BIOPHYS CHEM EX2

equilibrium for dissociation of ES complex

what is Ks?

the binding follows MM and is fast (Km=Ks)

what is Km when one ES complex is present?

Km estimates Ks and it follows the complete mechanism

what is Km when more than one ES complex is present?

Km = [ES][S] / ∑[ES]

Km equation with more than one ES present?

sum of all bound species

what is ∑[ES]?

equilibrium association constant of a complex

what is Ka?

equilibrium dissociation constant of a complex

what is Kd?

number of binding sites

what is n?

ligand binding to enzyme

what is L?

we want to know how many exist and how strong they are, to find Ka

what do you want to know when binding sites are unknown?

[EL]/[E][L]

equation for Ka?

[E] + [EL]

[E]₀ =

[L] [EL]

[L]₀ =

f = [EL] / [E]₀

what is the occupied sites fraction equation?

(1-f)= [E]/[E]₀

what is the unoccupied site fraction equation?

Ka = f / (1-f) [L]

what is the binding site occupation equation for Ka?

(1/Ka [L]) + 1 = 1 / f

what is the equation for graphically representing a single binding site?

a double reciprocal plot

how do you represent a single binding site to a graph?

slope: 1 / Ka

y-intercept: 1

x axis: 1 / [L]

y axis: 1 / f

what is the double reciprocal graph for a single binding site?

f = [EL] / n [E]₀ , measures the percentage of individual sites that are available

what is the equation for the fraction of occupied sites?

v = [EL] / [E]₀ , tracks the average number of bound ligands per single enzyme molecule

what is the equation for bound ligands?

slope: 1/nKa

y axis: 1/v

x axis: 1/[L]

y intercept: 1/n

compression at low [L]

what is the double reciprocal graph for a multiple binding site?

1/nKa[L] + 1/n = 1/v

what is the double reciprocal equation for multiple binding sites?

extremes and limitations, conceptually identical to looking at a reactions max capacity

what does this 1/nKa[L] + 1/n = 1/v focus on?

slope: - Ka

x axis: v

y axis: v / [L]

y intercept: nKa

sensitive to cooperative binding

what is the scatchard plot for multiple binding sites?

nKa - Kav = v/[L]

what is the scatchard plot equation?

the ratio of bound to free ligand against total ligand, focuses on how remaining capacity affects other sites

what does nKa - Kav = v / [L] focus on?

molecular interactions

forces between molecules and between atoms, that can be either attractive or repulsive

macromolecules and solvent environments and is highly variable

what does conformation depend on?

total # of independent coordinates or modes of motion required to fully specify the positions, orientations, and energy states of all the atoms in the system

doF

intermolecular interactions among molecules + intramolecular interactions among atoms within molecules

what is the total potential energy in a macromolecule system

total intramolecular potential energy and gives the PE landscape as a function of atom position

V_Total

V total = [ ∑_^Ni (V_bonding - V_nonbonding )]_intra

Vtotal equation?

bonding interactions

involves covalent bonds, where atoms share electrons to achieve stability (energy changes correspond to IR region of electromagnetic spectrum and absorb IR light)

stretching

movement along bond axis, involves 2 atoms and requires 1 covalent

bending

change in bond angle between 3 atoms and requires 2 covalent bonds

twisting

rotation around bond axis involving 4 atoms and requires 3 covalent bonds

nonbonding interactions

intermolecular forces attraction between molecules rather than within them, influences physical properties

ionic bond

electrostatic attraction between opposely charged ions, is very strong

dipole-dipole

attraction between polar molecules with permanent dipoles moderate strength, moderate strength

LDFS

temporary dipoles caused by electron movement, present in all molecules, weak interactions

VanDer Waals

collective term for all weak intermolecular interactions between surfaces, atoms, and molecules

y axis: potential energy

x axis: distance between nuclei

r0 : minimum value

what is the harmonic potential graph?

F = -kr

what is the force spring constant equation?

bonding energy (E) is modeled in a force field as distance dependent function

what does the harmonic potential graph model?

Vbond = kbond (r - r0)2

equation for bond length?

r0

standard length of a bond

HPG

bonding energy is modeled in a force field as distance dependent function

Vθ = kθ (θ - θ₀)²

what is the equation for V0?

bond angle and bond length graphs?

defines the dihedral angle phi around the central bond between atoms

the twisting of a bond

depends on the type of the bond connecting the central atoms

what does the potential energy function for rotation depend on?

are relatively free to rotate, while double bonds have very distinct energy minima at phi = 0, 180, 360

what is single bond rotation?

dihedral angle

measures how much one part of the molecule twists relative to another, determines molecular shape and flexibility energy function

the TYPE of bonds connecting the atoms

what is the V(ϕ) dependent on?

Torsional potential energy curves for single vs. double bond rotation ($V(\phi)$ vs. $\phi$)

• Plot A (Single bond): Shows a three-fold periodic curve with minima at staggered conformations and low energy barriers, allowing relatively free rotation.

• Plot B (Double bond): Shows distinct energy minima at trans ($0^\circ$) and cis ($\pm 180^\circ$) separated by high energy barriers, restricting rotation.

Vn:

torsion force constant (spring constant)

n:

period of the function

y (gamma);

phase angle (defines the minima occurs)

torsional potential

how energy changes as the molecule twists

peaks - unstable

valleys - stable

anharmonic function

true, nonparabolic potential energy of a molecular bond, moving beyond simple harmonic oscillator

forced toward r0 by potential energy surface

at r distance atoms are

the “spring” from r0 with K

what is Vbond dependent on deformation of

H-H repulsion

H—H attraction

H———H bond breaks

what is the graph for anharmonic function?

bond length

anatomical distance between nuclei with E at minimum (optimal)

the e-cloud overlaps gradually

what happens when the bond is compressed?

harmonic model

approximation is good around r0, it is symmetrical and shows molecules are tightly bonded than they actually are

ground vibration state, smallest amplitude, zero point energy

what does v=0 stand for?

dissociation energy from minimum to asymptote

what does De stand for?

energy and atoms vibrate with larger amplitude (farther from r0)

what increases as vibrational levels increase?

V1-3

potential for bond angle

non bonding potential

potential energy from interactions not dependent on covalent bonding and distance dependent to some power (n) of the distance between atoms {r}

V_nonbonding ∝ f (1/rⁿ )

what is the equation for intermolecular potential energy term derived from a power-law interaction?

It describes how a specific potential energy component of a chemical bond scales with the internuclear distance between the two bonded atoms.

what does this V_n ∝ f (1/rⁿ ) describe?

short range

when n is large the interaction is

large range

when n is small the interaction is

electrostatic

n=1 ?

dipole dipole

n=3?

London DF

n=6?

repulsion

n=12?

rⁿ

potential energy functions are inversely related to

n=12 → n=1

non bonding potential graph?

faster the function approaches 0

the higher the n exponent the

energy drops quickly

if n is high

energy drops slowly

if n is small

electrostatic

treatment of the electrostatic potential (V_e ) between two units charges Z1 and Z2

𝑉𝑒 = 𝑍1𝑒𝑍2𝑒/4𝜋𝜖0𝑟𝐷

what is the electrostatic potential energy equation?

𝑉𝑑𝑑 = + |𝜇1||𝜇2|/ Dr³

what is the dipole dipole parallel equation?

repulsion

dipole-dipole parallel

𝑉𝑑𝑑 = - |𝜇1||𝜇2|/ Dr³

what is dipole dipole antiparallel equation?

attraction

dipole-dipole antiparallel

𝑉𝑑𝑑 = −2 |𝜇1| |𝜇2| / 𝐷𝑟3

what is the dipole dipole head to tail equation?

the dipole moment, depends on length

what is µ?

𝑉𝑑𝑑 = + 2 |𝜇1| |𝜇2| / 𝐷𝑟3

what is the dipole dipole head to head equation?

attraction

dipole dipole head to tail

repulsion

dipole dipole head to head

electrical interactions between two or more atoms or molecules that are VERY close

what are VDW forces driven by?

London dispersion forces

VL ?

Nucleus-Nucleus repulsion forces

VR ?

VL + VR

VDW =