What is a net flow

Atoms, ions and molecules are in constant motion. They collide with each other and are thrown out of their path. In an ideal gas, the individual particles carry out unhindered, i.e. independent, movements. The particle distribution remains unaffected, so there is no predominant or preferred direction of movement. The speed is temperature-dependent and increases with increasing temperature. One speaks therefore of thermal movement (T). Movements are restricted in liquids, but movement in a real solution is subject to the same criteria as in an ideal gas. For many purposes the plasma of a cell can also be described as such a solution. However, the description cannot be extended to all situations (see problem of compartmentalization).

If a concentrated solution of any substance (e.g. sugar) is covered with water, a clear interface is formed between the two liquids. Since we have assumed that dissolved particles (here sugar molecules) move purely statistically, individual particles will initially penetrate more and more of the interface than f (t). Some, but not all, of them will return, creating a net movement (net flow) of particles towards regions that were originally devoid of them.

A movement from high to low concentration is called diffusion. Only after all particles have been evenly distributed in a system is no net movement detectable; the concentration equilibrium is achieved, the system has reached equilibrium.

How can this process be described quantitatively? The amount of particles that travel a certain distance by diffusion depends on the cross-sectional area of ​​the vessel to be considered (F) and a material constant (D).

Changes in concentration in certain cross-sectional areas of a vessel
due to diffusion as a function of time (details see text)

A net flow as a function of time can now be described as follows:

f (t) = DF (c1 - c2 / x1 - x0)

where c1 and c2 the concentrations in the cross-sectional areas under consideration, and x1 - x0 the distance between them is. Since the concentration decreases with increasing distance, the concentration gradient has a negative value. If you write the above formula for arbitrarily short periods of time, the values ​​must be given as differentials, and you come to

dm / dt = DF (dc / dx) [cm2 sec-1]

(= Fick's law of diffusion).

The dimensions of the sizes used are: m: [mole], F: [square centimeter], c: [mole / cubic centimeter], x: [cm].

The number of moles traversing a given area per second is called the net flux (Phi) designated. Written in a formula:

Phi = - D (dc / dx) [mole cm-2 sec-1]


Phi = - D (cl - c2 / x1 - x0)

resolved to D:

D = -Phi / (cl - c2 / x1 - x0)

The size (c1-c2) / (x1-x0) is called the concentration gradient (or concentration gradient), D is the diffusion constant, which is the amount of a substance (in moles) which diffuses per unit of time (sec) through a unit of area (square centimeter) at a concentration gradient of 1 (mol / cm), is defined.

Diffusion is very fast over short distances, but is extremely slow over long distances. The distance goes into the equation as a square and is proportional to the available area. Diffusion is important when looking at molecular movements within cells or between neighboring cells. However, it becomes less important when we examine whole tissues and is completely meaningless when we think, for example, of the transport of assimilates from leaves into the roots.

Permeability is understood as the diffusion of particles through membranes (interfaces). It is initially irrelevant whether we are looking at natural or artificial membranes (e.g. plastic foils). In order to obtain a quantitative statement, we assume as a rough approximation that the membrane is a solvent layer of thickness d.

Concentration profile on a membrane.
Concentration outside, concentration inside, concentration on the membrane outside, delta c concentration gradient outside / inside. delta c´: concentration gradient in the membrane, thickness of the membrane (after J. DAINTY, 1963)

Under this assumption, the flow through a membrane is directly proportional to the diffusion constant. It is consistently lower than in the water. The net flux through the membrane can therefore as

Phi = - D (c1 - c2 / d) = - D / d (c1 - c2)

can be described, where the term D / d is the permeability constant and has the dimension [cm / sec].

Biological membranes are not equally permeable to all substances. They are selectively permeable, i.e. the membranes are permeable to a substance A and impermeable to a substance B. Strictly speaking, they are only permeable to water and some gases such as oxygen, nitrogen, carbon dioxide, etc., because only these can overcome a membrane barrier through free diffusion. As derived above, this follows exclusively the laws of thermodynamics. Molecules are characterized by specific properties such as molecular size, ionizability or solubility in a membrane. Such lipophilic (fat-soluble) molecules can therefore pass them more easily than the hydrophilic ones.

In their lipid bilayer, membranes contain a number of other integral components, of which proteins are the most important for us. A specific arrangement of membrane components can create pores or channels through which certain ions and molecules can selectively diffuse through the membrane. Their permeability depends on the one hand on the pore diameter and on the other hand on its state of charge. Small anions like chloride can easily pass through positively charged pores. Cations are retained. In the case of negatively charged pores, the situation is reversed. One speaks here of restricted diffusion. A number of small molecules such as sugar and amino acids are apparently preferentially channeled through a membrane under certain conditions. However, the permeation kinetics does not follow the above formula, rather it is similar to enzyme-substrate turnover kinetics. Here we are dealing with a facilitated (or promoted) diffusion. The permeability is selective and depends on the presence of specific membrane-bound carrier or carrier molecules with an affinity for a limited group of chemically related substances. It is therefore not the substances (substrates) themselves that pass through the membrane, but a substrate-carrier complex. In summary, facilitated diffusion can be described by the following criteria:

  1. The membrane contains specific carrier or carrier molecules. One therefore also speaks of carrier-mediated transport.
  2. The carriers (mostly proteins, but also certain antibiotics such as valinomycin) bind the substrate to be transported, e.g. a sugar or an amino acid. In contrast to enzymes, it is not converted, but translocated through the membrane.

  3. Several substrates can compete for the same carrier. Your bond characteristics to him can be different; consequently, the transport kinetics are also substrate-specific.

  4. The loaded carrier crosses the membrane at a different speed than the unloaded one. Alone the concentration gradient of the substance to be transported.

  5. The driving force of facilitated diffusion is like simple diffusion

  6. The maximum transport speed depends on the number of carrier molecules present in the membrane.