Ligand-protein binding

Question 1

Write the simple equation for when one ligand binds to one protein and the equilibrium constant, K, for this same problem.

Answer 1

simple equation: P + L ⇔ PL

catalysed by K

Equilibrium constant: K= [PL] / [P][L]

P= protein, L= ligand, PL= protein-ligand complex

Question 2

Whats the equation that defines the average number of ligands binding to a protein?

Answer 2

Question 3

in the simplest case, of a single ligand binding to a protein. the eqaution for n is simply?

What can this be arranged to?

Answer 3

Question 4

Whats the fractional saturation of a protein?

Answer 4

The fractional saturation of the protein is the fraction of the proteins sites that are occupied by a ligand

Question 5

In general, how is fractional saturation denoted and how is it defined?

Tell me what each stands for and any variance ?

Answer 5

Fractional saturation is denoted, θ, and is defined as: θ = ñ/n

Where n is the total number of binding sites for the ligand.

θ varies between 0 and 1

Question 6

How is [L] and θ affected by changes in Kd

Answer 6

Question 7

How can we measure binding?

Answer 7

We can use the changes in concentration of the protein and ligand to tell us about binding

Question 8

The ligand can be titrated in as we know how much we have added.

How can you then test pure protein concentrations?

Answer 8

• Colorimtric assay
• UV spectrophotometry
• UV absorbance at 259 nm

Question 9

How does colorimetric assay work?

Answer 9

A dye is added to the protein solution that changes colour upon binding to the protein.

The amount of colour change (as determined by UV spec) is directly proportional to the protein concentration

Question 10

How does UV absorbance work?

Answer 10

Many proteins absorb light strongly at 280nm, due to tyrosine and tryptophan

For proteins of known sequence, the extinction coefficient (how much light at a given wavelength gets absorbed from a protein solution of a given concentration) can be calculated

Based on this, one can simply measure A280 and then calculate the protein concentration using Beer’s law

Question 11

UV absorbance at what wavelength is a standard way to measure the concentration of nucleic acids (RNA/DNA)?

Answer 11

259 nm

Question 12

Tell me how some affinities may change when proteins have multiple binding sites for a receptor?

Answer 12

many receptors have more than one binding sites for one or more ligands.

Even when all sites are for the same ligand, they may not have identical affinities and their affinites may vary depending on whether the other sites are filled or not

Question 13

What does ‘Affinity’ refer to?

What does ‘high affinity’ refer to?

Answer 13

‘Affinity’: How strong the binding is (as judged by K_d and ∆G˚)

‘High affinity’: refers to a very storng binding (large negative ∆G˚ and a very small K_d)

Question 14

What is the dissociation constant often referred to as?

Answer 14

The ‘affinity’ or ‘binding’ constant

Question 15

Why do we need to understand ideal solutions?

Answer 15

Ideality of solutions is analogous to ideality for gases, with the important difference that intermolecular interactions in liquids are strong and cannot simply be neglected as they can for ideal gases.

Question 16

Many of the important physical properties of a solution depend more directly on the concentration of the solvent. What properties do these include?

What are these properties referred to as?

Answer 16

These properties include the vapor pressure, the freezing point, the boiling point, and the osmotic pressure, they are referred to as the colligative properties of solutions.

Question 17

In an ideal solution or ideal mixture, there are forces of attraction between the molecules (unlike ideal gases). What do The molecules all interact with?

Answer 17

Identical magnitudes and distance dependencies

Question 18

What are the properties of a solution independent of?

Answer 18

composition

Question 19

Tell me the arrangement of molecules in solution and how this effects enthalpy change?

Answer 19

The arrangement of molecules is completely random; thus, the enthalpy change on mixing the components to make the solution is zero as is the volume change on mixing.

Question 20

For a real solution, the closer to zero the enthalpy of solution is means what?

Answer 20

The more ideal the behaviour of the solution becomes

Question 21

Ideal solutions are defined by an equation relating what?

Answer 21

The partial vapour pressure of the individual componetns to the composition

Question 22

Whats the equation to define an ideal solution?

What is this law called?

What does each component represent?

Answer 22

P_x = N_x x P_x*

This is known as Raoult’s law

P_x= partial vapour pressure of a component in solution

N_x= the mole fraction of x in solution

P_x^*= The vapour pressure of the pure liquid x

Question 23

Whats the equation of the mole fraction, of x, N_x?

Answer 23

Question 24

Write the equation which describes the concentration dependence of the chemical potential of a component in an ideal solution?

Write this in terms of molar concentrations as well

Answer 24

μ_x(solution) = μ_x°(liquid) + RTlogeN_x

In terms of molar concentrations: μ_x = μ_x° + RTloge[x]

Question 25

Very few compounds form ideal solutions over a wide concentration range. But in very dilute solutions what can happen?

Answer 25

Both the solvent and the solute can be treated as ideal

Question 26

In very dilute solutions the number of solute molecules is low. So what do solvent molecules spend most of their time doing?

How can this be effected?

Answer 26

Interacting with other solvent molecules.

Increasing the concentration of the solute will not affect this, until the number of solute molecules is high enough that the solvent molecules spend significant time interacting with solute molecules.

Question 27

What are the 3 equations to compare for ideal solutions?

Answer 27

Question 28

In a non-ideal solution, do the molecules in the solution interact with each other identically?

Answer 28

no

so the behaviour of a given molecule depends on the composiiton of the solution

Question 29

Is the arrangement of molecules in a non-ideal solution random?

Answer 29

No they are non-random.

This is a direct consequence of the fact that there are differing interactions between the different types of molecules

Explanation: Two molecules that attract each other strongly will be located closer together than predicted by a random distribution, likewise two molecules that repel each other will be further apart than predicted by a random distribution.

Question 30

Draw the graph of an ideal solution

(a plot of μ_x versus loge[x])

How is this effected by a non-ideal solution?

Answer 30

For a non-ideal solution because: μ_x ≠ μ_x° + RTloge[x], so the same plot will deviate from linearity. In the plot shown here, μ_x is lower (more stable) than that of the ideal solution.

Question 31

We can calculate the concentration of an ideal solution that would give the same chemical potential as the real solution.

This calculated concentration is called the effective concentration, or activity, a_x

Define an activity coefficient, g_x?

Answer 31

Question 32

When derived from ideality, how can the chemical potential now be written?

Answer 32

μ_x = μ_x° + RTlogeϒ_x[x]

Question 33

The activity coefficient converts the real concentration into an effective concentration. why is this useful?

Answer 33

it has physical significance - ϒ can be used as a measure of a solution’s deviation from ideality.

• if ϒ = 1, the solution behaves like an ideal solution,
• if ϒ < 1, x is more stable than predicted by the ideal model
• if ϒ >1, x is less stable than predicted by the ideal model

Question 34

Summary of an ideal and non-ideal solution

Answer 34

Question 35

Tell me the properties of simple ionic solutions?

Answer 35

Deviation of ideality is particularly important in ionic solutions.

Let’s think of a simple ionic solution:

NaCl in water ⇒ Na⁺ + Cl^- + H₂O

Water is strongly hydrogen-bonded:

• oxygen is far more electronegative than hydrogen

so, there is strong attraction between the solvent-solvent molecules

• When ions are added to water, the water-water hydrogen bonds are disrupted.
• They are disrupted by the hydration shells formed around the ions as a result of ion-water interactions.
• These are electrostatic interactions; this means they arise due to the charge of the ions and the partial charges on the atoms of water

Question 36

In dilute ionic solutions, do the strong interactions between ions and water cause non-ideal behaviour at low ion concentrations?

If no, what do these interactions effect?

Answer 36

no

These interactions do however have an effect on the enthalpy and entropy when ions are dissolved in solution.

Question 37

Tell me about enthalpy change in dilute ionic solutions

Answer 37

Enthalpy: The ion-water electrostatic interactions more than compensate for the loss of water-water hydrogen bonds, so the enthalpy changes of transferring an ion from gas phase to solution is negative.

Question 38

Tell me about entropy changes in dilute ionic solutons

Answer 38

Entropy: As we saw in the previous slide, water around ions are held in a particular arrangement (opposite charges pointing towards each other), so the entropy decreases when ions are added to water (there is less disorder).

Question 39

In general, what is seen in dilute ionic solutions?

Answer 39

In general, smaller ions cause the larger changes in entropy and enthalpy as they interact more strongly with water

Question 40

What happens between molecules as the concentration of ions in the solution increases?

Answer 40

The average distance between the ions decease (as volume is fixed)

Question 41

What happens in the interactions in a concentration ionic solution?

What does this lead to?

Answer 41

Ion-ion electrostatic interactions become significant. Like charges will repel, while opposite charges will attract.

This leads to a distribution of ions that is not random; ions will be surrounded by others of the opposite charge.

Question 42

How are ions stabilised in a concentrated ionic solution?

Answer 42

Each ion is stabilized relative to the hydrated ion (net attractive charge-charge interactions).

Question 43

How is chemical potential of a concentrated ionic solution different to that predicted by the ideal model?

Answer 43

Chemical potential is lower than that predicted by the ideal model, so ϒ < 1. As concentration of ions increases ϒ becomes smaller.

Question 44

Whats the equation used to quantify the deviation from ideality?

Answer 44

RTlogeϒ_x =μ_x(non-ideal) – μ_x(ideal) = Δμ_x

_{ϒ of a non-ideal solution can be calculated from the change in chemical potential on moving the ion from an ideal solution to a non-ideal solution.}

Question 45

What does the Debye-Huckel theory provide?

Answer 45

The Debye-Huckel theory provides a quantitative mode for calculating the solute-solute electrostatic interactions in an ionic solution.

Question 46

What do the following components in the reaction represent?

Answer 46

• A is a constant (0.51 M-1/2) for aqueous solution (298K),
• C_x is the concentration of ion x,
• Z_x is the charge of the ion x,
• The summation is taken over all the ions in solution
• Y_x is the activity coefficient of ion x in an ionic solution
• I is the ionic strength of the solution