Question 3(p.2)

College Answer

Good answers were based around Fick’s Law, Starling forces and the Gibb’s 
Donnan effect. 

It was expected that candidates would give Fick’s equation and describe the 
components : 
Fick’s Law J = -DA dc/dx

Candidates were also expected to describe Starlings equation and the equation for 
Osmotic Pressure. Starling Equation: 
Fluid movement = k[(Pc-Pi) – s(πp – πi)] 
Osmotic pressure : sRT(Ci-Co).

Gibb’s Donnan effect and, other mechanisms of transport (filtration and pinocytosis) 
was also expected for a good answer.

Syllabus: A combination C1c2.d, C21 2.e, C2b2.c, C2b2.e 
References: Pharmacology and Physiology in Anesthetic Practice, Stoelting pgs 
294-300, 322- 325

Discussion

This would have been a rather difficult question for the unprepared. Reading it carefully, one notices that "important factors" are asked for, not the mechanisms of molecular traffic. Judging by the college answer, those were required too, but clearly occupied some lower tier of importance. 

Those "important factors" would probably include 

• Factors which influence the movement of solvents (i.e. water)
• Factors which influence the movement of solutes (i.e. gases and larger molecules)

Even though water was not mentioned anywhere in the question, it's clearly a "substrate", so we will include it (or, rather, it's obvious that the examiners intended it that way).

Thus:

•  Factors which influence the movement of water between capillaries and tissues depend on a balance between hydrostatic and oncotic pressure gradients in the capillary lumen and the interstitial fluid.
  • This balance can be expressed as the Starling equation:
    
     Jv = L_p S [ (P_c - P_i) - σ (Π_c - Π_i) ]; 
    
    where
     
    • P_c - P_i is the capillary-interstitial hydrostatic pressure gradient
    • Π_c - Π_i is the capillary-interstitial oncotic pressure gradient
    • L_p S is the permeability coefficient of the capillary surface
    • σ is the reflection coefficient for protein permeability and is a dimensionless number which is specific for each membrane and protein
• Factors which influence the movement of gases and other molecules can be separated into passive and active factors.
  • Active transport mediated by  "pump" or exchanger protein, or through vesicle transport by endocytosis / pinocytosis 
  • Passive diffusion is the main mechanism of solute flux 
  • This is governed by Fick's Law of Diffusion:
    
    J = -D (dφ / dx )
    
    where
    • J is "diffusive flux", the magnitude and direction of the flow of a substance from one compartment to another
    • dφ is the concentration difference 
    • dx is the distance for diffusion (or the thickness of the membrane)
    • D is a diffusion coefficient 
• The Gibbs-Donnan effect affects the distribution of both water and charged solutes:
  • The product of diffusible ions on one side of the membrane will be equal to the product of diffusible ions on the other side of the membrane
  • The electrochemical gradients produced by unequal distribution of charged ions produces a transmembrane potential difference which can be calculated using the Nernst equation
  • The presence of impermeant ions on one side of the membrane creates an osmotic diffusion gradient attracting water into that compartment.

Wilson, David B. "Cellular transport mechanisms." Annual review of biochemistry 47.1 (1978): 933-965.

Yang, Nicole J., and Marlon J. Hinner. "Getting across the cell membrane: an overview for small molecules, peptides, and proteins." Site-Specific Protein Labeling. Humana Press, New York, NY, 2015. 29-53.

Stein, Wilfred. Transport and diffusion across cell membranes. Elsevier, 2012.

Cussler, E. L., Rutherford Aris, and Abhoyjit Bhown. "On the limits of facilitated diffusion." Journal of membrane science43.2-3 (1989): 149-164.

Wu, Ling-Gang, et al. "Exocytosis and endocytosis: modes, functions, and coupling mechanisms." Annual review of physiology 76 (2014): 301-331.