Quiz 5: Chapter 8: Motions of Biological Molecules Flashcards
Under what conditions does diffusion of molecules occur?
occurs if there is a concentration gradient dc/dx
What is net flux of molecules? (Diffusion)
- Flux is J, has units mol m^-2 s^-1
- it is the moles of molecules that moves through an area per second
What is Fick’s first law of diffusion?
- The net flux of molecules (J) is proportional to the gradient (dc/dx), the constant of proportionality is the diffusion coefficient D
What is the negative sign is Fick’s first law due to?
The negative sign is due to the flux being in the opposite direction of the gradient
What is the graph of a concentration gradient of a membrane between two reservoirs?
What is Fick’s second law of diffusion?
- relates the time dependent concentration change to the spatial variation of the concentration at that time point
What does Fick’s Second Law of Diffusion allow us to assume about this diagram?
- consider the slab with cross section A and thickness L (the slap extends from x to x + L)
- the number of molecules in moles that enter the slab in a time interval (dt) from the left is J(x)Adt
- Dividing this number by the volume AL gives the concentration change per time interval as:
dc/dt = (JAdt) / (ALdt) = J / L
*****What is the solution to Fick’s second law equation?
How does the solution to the diffusion equation change with time?
The solution of the equation for the diffusion from a point source is a Gaussian function that broadens with time
Describe Fick’s second law equation (order)?
Fick’s second law is a second-order differential equation in space and first order in time.
What is terminal velocity?
terminal velocity:
the limiting velocity due to friction with the air or for an object sinking in water
Why are calculated frictional coefficients lower than measured frictional coefficients?
- the hydrodynamic volume of macromolecules in the water (effective volume as they diffuse) is increased by tightly bound water molecules adhering to their surface (shell of hydration)
- spheriodal or ellipsoidal proteins have larger frictional coefficients than spheres of the same volume
- irregularities and clefts on the protein surface retard translational and rotational diffusion
What are the probability and average equations for a discrete variable?
What does a high diffusion coefficient mean?
diffuses quickly?
What is the average value of squared displacement for one dimensional diffusion?
x^2 = 2 D t
What is the average value of squared displacement for 3D diffusion?
d^2 = 6 D t
Flux is always___________
in the opposite direction of the gradient
What are the influx and outflux equations?
What does THE SOLUTION of Fick’s second law describe the behavior of?
diffusion of particles from a point source
What is Fick’s first law for?
steady state diffusion
What is Fick’s second law for?
time dependent concentration at position x
What is probability density?
probability of X falling in the interval between Xo to Xo + dx
What is the average equation for a continuous variable?
What is the friction coefficient equal to?
- r = radius of the sphere
- n = viscosity
What is a diagram illustrating stoke’s law?
How does the friction coefficient relate to force imbalance? For a pebble moving through water at CONSTANT velocity?
What is the equation for Ff?
Ff = (6 π n r) vt
Ff = f Vt
Force of friction = friction coefficient x terminal velocity
What is the equation for flux due to diffusion?
What is the equation for flux due to Fext?
What is the general equation for Fext? (always applies)
What are the units of J?
(this is FLUX)
mol / (m^2 s)
What are the units of v?
m / s
What should the units of concentration be in the flux and diffusion equations?
mol / m^3
What equations can you assume if two fluxes balance each other? No net flux?
What is an additional equation for flux due to external forces?
Jext = c x (Vt)
What do high and low concentrations indicate?
High or low potential energy
What are the units of the diffusion coefficient?
(m^2/s)
What is an equation for D?
What is the equation for the volume of a sphere?
What is D proportional to?
What proportional relationship is relevant to spheroids?
What are the forces involved in sedimentation?
What is bouyant force?
the weight of the solvent displaced by the particle
What is partial specific volume? What equation is it relevant to?
- relevant to bouyant force
What are the equations for buoyant force?
What is the equation for external force due to gravitation? (No frictional force) (Think about the sedimentation diagram)
What are the possible units of s?
-sedimentation coefficient
- svedbergs (S)
- 1 svedberg = 10 ^ -13 seconds
How does acceleration change in a centrifuge?
acceleration isnt g it is Arot
What are the angular rotation equations?
What is the first s equation?
What is X1/2?
the distance from the midpoint of the boundary to the center of the rotor
What is the second s equation?
What is the analytical centrifugation graph? Axes? Slope? What equation is it based off of?
How does diffusion affect centrifugation patterns?
- as the boundary migrates outward as a result of centrifugal force, diffusion causes the sharp step it forms at the beginning (b/c of sharpness of the solution air boundary) to be smeared out by diffusion
- sharp boundary - small D
- smeared boundary - large D
(in a graph of c vs x)
What is the equation for the standard sedimentation coefficient and what is is based on?
What can we assume if the values for s are significantly different from each other?
the macromolecule has different conformations in the two solvents
Long equation, relates x and c
Case 1
Case 2
What is viscosity?
net effect of retardation of momentum/ aka the rate of momentum transfer per unit time
What is an equation involving the viscosity coefficient?
What is electrophoretic mobility?
(u) the terminal velocity per unit electric field
What is the electrophoretic mobility equation?
What is the terminal velocity equation for electrophoresis?
What does net flux = 0 mean?
What is the equation for molar mass of the solute? (Mb)
List conversion equation
1 cm^3 = 1 mL = (1 x 10^-6) m^3
What is sedimentation? What determines its rate?
- in a gravitational field particles tend to settle towards the bottom in a column of solution
- the rate of this process is determined by the strength of the field, the shape and mass of the particles, and the solvent viscosity
What is the unit of viscosity?
n = Pa s or Ns/m^2
What is Jp?
flux of the x component of the momentum
What are two ways to experimentally measure viscosity?
- fill cylinder with known liquid, drop a bead in and bead travels with vt
- use vt and frictional coefficient equations to solve for n
- Oswald Viscometer
