Fick’s law basically describes the relationship between the different factors that affect the rate of diffusion:
Rate of Diffusion
The ‘∝’ sign means ‘proportional to’, so if the factors in the numerator increase, the Rate of Diffusion will increase
proportionally. If the factor on the denominator decreases, then the rate of Diffusion will increase proportionally
For example, if the Rate of Diffusion doubles, then the Surface Area or Concentration also doubles OR the Membrane Thickness will half.
Professor Emeritus, Department of Biology, Indiana University-Purdue University Indianapolis, Indianapolis, Indiana, USA
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Abstract
Life depends on a membrane's ability to precisely control the level of solutes in the aqueous compartments, inside and outside, bathing the membrane. The membrane determines what solutes enter and leave a cell. Transmembrane transport is controlled by complex interactions between membrane lipids, proteins, and carbohydrates. How the membrane accomplishes these tasks is the topic of this chapter.
Keywords: Biological membrane, Cells, Fick's laws, Membrane, Membrane transport, Semipermeability, Solutes
1. Introduction
Life depends on a membrane's ability to precisely control the level of solutes in the aqueous compartments, inside and outside, bathing the membrane. The membrane determines what solutes enter and leave a cell. Transmembrane transport is controlled by complex interactions between membrane lipids, proteins, and carbohydrates. How the membrane accomplishes these tasks is the topic of Chapter 19.
A biological membrane is semipermeable, meaning it is permeable to some molecules, most notably water, while being very impermeable to most solutes [various biochemicals and salts] found in the bathing solution. This very important concept of unequal transmembrane distribution and, hence, permeability between water and other solutes came out of the pioneering work of Charles Overton in the 1890s [see Chapter 2]. How does a biological membrane accomplish semipermeability? The barrier to solute movement is largely provided by the membrane's hydrophobic core, a very thin [∼40 Å thick], oily layer. The inherent permeability of this core varies from membrane to membrane. Generally, the more tightly packed the lipids comprising the bilayer, the lower its permeability will be. Lipid bilayers are very impermeable to most solutes because of their tight packing. Fig. 19.1 depicts the membrane permeability of a variety of common solutes [1]. Note the data are presented as a log scale of solute permeability [P in cm/s] and ranges from Na+ = 10−12 cm/s to water = 0.2 × 10−2 cm/s, spanning almost 10 orders of magnitude!
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Figure 19.1
Log of the permeability [P in cm/s] across lipid bilayer membranes for common solutes ranging from Na+ [10−12 cm/s] to water [0.2 × 10−2 cm/s]. This range spans almost 10 orders of magnitude [1].
Lipid bilayer permeability is not a constant but instead is affected by environmental factors. For example, LUVs [large unilamellar veicles] made from DPPC [16:0, 16:0 PC] have a sharp phase transition temperature, T m, of 41.3°C. At temperatures well below T m, the LUVs are in the tightly packed gel state and permeability is extremely low. At temperatures well above T m, the LUVs are in the loosely packed liquid disordered state [l d, also called the liquid crystalline state] and permeability is high. However, maximum permeability is not found in the l d state, but rather at the T m [2]. As the LUVs are heated from the gel state and approach the T m, domains of l d start to form in the gel state. Solutes can then pass more readily through the newly formed l d domains than the gel domains resulting in an increase in permeability. At T m there is a maximum amount of coexisting gel and l d state domains that exhibit extremely porous domain boundaries. It is through these boundaries that most permeability occurs. As the temperature is further increased, the LUVs pass into the l d state and the interface boundaries disappear, reducing permeability to that observed for the single-component l d state. Thus, maximum permeability is observed at the T m.
1.1. Fick's First Law
The tendency for solutes to move from a region of higher concentration to one of lower concentration was first defined in 1855 by the physiologist Adolf Fick [Fig. 19.2 ]. His work is summarized in what is now the very well-known Fick's Laws of Diffusion [3]. The laws apply to both free solution and diffusion across membranes. Fick developed his laws by measuring concentrations and fluxes of salt diffusing between two reservoirs through connecting tubes of water.
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Figure 19.2
Adolf Fick, 1829–1901.
Fick's First Law describes diffusion as:
Diffusionrate=−DAdcdx
Where D = diffusion coefficient [bigger molecules have lower Ds]; A = cross-sectional area over which diffusion occurs; dc/dx is the solute concentration gradient [diffusion occurs from a region of higher concentration to one of lower concentration].
The relationship between a solute's molecular weight and its diffusion coefficient is shown in Table 19.1 . Large solutes have low diffusion coefficients and therefore diffuse more slowly than small solutes. The diffusion rate for a particular solute under physiological conditions is a constant and cannot be increased. This defines the theoretical limit for an enzymatic reaction rate and also limits the size of a cell. If a solute starts at the center of a bacterial cell, it takes about 10−3 s to diffuse to the plasma membrane. For this reason, typical cells are microscopic [see Chapter 1]. At about 3.3 pounds and the size of a cantaloupe, the largest cell on Earth today is the ostrich egg. However a fossilized dinosaur egg in the American Museum of Natural History in New York is about the size of basketball. Since an egg's only function is to store nutrients for a developing embryo, its size is many orders of magnitude larger than a normal cell.
Table 19.1
Relationship Between a Solute's Molecular Weight and Its Diffusion Coefficient, D
CompoundO2Acetyl cholineSucroseSerum albuminD [cm2/s × 106]19.85.62.40.7Molecular weight3218234269,000
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1.2. Osmosis
Osmosis is a special type of diffusion, namely the diffusion of water across a semipermeable membrane. Water readily crosses a membrane down its potential gradient from high to low potential [Fig. 19.3 ] [4]. Osmotic pressure is the force required to prevent water movement across the semipermeable membrane. Net water movement continues until its potential reaches zero. An early application of the basic principles of osmosis came from the pioneering work on hemolysis of red blood cells by William Hewson in the 1770s [see Chapter 2]. It has also been discussed that MLVs [multilamellar vesicles, liposomes] behave as almost perfect osmometers, swelling in hypotonic solutions and shrinking in hypertonic solutions [see Chapter 3] [5], [6]. Liposome swelling and shrinking can be easily followed by changes in absorbance due to light scattering using a simple spectrophotometer. Therefore, osmosis has been investigated for many years using common and inexpensive methodologies and a lot is known about the process.
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Figure 19.3
Osmosis and osmotic pressure. Water is placed in a U-shaped tube where each of the tube arms is separated by a semipermeable membrane with pores of a size that water can easily pass through but a solute cannot. Upon addition of the solute to the tube's right arm, water diffuses from left to right [high water potential to low]. The column of water in the tube's right arm [the one containing the solute] rises until the extra weight of the column equals the osmotic pressure caused by the solute. A pump could then be used to counter the osmotic pressure whereupon the solution columns in the right and left arms of the tube are made the same. The pump pressure required to equalize the height of the two columns is the osmotic pressure [4]. Note a small amount of the solute leaks from right to left since no filter is perfect.
Membranes are rarely, if ever, perfectly semipermeable. Deviation from ideality is defined by a reflection coefficient [σ]. For an ideal semipermeable membrane where a solute is totally impermeable, σ = 1. If a solute is totally permeable [its permeability is equal to water], σ = 0. Biological membranes are excellent semipermeable barriers with σ = 0.75 to 1.0.
2. Simple Passive Diffusion
Movement of solutes across membranes can be divided into two basic types: passive diffusion and active transport [7]. Passive diffusion requires no additional energy source other than what is found in the solute's electrochemical [concentration] gradient and results in the solute reaching equilibrium across the membrane. Passive diffusion can be either simple passive diffusion where the solute crosses the membrane anywhere by simply dissolving into and diffusing through the lipid bilayer, or facilitated passive diffusion where the solute crosses the membrane at specific locations where diffusion is assisted by solute-specific facilitators or carriers. Active transport requires additional energy, often in the form of ATP, and results in a nonequilibrium, net accumulation [uptake] of the solute on one side of the membrane. The basic types of membrane transport, simple passive diffusion, facilitated diffusion [by channels and carriers] and active transport are summarized in Fig. 19.4 [8]. There are countless different examples of each type of membrane transport process [7]. Only a few representative examples will be discussed here.
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Figure 19.4
Basic types of membrane transport, simple passive diffusion, facilitated diffusion [by channels and carriers], and active transport [8].
Even simple passive diffusion requires energy to cross a bilayer membrane. In order to cross a membrane, the solute must first lose its waters of hydration, diffuse across the membrane, and then regain its waters on the opposite side. The limiting step involves the energy required to lose the waters of hydration. Table 19.2 shows the relationship between the waters of hydration [proportional to the number of —OH groups on a homologous series of solutes] and the activation energy for transmembrane diffusion. As the number of waters of hydration increases from glycol