Lecture 7 - Ligand Binding

Protein Function and Ligand Binding

General Description of Ligand Binding

Proteins often function by binding to specific molecules called ligands. Ligands can include small molecules, ions, DNA/RNA, or other proteins. The binding is typically reversible and non-covalent, allowing proteins to respond dynamically to changes in their environment.

• Ligand: A molecule that reversibly binds to a protein, affecting its activity or function.

• Apo form: The state of a protein without a bound ligand.

• Conformational changes: Ligand binding can induce structural changes in proteins, altering their activity (e.g., switching between "on" and "off" states).

Protein Structures Are Not Static

Proteins exhibit flexibility, and their structure can change depending on ligand binding, post-translational modifications (PTMs), or interactions with other partners. These conformational changes are essential for protein function.

• Rapidly reversible binding: Ligand binding and release can occur quickly, allowing proteins to adapt to cellular needs.

• Functional diversity: Different conformations correspond to different functional states.

Quantitative Description of Ligand Binding

Binding Equilibrium and Dissociation Constant (Kd)

The equilibrium between a protein (P) and ligand (L) is described by the dissociation constant (Kd), which quantifies the affinity of the protein for its ligand.

• Binding reaction: P + L → P•L

• Dissociation constant: $K_d = \frac{[P][L]}{[P\cdot L]}$

• Units: Concentration (typically Molar, M)

• Fractional occupancy (Θ): $\Theta = \frac{[P\cdot L]}{[P] + [P\cdot L]} = \frac{[L]}{[L] + K_d}$

Interpretation of Kd

The value of Kd indicates the affinity of the protein for its ligand:

• Smaller Kd: Higher affinity, tighter binding

• Larger Kd: Lower affinity, weaker binding

• At [L] = Kd: Half of the binding sites are occupied ($\Theta = 0.5$)

Oxygen Binding Proteins: Myoglobin and Hemoglobin

Myoglobin: Hyperbolic O2 Binding

Myoglobin (Mb) is a single polypeptide chain with a heme group that binds oxygen. It serves as an oxygen storage protein, especially in muscle tissue.

• Structure: 1 polypeptide, 8 α-helices, 1 heme group

• O2 binding: O2 binds to Fe in heme and to HisE7 in the protein

• Binding equation: $\Theta_{O_2} = \frac{pO_2}{pO_2 + p_{50}}$

• p50: Partial pressure of O2 at which half of the sites are occupied

Example: Myoglobin Oxygen Affinity

• p50 for Mb: 0.26 kPa

• In lungs (pO2 = 13.3 kPa): $\Theta_{O_2} = \frac{13.3}{13.3 + 0.26} \approx 0.98$ (98% occupied)

• In tissue (pO2 = 4 kPa): $\Theta_{O_2} = \frac{4}{4 + 0.26} \approx 0.94$ (94% occupied)

Hemoglobin: Sigmoidal O2 Binding and Cooperativity

Hemoglobin (Hb) is a tetrameric protein responsible for oxygen transport from lungs to tissues. Its O2 binding curve is sigmoidal, reflecting cooperative binding among its four subunits.

• Structure: 4 polypeptide chains, each with a heme group

• Function: Delivers O2 efficiently by releasing it in tissues

• Cooperativity: Binding of O2 to one subunit increases the affinity of the remaining subunits

• Sigmoidal curve: Steep transition between low and high affinity states

Example: Hemoglobin Oxygen Release

• In lungs (pO2 = 13.3 kPa): $\Theta_{O_2} \approx 1.0$

• In tissue (pO2 = 4 kPa): $\Theta_{O_2} \approx 0.6$

• O2 released: $1.0 - 0.6 = 0.4$ (40% of O2 released)

Mechanism of Cooperativity: T and R States

Hemoglobin can exist in two main conformational states:

• T (tense) state: Low affinity for O2

• R (relaxed) state: High affinity for O2

• Transition: Increasing pO2 shifts equilibrium from T to R state

• Positive cooperativity: Binding at one site increases affinity at other sites

General Expression for Multiple Ligand Binding

For proteins with multiple binding sites, the binding curve can be described by the Hill equation:

• Hill equation: $\Theta = \frac{[L]^n}{[L]^n + K_d}$

• N: Number of binding sites

• n: Hill coefficient (degree of cooperativity)

• As n increases: The curve becomes more sigmoidal (steeper transition)

Limiting Cases

• N=1, n=1: Hyperbolic binding (e.g., myoglobin)

• N>1, n=1: Independent binding sites

• N>1, n=N: Maximum cooperativity (steepest curve)

Summary Table: Myo1globin vs. Hemoglobin

Protein	Structure	O2 Binding Curve	Function	Cooperativity
Myoglobin	Monomer, 1 heme	Hyperbolic	O2 storage	None
Hemoglobin	Tetramer, 4 hemes	Sigmoidal	O2 transport	Positive

Key Concepts for Exam Preparation

• Understand the definition and role of ligands in protein function

• Be able to use the general expression for ligand binding to interpret binding curves and predict fractional occupancy

• Recognize the difference between hyperbolic (myoglobin) and sigmoidal (hemoglobin) binding curves

• Explain the concept of cooperative binding and its physiological significance

• Apply the Hill equation to describe binding behavior in proteins with multiple sites

Additional info: The notes expand on the original content by providing definitions, equations, and examples for clarity and completeness. All included images directly reinforce the explanation of protein structure, ligand binding, and cooperativity.