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Equations Biochemistry Section Amino Acids, Peptides, and Proteins

Equation Name Isoelectric point (pI)

Equation

p K a , NH

+ ¿group 3

+ p K a, COOH group

2 pI neutral aa=¿

pI acidic aa=

p K a , R group + p K a ,COOH group 2

p K a , NH

+ ¿ group 3

+ p K a, R group

2 pI basic aa=¿ Enzymes

Michaelis-Menten rates

k1 E+S ⇌ ES k cat E+ P → k −1

v max [ S] K m +[ S ]

Use / Description pI = the pH at which the molecule is electrically neutral Aa’s with non-ionizable side chains have pI around 6 Aa’s with acidic side chains have relatively low isoelectric points (well below 6) Aa’s with basic side chains have relatively high isoelectric points (well above 6)

k1 = rate E-S complexes forms k-1 = rate E-S complexes dissociate kcat = rate E-S complex turns into E + P v = velocity of enzyme vmax = maximum enzyme velocity Km = Michaelis constant (the [S] at which ½ E’s active sites are full)

Michaelis-Menten equation

v=

Turnover number (kcat)

v max =[ E ] k cat

vmax = maximum enzyme velocity kcat = # of S molecules “turned over” (converted to product)

Catalytic efficiency

k cat Km

kcat = # of S molecules “turned over” (converted to product) Km = Michaelis constant (the [S] at which ½ E’s active sites are full)

Nonenzymatic Protein Function & Protein Analysis

Migration velocity

Carbohydrate Structure & Function

# possible stereoisomers of a compound

Number of stereoisomers with common backbone=2

Biological Membranes

Osmotic pressure (P P)

Π =ℑ R T

Nernst equation

v=

E=

v = migration velocity of a molecule E = electric field strength z = net charge on the molecule f = frictional coefficient

Ez f

[ion]outside R T [ ion]outside 61.5 log ln = z z F [ ion]inside [ ion]inside

n

n = # of chiral Cs in the molecule

(of a solution) i = van’t Hoff factor 9the # of particles obtained from a molecule when in solution) M = the molarity of the solution R = the ideal gas constant T = the absolute temperature (kelvins) Used to determine the membrane potential (Vm) from the intra- & extracellular concentrations of various ions. R = the ideal gas constant T = the temperature (kelvins; assumed to be 310 K for body temp in simplified equation) z = the charge of the ion F = the Faraday constant (96,485 C/mol e-)

Bioenergetics & Regulation of Metabolism

Goldman-HodgkinKatz voltage equation

+¿ ¿ Na ¿ +¿ ¿ K ¿ −¿ ¿ Cl ¿ ¿inside ¿ +¿ Na¿ ¿ +¿ ¿ K ¿ −¿ ¿ Cl ¿ [¿ outside ¿¿] −¿ Cl ׿ ¿ +¿ K ׿ ¿ +¿ Na × ¿ ¿ Cl−¿ ׿ ¿ +¿ K ׿ ¿ +¿ Na × ¿ P¿ ¿ V m=61.5 log¿

Gibbs Free Energy (DG)

∆ G=∆ H−T ∆ S

Modified Standard State

∆ G=∆ G° + R T ln (Q)

'

Flows from the Nernst equation, taking into account the relative contribution of each major ion to the membrane potential.

DH = Enthalpy T = Temperature DS = Entropy DG°’ = Modified standard free energy R = the universal gas constant T = the temperature

Q = the reaction quotient

Respiratory quotient (RG) Body mass index (BMI)

RQ=

CO 2 produced O 2 consumed

mass BMI = 2 height

…for the complete combustion of a given fuel source (e.g., carbohydrates). Mass = kg Height = m Normal BMI = 18.5 – 25 Underweight = below 18.5 Overweight = 25 – 30 Obese = above 30...