30 Questions
What is the master equation that allows us to understand phase changes?
$\Delta G = VdP - SdT$
What occurs for living systems to exist?
They must be out of equilibrium and undergo dynamic processes.
What happens to an organism as it approaches closer to equilibrium?
It approaches closer to death.
What is the condition for spontaneous processes in an open system?
$\Delta \mu_{T,P} < 0$
What is the significance of considering equilibrium in connection with living organisms?
It helps define the direction of dynamic processes.
What is the equation for the molar free-energy surface as a function of temperature and pressure?
$\Delta G_{m} = G_{m,water} - G_{m,ice}$
In the Scatchard equation, what does 𝜈 represent?
The number of bound A molecules per polymer molecule
What does the parameter 𝝉 account for in the Ising model?
The interaction between two adjacent occupied sites
What is the statistical weight of the free species in the Ising model?
1
What does the concentration relative to a reference concentration represent in statistical weights?
Statistical weight of species I
What is the equilibrium constant for the binding of an A molecule to a site with one adjacent site occupied in the Ising model?
𝝉K
What does the parameter 𝝂 represent in the Scatchard equation?
The average number of molecules of A bound to the macromolecule
According to the Gibbs Phase Rule, how many degrees of freedom do pure substances have?
3
What is the additional constraint when two phases are present at equilibrium according to the Gibbs Phase Rule?
No additional constraint
What does the Clausius-Clapeyron Equation describe?
Pressure dependence of vapor-liquid equilibrium temperature
What is the special property of enthalpy of vaporization at pressures close to ambient according to the text?
It is independent of pressure and temperature
Which equation can be modified to increase its accuracy involving the enthalpy of vaporization and the standard state enthalpy of vaporization?
Clausius-Clapeyron Equation
What does Raoult’s Law govern in a 2-component system of gasoline and water?
Chemical potential of each component at equilibrium
What is the formula for the binding equation for cooperative, anticooperative, and excluded-site binding?
$\Delta = N - \Delta K_A \Delta z$
What type of plot characterizes cooperative binding?
Sigmoidal plot of fraction of sites occupied versus the number of occupied sites
What is used to represent the cooperative binding in hemoglobin?
Scatchard plot
What type of vesicles are formed by liposomes and have diameters between 1000 and 50,000 Å?
Multilayer vesicles (MLVs)
What is denoted as the temperature at which the gel to liquid-crystalline phase transition occurs in lipids, bilayers, and membranes?
Tm
What type of assembly of liposomes is entropy-driven, involving the release of water molecules from the solvation shell?
Liposomes
What does Henry's Law state?
The vapor pressure of a solute in a solution is proportional to its mole fraction in the solution
What is the equation for the chemical potential of the vapor in an ideal gas?
$\mu = \mu^\circ + RT \ln (P_{vap}/P^\circ)$
What does the Identical-and-Independent-Sites Model describe?
A polymer with identical and independent sites for binding a smaller molecule
What is the equilibrium constant for the binding of a small molecule to a polymer in the Identical-and-Independent-Sites Model?
$K = [AB]/[A][B]$
What is the relationship used to calculate the total binding of the polymer in the Identical-and-Independent-Sites Model?
$P_A = P_{A(1)} + P_{A(2)} + P_{A(3)} + P_{A(4)}$
How can the equilibrium constant for binding at different sites be calculated in the Identical-and-Independent-Sites Model?
$P_AK_1 = 4P_A, P_AK_2 = 4P_A, P_{A(2)}K = 4P_A, P_{A(3)}K = 4P_A, P_{A(4)}K = 4P_A$
Study Notes
Binding Equations and Cooperative Unit in Biochemistry
-
The general formula for defining the product K[A] as S involves the statistical weights and the number of occupied sites and nearest-neighbor interactions.
-
The average number of bound A per P is calculated as a function of the statistical weights and the fraction of sites occupied.
-
The binding equation for cooperative, anticooperative, and excluded-site binding is given by 𝝂= 𝑵−𝝂 𝑲 𝑨 𝝂z.
-
Cooperative binding is characterized by a sigmoidal plot of fraction of sites occupied versus the number of occupied sites, while the independent-sites model is not affected by the total number of sites.
-
For cooperative binding, the curve of fraction of sites occupied versus the number of occupied sites is dependent on the total number of sites per polymer molecule.
-
In the all-or-none limit, the reaction can be considered as 𝑷 + 𝟑𝑨 → 𝑷𝑨𝟑, and the fraction of sites occupied is calculated using the Hill constant.
-
The assembly of liposomes is entropy-driven, involving the release of water molecules from the solvation shell.
-
Liposomes are used as model systems for the cell membrane, as well as for drug delivery and cosmetic preparations.
-
Multilayer vesicles (MLVs) are formed by liposomes and have diameters between 1000 and 50,000 Å.
-
The gel to liquid-crystalline phase transition in lipids, bilayers, and membranes is highly cooperative, and the temperature at which phase transition occurs is denoted as Tm.
-
Near the Tm, the distance range of cooperation in the phase transition increases.
-
Scatchard plot is used to represent the cooperative binding in hemoglobin, showing the fraction of hemes occupied by oxygen as a function of the pressure of oxygen.
Chemical Equilibria and Partitioning in Solutions
- The equation for chemical potential of the vapor in an ideal gas is 𝜇 = 𝜇° + 𝑅𝑇 ln (𝑃𝑣𝑎𝑝/𝑃°)
- Henry's Law states that the vapor pressure of a solute in a solution is proportional to its mole fraction in the solution
- Partitioning refers to the distribution of a solute between two immiscible phases, such as liquid-liquid or liquid-solid
- Solubility measurements indicate that 𝜇°heptane - 𝜇°water = -38 kJ mol-1
- The binding of small molecules by a polymer can be described using the equation 𝐴 + 𝐵 ⇌ 𝐴𝐵, with the equilibrium constant 𝐾 = [𝐴𝐵]/[𝐴][𝐵]
- The Identical-and-Independent-Sites Model describes a polymer with identical and independent sites for binding a smaller molecule
- The model uses the equation 𝑃𝐴(1)𝐾 = 𝑃𝐴/𝑃𝐴(2)𝐾, 𝑃𝐴(2)𝐾 = 𝑃𝐴/𝑃𝐴(3)𝐾, 𝑃𝐴(3)𝐾 = 𝑃𝐴/𝑃𝐴(4)𝐾 to represent the binding at different sites
- The relationship 𝑃𝐴 = 𝑃𝐴(1) + 𝑃𝐴(2) + 𝑃𝐴(3) + 𝑃𝐴(4) can be used to calculate the total binding of the polymer
- The equilibrium constant for binding at different sites can be calculated using the equation 𝑃𝐴𝐾1 = 4𝑃𝐴, 𝑃𝐴𝐾2 = 4𝑃𝐴, 𝑃𝐴(2)𝐾 = 4𝑃𝐴, 𝑃𝐴(3)𝐾 = 4𝑃𝐴, 𝑃𝐴(4)𝐾 = 4𝑃𝐴
- The model also uses the equation 𝑃𝐴 = 4𝑃𝐴, 𝑃𝐴(2) = 6𝑃𝐴, 𝑃𝐴(3) = 6𝑃𝐴, 𝑃𝐴(4) = 4𝑃𝐴 to calculate the total binding
Test your knowledge of binding equations and cooperative units in biochemistry, as well as chemical equilibria and partitioning in solutions with this quiz. Covering topics such as statistical weights, cooperative binding, liposome assembly, and partitioning equations, this quiz is perfect for students and professionals in biochemistry and related fields.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
