Block 1 Equations Cheat Sheet

Thermodynamics

Enthalpy

ΔH=ΔU+PΔV\Delta H = \Delta U + P \Delta V

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

Gibbs Free Energy

ΔG=ΔHTΔS\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

KsxKs^x = Δ[products]time\frac{\Delta[products]}{time}

Ks = reaction rate
x = reaction order

Michaelis-Menten

V0=Vmax[S]Km+[S]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

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

Resting Potential

Voltage

V=IRV = IR

I = current
R = resistance

Capacitance

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

q = charge (coulombs)
V = voltage

Particle Movement Down Gradient

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

Ji=DiAC1C2xJ_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

Jx=Px(XoXi)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.

Eeq=60zlog([Xo][Xi])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.

Vm=60log(GNa[Na]out+GK[K]outGNa[Na]in+GK[K]in)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.

Vm=(ENaGNa)+(EKGK)GNa+GKV_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(VmEeq)I = G(V_m - E_{eq})

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

Action Potential Conduction

Space Constant

RmRi\frac{\sqrt{R_m}}{R_i}

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

Time Constant

RmCR_mC

Rm = membrane resistance
C = membrane capacitance

Heart Circulation

Mean Arterial Pressure

MAP=COTPRMAP = CO * TPR

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

MAP=DBP+(SBPDBP)3MAP = \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

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.

Body Fluid Compartments

Indicator Dilution Technique

For finding a compartment volume of unknown size.

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

CV=QQ/ViCV=\frac{Q}{Q/V_i}

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

Measuring Blood Volume

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

Hematocrit = % of blood that is cells

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

Osmosis and Fluid Shifts

Permeability to Water

σ=1PsolutePwater\sigma = 1 - \frac{P_{solute}}{P_{water}}

Ps = Permeability of solute
Pw = Permeability of water

Osmotic Pressure

π=σicRT\pi = \sigma icRT

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

Fluid Filtration Pressure

Jv=Kf((Pc+Πif)(Pif+Πp))J_v = K_f * ((P_c + \Pi_{if}) - (P_{if} + \Pi_p))

Jv=Pressure OutPressure InJ_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
Π\Pip = Plasma colloid osmotic pressure. Force pointing in from proteins (solute)
Π\Piif = Interstitial fluid colloid osmotic pressure. Force pointing out from proteins (solute) in the interstitial fluid

pH and Blood Buffering

Protons in Solution

pH=log1[H+]pH = log \frac{1}{[H+]}

pH=log[H+]pH = -log[H+]

Henderson-Hassall Bach

pH=pKa+log[conj. base][acid]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 (dominant)+q (recessive)=1 (total population)p \text{ (dominant)} + q \text{ (recessive)} = 1 \text{ (total population)}

p2+q2+2pq=1p^2 + q^2 + 2pq = 1

p2p^2 = homozygous dominant
q2q^2 = homozygous recessive
2pq2pq = heterozygous