Circular Dichroism Spectroscopy of Biomolecules

Nearly all molecules synthesized by living organisms are optically active.

If a meteorite contains optically active compounds this would suggest life elsewhere in the universe.

Why is nature dominated by chemical isomers of one handedness rather than the others (for example, L-amino acids predominate over D-amino acids in most living organisms).

Possible explanations involve the “seed” mechanism or the handedness of natural irradiation.

A molecule lacking a mirror plane or center of inversion is chiral and therefore modulates polarized light.

-phenylalanine

Plane polarized light is the sum of left and right circularly polarized light.
When plane polarized light passes through a solution containing an optically active substance the left and right circularly polarized components of the plane polarized light are absorbed by different amounts.
When these components are recombined they appear as elliptically polarized light.
The ellipticity is defined as q.

Optical Rotary Dispersion (ORD) is the ellipticity that results from absorption of linearly polarized light by chiral chromophores.
ORD has been replaced by Circular Dichroism (CD) spectroscopy.
Circularly polarized light is generated by:

Passing plane polarized light through a birefringent plate (in the z-direction) which splits the light into two plane-polarized beams oscillating along different axes (e.g., fast along x and slow along y). When one of the beams is retarded by 90º (using a quarter-wave retarder) then the two beams which are now 90º out of phase are added together, the result is circularly polarized light of one direction. By inverting the two axes such that the alternate beam is retarded than circularly polarized light of the other direction is generated.

The result of adding the right and left circularly polarized that passes through the optically active sample is elliptically polarized light, thus circular dichroism is equivalent to ellipticity.

Circular Dichroism Spectroscopy of Proteins

Back to the top

It is now possible to generate a wide variety of different proteins via solid-phase synthesis and recombinant DNA methods. There is a need to determine the structure of larger and larger numbers of proteins. High resolution techniques such as NMR and X-ray crystallography (that are complex and time-consuming) will be overwhelmed. Therefore, there is a need for quick low resolution techniques for determining protein structure. For example, absorption, Raman, fluorescence, and circular dichroism (CD).

Far-UV CD for determining protein structure

n -> p* centered around 220 nm

p -> p* centered around 190 nm

n -> p* involves non-bonding electrons of O of the carbonyl

p -> p* involves the p-electrons of the carbonyl

The intensity and energy of these transitions depends on f and y (i.e., secondary structure)

In a folded protein the amide is in a continuous array.

For example, the absorption spectrum of poly-L-lysine in an a-helix, b-sheet, and unordered (random coil) differ due to long-range order in the amide chromophore.

Far UV-CD of random coil (RC)

positive at 212 nm (p->p*)

negative at 195 nm (n->p*)

Far UV-CD of b-sheet

negative at 218 nm (p->p*)

positive at 196 nm (n->p*)

Far UV-CD of a-helix

exiton coupling of the p->p* transitions leads to positive (p->p*)_{perpendicular} at 192 nm and negative (p->p*)_parallel at 209 nm

negative at 222 nm is red shifted (n->p*)

Use far-UV CD to determine amounts of secondary structure in proteins

generate basis sets by determining spectra of pure a-helix, b-sheet, etc. of synthetic peptides

or deconvoluting CD spectra of proteins with know structures to generate basis sets of each of secondary structure

poly-L-lysine {(Lys)_n} can adopt 3 different conformations merely by varying the pH and temperature

random coil at pH 7.0

a-helix at pH 10.8

b-form at pH 11.1 after heating to 52°C and recooling

CD spectrum of unknown protein = f_aS_a(l) + f_bS_b(l) + f_RCS_RC(l), where S_a(l), S_b(l), and S_RC(l) are derived from poly-L-lysine basis spectra.

Recently S_a(l) was derived from the spectrum of myoglobin which is 80% a-helix

Recently b-turn has been added to the above equation {S_T(l)}. S_T(l) was derived from a combination of L-Pro-D-Ala, (Ala₂-Gly₂)_n and Pro-Gly-Leu

b-form is now (Lys-Leu)_n in 0.1 M NaF at pH 7

Random-coil is now (Pro-Lys-Leu-Lys-Leu)_n in salt free neutral solution.

a correction of chain-length for a-helix has been recently introduced:

The disadvantage of this method is that although these basis sets are easily determined by direct measurement, they do not always agree from one lab to another. In addition, chain length and aggregation effect the basis set spectra. However, this method is usually accurate to within 10% for a-helix content.

Technique Secondary Structure carboxypeptidase a-chymotrypsin myoglobin

a 23% 8% 68%

X-ray b 18% 22% 0%

RC + other 59% 70% 32%

a 13% 12% 68%

CD using (Lys)_n Basis Sets b 31% 23% 5%

RC + other 56% 65% 27%

If one has at least three proteins of known structure, then the following equation can be solved for S_i(l), where f_i(l) are determined from the X-ray structure:

spectrum of protein with known structure =

usually 5-15 proteins are used to generate basis set spectra

Disadvantages and problems with this method:

choice of reference proteins is arbitrary and effects results

determination of secondary structure from X-ray data is subject to error and disagreements among groups

secondary structures are NOT ideal in real proteins (e.g., a-helices can be bent, the spectrum of a 3₁₀-helix is different from a-helix, and b-turn can be twisted, non-planar, or perpendicular or parallel b-sheets.

Near-UV CD spectroscopy (250 - 350 nm) is dominated by Phe, Tyr, Trp and disulfides

If the aromatic residue is held rigidly in space than its environment is asymmetric, and it will exhibit circular dichroism.In a “molten globule” the far-UV CD is retained while the near-UV CD is lost.

Aromatics have allowed p->p* transitions (¹L_a and ¹L_b) that are directed in the plane of the p-bonding system and are orthogonal to each other.

Phe has a small extinction coefficient because of high symmetry and it is also the least sensitive to alterations in its environment. Absorption maxima at 254, 256, 262 and 267 nm (vibronic bands).

Tyr has lower symmetry then Phe and therefore has more intense absorption band. Tyr has absorption maximum at 276 nm and a shoulder at 283 nm. Hydrogen-bonding to the hydroxyl group leads to a red-shift of up to 4 nm. The dielectric constant effects the spectrum also.

Trp has the most intense absorption band centered at 282 nm. Hydrogen-bonding to the NH can shift the ¹L_a band by as much as 12 nm.

Disulfide (S-S) spectra have a broad band at 250 - 300 nm with no vibronic structure.

These groups can complicate the Far-UV CD region because of allowed p->p* transitions

Vacuum ultraviolet CD spectra of the models of aromatic side chain residues. Glutamyl tyrosine (Y); lysyl-phenylalanine (F); glutamyl-tryptophan (W).

Summary
Back to the top

CD has an important role in the structural determinants of proteins

However, the effort expended in determining secondary structure elements is usually not worth it because it is somewhat unreliable.

The real power of CD is in the analysis of structural changes in a protein upon some perturbation, or in comparison of the structure of an engineered protein to the parent protein.

CD is rapid and can be used to analyze a number of candidate proteins from which interesting candidates can be selected for more detailed structural analysis like NMR or X-ray crystallography.

Protein secondary structure and circular dichroism: A practical guide
Back to the top

q = ellipticity

[q] = ellipticity = , c = concentration, l = path length

q = 2.303 (A_L - A_R) 180/4p (in units of degrees)

[q]_MRW = (deg cm² dmole^-1) = mean residue weight ellipticity

n = number of amino acids

Monitoring q_222nm of a protein as a function of temperature or chemical denaturant yields information about protein stability.

The thermodynamic parameters, DG_u, DH_u, DS_u, T_m, DC_p can be determined

DG = ((DH(1-(T/T_m)) - DC_p((T_m-T) + T ln(T/T_m))

Fraction Unfolded = 1 - (1/(1 + (exp((DH + DC_p (T-T_m) - T DH/T_m - T DC_p ln(T/T_m))/R/-1/T))))

The goal is to determine the fraction of basis set spectra that add up to give the CD spectrum of the protein (hemoglobin, elastase, lysozyme)

The absorption should be less than 1.0 (usually < 0.3) for cell pathlengths of 0.05 to 1 cm in order to maintain reasonable signal-to-noise ratios and accurate CD measurements.

Protein concentration is typically 1 mg/mL

Buffer is typically 10 mM phosphate with low salt if any.

Solvent Cut-Off (A=1.0) for

Two Different Cell Pathlengths

Compound 1.0 mm 0.05 mm

H₂O 182 176

F₆iPrOH 174.5 163

F₃EtOH 179.5 170

MeOH 195.5 184

EtOH 196 186

MeCN 185 175

Dioxane 231 202.5

Cyclohexane 180 175

n-Pentane 172 168

Must calibrate the instrument: typically an aqueous solution of (+)-10-camphorsulfonic acid (CSA): 1 mg/mL in 1 mm cell: De = 2.36 at 290.5 nm, DA = 1.02¥10^-3, ellipticity = 33.5 mdeg. At 192.5 nm ellipticity = 69.6 mdeg. To accurately determine concentration of CSA solution: A_285nm = 0.743 in 5 cm cell, e_285nm = 34.5 M^-1 cm^-1.

Need to know protein concentration accurately.

e_190nm = 8,500 - 11,400 M^-1 cm^-1 per residue (this is not accurate enough: as you know the e in the far UV of proteins depends on the secondary structure).

e_280nm (in 6 M GdmCl) = # of Trp residues ¥ 5,690 + # of Tyr residues ¥ 1,280 M^-1 cm^-1

Protein Technique a-helix
H
antiparallel-b-sheet
A
parallel-b-sheet
P
b-turn
T
other
O

EcoRI endonuclease X-ray 26 20 8 25 21

EcoRI endonuclease Deconvolution of CD spectrum 33 20 5 17 25

calmodulin X-ray 59 3 0 - 41

calmodulin Deconvolution of CD spectrum 61 2 2 - 35

Thymidylate synthetase is 33% H, 24% A, 2% P, 21% T, 20% O. Upon binding of FdUMP and 5,10-methylenetetrahydrofolate CD shows -5% A, -6% T, +8% O.

Circular dichroism spectroscopy has been used to determine the preference for amino acids in the first or last position of an a-helix.

The CD spectra of the following peptides were measured for X = all 20 amino acids

NH₂-XAKAAAAKAAAAKAAGY-CONH₂

Ac-YGAAKAAAAKAAAAKAX-CO₂H

Helix contents for peptides with varying N-terminal amino acid, X.

If Asn, Asp, Ser, Thr, Cys are the first residue in a helix they can form H-bond with otherwise free backbone NH group and therefore have a high preference for being located at the beginning of helices.

Left Figure: Helix turn indicating main chain C=O/NH hydrogen bond

Right Figure:Asn as the first amino in a helix indicating side chain/main chain hydrogen bond

Also negatively charged residues are located more often at the beginning of helices because of helix-dipole stabilization.

The C-terminal preferences are uninteresting, however, positively charged residues have a slight preference for the end of a-helices.

Conformational studies of membrane proteins lag far behind those of soluble proteins:

mainly due to the difficulties associated with crystallization of membrane proteins for X-ray diffraction studies and to the restricted movement of the proteins embedded in the membrane for NMR studies.

CD spectra of membrane proteins often are distorted compared to soluble proteins.

Why?

One of the reasons is that transmembrane helices (a_T helices) may differ from peripheral a-helices.

Remember the CD of soluble proteins:

a-helix positive p->p* 190-195 nm 60,000 to 80,000 deg cm² dmol^-1

negative p->p* 208 -36,000 ± 3,000

negative n->p* 222 -36,000 ± 3,000

b-sheet positive p->p* 195 - 200 30,000 to 50,000

negative n->p* 215 - 220 -10,000 to -20,000

random negative p->p* ca. 200 -20,000

positive n->p* 220 small

Deconvolution of CD spectra of 5 transmembrane helices of known structure:

a_T-helix positive p->p* 195-200 nm 95,000 deg cm² dmol^-1

negative p->p* 208 -50,000

negative n->p* 222 -60,000

a-helix positive p->p* 190-195 nm 60,000 to 80,000 deg cm² dmol^-1

negative p->p* 208 -36,000 ± 3,000

negative n->p* 222 -36,000 ± 3,000

Transmembrane helices are longer (22-28) and are therefore expected to exhibit large extinction coefficients.

Method a-helix a_T-helix b-sheet b-turn Random

Reaction Center from R. viridis X-ray 16 23 7 - 54

CD 8 22 9 10 52

CD spectroscopy of hemoproteins
Back to the top

Heme group is optically INACTIVE

However, the CD spectrum above 300 nm of hemoproteins are rich in detail

Why?

In myoglobin and hemoglobin the dipole-dipole coupling involving heme transitions and allowed p->p* transitions of nearby aromatic side chains gives rise to circular dichroism.

Residues as far as 12 Å away depending on the relative orientation can yield CD of heme groups

Simple alterations of the polarization direction or orientation of a distal aromatic chromophore could result in significant alterations of both the complexity and magnitude without implying any major conformational change in the protein structure or the heme group.

In model compounds, axial ligands also effect CD spectrum of heme group

CD spectroscopy has been recognized for its utility and simplicity in operations for conformational studies, even though interpreting the data has not been simple and there have been major controversies concerning the technique.

CD of nucleic acids
Back to the top

For nucleic acids, unlike proteins, one cannot ignore spectral differences between different monomeric residues.

The bases themselves are directly involved in close interactions in all common secondary structures.

Even some actual sequence information must be taken into account to explain CD spectra. For example the CD spectrum of the dinucleoside phosphate ApG is different from the sum of the CD spectra of A and G monomers.

The CD spectra of ApG and GpU are the sum of the two monomers plus and an additional term to account for the base-base interactions:

2[q_ApG(l)] = [q_A(l)] + [q_G(l)] + I_AG(l)

2[q_GpU(l)] = [q_G(l)] + [q_U(l)] + I_GU(l)

In a trinucleoside diphosphate such as ApGpU, there would be contributions from three monomers, two interactions between neighboring bases, and a final contribution due to interaction between the next-nearest neighbors, A and U:

3[q_ApGpU(l)] = [q_A(l)] + [q_G(l)] + [q_U(l)] + I'_AG(l) + I'_GU(l) + I”_AU(l)

One can assume that I_AG(l) = I'_AG(l) and that I”_AU(l) is negligible, therefore:

3[q_ApGpU(l)] = 2[q_ApG(l)] + 2[q_GpU(l)] - [q_G(l)]

The spectrum of a random coil can be estimated as simply the average of the properties of the four monomers.

The spectrum of a single-strand stacked helix would contain optical contributions from each of the 16 possible dinucleoside phosphates, weighted by their frequencies of occurrence. The spectrum of a double-strand is accounted for in an analogous way, by adding the contributions of each of the 10 possible double-strand dimers (ApG base paired with CpU, and so on).

In practice, a total of up to 30 different spectral contributions must be combined to compute the CD of a molecule such as tRNA that has both single-strand and double-strand regions.

This approach is very complex!

CD of DNA bound to racemic mixtures of intercalators is useful

For example:

A racemic mixture of D,G-Co(phen)₃ + DNA followed by dialysis Æ circular dichroism because one enantiomer binds (intercalates) preferentially over the other to DNA.
Back to the top

Return to the Chemistry Home Page

Technique	Secondary Structure	carboxypeptidase	a-chymotrypsin	myoglobin
	a	23%	8%	68%
X-ray	b	18%	22%	0%
	RC + other	59%	70%	32%

	a	13%	12%	68%
CD using (Lys)_n Basis Sets	b	31%	23%	5%
	RC + other	56%	65%	27%

Compound	1.0 mm	0.05 mm
H₂O	182	176
F₆iPrOH	174.5	163
F₃EtOH	179.5	170
MeOH	195.5	184
EtOH	196	186
MeCN	185	175
Dioxane	231	202.5
Cyclohexane	180	175
n-Pentane	172	168

Protein	Technique	a-helix H	antiparallel-b-sheet A	parallel-b-sheet P	b-turn T	other O
EcoRI endonuclease	X-ray	26	20	8	25	21
EcoRI endonuclease	Deconvolution of CD spectrum	33	20	5	17	25
calmodulin	X-ray	59	3	0	-	41
calmodulin	Deconvolution of CD spectrum	61	2	2	-	35

a-helix	positive	p->p*	190-195 nm	60,000 to 80,000 deg cm² dmol^-1
	negative	p->p*	208	-36,000 ± 3,000
	negative	n->p*	222	-36,000 ± 3,000
b-sheet	positive	p->p*	195 - 200	30,000 to 50,000
	negative	n->p*	215 - 220	-10,000 to -20,000
random	negative	p->p*	ca. 200	-20,000
	positive	n->p*	220	small

a_T-helix	positive	p->p*	195-200 nm	95,000 deg cm² dmol^-1
	negative	p->p*	208	-50,000
	negative	n->p*	222	-60,000
a-helix	positive	p->p*	190-195 nm	60,000 to 80,000 deg cm² dmol^-1
	negative	p->p*	208	-36,000 ± 3,000
	negative	n->p*	222	-36,000 ± 3,000

	Method	a-helix	a_T-helix	b-sheet	b-turn	Random
Reaction Center from R. viridis	X-ray	16	23	7	-	54
	CD	8	22	9	10	52

Circular Dichroism Spectroscopy of Biomolecules

Circular Dichroism Spectroscopy of Proteins

Summary

Protein secondary structure and circular dichroism: A practical guide

CD spectroscopy of hemoproteins

CD of nucleic acids

Nearly all molecules synthesized by living organisms are optically active.

If a meteorite contains optically active compounds this would suggest life elsewhere in the universe.

Why is nature dominated by chemical isomers of one handedness rather than the others (for example, L-amino acids predominate over D-amino acids in most living organisms).

Possible explanations involve the “seed” mechanism or the handedness of natural irradiation.

A molecule lacking a mirror plane or center of inversion is chiral and therefore modulates polarized light.

-phenylalanine

Plane polarized light is the sum of left and right circularly polarized light.

When plane polarized light passes through a solution containing an optically active substance the left and right circularly polarized components of the plane polarized light are absorbed by different amounts.

When these components are recombined they appear as elliptically polarized light.

The ellipticity is defined as q.

Optical Rotary Dispersion (ORD) is the ellipticity that results from absorption of linearly polarized light by chiral chromophores.

ORD has been replaced by Circular Dichroism (CD) spectroscopy.

Circularly polarized light is generated by:

The result of adding the right and left circularly polarized that passes through the optically active sample is elliptically polarized light, thus circular dichroism is equivalent to ellipticity.

Circular Dichroism Spectroscopy of Proteins

Far-UV CD for determining protein structure

n -> p* centered around 220 nm

p -> p* centered around 190 nm

n -> p* involves non-bonding electrons of O of the carbonyl

p -> p* involves the p-electrons of the carbonyl

The intensity and energy of these transitions depends on f and y (i.e., secondary structure)

In a folded protein the amide is in a continuous array.

For example, the absorption spectrum of poly-L-lysine in an a-helix, b-sheet, and unordered (random coil) differ due to long-range order in the amide chromophore.

Far UV-CD of random coil (RC)

positive at 212 nm (p->p*)

negative at 195 nm (n->p*)

Far UV-CD of b-sheet

negative at 218 nm (p->p*)

positive at 196 nm (n->p*)

Far UV-CD of a-helix

exiton coupling of the p->p* transitions leads to positive (p->p*)perpendicular at 192 nm and negative (p->p*)parallel at 209 nm

negative at 222 nm is red shifted (n->p*)

Use far-UV CD to determine amounts of secondary structure in proteins

generate basis sets by determining spectra of pure a-helix, b-sheet, etc. of synthetic peptides

or deconvoluting CD spectra of proteins with know structures to generate basis sets of each of secondary structure

poly-L-lysine {(Lys)n} can adopt 3 different conformations merely by varying the pH and temperature

random coil at pH 7.0

a-helix at pH 10.8

b-form at pH 11.1 after heating to 52°C and recooling

CD spectrum of unknown protein = faSa(l) + fbSb(l) + fRCSRC(l), where Sa(l), Sb(l), and SRC(l) are derived from poly-L-lysine basis spectra.

Recently Sa(l) was derived from the spectrum of myoglobin which is 80% a-helix

Recently b-turn has been added to the above equation {ST(l)}. ST(l) was derived from a combination of L-Pro-D-Ala, (Ala2-Gly2)n and Pro-Gly-Leu

b-form is now (Lys-Leu)n in 0.1 M NaF at pH 7

Random-coil is now (Pro-Lys-Leu-Lys-Leu)n in salt free neutral solution.

a correction of chain-length for a-helix has been recently introduced:

If one has at least three proteins of known structure, then the following equation can be solved for Si(l), where fi(l) are determined from the X-ray structure:

spectrum of protein with known structure =

usually 5-15 proteins are used to generate basis set spectra

Disadvantages and problems with this method:

choice of reference proteins is arbitrary and effects results

determination of secondary structure from X-ray data is subject to error and disagreements among groups

secondary structures are NOT ideal in real proteins (e.g., a-helices can be bent, the spectrum of a 310-helix is different from a-helix, and b-turn can be twisted, non-planar, or perpendicular or parallel b-sheets.

Near-UV CD spectroscopy (250 - 350 nm) is dominated by Phe, Tyr, Trp and disulfides

If the aromatic residue is held rigidly in space than its environment is asymmetric, and it will exhibit circular dichroism.In a “molten globule” the far-UV CD is retained while the near-UV CD is lost.

Aromatics have allowed p->p* transitions (1La and 1Lb) that are directed in the plane of the p-bonding system and are orthogonal to each other.

Phe has a small extinction coefficient because of high symmetry and it is also the least sensitive to alterations in its environment. Absorption maxima at 254, 256, 262 and 267 nm (vibronic bands).

Tyr has lower symmetry then Phe and therefore has more intense absorption band. Tyr has absorption maximum at 276 nm and a shoulder at 283 nm. Hydrogen-bonding to the hydroxyl group leads to a red-shift of up to 4 nm. The dielectric constant effects the spectrum also.

Trp has the most intense absorption band centered at 282 nm. Hydrogen-bonding to the NH can shift the 1La band by as much as 12 nm.

Disulfide (S-S) spectra have a broad band at 250 - 300 nm with no vibronic structure.

These groups can complicate the Far-UV CD region because of allowed p->p* transitions

Vacuum ultraviolet CD spectra of the models of aromatic side chain residues. Glutamyl tyrosine (Y); lysyl-phenylalanine (F); glutamyl-tryptophan (W).

Summary

CD has an important role in the structural determinants of proteins

However, the effort expended in determining secondary structure elements is usually not worth it because it is somewhat unreliable.

The real power of CD is in the analysis of structural changes in a protein upon some perturbation, or in comparison of the structure of an engineered protein to the parent protein.

CD is rapid and can be used to analyze a number of candidate proteins from which interesting candidates can be selected for more detailed structural analysis like NMR or X-ray crystallography.

Protein secondary structure and circular dichroism: A practical guide

q = ellipticity

[q] = ellipticity = , c = concentration, l = path length

q = 2.303 (AL - AR) 180/4p (in units of degrees)

[q]MRW = (deg cm2 dmole-1) = mean residue weight ellipticity

n = number of amino acids

Monitoring q222nm of a protein as a function of temperature or chemical denaturant yields information about protein stability.

The thermodynamic parameters, DGu, DHu, DSu, Tm, DCp can be determined

exiton coupling of the p->p* transitions leads to positive (p->p)_{perpendicular} at 192 nm and negative (p->p)_parallel at 209 nm

poly-L-lysine {(Lys)_n} can adopt 3 different conformations merely by varying the pH and temperature

CD spectrum of unknown protein = f_aS_a(l) + f_bS_b(l) + f_RCS_RC(l), where S_a(l), S_b(l), and S_RC(l) are derived from poly-L-lysine basis spectra.

Recently S_a(l) was derived from the spectrum of myoglobin which is 80% a-helix

Recently b-turn has been added to the above equation {S_T(l)}. S_T(l) was derived from a combination of L-Pro-D-Ala, (Ala₂-Gly₂)_n and Pro-Gly-Leu

b-form is now (Lys-Leu)_n in 0.1 M NaF at pH 7

Random-coil is now (Pro-Lys-Leu-Lys-Leu)_n in salt free neutral solution.

If one has at least three proteins of known structure, then the following equation can be solved for S_i(l), where f_i(l) are determined from the X-ray structure:

secondary structures are NOT ideal in real proteins (e.g., a-helices can be bent, the spectrum of a 3₁₀-helix is different from a-helix, and b-turn can be twisted, non-planar, or perpendicular or parallel b-sheets.

Aromatics have allowed p->p* transitions (¹L_a and ¹L_b) that are directed in the plane of the p-bonding system and are orthogonal to each other.

Trp has the most intense absorption band centered at 282 nm. Hydrogen-bonding to the NH can shift the ¹L_a band by as much as 12 nm.

q = 2.303 (A_L - A_R) 180/4p (in units of degrees)

[q]_MRW = (deg cm² dmole^-1) = mean residue weight ellipticity

Monitoring q_222nm of a protein as a function of temperature or chemical denaturant yields information about protein stability.

The thermodynamic parameters, DG_u, DH_u, DS_u, T_m, DC_p can be determined

DG = ((DH(1-(T/T_m)) - DC_p((T_m-T) + T ln(T/T_m))

Fraction Unfolded = 1 - (1/(1 + (exp((DH + DC_p (T-T_m) - T DH/T_m - T DC_p ln(T/T_m))/R/-1/T))))

e_190nm = 8,500 - 11,400 M^-1 cm^-1 per residue (this is not accurate enough: as you know the e in the far UV of proteins depends on the secondary structure).

e_280nm (in 6 M GdmCl) = # of Trp residues ¥ 5,690 + # of Tyr residues ¥ 1,280 M^-1 cm^-1

NH₂-XAKAAAAKAAAAKAAGY-CONH₂

Ac-YGAAKAAAAKAAAAKAX-CO₂H

One of the reasons is that transmembrane helices (a_T helices) may differ from peripheral a-helices.

2[q_ApG(l)] = [q_A(l)] + [q_G(l)] + I_AG(l)

2[q_GpU(l)] = [q_G(l)] + [q_U(l)] + I_GU(l)

3[q_ApGpU(l)] = [q_A(l)] + [q_G(l)] + [q_U(l)] + I'_AG(l) + I'_GU(l) + I”_AU(l)

One can assume that I_AG(l) = I'_AG(l) and that I”_AU(l) is negligible, therefore:

3[q_ApGpU(l)] = 2[q_ApG(l)] + 2[q_GpU(l)] - [q_G(l)]

A racemic mixture of D,G-Co(phen)₃ + DNA followed by dialysis Æ circular dichroism because one enantiomer binds (intercalates) preferentially over the other to DNA.