Biochemistry Exam 3

molecular chaperones

• prevent/reverse improper associations → especially in multidomain & multi-subunit proteins

  • bc unfolded prot in vivo have great tendency to form intra and intermolec aggregates

    • exposed hydrophob regions (release water molecs = drives protein folding to hide hydrophob regions)

• function by binding solvent-exposed hydrophob surfaces to reversibly promote proper folding

• many chaperones are ATPases

  • contain phosphoanhydride ( increase energy when released)

  • ATP → ADP

classes of chaperones

• heat shock proteins 70

• chaperonins

• Hsp90

• nucleoplasmins

heat shock proteins 70

70 kD monomeric proteins

chaperonins

• form large multi-unit cage-like assemblies

  • from cavity for unfolded prot

• ATPases

Hsp 90

involved in signal transduction ; very abundant in eukaryotes

nucleoplasmins

acidic nuclear proteins involved in nucleosome assembly

GroEL/ES system

• from bacteria

• chaperonin

• 14 identical (60 kD) subunits in 2 rings = creates central cavity

  • each ring = 7 identical subunits

  • stack tg

• rings interact noncovalently

• GroES = cap

• GroEL = cavity

  • can have cis and trans config

GroES function

• cap to out on top of GroEL donut system = creates cavity to insert misfolded protein

• adding cap = functional form of GroES/EL

GroEL cis/trans

• cis ring = genetically distinct

  • induced upon cap binding

• trans ring = no cap = thinner

• widths are of ring are the same w/out cap

• binding: induces conf change of all 7 subunits = leads to overall change (elongation)

  • C-shaped structure → elongated struc

• each of 7 subunits have 3 domains (made of 1 polypep chain)

  • contain apical domain, intermed domain (linkages), and equatorial domain)

    • equatorial domain imparts mobility via Pro and Gly residues

    • ADP binds to equatorial

GroEL/GroES binding process

• ATP binds to GroEL = becomes cis ring

• prot enters cavit

• GroES cap binds via hydrophobic interactions → further exposes hydrophob binding sites on apical domain of GroEL

• misfolded prot binds via hydrophob patches in cavity

• protein begins to refold in cavity

  • thermally denature & refold prot due to increased exothermic reaction

  • gamma hydrolysis of 7 bound ATP → release of P weakens interactions of binding between GroEs and GroEL

• second misfolded prot enters trans ring w/ ATP

• cis ring releases GroES cap, ADP, and better-folded substrate protein

  • may not be refolded but unfolded to refold better later

• 1 cycle = 7 ATP

  • a lot of ATP but less than hydrolyzing

  • multiple cycles can occur

anfinsen cage model of GroEL/ES action

• folding w/in the complex

• = fully properly folded prot upon exit

• probably not accurate

iterative annealing

• reversible release of partially folded intermediates

• must go thru cavity several times or comes out unfolded and must refold by self

  • thru use of many GroEL/ES proteins

• supported by experimental evidence

protein dynamics

proteins undergo structural motions that have fxnal significance

conformational fluctuations (breathing motions) in myoglobin

• space-filled model

  • heme = buried

  • O2 must find channel to get in

    • crystal struc will not tell us how O2 is able to penetrate core

    • need dynamic motion

      • prot breathing = transiently opening channel to allow O2 to enter

time-scales of protein motions

• atomic fluctuations (very short timescale = limited motion)

• collective motions (still small but bigger than atomic)

  • groups of atoms moving tg = move further & increase time scale

• triggered conformational changes

  • slowest time scale = greatest atomic displacement

  • when prot has more than 1 domain & can switch between configs (changing dispositions of domains)

techniques for studying protein motion

• show change in protein dynamic over time

• crystallography = solid state but can get some info from e- density (spreading out if experiencing motion)

• NMR = more effective = motional study

• molecular dynamics (MD) simulations = use crystal struc at t=0 → computer sim → force field = sim motions of prot over time

  • shows how prot moves & use as comparison to experiment

MD simulation of myoglobin

• shows internal motion via overlay of multiple MD simulation results

• can see that backbone has some motion but is limited

• more motion occurs w/ R groups

conformational equilibrium

• many prot have similar energies for dif geomtries

  • = multiple native configs

conformational dynamics

• how fast/efficient are these configs

• answered by MD simulation

conformational diseases: amyloid and prions

• form plaques from protein misfolding

• examples: Alzheimer & Huntington diseases, transmissible spongiform encephalopathies (TSE’s), amyloidoses

• common characteristics = formation of amyloid fabrils (insoluble plaques_

• involved proteins assume 2 dif stable conformations (native and amyloid)

  • coax prot to associate w/ self

  • plaque / aggregate

  • form hydrophob patches

amyloid fibrils

• fibrils consist mainly of beta sheets whose beta strands are perpendicular to fibril axis

• folded native → converted to amyloid

  • more beta found = self-association

  • extensive network of beta (that’s not allowed in native)

• self-association triggered by increased beta in amyloid form

amyloid proteins

• mutant forms of normally occurring proteins

  • consequence of gene mutations = predisposed to adapt amyloid form

• in mutant = equilibrium / convesion between amlyoid much more likely

  • much lower activation barrier

• ex. lysozyme mutants

  • turn neg side chain into no charge/pos charge side chain

prion diseases

• can be spread from one organism to another

• may be cell-surface signal receptor

• evidence that scrapie is protein

  • inactivated w/ diethylpyrocarbonate (only reactions w/ proteins that have His side-chains)

  • unaffected by hydroxylamine = reacts w/ cytosine residues (shows scrapie is protein not nucleic acid)

• conversion of native prion to scrapie:

  • normally very unlikely but equlib shifted by increased beta = promotes self-aggregation

  • may be mediated by molec chaperone

    • neg effect (make scrapie more likely form)

mechanisms of amyloid plaque formation

• 2 models = both valid

• Model A : nucleation-polymerization mechanism

  • body has natural/intrinsic tendency to adopt scrapie/amyloid form (pre-existing equlib)

  • usually native favored → when equlib changed = scrapie forms

• Model B : template-directed mechanism

  • no pre-existing equilib = dif external factor that promotes conversion

  • when gen small amount of Sc form = coax C (native) form to induce into SC

  • equlib forms after external trigger

lock and key model of ligand-receptor binding

• older model

• no catalytic event

• already have complementary surface

induced fit model of ligand-receptor binding

• requires plasticity = protein can adopt more than 1 geometry

• can also induce new config of ligand as well (not just receptor)

types of ligand-receptor binding

1. single binding site for the ligand on the receptor (non-cooperative)

2. multiple equivalent binding sites for two or more ligands on the receptor (non-cooperative)

3. multiple non-equiv binding sites for ligands on the receptor (cooperative)

Kd

• dissociation constant

• shows strength of binding

• = [P][A] / [PA]

• lower Kd = strong/tight binding

• also can be written as p50 w/ partial pressues

fractional saturation

• represented as “r” or YO2 (partial pressures)

• when r=.5 → [A]  = Kd

• Kd = [A] to get P ½ saturated

Hughes-Klotz plot (double-reciprocal)

• plot of 1/r v. 1/ [A]

• varied distrib of points = unreliable

• if 1 pt in experiment off = big change in slope

• slope = Kd/n

• y-intercept = n

Scatchard plot (single reciprocal)

• more reliable

  • pts more uniformly distributed

  • more accurately evaluate slope

• slope = -1/Kd

• x-intercept = n

n sites of multiple binding sites

• n = number of equivalent binding sites

• assumed to be equivalent and independent (free energy of binding is the same for each site) → no cooperation

• in Scatchard: n = x-intercept

• in Hughes-Klotz: 1/n = y-intercept

biological functions of myoglobin & hemoglobin

• both O2 binding proteins

  • myo = mostly storage

  • hemo = transport

    • tetramer w/ 4 subunits

• process:

  • O2 enters lungs → transported to tissues via oxyhemoglobin

    • non cov attachment to hemo

  • myoglobin stores O2 in tissues = affinity for O2 > hemo

  • CO2 released via HCO3

  • covalently bind to hemo as deoxyhemoglobin → transported to lungs

  • lungs release CO2

the heme group

• = O2 binding site = prosthetic group tightly bound between helix E and helix F

• ion oxidation state is important (Fe2+ not Fe3+)

• only Fe2+ binds O2 (must protect from aq spont. oxidation into Fe3+)

• 1 in myo and 4 in hemo

• 6 ligands of Fe 2+

  • 4 from heme

  • proximal His93 (F helix)

  • variable ligand (O2, CO, H2O)

• also have distal His64 (E-helix)

  • influences variable ligand affinity; not directly bound to iron center

  • weak interaction w/ Fe but can still influence

myoglobin v hemoglobin structures

• myo

  • monomer

  • single polypep chain

  • non cooperative

• hemo

  • tetramer

  • 2 polypep chains (2 beta, 2 alpha)

  • 4 subunits = not identical but symmetrical

    • all have dif Kd

    • 4th site = much lower Kd than 1st

    • = pos cooperativity = 1 site becomes bound = increase binding affinity for other sites

• primary structures not similar but same tertiary (fold the same)

deoxyhemoglobin v oxyhemoglobin

• deoxy = no O2 bound

• different UV spectra

  • use to differentiate

fractional saturation of Mb v Hb

• YO2 = fractional saturation = fraction of O2 binding sites occupied by O2

• Mb = hyperbolic = non-coop

  • p50 = 4 mm

• Hb = sigmoidal = implies coop

  • p50 = 30 mm (weaker affinity to O2)

O2 saturation curves

• fractional saturation

  • sigmoidal = coop

  • hyperbolic = non-coop

• double reciprocal / single reciprocal (Scatchard)

  • non-linearity = coop

  • linearity = non-coop

hill equation

describes the degree of saturation of a multi-subunit protein as function of ligand concentration

Hill constant

• n = non-integer parameter related to degree of cooperativity among interacting ligand binding sites

• increases w/ degree of cooperativity

• n=1 → non-coop

• n>1 → pos coop

  • greater n = greater coop

  • lower n = reduces ability of hemoglobin to transport / bind O2 (loading/unloading)

• n<1 → neg coop

• steepest slope on Hill plot = value of n

optimizing O2 storage and O2 transport proteins

• situation 1: both hemo and myo are non-coop

  • transport protein efficient in binding but inefficient in unloading

  • O2 is too tightly bound = hemo cannot unload after transfer

• situation 2: transport protein binds weaker but still non-coop

  • transport prot efficient in unloading but inefficient in binding

• situation 3: sigmoidal curve transport protein binding

  • at low O2 sat (ie in the tissues) = low binding of O2 to hemo

    • able to unload

  • at high O2 sat (ie in lungs) = strong binding

    • able to load/store O2

  • transport protein efficient in both binding and unloading

the Bohr effect

• hemoglobin releases H+ ions upon binding O2

• tissues are actively metabolizing = more CO2 = bicarbonate produced from H+ ions

• pH decreases = reduce Hb affinity for O2

• catalyzed by carbonic anhydrase = decreased pH of actively metabolizing tissues results in enhanced release of O2 from Hb

CO2 and O2 production in the body

• in tissues:

  • CO2 enters from cells of tissues

  • carbonic anhydrase catalyzes carbamate production and bound hemoglobin

  • promotes O2 release to tissue & carbonic acid production → transport via plasma to lungs

• in lungs

  • HCO3- from plasma & O2 from air enters lungs 

  • high concen of O2 in lungs forces oxygenation of Hb

  • HCO3- cleaved by carbonic anhydrase to become CO2

covalent transport via Hb (carbamate formation)

• carbamate formation via the N-termini and CO2 = forms H+ ion

• also acidifies environ

• lower pH = coax Hb to release O2

• deoxyHb binds more CO2 as carbamate than does oxyHb

  • CO2 forces deoxy to give up O2 bc carbamate binds less tightly

• 2 amino groups per HB able to covalently bind O2 on N-termini (not all 4 subunits)

carbamate and CO2 in the body

• in the tissues:

  • CO2 enters from cells of tissues

  • combines w/ HBNH2

  • carbamate and H+ ion forms w/ oxyHb

  • Hb coaxed to release O2 and bind to H+

    • carbamate stabilizes deoxyHb in tissues

    • O2 to cells of tissues

• in the lung

  • O2 from air enters lungs and combines w H+Hb

  • O2 binds w/ Hb = carbamate formed

  • carbamate breaks down = CO2 + HbNH2

  • CO2 to air

effect of 2,3 BPG

• one 2,3-BPG molec binds per Hb tetramer

• highly neg charged molec = net charge of -5

• BPG binding pocket lined w/ pos charge = electrostatic interactions

  • Lys, His, N-termini

• 2,3 BPG pref binds to deoxyHb

  • central cavity is too small in oxyHb to for BPG to bind

• higher BPG = increased p50 = weaker binding = reduced affinity for for O2

effects of 2,3 BPG and CO2 on O2 dissociation curve of Hb

• whole blood = furthest left

• Hb + CO2 → gen carbamate = favor deoxy form = weaker affinity O2 by Hb

  • CO2 = produce H+ ion = HCO3- = also weaken Hb affinity

• Hb + BPG → Hb binds in favored deoxy form = want to release O2

• Hb + BPG + CO2 → Bohr + BPG (most right shifted)

importance 2,3 BPG effect in blood

• level of BPG in blood is dep on

  • relative activity of 2 molecs

    • synthesizing enzyme: 2,3 BPG mutase

    • degradating enzyme: 2,3 BPG phosphatase

  • altitude = increased altitude = increased BPG

    • enzyme responsible for biosynth wins out over degradation in high altitudes

• w/o BPG acting at increased altitude: not enough O2 released in tissues = become anoxic

  • by shifting curve (due to increased BPG) = keep O2 level at same as sea level about 38% released

• also active in fetal HB

  • fetal Hb = sub His for Ser (lose 2 pos charges)

    • remove 2 pos charge in BPG binding pocket = lower affinity for BPG and increase affinity for O2 in fetuses

    • fetus can steal O2 from mother

deoxy Mb and oxyMv

• heme located in hydrophobic pockets formed by helices E and F

  • maintains Fe2+ state

• oxyMb: Fe is .22 A out of plane on proximal His(3

  • O2 is bound in a bent geometry

• deoxyMb: Fe is .55 A out of plane 

• structures of oxyMb and deoxyMb are largely superimposable

  • very dif primary but similar similar tertiary

deoxyHb and oxyHb

• interactions between alpha 1 - beta 1 and alpha 2- beta 2 = hydrophobic

  • abundant and fixed

• alpha 1 - beta 2 and alpha 2 - beta 1 = polar

  • few & connects like subunits

  • dep on O2 binding = change based on oxy/deoxy state

  • oxygenation = 15 degree rotation of alpha 1 - beta 1 dimer

    • leads to differences in quaternary structures

  • dynamic = any mutations that occur here are detrimental

• deoxyHb = T state (tense)

• oxyHb = R state (relaxed)

cooperativity of hemoglobin

• out of plane Fe in deoxyHb (.55 A) moves nearly in-plane in oxyHb (.22A) and pulls on prox His 93 → moves F helix due to Fe being pulled in plane

  • distal His also affected = changes backbone

symmetry model of allosteric regulation

• conf changes alters affinity for ligand = molec symm is conserved

• multiple equlibs as increase amount of ligand

• predicts sigmoidal binding curve

sequential model of allosterism

• conformational change for liganded + unliganded subunits

• intermediate conf/affinity state = breakage of symmetry

  • multiple intermed shapes

• symmetry not maintained thru intermediates = leads to mutliple Kds

• also predicts sigmoidal curve

• more accurate = supported via experimental evidence

sickle cell anemia

• single state mutation: Val replaces Glu A3(6)beta

• mutate one Hb tetramer beta chain

  • non conserved = neg polar → np

  • self associates to form insoluble fibers (multiple beta 1 and beta 2 chains interacting)

    • mutating self-associating chain created

  • np can fit into hydrophobic pocket & self-associate

enzyme classification by type

1. oxidoreductases → redox reactions

2. transferases → transfer of fxnal groups

3. hydrolases → hydrolysis rxns

4. lyases → group elimination to form double bonds

5. isomerases → isomerization

6. ligases → bond formation couples w/ ATP hydrolysis

classification of enzymes (name)

• ex. carboxypeptidase A = EC 3.4.17.1

• enzyme major class = hydrolase (3)

  • cleave fxnal group

• subclass of hydrolase →  peptide hydrolase (4)

  • cleave peptide bond

• sub-subclass → metallocarboxypeptidase (17)

  • carboxypeptidase A has a Zn2+ ion bound in its active site

• arbitrarily assigned serial number in its sub-subclasses (1)

cofactors

• non protein components req by an enzyme for activity

• can be inorganic (ion) or organic

• very general

  • ex. heme group in Hb

• can be strongly bound by protein or reversibly associate w/ protein

coenzyme

• an organic cofactor

• can be strongly bound by protein or reversibly associate w/ protein

prosthetic group

• a strongly bound cofactor

• ex. heme group

• weaker binding = substrate diffuses into active site and then leaves

holoenzyme

an enzyme and all the cofactors req for activity

apoenzyme

just the enzyme (protein)

coenzymes and their vitamin precursors

• vitamins create scaffold used by enzymes to convert to coenzymes

• must ingest vitamins from outside sources

• examples:

  • biotin synthesizes the biocytin coenzyme

  • nicotinamide is enzymatically converted to nicotinamide coenzyme

common coenzymes and enzyme rxns they mediate

• coenzymes are neccessary for enzyamtic fxn

• examples:

  • coenzyme A = acyl transfer

  • flavin coenzymes = redox rxns

  • nicotinamide coenzymes = redox rxns

    • critical for metabolic rxns

NAD+ / NADP+ coenzyme reactions

• 2 e- , 2 proton redox rxn NAD+ (NADP+) accommodates 2 e_ and 1 p during reduction of nicotinamide ring

• 2nd proton released into solution

• in reduced form: C4 carbon of nicotinamide ring = prochiral

  • either pro-R or pro-S sit involved in redox depending n dehydrogenase

    • w/ NAD+ or NADP+ as coenzyme

  • selectivity determined via conducting rxns w/ deuterated substrates and/or deuterated NADH

• NAD+/NADH = primarily catabolic (break down) & mitochondrial

• NADP+/NADPH = primarily anabolic (biosynth) & cytosolic

• in vivo (cell):

  • NAD+/NADH ratio is high & NADP+/NADH ratio low

  • this consistent w/ NAD+ as oxidizing agent & NADPH as reducing agent

    • NAD+ = want to accept as many e- during oxidation

    • NADPH = want it to be source of e- so want more NSDPH as reducing

flavin coenzyme structure and reactions

• vitamin B2 responsible for construction of flavin coenzyme 

  • phosphorylate ester of B2 to create phosphomonoester of flavin mononucleotide 

    • this creates oxidized form (FMN)

    • can also reduce = FMNH2

  • if more complex group attached (ATP) = FAD / FADH2

• unlike NAD+ = FMN/FAD coenzymes can undergo 1 e- / 1 p reduction to form stable intermediate (semiquinone form)

  • important for e- transport

  • transfer 1 e- at a time

• can also further reduce to 2e-/2p reduction with next step

enzyme-substrate complex interactions

• geometric & physical complementarity between the enzyme active sit & the substrate 

  • also applies to other types of binding

  • many non-cov reactions happening in active site that lead to specificity

• via induced fit = complementarity = protein-protein, electrostatic, donor/acceptor, hydrophob, H-bond, etc.

prochiral centers in substrates

• pro-chiral = right before becoming chiral

• prochiral differentiation in a chiral protein binding site 

  • can tell dif between pro-R and pro-S substates bc only one will bind to active site = becomes chiral

• examples;

  • ethanol: between pro-R H and pro-S H

  • citric acid: two identical groups but once bound to active site = can tell difference bc one site changed via binding

protein phosphorylation

• major form of reversible post-trans covalent modif that affects enzyme structure and activity

  • introduction of neg charge = substantial conf change (tertiary)

    • phosphate group = 2 ionizations = 2 new neg changes

    • conf change = affects activity of enzyme to bind substrate or convert substrate to product

  • introduction of new binding site

enzyme-catalyzed phosphorylation & dephosphorylation of protein

• ex. serine phosphomonoester (serine = primary phosphorylated side chain)

  • but threonine & tyrosine also options (all have OH)

• protein kinase = transfer phos group = activates enzyme

• protein phosphatase = recog phosphorylated form of enzyme = remove phos group = deactivate enzyme

• (phosphorylation can also deactivate)

• regulate expression of control enzymes (kinase & phosphatase) based on desired enzyme activation sate

enyzme catalysis basic principle

• substate binds enzyme active site → forms ES complex → converted to product

• rate constant K2/Kcat associated w/ conversion of ES complex to product

allosteric regulation of an enzyme

• ex. ATCase in UTP/CTP biosynth pathway

• regulatory enzyme = created early in pathway

• catalyze the initial rxn of metabolic pathway

• ATCase = reg enzyme

  • converts UTP → CTP

  • high levels of CTP = feedback inhibition = shut down enzyme activity bc enough product made

  • catalyzes 2-sub (carbamoyl phosphate & aspartate) reaction to give single product (CTP)

rate vs [S] curves of allosteric regulation

• ATCase = reg enzyme

  • catalyzes 2-sub (carbamoyl phosphate & aspartate) reaction to give single product

• cooperativity = sigmoidal curve

• ATP = positive effector = shift curve left

  • increase activity of enzyme

  • less reactant for greater rate

• CTP = negative effector = shift curve right

  • slow down catalytic activity

  • need higher concen of aspartate (substrate) to achieve activity

benefits of cooperativity

• w/ increased subunit cooperativity: minor changes in concen of intercellular effector molec = big changes in catalytic activity

  • increased subunits = increased sigmoidal

• no cooperativity = need large amounts of effector to change catalytic activity

enzymatic rate acceleration

• enzymes leads to substantial rate enhancements relative to uncatalyzed

  • accelerations range from 10⁹ to 10²³

• due to acid-base catalysis & proximity/orientation effects

proximity/orientation effects on enzymatic rates

• without enzyme = bimolecular process (intermolecular)

  • 2 reactants

  • angle of attack has a very specific preferred trajectory 

  • very inefficient and time-consuming

• with enzyme = unimolecular (intramolecular)

  • enzyme reorients reactants/substrates to enhance rate

    • tethers molecs together

    • = greater propensity for nuc attack bc closer tg

  • removes time needed for O- to find perfect angle = increase rate

acid-base catalysis on enzymatic rates

• peptide (amide) bond hydrolysis

• no catalysis = no charge involved = O slow to attack C

• acid catalysis = enhance electrophilic character of carbonyl

  • add protonated group/proton donor

  • leads to formal pos charge on carbon

  • H2O much more likely to attack carbonyl

• base catalysis = enhance nucleophilic character of water = activating oxygen

  • add neg charge on oxygen

  • H2O much more likely to attack

• both acid & base catalysis

  • both carbonyl & oxygen have charge

  • very fast nuc attack = increased rate of enzyme

enthalpic and entropic factors affecting strength of enzyme-substrate binding

• entropy/disorder in the substrate

  • substrates go from highly disordered, high entropy → highly ordered, low entropy complex once bound to enzyme

• solvation effects

  • substrate starts in solvation shell → water released to environ upon binding to enzyme

  • too tightly bound for water to get in

• electrostatic interactions

  • complementary charges on substrate and enzyme surface can strengthen binding

reaction coordinate diagrams

• enzyme-catalyzed

  • leads to lower activation energy due to formation of ES complex

  • turns to EP complex

  • dissociates into enzyme and product

• acid-catalyzed

  • also leads to lower activation energy but less so

  • creates protonated intermediate

  • turns to protonated product

  • product is deprotonated

• all reactions = same overall change in free energy, only activation energy changes

enzyme catalysis and activation energy

• enzyme must bind transition state more tightly than substrate for catalysis to occur

  • amount stabilize transitions state must be greater than formation of ES complex

  • only way for activation barrier to actually go down

catalytic antibodies

• antibody generation against a molec that mimics the putative transition state of amide hydrolysis

  • unstable tetrahedral intermediate formed post H2O attack

• create stable analog of tetra intermed in lab → create antibodies that bind tightly → introduce antibodies to binding site (already predisposed to those antibodies) → catalyze hydrolysis of analog → form tetrahedral intermed

• = stabilize and create more product than normal amide hydrolysis

common mechanisms of enzyme catalysis

• acid-base catalysis

• covalent catalysis

  • serine protease

• metal ion catalysis

  • cofactor to enzyme catalysis in many cases

• electrostatic catalysis

• catalysis via proximity/orientation effects

  • fxnal sites closer tg in active site = promote reactions

• catalysis via preferential transition binding

  • enzyme binds TS more tightly than substrate to lower activation energy barrier

Michaelis-Menten: Vo v [S]

• Km = Michaelis constant

• Km = [S] at ½ Vmax

• enzyme sat is achieved at [S] > 10 Km

• simple = hyperbolic (no allosterism)

• at Vmax = high substrate and low free enzyme

  • all ES complex (fully sat)

Michaelis constant

• Km

• sometimes used as Kd in enzymatic reactions

  • shows affinity of substrate for enzyme

• [S] at ½ Vmax = Km

initial velocity as a function of [S]

• increasing substrate concentrations = increased vo

• vo = tangent slopes of reactions curves

initial velocity as a function of [E]

• initial velocity directly proportional to concentration of E

• increasing amount of enzyme = increases rate of catalysis

• important for specific activity of an enzyme

enzyme-catalyzed reaction steps

• binding step

  • fast, reversible

  • E+S ←> ES

  • k1 / k-1

• catalytic/conversion step

  • slow, rate determining

  • reaction rate proportional to [ES]

  • when [Ef] is small = rate is maximal (saturating conditions)

    • more ES = more propensity for enzyme to convert reactant to product = increase rate

  • ES ←> E + P

  • k2 / k-2 (kcat)

Michaelis-Menten equation

• Vo = k2 [ES] = Vmax [S] / [S] + Km

• describes hyperbolic, saturation kinetics curve

  • only simple enzymes: bind 1 substrate, not regulatory

• Vmax = max initial rate

• Km = MM constant = [S] at which ½ Vmax is observed

• [S] = concentration of free S

• based on

  • rate of formation of ES = rate of breakdown of ES

steady state principle

• overtime of reaction = [S] decreases and [P] increases

• enzyme concentration stays steady

  • initial drop in free E then steady

  • initial rise in ES then steady

  • slight rises & falls over time are very fast → can generalize as unchanging / “steady”

• thus

  • rate of formation of ES = rate of breakdown of ES

comparing Km and Kd for formation of ES complex

• Km = Michaelis constant

  • obtained from kinetics (catalytic activity) measurements

  • k2 + k-1 / k1 = Km

• Kd = dissociation constant 

  • obtained from Scatchard or related plots

  • binding of ligand to protein

  • k-1 / k1 = Kd

• Kd is formal measure of enzyme affinity for S

• Km is commonly interpreted as a measure of this affinity

  • can be reasonable estimate of Kd when k2 < < k-1

    • makes k2 irrelevant

k2/Km

• measure of catalytic efficiency

  • k2 = conversion of enzyme to product

  • km = binding of substrate to enzyme

• second order rate constant for formation of ES complex

• maximal when k2 is large and Km is small (small Km = stronger binding)

• maximal ratio when k2 > > than K -1

  • = k1 can only be as fast as the rate of diffusion

    • limits how fast enzyme can bind substrate

  • diffusion limit = 10⁸- 10⁹ M-1 s-1 = maximal rate

outcomes of Km and Kcat relationship

• [S] > > Km

  • v = kcat [E0]

  • enzyme sat w/ substrate

  • all ES complex

• [S] = Km

  • v = kcat/2 x [E0]

  • enzyme ½ sat w/ substrate

  • ½ free E and S and ½ ES complex

• [S] < < Km

  • v = kcat/Km x [E0] x [S]

  • mostly unbound/free substrate

  • uncatalyzed = higher Eact

Lineweaver-Burk plot

• linearizes MM equation

• double-reciprocal plot

  • plot 1/vo vs 1/[S]

• slope = Km/Vmax

• y-intercept = 1/Vmax

• x-intercept = -1/Km

• large extrapolations so less accurate

Eadie-Hofstee plot

• linearizes MM eq

• single reciprocal

• 2 forms = either can be used

• form 1:

  • plot vo / [S] vs vo

  • slope = -1/Km

  • x-intercept = Vmax

  • y-intercept = Vmax/Km

• very well-dispersed = less error and extrapolation (compared to single recip)

bi-substrate reactions

• can be catalyzed directly by enzyme or by using coenzyme as reactant/substrate

  • ex redox coenzyme (NAD+)

• 2 substrates = very common

• more than 2 = too much competition/collisions = hinders binding = uncommon

sequential mechanism

• bi product, bi substrate

• single displacement reactions

• ordered bi bi = specific order of binding

  • A before B (EA before EAB)

  • Q leaves before P

• characterized by formation of ternary complex (EAB) & interception of lines in double reciprocal plots

• steps:

  • E+A → EA (binding)

  • EA → EAB (binding)

  • EAB → EPQ (conversion/catalytic)

  • EPQ → EP + Q (dissociation)

  • EP → E + P (dissociation)

• also random bi bi = no order to substrates binding/dissociation

  • kinetically indistinguishable from ordered bi bi plots

ping pong mechanism

• bi product, bi substrate

• double displacement reaction

• characterized by parallel lines on double reciprocal plot and E’

  • E’ = covalently modified enzyme

    • enzyme steals fnxal group of A to later pass to B

• order matters = A binds before B

• steps:

  • E + A → EA (binding)

  • EA → E’ + P (catalytic/conversion & dissociation step)

  • E’ + B → E’B binding

  • E’B → E + Q  (catalytic/conversion & dissociation step

assaying an enzyme

• important for enzyme isolation

• need to look at how much enzyme is there

  • in solution w/o destroying activity

  • use catalytic activity to answer

purifying proteins

• scheme A: traditional chromatography

  • many steps and inefficient

  • lower yield, fold purification, and specific activity

• scheme B: affinity chromatography

  • fewer steps & more pure product

  • higher yield, fold purification, and specific activity

specific activity of an enzyme

• units of activity / mg protein

• fnxal definition to measure amount of enzyme in solution

  • “converts this much reactant to product at this rate”

  • nkat / g

• as purify = systematic increase in sp. activity

  • g decreases as junk removed

  • nkat should stay same is enzyme is retained as it should

  • shows effectiveness of purification step

  • want to retain as much enzyme and get rid of as much junk as possible

steps to creating protein purification protocol

• need to know eq of rxn, cofactor req, Km, and optimum pH

• need experimental method to measure rate of disappearance / appearance of product

• procedure:

  • measure initial vo at dif [E] and w [S] at sat levels

    • S > 10 Km

  • plot vo against [E]

  • define one unit of activity (sp activity = units of activity / mg protein)

  • observe turnover number