Material up to Prelim 1

1) Meaning of the association equilibrium constant K_eq (=K_A)

Note: know the difference between K and k

1) Equilibrium: reverse and forward reactions occur simultaneously, no net changes in products/reactants (the rate of change is equal not the amount)

• K_eq = [MbO2]/[Mb] [O2] = k_assoc/k_dissoc = Association equilibrium constant, K_A

Note: K = equilibrium constant(equilibrium ratio); k = rate constant(kinetics)

What is the Rate constant for association (k_assoc), using Mb as an example

What is the Rate constant for dissociation (k_dissoc), using Mb as an example

• Relationship between them

k_assoc (Association rate constant), where observed association rate(R) = k_assoc [Mb][O2]

k_dissoc (Dissociation rate constant), where observed dissociation rate(R) = k_dissoc [MbO2]

• Relationship between these: At equilibrium, k_assoc = k_dissoc, meaning the following 2 equations apply:

  • k_assoc [Mb]x[O2] = k_dissoc [MbO2]

  • K_eq =k_assoc/k_dissoc = [MbO2]/[Mb] [O2]

Apply this relationship to calculate one parameter if values for the other parameters are given(Boltzmann equation).

Keq application to Boltzmann Distribution: Keq = e^-ΔG°/RT →

rearranged to -RT ln(Keq) = ΔG°

From this graph what can be inferred about the concentration amounts at equilibrium

Left Diagram

• More product is favored at equilibrium as the energy is lower = more stable

Right Diagram

• More reactant is favored at equilibrium as the energy is lower = more stable

Meaning & usefulness of Hill Equation;

Meaning of n and P50

P50 when theta = 0.5 meaning

Relationship between P50 and O2 affinity

Hill Equation: cooperativity and affinity of O2 binding

• n: cooperativity coefficient (higher = more cooperative)

• P50: corresponding O2 pressure at which ½ (50%) of hemes are bound to O2

• p50 = theta = 0.5; rely on this to check for cooperativity on graph where intersection occurs and go straight down looking at p50

Relationship between P50 and O2 affinity: ↓ P50 = ↑ O2 affinity and ↑ P50 = ↓ O2 affinity

Apply the concepts of Hill equation to identify the plots of O2 binding curves for different forms of Hb

• Adult,

• Fetal

• Myoglobin

• Hb w/o BPG

• Isolated subunits of Hb,

• Locked T state & R state

State the n and P50 values of Hb, HbF, and Mb

Different forms of Hb under different conditions:

1) Adult hemoglobin: n = 2.8, P50 = 26

2) Fetal hemoglobin: n = 2.8, P50 = 19-20(Hb graph shift to left)

3) Myoglobin: n = 1, P50 ~ 1

4) Hb w/o BPG has same/similar graph as myoglobin

5) Isolated subunits will be like myoglobin

6) T state is linear near the bottom

7) R state is like myoglobin

What is 2,3-BPG?

What happens in the O2 binding

Ratio between hemoglobin

2,3-biphosphoglycerate (BPG): small molecule with many negative groups that stabilizes ion pairs in hemoglobin’s T state

When O2 binds and favored R state → BPG exclusion

1:1 hemoglobin-to-BPG molecule ratio(AKA 1 2,3 BPG per hemoglobin)

Hemoglobin’s Properties

• In lungs

• O₂ and CO₂ transport/pickups

• Fetal Hb

1) Hemoglobin Properties 

• Saturated with O₂ in lungs 

• Transports O₂ to tissues where pH is low + picks up CO₂ from metabolically active tissue(Transport CO₂)

• Fetal hemoglobin has higher O₂ affinity than adult hemoglobin (shifted more to left)

Hemoglobins Function in regards to as enzymatic

Hemoglobin is not an enzyme (no chemical reaction catalyzed)

Hemoglobins cooperativity (how it works!) & Evidence/Rasoning for Cooperativity

Overview: Hemoglobin can bind up to 4 O2 molecules (The O2 molecules that are already bound “cooperate” to make the next O2 binding more favorable to bind to hemoglobin)

Reasoning for Cooperativity

• Formation of crystals under N2, then observe deoxyHb Crystal -Add O2--> crystal shatters(means a change from T-R state)

• Utilize x-ray, NMR studies to find 3D structure of each alpha and beta subunit

Hemoglobins relationship between cooperativity and salt bridges; How many amino acids paris have ion pairs in the deoxy-Hb(T-state)

When the first O2 binds to the hemoglobin (deoxy-Hb → oxy-Hb), it has to break some of the ion pairs or salt bridges so that binding can occur effectively. Therefore, the binding is weak.

When the next few O2 bind, they do not need to break ion pairs or salt bridges, so binding happens readily.

→ Overall, 8 amino acid pairs have ion pairs/salt bridges in the deoxy-Hb(T-State), not present in oxy-Hb

Hemoglobins meaning of R and T states;

• R(oxyhemoglobin) and T(Deoxyhemoglobin) states 

  • R state: Relaxed state that has high oxygen affinity with low ion pairs/salt bridges

    • Right side of graph

  • T state: Tense state that has low oxygen affinity with high ion pairs/salt bridges

    • Left side of graph

Role of salt bridges in stabilizing the T state with respect to the Bohr Effect, & how does 2,3 BPG contribute to

• Bohr Effect: The Bohr effect states that lower pH (more CO2 + H2) causes hemoglobin to release O2. This leads to more ion pairs, or salt bridges, forming to stabilize hemoglobin's T-state quaternary structure. Overall, the hydrogen ions stabilize the T-state of hemoglobin through increased salt bridge formation.

→ 5 ion pairs also contributed from BPG. Overall, there are 13 ion pairs. 

Draw O2 binding curve for Mb and Hb. Know what is plotted on each axis!

Remeber to plot

1) Correct Shapes: Hyperbolic vs Sigmoidal

2) Correct Axes Labeled: theta vs PO2(mmHg)

3) Axes values: theta = 0,0.5,1; PO2 = 0, 25, 50, 75

4) Dashed lines for at 1 and 0.5 theta

5) Label what line is what

The Bohr Effect (mechanism for how it works!). Be able to explain how Hb acts as a “pH sensor” to regulate its O2 binding affinity.

Draw O2 binding curves for Hb at ~pH 7.2 and pH 6.7.

Know how to label each axis, and what values on each axis are relevant (e.g., P50 value for HbA, HbF, what q value this corresponds to, and what the maximum value of q is)!

• Overall Bohr Effect process: When lower pH is detected in physiological condition, there is an increase in hydrogen ions in the environment, which acts as negative allosteric effect, lowering the oxygen affinity. The hydrogen ions stabilize the T-state of hemoglobin’s quaternary structure because of the increased ion pairs and salt bridge formation. The ion pairs and salt bridge formation is made ONLY possible due to the protonation of the histidine and N-terminus. Finally, the stabilization of the T-state enables hemoglobin to release O₂. 

  • Histidine is particularly sensitive to pH changes due to its pKa of ~6

Note:

pH 7.2: theta = 0.5, p50 = 26

pH 6.7 theta =0.5, p50 = increased

Describe and differentiate between the positive and negative allosteric effectors

• Positive allosteric effectors: favors the R-state (e.g. O2, CO) → increased O2 affinity

• Negative allosteric effectors: favors the T-state (e.g. H+, 2,3-BPG, CO2) → decreased O2 affinity

Draw O2 binding curves for fetal vs adult Hemoglobin. State reasons for why O2 is transferred from maternal Hb to fetal Hb. Know what is plotted on each axis!

• O₂ binding curve for fetal vs. adult hemoglobin 

• → Adult hemoglobin has 𝛼₂β₂ subunits while fetal hemoglobin has 𝛼₂ɣ₂ subunits in amino acid position #143. At this position, the histidine amino acid is replaced by serine amino acid. Serine does not form ion pairs, which means the T-state is favored less with lower stability. Therefore, oxygen is transferred from higher pressure to lower pressure, meaning maternal side to fetal side. 

  
  

Explain how Hb can serve as O2 carrier from lung to metabolically active tissue and Mb cannot

• # of subunits

• curve

• Respond to physiological changes

• Found in where

Why Hb Can Transport O₂

Has 4 subunits → cooperative binding

Sigmoidal curve allows dynamic binding & release

Responds to pH and CO₂ (Bohr Effect)

Found in blood → ideal for system-wide O₂ delivery

Why Mb Cannot

Only 1 subunit → no cooperativity

Hyperbolic curve = binds O₂ tightly, doesn't release easily

Does not respond to physiological changes

Found in muscle → localized O₂ storage only

Enzymes: How catalysts speed up reactions (two ways)

1) Direct binding to the transition state 

• Example from organic chemistry (Nickel catalyst):

2) Changing reaction pathway of acid-catalyzed vs. uncatalyzed reactions (new transition state has lower G°)

• Example from ester hydrolysis (uncatalyzed vs. acid catalyzed): The uncatalyzed has charged intermediates that involve charge separation, which is unfavorable (high energy). On the other hand, catalyzed has uncharged intermediates and incorporates resonance stability, which is favorable (low energy)

Enzymes

How they work

• by binding to the TS better than to reactants

  • What is the TS

• changing reaction pathway(3 ways);

• Simple examples of Nickel surface and acid catalysis given in lecture)

Transition state: The least stable, highest-energy intermediate → highest G° structure

Enzyme Specificity (ranges from absolute to relative functional group)

1) Absolute specificity: enzyme acts only on 1 substrate (doesn’t act on anything else)

• Urease

2) Absolute functional group specificity: enzyme acts on specific functional group such as alcohol

• Alcohol dehydrogenase that precisely fits to -OH and NAD+ or NADPH+

3) Relative functional group specificity: enzyme acts on peptide or ester bond(any function group)

• Trypsin specificity for Lysine or Arginine “on carbonyl side” of either peptide or ester bond

Enzymes
The Gibbs Function

• be able to write the Gibbs function for a given reaction with standard gibbs energy along with concentrations of reactant/product

• Given that the reaction is A + B ⇌ C + D,

• ΔG = ΔG° + RT ln ([C]x[D] / [A]x[B])

  
  

Enzymes
The Gibbs Function(explain each variable)

• It expresses the tendency for reaction to occur, and includes delta Go and mass action term.

ΔG: the overall difference in free energy between reactants and products, given the condition(tendency for rxn to occur)

ΔG°: the relative stability of reactants and products per molecule, independent of concentration (e.g. 1M concentration under standard state).

RT: constant temperature and pressure 2.5

ln ([C} x [D}/[A} x [B]): the “mass action” or “concentration tendency”

Enzymes
The Gibbs Function

• Know what happens when concentrations are at the Standard State.

• ΔG = ΔG° since concentrations are all at 1M under standard state conditions.

• ln(1) = 0

Enzymes
The Gibbs Function

• Know what happens when concentrations are at their equilibrium values.

• Concentrations of reactants and products adjust till ΔG = 0  as there is no net rate of change of reactants and products concentrations

Enzyme

Defintion of inital velocity

Determined via primary or raw data

• The initial velocity is determined at the very beginning of the forward reaction, where products are not formed yet. V_initial = V_in = k₁ [A]_in x [B]_in. Defined by the change in product concentration over the change in time, assuming that the reaction hasn’t started/proceeded (no product formed). 

• Initial velocity is determined from the primary data, not from raw data measurements

• The overall velocity of rxn measures change in concentration over change in time (concentration of products over the concentration of reactants) 

• At equilibrium, V_in = 0 because the tangent line slope is 0 when the reaction has proceeded to form the product. From a kinetics standpoint, no useful info is provided.