Untitled Flashcard Set

Ligand Binding and KDK_DKD​

Ligand binding involves a simple equilibrium between:

L+R⇌LRL + R \rightleftharpoons LRL+R⇌LR

  • LLL = ligand

  • RRR = receptor

  • LRLRLR = ligand–receptor complex

The dissociation constant is:

KD=[L][R][LR]K_D = \frac{[L][R]}{[LR]}KD​=[LR][L][R]​

Also:

KD=1kaK_D = \frac{1}{k_a}KD​=ka​1​

where kak_aka​ is the association/affinity constant.

Key meanings

  • Low KDK_DKD​ = strong binding/high affinity

  • High KDK_DKD​ = weak binding/low affinity

Scatchard Plot

Used to determine KDK_DKD​.

Plot:

  • BoundFree\frac{\text{Bound}}{\text{Free}}FreeBound​ on Y-axis

  • Bound on X-axis

Equation:

BF=−1KD(B)+nKD\frac{B}{F} = -\frac{1}{K_D}(B) + \frac{n}{K_D}FB​=−KD​1​(B)+KD​n​

Where:

  • slope = −1KD-\frac{1}{K_D}−KD​1​

  • nnn = number of binding sites

Important correction from transcript:

  • It is Bound/Free vs Bound

  • NOT Bound/Free vs Free

Exam Tips

  • Scatchard analysis is less common than enzyme kinetics questions.

  • If asked to calculate KDK_DKD​, remember:

    • slope = −1/KD-1/K_D−1/KD​

  • Always label axes and include units.

Michaelis–Menten Enzyme Kinetics

Core Definitions

KMK_MKM​

Substrate concentration at half maximal velocity.

V=Vmax2V = \frac{V_{max}}{2}V=2Vmax​​

Meaning

  • Low KMK_MKM​ = high substrate affinity

  • High KMK_MKM​ = low substrate affinity

Units:

  • concentration units only

  • usually mM, µM, nM, etc.

VmaxV_{max}Vmax​

Maximum possible reaction rate when enzyme is saturated with substrate.

Units:

  • concentration/time

  • e.g. µmol L−1^{-1}−1 min−1^{-1}−1

kcatk_{cat}kcat​ (Turnover Number)

kcat=Vmax[active sites]k_{cat} = \frac{V_{max}}{[\text{active sites}]}kcat​=[active sites]Vmax​​

Measures catalytic speed of enzyme.

Units:

  • time−1^{-1}−1

  • e.g. s−1^{-1}−1, min−1^{-1}−1

Interpretation

  • High kcatk_{cat}kcat​ = efficient catalysis

  • Low kcatk_{cat}kcat​ = slower enzyme

Important

Do not compare VmaxV_{max}Vmax​ values between enzymes unless enzyme concentrations are equal.

Specificity Constant

kcatKM\frac{k_{cat}}{K_M}KM​kcat​​

Combines:

  • catalytic efficiency

  • substrate affinity

Interpretation

  • High specificity constant = very efficient enzyme

  • Low specificity constant = poor enzyme

Why KMK_MKM​ Reflects Affinity

Reaction scheme:

E+S⇌ES→E+PE + S \rightleftharpoons ES \rightarrow E + PE+S⇌ES→E+PKM=k−1+k2k1K_M = \frac{k_{-1}+k_2}{k_1}KM​=k1​k−1​+k2​​

Usually:

k−1≫k2k_{-1} \gg k_2k−1​≫k2​

Therefore:

KM≈k−1k1K_M \approx \frac{k_{-1}}{k_1}KM​≈k1​k−1​​

which resembles KDK_DKD​.

Important wording

Do NOT say:

  • “KMK_MKM​ equals affinity”

Instead say:

  • “KMK_MKM​ is related to substrate affinity”

Linear Transformations of Michaelis–Menten

Lineweaver–Burk Plot

Double reciprocal plot:

1V vs 1[S]\frac{1}{V} \text{ vs } \frac{1}{[S]}V1​ vs [S]1​

Easy to remember but introduces large errors.

Eadie–Hofstee Plot (preferred)

Plot:

  • VVV vs V[S]\frac{V}{[S]}[S]V​

Equation:

V=−KM(V[S])+VmaxV = -K_M\left(\frac{V}{[S]}\right) + V_{max}V=−KM​([S]V​)+Vmax​

V=−KM(V[S])+VmaxV=-K_M\left(\frac{V}{[S]}\right)+V_{max}V=−KM​([S]V​)+Vmax​

Therefore:

  • slope = −KM-K_M−KM​

  • Y-intercept = VmaxV_{max}Vmax​

Exam Tips

  • Include units on axes

  • Label graphs carefully

  • Always give units in answers

Typical units

Parameter

Units

V0V_0V0​, VmaxV_{max}Vmax​

concentration/time

KMK_MKM​

concentration

kcatk_{cat}kcat​

time−1^{-1}−1

Beer–Lambert Law

Used to convert absorbance changes into concentration changes.

Equation:

A=εclA = \varepsilon c lA=εcl

A=εclA=\varepsilon c lA=εcl

εεε

ccc

lll

Where:

  • AAA = absorbance

  • ε\varepsilonε = molar extinction coefficient

  • ccc = concentration

  • lll = cuvette path length (usually 1 cm)

Important Notes

  • Usually used with NADH absorbance at 340 nm

  • Common extinction coefficient:

    • 6220 M−1cm−16220 \ \text{M}^{-1}\text{cm}^{-1}6220 M−1cm−1

Exam Tips

  • Watch for dilution factors

  • Convert absorbance changes into concentration changes

  • Questions may already provide rates

Exponential Growth and Decay

Growth

Nt=N0ektN_t = N_0 e^{kt}Nt​=N0​ekt

Nt=N0ektN_t=N_0e^{kt}Nt​=N0​ekt

Decay

Nt=N0e−ktN_t = N_0 e^{-kt}Nt​=N0​e−kt

Nt=N0e−ktN_t=N_0e^{-kt}Nt​=N0​e−kt

Where:

  • NtN_tNt​ = amount at time ttt

  • N0N_0N0​ = initial amount

  • kkk = rate constant

Half-Life

Linearised form:

log⁡Nt=log⁡N0−kt\log N_t = \log N_0 - ktlogNt​=logN0​−kt

Slope = −k-k−k

Half-life equation:

t1/2=log⁡2kt_{1/2} = \frac{\log 2}{k}t1/2​=klog2​

t1/2=log⁡2kt_{1/2}=\frac{\log 2}{k}t1/2​=klog2​

Practical Half-Life Estimation

If graph does not reach 50% decay:

  • use 25% or 10% decay

  • scale proportionally

Example:

  • 25% decay in 10 min

  • therefore 50% decay in 20 min

Protein Purification Techniques

1. Surface Properties

Ion Exchange Chromatography

Separates by charge.

  • Protein binds charged resin

  • Salt gradient elutes protein

Hydrophobic Interaction Chromatography

Separates by hydrophobicity.

  • High salt promotes binding

  • Lower salt elutes proteins

Example:

  • phenyl sepharose

Salting Out

Usually uses ammonium sulfate.

  • proteins precipitate at different salt concentrations

2. Size-Based Separation

Size Exclusion Chromatography

Also called:

  • gel filtration

Separates proteins by size.

Other Size Methods

  • SDS-PAGE

  • native PAGE

  • ultrafiltration

  • sucrose gradient centrifugation

Important

SDS denatures proteins, so not usually used for purification.

3. Affinity Chromatography

Separates proteins by specific binding interactions.

Common Examples

Tag/Protein

Ligand on Resin

GST

glutathione

His-tag

nickel/cobalt

Protein A

antibody Fc region

MBP

maltose

Elution

Usually by competition:

  • free ligand added in excess

Examples:

  • glutathione elutes GST

  • imidazole elutes His-tag proteins

Protein Tags

His-tag

  • small tag

  • purification using nickel affinity

GST

  • improves bacterial expression

  • purification with glutathione resin

GFP

Used for:

  • localisation in living cells

Advantages:

  • live-cell imaging

  • dynamic studies

Disadvantages:

  • large tag

  • may affect protein function

Other Tags

  • FLAG

  • HA

  • Myc

  • TAP tag

  • Halo tag

Small epitope tags are mainly used with antibodies.

Antibody Techniques

Immunofluorescence

Determines subcellular localisation.

Western Blotting

Determines:

  • protein size

  • protein abundance

Immunoprecipitation (IP)

Uses antibodies to isolate proteins.

Native IP

Can pull down interacting proteins.

ELISA

Highly quantitative protein detection.

Immunogold Electron Microscopy

Uses gold-labelled antibodies for high-resolution localisation.

FACS (Fluorescence Activated Cell Sorting)

Separates cells based on fluorescence intensity.

Applications:

  • cell sorting

  • quantifying surface expression

Experimental Controls

Very important exam topic.

Common Controls

Non-related antibody

Shows specificity of antibody binding.

Untagged cells/protein

Confirms signal depends on tag.

Resin-only control

Checks for non-specific binding to beads/resin.

Key Exam Phrase

“Negative control to test for non-specific binding.”

Post-Translational Modifications (PTMs)

Phosphorylation

Target residues

  • serine

  • threonine

  • tyrosine

Need free hydroxyl group.

Detection Methods for PTMs

Radioactive Labelling

Using:

  • 32P^{32}P32P

  • 33P^{33}P33P

Mass Spectrometry (MS/MS)

Can determine:

  • mass changes

  • modification type

  • exact modification site

  • peptide sequence

Very important technique.

MS vs MS/MS

  • MS = peptide mass

  • MS/MS = fragments peptide and determines sequence

Antibodies

Modification-specific antibodies can recognise:

  • phosphorylated proteins

  • specific histone modifications