Formulas

Molecular Biology & Biochemistry

Concentration & Dilutions

Molarity
M = moles of solute / liters of solution
M Molarity
moles of solute Amount of Substance
liters of solution Total Volume

Dilution Formula
C₁V₁ = C₂V₂
C₁ Initial Concentration
V₁ Initial Volume
C₂ Final Concentration
V₂ Final Volume

pH
pH = -log₁₀[H⁺]
pH Measure of Acidity
[H⁺] Hydrogen Ion Concentration

pOH
pOH = -log₁₀[OH⁻]
pOH Measure of Alkalinity
[OH⁻] Hydroxide Ion Concentration

pH and pOH Relationship
pH + pOH = 14
pH Measure of Acidity
pOH Measure of Alkalinity

Henderson Hasselbalch Equation
pH = pKa + log₁₀([A⁻]/[HA])
pH Measure of Acidity
pKa Acid Dissociation Constant
[A⁻] Concentration of Conjugate Base
[HA] Concentration of Weak Acid

Enzyme Kinetics

Michaelis Menten Equation
V₀ = (V_max * [S]) / (K_m + [S])
V₀ Initial Reaction Velocity
V_max Maximum Velocity
[S] Substrate Concentration
K_m Michaelis Constant

Lineweaver Burk Equation
1/V₀ = (K_m / V_max) * (1/[S]) + 1/V_max
V₀ Initial Reaction Velocity
V_max Maximum Velocity
[S] Substrate Concentration
K_m Michaelis Constant

Catalytic Efficiency
k_cat / K_m
k_cat Turnover Number
K_m Michaelis Constant

Turnover Number
k_cat = V_max / [E_t]
k_cat Turnover Number
V_max Maximum Velocity
[E_t] Total Enzyme Concentration

Nucleic Acids

Melting Temperature of DNA
T_m = 4(G+C) + 2(A+T)
T_m Melting Temperature
G C Number of Guanosine and Cytosine Bases
A T Number of Adenosine and Thymine Bases

DNA Concentration
μg/mL = A₂₆₀ * 50 * dilution factor
A₂₆₀ Absorbance at 260 nm
dilution factor Factor of Dilution

DNA Purity Ratio
Purity = A₂₆₀ / A₂₈₀
A₂₆₀ Absorbance at 260 nm
A₂₈₀ Absorbance at 280 nm

Protein Biochemistry

Beer Lambert Law
A = ε * c * l
A Absorbance
ε Molar Extinction Coefficient
c Concentration
l Path Length

Protein Concentration Bradford Assay
Concentration from Standard Curve
Absorbance Measured Absorbance
Standard Curve Plot of Known Concentrations

Isoelectric Point Estimation
pI = (pKa₁ + pKa₂) / 2
pI Isoelectric Point
pKa₁ pKa₂ pKa Values for Amino and Carboxyl Groups

Genetics

Population Genetics

Hardy Weinberg Equilibrium
p² + 2pq + q² = 1
p² Frequency of Homozygous Dominant Genotype
2pq Frequency of Heterozygous Genotype
q² Frequency of Homozygous Recessive Genotype

Allele Frequency
p + q = 1
p Frequency of Dominant Allele
q Frequency of Recessive Allele

Expected Genotype Frequency
p² = (AA) 2pq = (Aa) q² = (aa)
p² Expected Frequency of AA
2pq Expected Frequency of Aa
q² Expected Frequency of aa

Chi Square Test
X² = Σ[(O – E)² / E]
X² Chi Square Statistic
O Observed Value
E Expected Value

Inbreeding Coefficient
F = (H_e – H_o) / H_e
F Inbreeding Coefficient
H_e Expected Heterozygosity
H_o Observed Heterozygosity

Linkage & Mapping

Recombination Frequency
RF = (# Recombinant Offspring / Total Offspring) * 100%
RF Recombination Frequency
# Recombinant Offspring Number of Recombinants
Total Offspring Total Number of Offspring

Map Distance
Map Distance = RF (%)
RF Recombination Frequency

Coefficient of Coincidence
C = observed double crossovers / expected double crossovers
C Coefficient of Coincidence
observed double crossovers Number of Observed DCOs
expected double crossovers Product of Two Single RFs

Interference
I = 1 – C
I Interference
C Coefficient of Coincidence

Heritability

Broad Sense Heritability
H² = V_G / V_P
H² Broad Sense Heritability
V_G Genetic Variance
V_P Phenotypic Variance

Narrow Sense Heritability
h² = V_A / V_P
h² Narrow Sense Heritability
V_A Additive Genetic Variance
V_P Phenotypic Variance

Response to Selection
R = h² * S
R Response to Selection
h² Narrow Sense Heritability
S Selection Differential

Cell Biology & Physiology

Cell Counting

Cell Concentration
Cells/mL = (Total Counted / Number of Squares) * Dilution Factor * 10⁴
Total Counted Number of Cells Counted
Number of Squares Hemocytometer Squares Used
Dilution Factor Factor of Dilution

Total Cell Count
Total Cells = Cells/mL * Total Volume (mL)
Cells/mL Cell Concentration
Total Volume Total Volume of Cell Suspension

Viability Percentage
% Viability = (Viable Cells / Total Cells) * 100
Viable Cells Number of Live Cells
Total Cells Number of Live and Dead Cells

Membrane Potentials

Nernst Equation
E_ion = (RT / zF) * ln([ion]_out / [ion]_in)
E_ion Equilibrium Potential for Ion
R Gas Constant
T Temperature in Kelvin
z Valence of Ion
F Faraday Constant
[ion]_out Extracellular Ion Concentration
[ion]_in Intracellular Ion Concentration

Goldman Hodgkin Katz Equation
V_m = (RT / F) * ln( (P_K[K⁺]_out + P_Na[Na⁺]_out + P_Cl[Cl⁻]_in) / (P_K[K⁺]_in + P_Na[Na⁺]_in + P_Cl[Cl⁻]_out) )
V_m Membrane Potential
R Gas Constant
T Temperature in Kelvin
F Faraday Constant
P_ion Permeability of Ion
[ion] Ion Concentration

Respiratory & Cardiac Physiology

Cardiac Output
CO = HR * SV
CO Cardiac Output
HR Heart Rate
SV Stroke Volume

Ejection Fraction
EF = (SV / EDV) * 100%
EF Ejection Fraction
SV Stroke Volume
EDV End Diastolic Volume

Vital Capacity
VC = TV + IRV + ERV
VC Vital Capacity
TV Tidal Volume
IRV Inspiratory Reserve Volume
ERV Expiratory Reserve Volume

Total Lung Capacity
TLC = VC + RV
TLC Total Lung Capacity
VC Vital Capacity
RV Residual Volume

Alveolar Ventilation
V_A = (TV – VD) * RR
V_A Alveolar Ventilation
TV Tidal Volume
VD Dead Space Volume
RR Respiratory Rate

Renal Physiology

Filtration Fraction
FF = GFR / RPF
FF Filtration Fraction
GFR Glomerular Filtration Rate
RPF Renal Plasma Flow

Clearance
C_x = (U_x * V) / P_x
C_x Clearance of Substance X
U_x Urinary Concentration of X
V Urine Flow Rate
P_x Plasma Concentration of X

Ecology

Population Ecology

Exponential Growth
dN/dt = rN
dN/dt Growth Rate
r Per Capita Growth Rate
N Population Size

Exponential Growth Integrated
N_t = N₀ * e^(rt)
N_t Population Size at Time t
N₀ Initial Population Size
e Base of Natural Logarithm
r Per Capita Growth Rate
t Time

Logistic Growth
dN/dt = rN * (1 – N/K)
dN/dt Growth Rate
r Intrinsic Growth Rate
N Population Size
K Carrying Capacity

Logistic Growth Integrated
N_t = K / (1 + ( (K – N₀)/N₀ ) * e^(-rt) )
N_t Population Size at Time t
K Carrying Capacity
N₀ Initial Population Size
e Base of Natural Logarithm
r Intrinsic Growth Rate
t Time

Per Capita Growth Rate
r = (dN/dt) / N
r Per Capita Growth Rate
dN/dt Growth Rate
N Population Size

Doubling Time Exponential
T_d = ln(2) / r
T_d Doubling Time
ln(2) Natural Log of 2
r Per Capita Growth Rate

Community Ecology

Species Richness
S = Total Number of Species
S Species Richness

Shannon Wiener Index
H’ = -Σ (p_i * ln(p_i))
H’ Shannon Wiener Diversity Index
p_i Proportion of Individuals of Species i
ln(p_i) Natural Log of that Proportion

Simpsons Diversity Index
D = 1 – Σ (n_i (n_i – 1) / (N (N – 1))
D Simpsons Diversity Index
n_i Number of Individuals of Species i
N Total Number of Individuals

Species Evenness
J’ = H’ / H’_max
J’ Species Evenness
H’ Observed Shannon Wiener Index
H’_max ln(S) Maximum Possible Diversity

Energy Flow

Primary Productivity
NPP = GPP – R
NPP Net Primary Productivity
GPP Gross Primary Productivity
R Autotrophic Respiration

Trophic Efficiency
TE = (Production at Trophic Level n) / (Production at Trophic Level n-1) * 100%
TE Trophic Efficiency
Production Energy or Biomass Production

Evolution

Rates of Evolution

Nucleotide Substitution Rate
K = (d) / (2T)
K Substitution Rate
d Number of Substitutions
T Time since Divergence

Jukes Cantor Model
d = -3/4 * ln(1 – 4/3 * p)
d Estimated Number of Substitutions
p Proportion of Different Sites

Jukes Cantor Distance
D = d / L
D Genetic Distance
d Estimated Number of Substitutions
L Sequence Length

Biophysics & Thermodynamics

Energy

Gibbs Free Energy
ΔG = ΔH – TΔS
ΔG Change in Free Energy
ΔH Change in Enthalpy
T Temperature in Kelvin
ΔS Change in Entropy

Free Energy and Equilibrium
ΔG = ΔG°’ + RT ln(Q)
ΔG Change in Free Energy
ΔG°’ Standard Free Energy Change
R Gas Constant
T Temperature in Kelvin
Q Reaction Quotient

Standard Free Energy Change
ΔG°’ = -RT ln(K_eq)
ΔG°’ Standard Free Energy Change
R Gas Constant
T Temperature in Kelvin
K_eq Equilibrium Constant

Membrane Transport

Osmotic Pressure
π = iMRT
π Osmotic Pressure
i Van’t Hoff Factor
M Molarity
R Gas Constant
T Temperature in Kelvin

Ficks Law of Diffusion
J = -D * (dc/dx)
J Flux
D Diffusion Coefficient
dc/dx Concentration Gradient

Microbiology

Generation Time
g = t / n
g Generation Time
t Elapsed Time
n Number of Generations

Number of Generations
n = (log₁₀(N_t) – log₁₀(N₀)) / log₁₀(2)
n Number of Generations
N_t Final Population Size
N₀ Initial Population Size

Growth Rate Constant
k = ln(2) / g
k Growth Rate Constant
ln(2) Natural Log of 2
g Generation Time

Pharmacology

Hill Equation
Y = ( [L]^n ) / ( K_d + [L]^n )
Y Fractional Saturation
[L] Ligand Concentration
n Hill Coefficient
K_d Dissociation Constant

Dissociation Constant
K_d = [P][L] / [PL]
K_d Dissociation Constant
[P] Free Protein Concentration
[L] Free Ligand Concentration
[PL] Bound Protein Ligand Complex Concentration

IC₅₀
Concentration for 50% Inhibition
Inhibition Percent Inhibition of Activity

Statistics for Biology

Standard Error of the Mean
SEM = SD / √n
SEM Standard Error of the Mean
SD Standard Deviation
n Sample Size

95% Confidence Interval
CI = mean ± (1.96 * SEM)
CI Confidence Interval
mean Sample Mean
SEM Standard Error of the Mean

Students t test
t = (x̄₁ – x̄₂) / (s_p * √(1/n₁ + 1/n₂))
t t statistic
x̄₁ x̄₂ Means of Groups 1 and 2
s_p Pooled Standard Deviation
n₁ n₂ Sample Sizes of Groups 1 and 2

Pooled Standard Deviation
s_p = √( ((n₁-1)s₁² + (n₂-1)s₂²) / (n₁ + n₂ – 2) )
s_p Pooled Standard Deviation
n₁ n₂ Sample Sizes
s₁² s₂² Variances of the Two Groups