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# Binding Affinity

You must have heard about the catalyst which increases the rate of reaction without involving in the reaction. The biological catalyst or enzymes bind with the substrate molecules and convert them into products. There is a certain binding affinity between catalyst and subtract molecules. Catalysts are specific in their activities for particular substrate.

In other words, a specific enzyme can bind with a particular substrate only because of fix active sites on them. The combination of catalyst and substrate make a perfect pair which initiates the reaction and form product. Similar binding is found in between drugs and their receptor. It is binding between drugs and receptors depends on the strength of interaction between these two species. Here weak attraction forces balance the affinity of a drug and the receptor.

The binding surface of receptor plays an important role in the bonding of drugs and receptor. As the distance between drug and receptor increases, the strength of electrostatic forces between them also reduces. For example strength of hydrogen bonding is inversely proportional to the fourth power of the distance between drug and receptor. Other interactions between drug and receptors are Van der Waals forces and hydrophobic bonds. Because of these interactions, drugs are arranged in a certain position within the proteins or receptors.

## Binding Affinity Definition

In coordination chemistry, ligand is an atom, molecule or ion which has one or more pair s of electrons which could be donated to the metal atom or ion to form the coordination bond. Such compounds are known as coordination compounds or complex compounds.
The binding affinity term stands for the capability of ligands to form coordination bonds with a receptor. The binding affinity of a ligand with a receptor depends upon the interaction force of attraction between the ligands and their receptor binding sites.Strong intermolecular force of attraction results to show high bonding affinity ligand binding, while the ligand binding of low-affinity involves lower and weak intermolecular force between ligands and their receptors. In other words, a ligand with high-affinity binding shows a long residence time at the receptor binding site compared to low-affinity binding.
1. This binding affinity of ligand to receptor is physiologically important as some amount of the binding energy is utilized in the receptor to bring a conformational change. This leads to altered behavior of an associated ion channel or the enzyme.
2. Hence binding affinity describes the strength with which a ligand, like a drug , binds to a receptor.
3. In any living body the smallest unit, that is, the cell only communicates with ligands. A ligand can be any drug or releasing chemical which can be detected by the target cell.
4. Some common ligands are hormones, mediators, and neurotransmitters, etc. There must be a suitable receptor on target cell which can detect and respond for coming ligand. Generally, ligands are endogenous in nature as they are produced naturally in the body.
5. For every ligand there is a specific receptor and they must be complementary to each other in their size and geometry. It is just like lock and key, as there is always a certain key for a lock, no other key can be fitted in a lock, in the same way each receptor is a protein with specific shape which is complementary to a certain ligand. If the particular cell does not have appropriate shape, the ligand can't be bounded with receptor.

• Hence for a strong binding between ligand and receptor, there must be appropriate shape of both substances. If there is a strong binding between ligand and receptors, there will be some physiological changes triggered on receptor sites.
• For example, peptide hormones trigger a secondary messenger within the cell which initiates a biochemical reaction.
• While other ligands like neurotransmitters and some mediators, when bounded with receptors, trigger the opening of ion channels which allows the transmission of ions in or out of a cell.
• Ligands, like drugs, also have some specificity for the binding sit on the receptor like target protein. If the specificity is less, it means binding affinity is less; a greater dose of drug will be required, which is associated with some side effects.
• Hence the potency of a drug depends on its binding affinity for the binding site as well as its binding ability to bring about the desired effects.
• If any enzyme is bounded on the active site of a receptor, the ligand will mimic the enzymatic substance that the active site of the enzyme recognizes.
• Such type of ligands or drugs that can copy the ligand structure close enough may respond similarly to the original ligand and are better known as agonists.
• Those substances, which are similar in shape to the original ligand but binding affinity is not same, which means they bind to and block the receptor without producing any response and also prevent the original ligand from binding, are known as antagonists.

## Binding Affinity Constant

The binding of a Ligand to a receptor affects the function of the receptor and triggers its physiological response. This property of the receptor is known as agonist. Agonist binding can be referred both in terms of change in response we observe physiologically as well as in terms of the agonist concentration required to produce the physiological response.

In the case of a ligand with high binding affinity, it requires a comparatively low concentration to occupy maximum ligand-binding site, resulting in a physiological response triggering. While the low-affinity binding shows that a comparative high concentration of any ligand is essential before the binding site is maximally occupied and a large physiological response to the ligand is received.

If a couple of different ligands bind to the same receptor binding site, then only one of the agonists can show maximal stimulation on the receptor and, hence, could be defined as a "full agonist"

The agonist which can only partially activate the physiological response of receptor is known as "partial agonist"

While the ligands which although they bind to a receptor, fail to initiate the physiological response are termed as antagonist receptors.

The best example to explain the binding affinity is the binding of carbon monoxide and oxygen as ligand on hemoglobin as receptor in living bodies. Out of these two ligands; carbon monoxide has high binding affinity towards hemoglobin and cause carbon monoxide poisoning.

When a drug is diffused towards receptor site, the association constant is termed as K1 and the rate constant for backwards reaction is K-1. The binding of a drug D to the receptor R can be represented as, at equilibrium state, the concentration of product that will be equal to the concentration of reactant.

Hence,
[D] [R] k1 = [DR] k-1
$\frac{k_1}{k-1}$ =$\frac{[DR]}{[D] [R]}$

Binding Affinity = $\frac{k1}{k-1}$

Kd =
$\frac{k-1}{k1}$
Here, Kd is called as binding affinity constant or Kd binding affinity.
Each ligand or drug has a unique binding affinity constant for a certain receptor system which can be used to identify distinct receptors. The high magnitude of binding affinity (large magnitude of K1) shows good binding capacity of the drug to bond with receptors.

Kd, that is the equilibrium dissociation constant or binding affinity constant, is the reciprocal of the affinity. It can be widely used to explain the binding of drugs to a receptor. The units of the dissociation constant can be molar, millimolar, or micromolar, etc. In general dissociation constants are small numbers, less than 1, such as 1 x 10-8M or in nanomolar.

Kd a Binding affinity

The magnitude of the physiologic response (E) is directly proportional to the amount of drug bound to the receptor ([DR]).

$\frac{E}{E_max} a \frac{[DR]}{[RT]}$

or $\frac{E}{Emax} a \frac{[DR]}{[RT]} a \frac{[DR]}{([D] Kd)}$

Hence the effect observed (E/Emax) can be determined by both the concentration of the drug and Kd for the receptor.

## Binding Affinity Equation

Consider the following equation that describes the formation of ABC when both AB and AC complexes can form but BC cannot.

This model can also be depicted by the combination of two linear equations.

KD(AB) is the equilibrium dissociation constant for B binding A and KD(AC) is the equilibrium dissociation constant for C binding A.
1. The term α describes the co-operativity in the system.
2. For example, the effect of C on the KD for the interaction of A with B is represented by α, in that KD(AB) becomes αKD(AB) in the presence of C.
3. If there is positive co-operativity, alpha is less than 1; the presence of C increases the affinity of A for B.
4. If there is negative co-operativity, alpha is greater than 1; the presence of C decreases the affinity of A for B.
5. If C affects the affinity of A and B by the factor α, then B affects the affinity of A for C by the same factor of α.

 Value of α Co-operativity Effect on affinity Effect on KD α < 1 Positive Increase Decrease α = 1 None None None α > 1 Negative Decrease Increase

The following equation relates the rate constant to affinity constant:

## Binding Affinity Calculation

The understanding of the principles of ligand-protein binding thermodynamics and the calculation of ligand-protein binding affinity is difficult and the most general level is from the vital contribution, in the area of structure based drug design.

In aqueous solution the ligand (L) - Protein (P) binding affinity or absolute binding free energy ΔGb is given by

ΔGb(LP) = Gaq (LP) - Gaq (L) - Gaq (P)

This quantity is difficult to calculate because it is far smaller than the individual free energies of the ligand Gaq (L), the protein Gaq (P) and the ligand protein Gaq (LP).

Accurate calculations of the reactant and product free energies are then needed in order to obtain the nearby complete cancellation of free energies necessary for estimates of ΔGb that are typically on the order of a few kcal / mol.

However, accurate calculation of absolute estimate of free energies for complex systems such as enzymes and substrates is currently beyond the scope of computational methods.

Therefore, if any reasonable estimate of the binding free energy is to be obtained there must be a significant cancellation of errors as well.

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