Canonical Question

Cell Transport

V5 A.iv Historical V4 E.ii 1 appearance

Master answer

Based on 3 main physical principles

Diffusion via Fick’s Law

Rate of movement of solute across semi-permiable membrane J is

\[J\;={{D\;A\;\Delta C}\over{T}} \]

where

\[D=Diffusion\;constant\;\propto\;{{Solubility}\over{\sqrt{Molecular\;Weight}}}\]

C = concentration (or partial pressure for gasses)
A = cross-sectional area
T = thickness of the membrane or distance over which diffusion takes place.

These factors alter the rate of transfer as per the equation above.
Valid for Most medium – small substances
- Water soluble (H2O, electrolytes, glucose, urea) via intercelular clefts
- Lipid soluble substances (O₂, CO₂) via endothelial cells themselves.

Starling Forces

The NET flux across the membrane is the balance of hydrostatic pressure and oncotic pressure, as defined by the Classic Starling Equation:

\[J_v={\kappa \; ([P_{capil} – P_{interstit}] – \sigma \; [\pi_{plasma} – \pi_{interstit}])}\]

where
J_v is the trans endothelial solvent filtration volume per second
( [ P_c – P_i ] – σ [ π_p – π_i ] ) is the net driving force
P = hydrostatic pressure
π = oncotic pressure
σ = Staverman’s reflection coefficient ie. Permeability of membrane to protein
κ = filtration constant = L_pS = Hydraulic conductivity x Surface Area

\[P_{cap} \; \propto \; {{Post-capil\;resist} \over {Pre-capil \; resist}}\]

Typically quoted values for the variables in the classic Starling equation:

Hydrostatic pressure	Oncotic pressure
Pressure moving fluid	pressure exerted by proteins which draw water into and keep it within a compartment
P_c ~35 → 15mmHg (Arterial → venous) Capillary hydrostatic pressure Pressure moving fluid out of capillary	π_p ~ 20mmHg Plasma oncotic pressure Pressure keeping fluid within capillary
P_if = 5mmHg Interstitial hydrostatic pressure Pressure moving fluid into capillary	π_if ~ 0mmHg Interstitial fluid oncotic pressure Pressure keeping fluid out of capillary

Gibbs-Donnan Effect:

“Opposing osmotic and electro-chemical gradients in the presence of a nondiffusable ion resulting in unequal distribution of the diffusable ions”

Diffusible ions move ↓ [ ] gradient
Because of non-diffusable ion, significant opposing electrical potential develops.
This prevents further movement of ions, and an electrochemical equilibrium is reached.
Because of the presence of non-diffusable ions, there is an osmotic disequilibrium.

Osmotic pressure itself can be determined from the Vant Hoff Equation

\[Osmotic \; pressure \; (\pi) \; = \; {{nRT \times c} \over {M}} \]

where
n = # of particles into which substance dissociates
c = [ ] (in g/L)
T = Absolute temperature
R = Universal Gas Constant (8.314 J⋅K⁻¹⋅mol⁻¹)
M = Molecular weight of molecules

It depends on:

# of particles
[ ] or molarity of the solution
Temperature
Inversely to the molecular weight

Active Processes

Serve to establish Starlings forces and G-D equlibrium

Facilitated diffusion
◦ Diffusion through the membrane using a specific carrier protein to help
Active transport
◦ Movement of ions or other substances across the membrane in combination with a carrier protein
against an energy gradient.
◦ May be primary (energy derived directly from ATP)
◦ or secondary (occurs via co-transport or counter transport)
Endocytosis/Exocytosis
◦ Vesicular transport by engulfment/extrusion of particle by cellular contents

Gladwin 2016

Answer by Gladwin

Exam appearances

Exam	Exact wording	Relationship	Success
2010A Q15	Discuss the important factors in exchange of gases and substrates between capillaries and tissue cells.	historical_member	—