2. From the perspective of thermodynamics, the total free energy change of antibody (Ab) andantigen (Ag) interaction can be expressed as AG = -RTln(K·1M), where R = 8.3145 J/(mol·K) isthe gas constant, T is the temperature in the unit of Kelvin (K = °C + 273.15), and K is affinityconstant of Ab-Ag interaction. Note: 1M here means 1 Molar, so that affinity constant K has theunit of 1/M. A negative value of free energy change AG indicates energy release, while a positivevalue of free energy change AG indicates energy absorption.a) At body temperature T = 37°C, if we know the affinity constant K = 108/M, please compute thetotal free energy change AG.b) The presence of a single charged group on epitope or antigenic determinant of an antigen,typically increases the energy release by 20 kJ/mol for Ab-Ag interaction. Please compute the updated affinity constant K based on the presence of such a single charged group, and quantify theratio between the updated affinity constant K and original affinity constant K = 108/M in a).From the perspective of reaction kinetics, Ab + Ag: Ab-Ag, where Ab-Ag indicates thek₁kdcomplex of antibody and antigen, ka is the association rate constant, and ka is the dissociation rateconstant. In this way, the affinity constant K can be computed as K = k₁/ka.c) For a high-affinity antibody, K = 109/M, and a typical association rate constant ka = 108 /(M·s),please compute the dissociation rate constant ka-High. For a low-affinity antibody, K = 107/M, if theassociation rate constant is still kept as ka 108/(Ms), please compute the dissociation rateconstant kd-Low.=We know the Ab-Ag interaction also follows the first-order kinetics, i.e. the half-life of the Ab-Aginteraction t1/2 can be expressed as t1/2 = ln2 / kd = 0.693 / ka.d) Please compute the half-life of the Ab-Ag interaction t1/2-High for high-affinity antibody, and t1/2-Low for high-affinity antibody respectively.

“Since you have posted multiple questions, we will provide the solution only to the first question…

= 2. From the perspective of thermodynamics, the total free energy change of antibody (Ab) and antigen (Ag) interaction can be expressed as AG = -RTln(K-1M), where R 8.3145 J/(mol·K) is the gas constant, T is the temperature in the unit of Kelvin (K = °C + 273.15), and K is affinity constant of Ab-Ag interaction. Note: 1M here means 1 Molar, so that affinity constant K has the unit of 1/M. A negative value of free energy change AG indicates energy release, while a positive value of free energy change AG indicates energy absorption. a) At body temperature T = 37°C, if we know the affinity constant K = 108/M, please compute the total free energy change AG.

= 2. From the perspective of thermodynamics, the total free energy change of antibody (Ab) and antigen (Ag) interaction can be expressed as AG = -RTln(K-1M), where R 8.3145 J/(mol·K) is the gas constant, T is the temperature in the unit of Kelvin (K = °C + 273.15), and K is affinity constant of Ab-Ag interaction. Note: 1M here means 1 Molar, so that affinity constant K has the unit of 1/M. A negative value of free energy change AG indicates energy release, while a positive value of free energy change AG indicates energy absorption. a) At body temperature T = 37°C, if we know the affinity constant K = 108/M, please compute the total free energy change AG.

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Concept explainers

Catalysis and Enzymatic Reactions

Catalysis is the kind of chemical reaction in which the rate (speed) of a reaction is enhanced by the catalyst which is not consumed during the process of reaction and afterward it is removed when the catalyst is not used to make up the impurity in the product. The enzymatic reaction is the reaction that is catalyzed via enzymes.

Lock And Key Model

The lock-and-key model is used to describe the catalytic enzyme activity, based on the interaction between enzyme and substrate. This model considers the lock as an enzyme and the key as a substrate to explain this model. The concept of how a unique distinct key only can have the access to open a particular lock resembles how the specific substrate can only fit into the particular active site of the enzyme. This is significant in understanding the intermolecular interaction between proteins and plays a vital role in drug interaction.

Question

2. From the perspective of thermodynamics, the total free energy change of antibody (Ab) and
antigen (Ag) interaction can be expressed as AG = -RTln(K·1M), where R = 8.3145 J/(mol·K) is
the gas constant, T is the temperature in the unit of Kelvin (K = °C + 273.15), and K is affinity
constant of Ab-Ag interaction. Note: 1M here means 1 Molar, so that affinity constant K has the
unit of 1/M. A negative value of free energy change AG indicates energy release, while a positive
value of free energy change AG indicates energy absorption.
a) At body temperature T = 37°C, if we know the affinity constant K = 108/M, please compute the
total free energy change AG.
b) The presence of a single charged group on epitope or antigenic determinant of an antigen,
typically increases the energy release by 20 kJ/mol for Ab-Ag interaction. Please compute the

updated affinity constant K based on the presence of such a single charged group, and quantify the
ratio between the updated affinity constant K and original affinity constant K = 108/M in a).
From the perspective of reaction kinetics, Ab + Ag: Ab-Ag, where Ab-Ag indicates the
k₁
kd
complex of antibody and antigen, ka is the association rate constant, and ka is the dissociation rate
constant. In this way, the affinity constant K can be computed as K = k₁/ka.
c) For a high-affinity antibody, K = 109/M, and a typical association rate constant ka = 108 /(M·s),
please compute the dissociation rate constant ka-High. For a low-affinity antibody, K = 107/M, if the
association rate constant is still kept as ka 108/(Ms), please compute the dissociation rate
constant kd-Low.
=
We know the Ab-Ag interaction also follows the first-order kinetics, i.e. the half-life of the Ab-Ag
interaction t1/2 can be expressed as t1/2 = ln2 / kd = 0.693 / ka.
d) Please compute the half-life of the Ab-Ag interaction t1/2-High for high-affinity antibody, and t1/2-
Low for high-affinity antibody respectively.

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