40 SOME PHYSICAL FORCES EXEMPLIFIED IN MAN 



The electric field strength (see Figure 2-4) is denned as the voltage gradient, 

 X), dV/dx, i.e., the voltage change per centimeter of effective thickness of 

 membrane across which the force acts. In cells it has been variously esti- 

 mated that the effective part of the membrane is only about 100 angstroms 

 (100 A), 100 x 10 -8 cm, thick. The field strength across the membrane is 

 therefore a phenomenal 85,000 v/cm, or over 200,000 v/in.! 



Electric field strength enters many phases of biophysics, and will appear 

 often throughout this book, e.g., whenever membranes or bioelectric phe- 

 nomena, such as those which give rise to the electrocardiogram and en- 

 cephalogram, are introduced. 



The voltage gradient, TJ, (i.e., electric field strength) is the force which 

 causes charge to flow — for positive charges, in the direction from higher to 

 lower potential. The rate at which they flow (the current, i) is proportional 

 to the forced. Thus 



l oc 



V 



Since the potential difference acts over the same path as the charges flow, 

 the path length can be taken into the proportionality constant, and the 

 result becomes 



i = AT amperes 



where K is the current if the impressed voltage is 1 v. This is Ohm's law. 

 Transfer of charge is discussed further in Chapter 8. 



Colloids 



At the microscopic level the most important electrostatic forces are those 

 which help to stabilize colloids. Colloids are suspensions of liquid or solid 

 particles in a liquid medium (water, in our case). The particles are of the 

 order of microns (1/i = 10 -4 cm) in diameter, and may be single macro- 

 molecules, heavily hydrated, or collections or agglomerates of molecules. 

 Characteristically, stable colloid particles (which do not agglutinate or 

 precipitate) have excess like charge, and so repel each other. The repulsion 

 promotes stability. The excess charge usually arises ultimately from the fact 

 that the agglomerate contains acidic and basic chemical groups (e.g., 

 — COO - , — NH 3 + , — P0 4 = ) whose extent of ionization at the tissue pH 

 (~7) depends upon electrostatic interactions with other chemical groups 

 nearby in the molecule. Since these interactions will differ from molecule 

 to molecule, a chemical change in the colloid, an increased salt concentra- 

 tion, or a shift in pH can weaken electrostatic repulsion and coagulate the 

 colloid .... This is considered by some to be the mechanism by which anti- 

 bodies work, and to be the reason why the blood groups are incompatible. 



