Block 1 Equations Cheat Sheet

Thermodynamics

Enthalpy

$\Delta H = \Delta U + P \Delta V$

U = the change in energy
P = pressure
V = is volume

Gibbs Free Energy

$\Delta G = \Delta H - T \Delta S$

Gibbs (G) = free energy of a system
S = entropy (a measure of disorder)
T = temperature

Enzymes

Reaction Velocity

$Ks^x$ = $\frac{\Delta[products]}{time}$

Ks = reaction rate
x = reaction order

Michaelis-Menten

$V_0 = \frac{V_{max}[S]}{K_m + [S]}$

Vmax = maximum velocity
Km = half of the maximum velocity

Enzyme Binding

Dissociation Constant

Receptor (R) + Ligand (L) → RL

$K_d = \frac{[R][L]}{[RL]}$

Resting Potential

Voltage

$V = IR$

I = current
R = resistance

Capacitance

$C = \frac{q}{V}$

q = charge (coulombs)
V = voltage

Particle Movement Down Gradient

AKA, Fick's Law. Measured in Flux (J).

$J_i = D_i A \frac{C_1 - C_2}{x}$

Di = diffusion coefficient
A = cross sectional area
(C1 - C2) = concentration difference
X = distance over which the diffusion takes place

Movement Across Membranes

$J_x = P_x (X_o - X_i)$

Px = permeability coefficient
(Xo - Xi) = concentration difference between outside (o) and inside (i) the cell

Membrane Equilibrium Potential (Simplified)

AKA, Nernst Equation.

$E_{eq} = \frac{60}{z} * log(\frac{[X_o]}{[X_i]})$

z = valence (charge of ion, Ca2+ = 2, K+ = 1)
Xo = concentration outside the cell
Xi = concentration inside the cell

Membrane Potential (Multiple Ions)

AKA, Goldman-Hodgkin-Katz. This example considers the flow of Potassium (K) and Sodium (Na) ions.

$V_m = -60 * log(\frac{G_{Na} * [Na] _{out} + G_K * [K] _{out}}{G _{Na} * [Na] _{in} + G_K *[K] _{in}})$

G = conductance
out = concentration outside membrane
in = concentration inside membrane

Membrane Potential (Steady State)

A modification of Goldman-Hodgkin-Katz using the current equation at steady state. This example considers the flow of Potassium (K) and Sodium (Na) ions.

$V_m = \frac{(E_{Na} * G_{Na}) + (E_K * G_K)}{G_{Na} + G_K}$

G = conductance
E = membrane potential

Current Equation (Single Ion)

$I = G(V_m - E_{eq})$

I = current
G = conductance
(Vm - Eeq) = driving force

Action Potential Conduction

Space Constant

$\frac{\sqrt{R_m}}{R_i}$

Rm = membrane resistance
Ri = internal resistance (inverse of axon diameter)

Time Constant

$R_mC$

Rm = membrane resistance
C = membrane capacitance

Heart Circulation

Mean Arterial Pressure

$MAP = CO * TPR$

CO (Cardiac Output) = stroke volume (SV) * heart rate (HR)
TPR (Total Peripheral Resistance) = The resistance of the entire circulatory system

$MAP = \frac{DBP + (SBP - DBP)}{3}$

SBP = The contracting pressure, which correlates with the cardiac output (CO). Normally between 90-120 mmHg.
DBP = The arterial pressure when the heart is relaxes, which correlates with total peripheral resistance (TPR). Normally between 60-80 mmHg.

Pulse Pressure

PP = SBP - DBP

Body Fluid Compartments

Indicator Dilution Technique

For finding a compartment volume of unknown size.

$CV=\frac{\text{quantity injected (mmol)}}{\text{fluid concentration (mmol/L)}}$

$CV=\frac{Q}{Q/V_i}$

Quantity (Q) = concentration * volume
Vi = volume injected

Measuring Blood Volume

$\text{Blood volume} = \frac{\text{plasma volume}}{[1 - \text{hematocrit}]}$

Hematocrit = % of blood that is cells

$\text{Blood volume} = \frac{\text{total injected CPM}}{\text{blood sample (CPM/ml)}}$

Osmosis and Fluid Shifts

Permeability to Water

$\sigma = 1 - \frac{P_{solute}}{P_{water}}$

Ps = Permeability of solute
Pw = Permeability of water

Osmotic Pressure

$\pi = \sigma icRT$

σ = permeability to water
c = concentration
R = gas constant
T = the temperature (in k) of the fluid

Fluid Filtration Pressure

$J_v = K_f * ((P_c + \Pi_{if}) - (P_{if} + \Pi_p))$

$J_v = \text{Pressure Out} - \text{Pressure In}$

Pc = Capillary pressure. Force pointing out from pumping of the heart
Pif = Interstitial fluid pressure. Force pointing in from hydrostatics
$\Pi$p = Plasma colloid osmotic pressure. Force pointing in from proteins (solute)
$\Pi$if = Interstitial fluid colloid osmotic pressure. Force pointing out from proteins (solute) in the interstitial fluid

pH and Blood Buffering

Protons in Solution

$pH = log \frac{1}{[H+]}$

$pH = -log[H+]$

Henderson-Hassall Bach

$pH = pKa + log \frac{[\text{conj. base}]}{[\text{acid}]}$

pKa = the point at which half the molecules are protonated
pKa = -log(Ka)

Inheritance in Populations

Hardy-Weinberg

$p \text{ (dominant)} + q \text{ (recessive)} = 1 \text{ (total population)}$

$p^2 + q^2 + 2pq = 1$

$p^2$ = homozygous dominant
$q^2$ = homozygous recessive
$2pq$ = heterozygous