Unit 3: Myoglobin, Hemoglobin, Enzymes, and Enzyme Kinetics
Km=(K2+K-1)/K1
Km in terms of rate constants
The substrate concentration when Vo is half Vmax (Km=1/2 Vmax)
Km or Michaelis Constant
rxn velocity=V=k[S]. Units: sec⁻¹
1st Order Rate Constant
Rxn dependent on two molecules of substrate. V=k[A][B]. Units: M⁻¹sec⁻¹
2nd Order Rate Constant
activting homotropic modulator. the binding of O2 changes the affinity of remaining unfilled binding sites
is O2 a homotropic or heterotropic modulator
the effect of pH and CO2 concentration on the binding and release of oxygen by hemoglobin. Both O2 and H+ are bound by Hb but with inverse affinity: when O2 concentration is high (lungs) Hb binds O2 and releases H+. When O2 concentration is low (tissue) H+ binds and O2 is released.
Bohr effect
A high value of Kd or Km indicates a low affinity of E and S for each other because k-1 is higher.
High value of Kd or Km
Equilibrium constant [Products]/[Reactants] if P is lower than S, there is a higher [P] because the rxn is favorable and exergonic so Keq>1. Keq=[B]/[A]=kR/kF
Keq
Vo=Vmax[S]/Km + [S]
M-M Equation
substrate concentration is plotted against initial velocity
Michaelis-Menton plot
Occurs with loops that bring the non-polar residues into the center and keep the polar, hydrophilic molecules near the surface.
Myoglobin Folding
The oxygen binding site in myoglobin involves the heme group and 2 histidine residues. The aromatic structure of the His residue explains why the residue would be inside the protein core, however, the nitrogen is a polar molecule, but it can participate in H-bonding to stabilize the native tertiary structure.
Oxygen Binding Site in Myoglobin
Aromatic organic compound, a five-membered ring with the formula C4H4NH.
Pyrrole Ring
the maximum initial rate of the catalyzed reaction observed when virtually all the enzyme is present as the ES complex and [E] is vanishingly small; the enzyme is saturated with substrate so that further increases in [S] will have no effect on reaction rate. The plateau-like region. µM/min
Vmax
The oxygen binding sites are rather far apart given the size of the molecule, roughly 2.5nm from each other.
are the oxygen binding sites far or close in hemoglobin
hemoglobin is more sensitive to small difference in O2 concentration between the tissues and lungs, allowing it to bind O2 in lungs and release in tissue
at physiologically relevant O2 concentrations, is myoglobin or hemoglobin more sensitive to small changes in oxygen concentration
where a ligand binds on the protein; complementary to the ligand in shape, size, charge, and hydrophilic/ hydrophobic character; allows the interaction to be SPECIFIC. The crevice or pocket where the ligand binds. A given protein may have separate binding sites for several different ligands.
binding site
a substance that increases the rate of a chemical reaction without itself being changed or consumed in the overall process. Most biological catalysts are protein enzymes. If an enzyme is denatured or dissociated into subunits, catalytic activity is ususally lost. Thus, the primary, secondary, tertiary, and quaternary structures of protein enzymes are essential to their catalytic activity.
catalyst
the upper diffusion-controlled limit is 10^8 to 10^9 M-1 s-1; when enzymes have a kcat/Km near this range they are said to have achieved catalytic perfection
catalytic perfection
the ligand binding site, the enzyme-substrate binding site. The position of the enzyme that is complimentary to the substrate
catalytic site or active site
organic or metalloorganic molecule bound to enzymes and is necessary for enzymatic activity; often contains a vitamin component. Acts as a transient carrier of specific functional groups.
coenzyme
inorganic ions or coenzymes required for enzymatic activity and are bound to enzymes. So, not all enzymes that have a cofactor have a coenzyme. But all enzymes that have a coenzyme have a cofactor.
cofactor
"R"- relaxed; "T" - tense - R is more stable when O2 bound and T is more stable when no O2 bound; in the "T" state the porphyrin is slightly puckered, causing heme iron to protrude on the proximal His, the binding of O2 causes heme to assume a more planar conformation which shifts the conformation of the proximal His and attached F helix. The His residues at the carboxyl termini of the β subunits, which are involved in ion pairs at the T state, rotate toward the center in the R state, when they are no longer in ion pairs.
compare conformation of hemoglobin T and R states
1) CO2 binds to H2O to release H+ which binds to the hemoglobin, lowering oxygen affinity. 2) CO2 also binds as a carbonate group to the alpha amino group at the N terminal of the globin chain which makes carbaminohemoglobin, this reaction also produces H+, bound carbamates also form salt bridges to help stabilize the T sate and promote the release of O2.
describe 2 ways CO2 allosterically lowers oxygen affinity
by taking the reciprocal of both sides of the M-M equation (double-reciprocal plot); 1/Vo vs 1/[S]
describe how a Lineweaver-Burke plot can be generated from a M-M plot
The heme is bound in a pocket made largely of E and F helices; deeply buried in the folded polypeptide
describe the location of the heme group
homotropic is when the normal ligand and modulator are identical. heterotropic is when the modulator is a molecule other than the normal ligand.
differentiate between heterotropic and homotropic modulators
iron only binds reversibly in the ferrous (Fe2+) state; the coordinated nitrogen atoms have electron-donating character which helps prevent the conversion of heme iron to the ferric (Fe3+) state, which does not bind oxygen.
discuss the oxidation state of iron in myoglobin (and hemoglobin)
when K2 is rate-limiting (K2 <<<K-1), and Km reduces to K-1/K1; under these conditions Km represents a measure of the affinity of the enzyme for its substrate in the ES complex. Units of M⁻¹sec⁻¹
dissociation constant (Kd)
Both are free energy and the energy in biological systems is described in terms of free energy. ∆G: standard free-energy change under conditions 298K, 1atm/101.3kPa and 1M conc. ∆G': the biochemical standard free-energy change at pH 7.0
distinguish between ∆G and ∆G'
Yes. O2 binding to individual subunits alters the affinity for O2 in adjacent subunits- the first molecule of O2 that interacts with deoxyhemoglobin binds weakly (in T state), but its binding leads to conformational changes that are communicated with adjacent subunits (a single subunit protein with a single ligand-binding site cannot produce a sigmoidal curve, because the ligand binds independently and cannot affect ligand binding to another molecule.)
do isolated hemoglobin subunits exhibit cooperativity in O2 binding
no. rates of reactions are determined by activation energy not by favorable equilibrium. favorable reactions have large Kc and have a large negative ∆G'
does a favorable equilibrium mean that the rate of the forward reaction is fast
slower reaction rate
does a higher standard free energy of activation correspond to a slower or faster reaction rate
no. catalysts increase the rate of reaction and bring it to equilibrium faster but they have no effect on the equilibria constants or the position of equilibrium or its favorablility.
does the presence of a catalyst have any effect on the position of equilibrium
P₅₀ for Hb=3.5kPa and P₅₀ for Mb= 0.26. Myoglobin has the higher affinity for oxygen. Hb is more sensitive to small changes in oxygen concentration because of its cooperative binding. This allows it to bind oxygen in the lungs and release it in the tissues.
estimate P50 of oxygen binding for hemoglobin. compare to myoglobin
weak binding interactions between the enzyme and the substrate provide a substantial driving force for enzymatic reactions, by lowering the Ea by providing an alternative, lower energy rxn. path. Formation of each weak interaction in the ES complex is accompanied by the release of a small amount of free-energy that stabilizes the interaction, this energy is the binding energy and it is a major source of free-energy used by enzymes to lower Ea of reactions. This binding energy also contributes to the specificity. Weak interactions are optimized in the reaction transition state. Enzyme active sites are complimentary not to the substrates per se, but to the transition state through which the substrates pass as they are converted to products.
explain enzymes accelerate reactions by stabilizing the transition state
the enzyme lowers ∆G⁺; to lower the activation energy for a reaction the system must acquire an amount of energy equal to the amount at which ∆G⁺ is lowered. much of this energy comes from binding energy contributed by formation of weak non-covalent interactions between substrate and enzyme in transition state. The catalyst lowers the the activation energy and increases the reaction rate by going through stable reaction intermediates, which are stable trnasient chemical species that have a finite chemical lifetime.
explain the affect of an enzyme on the standard free energy of activation
initial velocity can be explored as a function of [S]. data is generated by varying [S] and holding enzyme concentration constant. At low [S], Vo increases almost linearly with an increase in [S]. At higher [S], Vo increases by smaller and smaller amounts in response to [S]. Finally, a point is reached beyond which increases in Vo are vanishingly small as [S] increases. This plateau-like Vo region is close to the max velocity or Vmax.
how can Vo be determined at a number of different [S]
more rigid; more salt bridges; more stable when no oxygen is bound; heme group is puckered which shifts the proximal His. Interactions betweek ion pairs like His and Asp of the β subunit and Lys of the α subunit and His of the β Subunit.
how do salt bridges stabilize the Tense conformation (T State) of deoxyhemoglobin
They lower hemoglobins affinity for oxygen by stabilizing the T state; the transition to the R state narrows the binding pocket for BPG and prevents it from binding - hemoglobin is converted to the R state more easily when BPG isn't bound
how do the BPG interactions affect hemoglobin's oxygen binding affinity
the binding of H+ and CO2 is inversely related to the binding of oxygen: at low pH (high H+ and CO2) the affinity of hemoglobin for oxygen decreases since H+ and CO2 are bound and O2 is released into the tissue
how does H+ promote the delivery of O2 from lungs to tissues
T→R transition is triggered by changes in positions of key amino acid side chains surrounding the heme. In the T State the porphyrin ring is slightly puckered, causing the heme iron to protrude somewhat on the proximal His side. The binding of O₂ causes the heme to assume a more planar conformation, shifting the position of the proximal His and the attached F helix. These changes lead to adjustments in the ion pairs at the α₁β₂ interface. T→R transition also narrows the pocket between the β subunits.
how does binding of O2 lead to conformational changes in the ligand binding site? how are these changes submitted to the subunit interface
free heme molecules (not bound to protein) leave Fe2+ with 2 open coordination bonds - reaction of 1 O2 with 2 free heme molecules can result in irreversible conversion of Fe2+ to Fe3+; this reaction is prevented by sequestering heme deep within the protein structure. One of the two coordination bonds is occupied by an N of histidine residue (proximal Histine) and the other coordination bond is the binding site for molecular oxygen.
how does the globin protein prevent heme iron oxidation
at low substrate concentration; Km >> [S]; Vo exhibits a linear dependence. Vo = Vmax[S] /Km
in what part of M-M plot is the velocity directly proportional to the substrate concentration
At high substrate concentration where [S]>>Km. Vo = Vmax
in what part of the M-M plot is the velocity independent of the substrate concentration
the binding of a protein and ligand is often coupled to a conformational change that makes the binding site more complementary to the ligand, to allow tighter binding; also can affect conformation of other subunits in multi-subunit protein. A change in the conformation of an enzyme in response to substrate binding that renders the enzyme catalytically active.
induced fit
not a realistic variable because biological enzymes have certain temperatures where they work optimally.
is temperature control a realistic variable to increase reaction rate in a biological system
ES --> E + S breakdown to reactants
k-1
P-->S; this can be ignored because early in the reaction, [P] is negligible
k-2
E + S --> ES pre-steady state when enzyme is mixed with excess of substrate and the concentration of ES is building.
k1
ES --> E + P breakdown to products
k2
a molecule bound reversibly by a protein; may be any kind of molecule including another protein
ligand
the partial pressure of oxygen at which the oxygen-carrying protein is 50% saturated (half of the available ligand-binding sites are occupied [O₂]₀.₅) In experiments using oxygen as the ligand, it is the partial pressure (pO₂) in the gas phase above the solution that is varied.
meaning of P50
there are certain binding sites in hemoglobin that are of higher affinity in the deoxy form than the oxy form - reflects increase in affinity for H+ reflects that the pKs for some groups are higher in the deoxy form. O2 binds to the iron atoms of the hemes and H+ binds to any of several amino acid residues in the protein.
mechanism of Bohr effect
sigmoidal (s-shaped) curve; hemoglobin undergoes transition from low-affinity state (T state) to high-affinity state (R state) as more O2 molecules bind
name the shape of the hemoglobin oxygen binding curve
oxygen binds to heme with O2 axis at an angle; curve of O2 binding follows rectangular hyperbolic shape
oxygen binding behavior of myoglobin
facilitates oxygen diffusion into muscle tissue; also have O2 storage function (in muscles of diving marine animals during prolonged excursions - rapid molecular flexing of amino acid side chains produce transient cavities allowing O2 to come in and out; better as storage protein than carrier (see curve)
physiological role of myoglobin
they have some of the same residues but most are different. Hbα and Hbβ are more similar to each other than to Mb; only have 27 identical positions
primary sequence of myoglobin vs. hemoglobin
features strong interactions between unlike subunits; the α1β1 (and α2β2) involves more than 30 residues; mild treatment with urea disassembles the tetramer into αβ dimers that remain intact; hydrophobic interactions predominate at all interfaces, but there are also hydrogen and ionic bonds. Tetrameric protein containing 4 heme prosthetic groups, one associated with each polypeptide chain, 2 per subunit.
quaternary structure of hemoglobin
when several steps occur in a reaction, the overall rate is determined by the step(s) with the highest activation energy; can vary with reaction conditions; the highest point in the diagram for the interconversion of S and P; for a first order reaction the RLS depends only on the amount of substrate
rate-limiting step
transports oxygen from lungs to tissues in hemoglobin of red blood cells or erythrocytes.
role of hemoglobin
1 subunit; made up of 8 alpha-helical segments (labeled A-H) connected by 6 bends. About 78% of amino acid residues in the protein are found in these alpha-helices.
secondary and tertiary structure of myoglobin
1/Vmax is y-intercept on 1/Vo axis -1/Km is x-intercept on 1/[S] axis slope=Km/Vmax
show how the axis intercepts on a L-B plot can be used to determine the Km and Vmax of the enzyme
molecules that act upon enzymes (proteins), (rather than ligands). A molecule bound reversibly by an enzyme.
substrates
very similar; globin family has similar structure
tertiary structure of myoglobin vs. hemoglobin
at the top of the free energy hill where the decay to products is optimal; the point at which decay to the S or P state is equally probable (downhill either way)
transition state
equivalent to the number of substrate molecules converted to product in a given unit of time on a single enzyme molecule when the enzyme is saturated with substrate. First order rate constant. To find: (M[S]/M[E])/time
turnover number (Kcat)
ES complex can revert back to enzyme and substrate or proceed forward and make product free up enzyme. So, enzyme can be in complex form ES or unbound as E. At any given instant in an enzyme-catalyzed reaction, the enzyme exists in two forms. At low [S] most of the enzyme is uncombined i.e. E. The Vmax is observed when virtually all the enzyme is present as the ES complex and [E] is vanishingly small. ES is observed on M-M plot as the plateau region.
two fates of ES
when K2 <<< K-1 (K2 is rate-limiting
under what conditions does Km=Kd
Vo=Vmax(Km)/2Km= 1/2Vmax
use M-M to show that the velocity will be half Vmax when [S] = Km
4 to the nitrogen atoms that are in the plane of, and bonded to the flat porphyrin ring system and 2 perpendicular to it
what are the 6 coordination points
Pocket on the enzyme where the enzyme-catalyzed rxn occurs. The surface of the active site is lined with amino acid residues with substituent groups that bind the substrate and catalyze its chemical transformation. Often the active site encloses a substrate, separating it completely from solution.
what are the key features of the active site of an enzyme
Vmax plateau; implies ES complex - initial rate is dictated by level of enzyme when substrate concentration is high
what aspect of the M-M plot suggests an ES intermediate
the activation energy ∆G⁺. the higher the activation energy, the slower the reaction; reaction rates can also be increased by raising the temp and/or pressure thereby increasing the number of molecules with sufficient energy to overcome the energy barrier. Also, ∆G⁺ can be lowered by adding a catalyst.
what determines the rate of a reaction
myoglobin is more sensitive to binding when ligand concentration is low. As ligand concentration increases, it is less crucial to bind ligand and therefore sensitivity decreases and myglobin functions better as an oxygen-storage protein.
what does the hyperbolic shape of the binding curve tell you about the sensitivity of myoglobin to changes in ligand concentration
interactions are mostly hydrophobic (non-specific); hydrogen bonds and ionic pair (salt bridges) keep specificity of binding (so units don't rotate)
what forces holds the subunits together
CO₂ + H₂O forms H₂CO₃ which ionizes to HCO₃⁻ and H⁺. This reaction is catalyzed by carbonic anhydrase, an enzyme abundant in red blood cells. [CO₂ + H₂O ↔ HCO₃⁻ + H⁺] CO₂ is not soluble, and bubbles would form in the tissues and blood if it were not converted to bicarbonate (HCO₃⁻). The hydration of CO₂ results in an increase in H⁺ concentration, lowering the pH, in the tissues. The binding of O₂ by Hb is profoundly influenced by pH and CO₂ concentration. The binding of H⁺ and CO₂ is inversely related to the binding of O₂. Low pH and high CO₂ concentration, the affinity of Hb for O₂ decreases as H⁺ and CO₂ are bound. CO₂ is excreted and the blood pH rises, the affinity of Hb for O₂ increases.
what happens to CO2 in Red Blood Cells
it narrows and makes it harder for BPG to bind
what happens to the BPG binding sire in oxygenated hemoglobin
the heme molecule is buried deep in the folded polypeptide with no direct path for oxygen to move from the surrounding solution to the ligand-binding site; the "breathing" (rapid flexing of amino acid side chains) produces transient cavities in the protein structure and allows O2 to make its way in and out
what is "molecular breathing" and why is it important
2,3 - bisphosphoglycerate (heterotropic allosteric modulation)
what is BPG
the initial rate,initial velocity. It is the slope=∆[P]/time
what is Vo
the breakdown of ES to form product, which is determined by [ES]; Vo = k2[ES]
what is Vo determined by
widespread family of proteins having similar primary and tertiary structure; most function in O2 transport or storage
what is a "globin"
substrate concentration
what is a key factor that affects the rate of a reaction catalyzed by a substrate
A ligand that induces conformational changes
what is a modulator
after one molecule of O2 is bound, the binding affinity for more O2 molecules increases. The first molecule of O₂ that interacts with with deoxyhemoglobin binds weekly, because it binds to a subunit in the T state. Its binding leads to conformational changes that are communicated to adjacent subunits, making it easier for additional O₂ molecules to bind.
what is meant by cooperative binding
0.26 kPa
what is the P50 of oxygen binding to myoglobin
the reaction reaches equilibria much faster. The relationship between K and the activation energy is inverse and exponential. So, when an enzyme lowers activation energy, kF increases and the ratio of kF/kR increases.
what is the effect of an enzyme on kF and kR? on kF/kR
An enzyme will carry a reaction to equilibrium at a faster rate, but it will not have much effect on the concentrations of the reactants and products at equilibrium because an enzyme does not effect the position of equilibrium or which molecules are favored.
what is the effect of an enzyme on the concentrations of reactants and products at equilibrium
Kcat/Km is the specificity constant and it is the rate constant for the conversion of E+S to E+P. Upper limit imposed by the rate at which E and S can diffuse together in an aqueous solution. It is 10⁸ to 10⁹ M⁻¹sec⁻¹
what is the upper limit on Kcat/Km
iron in ferrous Fe 2+ state and the complex organic ring structure called the protoporphyrin ring
what makes up a heme group
BPG greatly reduces the affinity of hemoglobin for oxygen (inverse relationship); BPG binds at a site distant from the O2 binding site and regulates O2-binding affinity of hemoglobin in relation to pO2 (important for the physiological adaptation to the lower pO2 at high altitudes - increases release of O2 into the tissues; without BPG hemoglobin has very steep sigmoid curve (don't want this - very similar to myoglobin)
what role does BPG play in influencing oxygen affinity of hemoglobin
CO binds to free heme molecules more than 20,000 times more readily than O2 but when heme is bound to myoglobin the rate drops to 200 due to steric hindrance (C=O is linear); the distal His forms a H bond with O2 but preclude the linear binding of O2; this is physiologically important, because CO is a low-level byproduct of cellular metabolism.
what role does the distal histidine play in myoglobin binding
has the advantage of allowing a more accurate determination of Vmax which can only be approximated from a simple plot of Vo vs. [S]
what shortcoming of the Michaelis-Menten plot is overcome in the L-B plot
Ionic interaction is occurring here between negative BPG and positive amino acid residues
what types of interactions are involved in binding of BPG to deoxyhemoglobin
embedded in the middle of the subunit, 4 heme groups associated with each polypeptide chain. 2 per subunit. Folding pattern that strongly binds the heme group
where are the heme groups located in each subunit of hemoglobin
binds to cavity/pocket between the β subunits in the T state, lined with positively charged amino acids that interact with negatively charged BPG groups; only one molecule BPG binds to each hemoglobin tetramer
where does the binding of BPG occur in deoxyhemoglobin
when histidine residue is protonated, it forms ion pairs to aspartate which helps stabilize deoxyhemoglobin in the T state and gives it a high pKa. In the R state the pKa drops to normal value of 6.0 since the ion pair cannot form - this residue is largely unprotonated in oxyhemoglobin at pH 7.6. As H+ concentration rises, oxygen gets released favoring transition to the T state.
which residues participate in the Bohr effect
1)oxygen is poorly soluble in aqueous solutions 2)larger organisms depend on proteins that can transport and store O2 but no amino acid side chains can reversibly bind O2 3)iron is used to bind to the O2 but because free iron promotes the formation of reactive oxygen species iron is sequestered in a protein-bound prosthetic group called heme, which makes the iron less reactive.
why do multicellular organisms transport O2 on Fe2+ in a heme group
when histidine is protonated, the residues can form ion pairs with the anion which is very stabilizing in the T state
why does a closely positioned anion increase the pK of histidine
The use of Vo allowed Michaelis and Menten to make the simplifying assumption that the reverse rxn. P→S, described by k-2 can be ignored, because early in the reaction, the concentration of the product [P] is negligible.
why does the use of Vo allow Michaelis and Menton to ignore the reverse reaction (k-2) in their analysis of how Vo varies with [S]
because it is an estimation of the slope of the curve; tangent to each curve at time=0 defines the initial velocity. If you are holding [S] constant, even though in reality [S] is changing during the course of a rxn, and you are only observing the very beginning of the reaction varying [S] experimentally, and holding [E] constant because it is present in nanomolar quantities.
why is Vo a simplification
binding of a ligand to one site affects the binding properties on another site of the same protein; conformational changes interconvert more-active and less-active forms of the protein. There is only one binding site for O₂ on each subunit, so the allosteric effects giving rise to cooperativity are mediated by conformational changes transmitted from one subunit to another via subunit-subunit interactions.
why is hemoglobin an allosteric protein
