diffusion depends on altering the pKa of outer membrane-adsorbed free fatty acids (around 7.5) relative to free fatty acids in solution (around 4.5). The protonated fatty acid adsorbed to the membrane would move into the outer leaflet.  It would flip to the inner leaflet and be picked up by cytoplasmic and/or peripheral membrane proteins. This process would also be associated with the movement of H+ across the leaflet. This type of diffusion has been observed in protein-free lipid vesicles and cells. Likewise, long-chain fatty amines (instead of carboxylic acids) can diffuse into vesicles and cells, supporting this passive diffusion if fatty acid-binding proteins don't bind the amine forms.

Summary

(Summary written by Claude, Sonnet 4.6, Anthropic)

This chapter addresses one of the fundamental challenges of cell biology: how molecules and ions cross the hydrophobic barrier of the lipid bilayer, either spontaneously or with protein assistance, and what thermodynamic and kinetic principles govern these processes.

The chapter opens by establishing why membrane permeability is not uniform. The permeability coefficient of a solute reflects both its size and polarity — small, uncharged molecules such as water and CO₂ cross readily, while larger polar molecules and ions cross poorly or not at all without assistance. For charged species, the relevant driving force is not simply the concentration gradient but the electrochemical potential, which combines the chemical potential (arising from the concentration gradient) with the electrical potential arising from charge separation across the membrane.

Passive diffusion of an uncharged solute obeys Fick's First Law: flux J is proportional to the concentration gradient and to the permeability coefficient P = D/Δx, where D is the diffusion coefficient, and Δx is the membrane thickness. A plot of J versus the transmembrane concentration difference is linear, with slope equal to P. At equilibrium, chemical potentials are equal on both sides, net flux is zero, and ΔG = 0 — though individual molecules continue to cross in both directions dynamically. When the diffusing solute carries a charge, the situation changes qualitatively. Using a model system of K⁺-selective vesicles treated with the ionophore valinomycin — a cyclic peptide that desolvates and shuttles K⁺ across the membrane by presenting inward-facing carbonyl oxygens and an outward-facing hydrophobic surface — the chapter demonstrates how selective ion efflux generates a transmembrane electrical potential that opposes further efflux. Net ion flux stops when the chemical driving force (favoring efflux down the concentration gradient) exactly equals the electrical driving force (opposing it), a condition described quantitatively by the Goldman equation, which generalizes the familiar Nernst equation to account for multiple permeant species and finite membrane permeability.

For many solutes, particularly polar molecules such as glucose, passive diffusion is kinetically too slow to meet cellular needs. Facilitated diffusion — movement down a concentration gradient assisted by a membrane protein — overcomes the kinetic barrier without violating thermodynamics: the process remains spontaneous (ΔG < 0) and requires no external energy input. The chapter derives the kinetic equation for facilitated diffusion by treating the carrier protein (R) as a receptor with a dissociation constant K_D. Under initial-rate conditions, with external solute concentration A₀ >> R₀ and with the rate of transport (k₃) much slower than the rate of dissociation (k₂), the relative concentrations of free and carrier-bound solute are governed by K_D, yielding a hyperbolic J versus A₀ relationship formally identical to the equilibrium binding equation: J = J_max · A₀ / (K_D + A₀). This treatment reveals that J_max is reached when all carriers are saturated, and that the concentration giving half-maximal flux equals K_D — parameters directly analogous to those used in enzyme kinetics and binding analyses developed earlier in the course.

Two classes of proteins facilitate passive diffusion. Carrier proteins (permeases or transporters) bind solutes and undergo a conformational change that alternately exposes the binding site to one side of the membrane, then the other, physically translocating the solute. The glucose transporter GLUT1 exemplifies this mechanism: its inward-open conformation binds glucose on the extracellular face, a conformational transition occludes and then opens the binding site to the cytoplasm, and glucose is released down its concentration gradient. GLUT1 is constitutively expressed in most cells, while GLUT4 provides insulin-regulated glucose uptake in muscle, heart, and adipose tissue. The mitochondrial ADP-ATP carrier illustrates facilitated exchange: because ATP is synthesized in the matrix and consumed in the cytoplasm, while ADP follows the opposite gradient, the carrier can shuttle ATP outward and ADP inward simultaneously, each moving downhill, without requiring ATP hydrolysis to power the exchange.

Channel proteins operate differently: rather than translocating solute through conformational cycling, they form a continuous hydrophilic pore that allows many ions to pass simultaneously when open. Channels can be gated by ligand binding (ligand-gated channels) or by changes in transmembrane voltage (voltage-gated channels), and the mathematical treatment derived for carriers does not apply to them because the stoichiometric binding assumption breaks down.

The chapter closes with the special and contested case of long-chain fatty acid transport. Although free fatty acids are largely nonpolar, size considerations and their very low aqueous concentration complicate simple passive diffusion models. Multiple proteins have been identified as potential participants: CD36 and the FATP family of transmembrane proteins appear to facilitate fatty acid delivery into the outer leaflet, while cytoplasmic FABPs and albumin buffer extracellular free fatty acid concentrations and prevent them from reaching the critical micelle concentration at which they would act as detergents and lyse membranes. An alternative model proposes that protonation of adsorbed fatty acids at the membrane surface (raising the effective pKa from ~4.5 in solution to ~7.5 at the membrane) enables passive flip-flop across the bilayer, supported by observations in protein-free vesicles. The mechanistic debate remains unresolved, illustrating that even apparently simple membrane transport processes can involve unexpected complexity. Throughout, the chapter reinforces the overarching theme: thermodynamics determines whether transport is possible and in what direction; structure — of both the solute and the transport protein — determines whether and how fast it occurs.