Physical Biochemistry

Kwan Hee Lee, Ph.D.

Handong Global University

Week 16

Chapter 7

Molecular Structures and Interactions: Spectroscopy

Spectroscopy is the energy of the interaction of electromagnetic radiation with matter.

Ultraviolet and visible spectroscopy monitors changes between electronic states; infrared spectroscopy probes vibrational states.

Circular dichroism is the differencal absorption of right- and left-circularly polarized light.

NMR is the absorption of radiofrequency electromagnetic radiation by nuclei placed in a static magnetic field.

All matters scatters electromagnetic radiation. In Rayleigh scattering only the direction of incident light is

changed, in Raman scattering there is also a change in wavelength.

Introduction

Wavelength regions of the electromagnetic spectrum

Quantitative analysis Identities Concentrations Probe molecular structure Circular dichroism reveals the helical content of proteins or

nucleic acids. Fluorescence and NMR spectroscopy monitor the relative

separations of atoms or chemical groups, which provides three dimensional conformational information on proteins and nucleic acids.

NMR can reveal their structures in solutions at atomic resolution.

Spectroscopy can be used to measure changes in biochemical systems including the binding of molecules and chemical reactions.

Applications

Color is an obvious property of a substance.

The color is characteristic of the spectrum of light in the visible region transmitted by the substance when white light shines through it or when light is reflected from it or when light is reflected from it.

The quantitative measure of color that we use is the absorption spectrum, which is a plot of the wavelength or frequency of the absorption of radiation by the substance.

The absorptions spectrum is complementary to the transmission of light.

Color and Refractive Index

The refractive index n is simply a measure of the ratio of velocity of light in vacuum to the velocity in the medium v.

n= c/v The reason that we are able to see objects that are not

colored is because the changes of refractive index at the boundary result in bending of the light rays.

Techniques such as phase contrast have been used in microscopy to increase the contrast between different regions of biological organelles.

Objects such as single crystals or biological cells exhibit different refractive indices, depending on the direction of polarization of the light relative to the object.

Color and Refractive Index

RI for some substances

Light that is incident on a colored sample is partly absorbed by it => at certain wavelengths there is less intensity transmitted.

There is no breakdown in the law of conservation of energy.

The result of the absorption may appear as heat producing a temperature rise, imminescence in which a photon of the same or lower energy is emitted, chemistry that incorporates energy into altered bonding structures, or a combination of these.

The total energy change of the processes is always exactly equal to the energy of the photon that was absorbed.

Absorption and Emission of Radiation

The interactions leading to absorption of light are essentially electromagnetic in origin.

The oscillating electromagnetic field associated with the incoming photon generates a force on the charged particle in a molecule.

If the electromagnetic force results in a change in the arrangement of the electrons in a molecule, we say that a transition to a new electronic state has occurred.

The absorbed photon results in the excitation of the molecule from its normal, or ground, state G to a higher energy, or excited state E.

Absorption and Emission of Radiation

The excited electronic state has a rearranged electron distribution.

It can be described approximately as a promotion of one of the ground-state electrons to an orbital of higher energy.

This completes the absorption process, which usually occurs very rapidly, but the excited state is usually not stable for very long.

At ordinary intensities, the relaxation of the system back to the ground state is so rapid that the light produces very little change in the population of molecules in the ground state.

Absorption and Emission of Radiation

The dynamics of an atom or molecule placed in a radiation field can be explained using a simple model.

Consider any two states of a molecule, the states will differ in energy by an amount ΔE=hν.

If the energy separation is large compared with kT, virtually all molecules will be in the ground state in the dark at ordinary temperatures.

Radiation-Induced Transitions

Radiation Density

In the presence of a radiation field, this population distribution will be slightly disturbed.

We can characterize the radiation field by a radiation-energy density ρ(ν), which is the amount of energy near frequency ν and per unit volume of the sample.

I(ν) = c/n ρ(ν), where n is the refractive index of the medium.

Radiation-Induced Transitions

As a consequence of the introduction of the radiation field to an absorbing sample, three processes are included.

Absorption: the rate of this absorption process will depend on the number of molecules in state G, on the radiation density, and on the absorption coefficient of the molecule.

Stimulated emission: once molecules are present in the excited state, E, the radiation field can stimulate transitions down to the lower state, giving emission of radiation.

Spontaneous emission: molecules put into the excited state E by the radiation field are substantially out of equilibrium. Spontaneous relaxation processes restore the system to equilibrium.

Radiation-Induced Transitions

Einstein derived expressions for the rate of absorption, and of stimulated and spontaneous emissions of radiation.

The intensity of absorption depends on the difference in population of two states that are connected by a spectroscopic transition.

For transitions involving electronic or vibrational energy levels at room temperature, the energy difference involved (10-400 kJ/mol) is much greater than kT (2.5 kJ/mol); this means that only the ground state is significantly populated at room temperature.

Quantum Mechanical Description

In contrast, rotational or nuclear states, which give rise to microwave and NMR signals, have energy separations smaller than kT, such that ground and excited states are both significantly populated.

NMR is a significantly sensitive technique than UV spectroscopy because of the nearly equal populations of the energy levels.

The rates of stimulated and spontaneous emission are related by A = 8πhν3/c3

Quantum Mechanical Description

Spectroscopic Relations

We consider the return of excited states to equilibrium after absorbing energy as first-order reactions.

The inverse of the rate constant for return to the ground state, which for electronic transitions is dominated by the rate of spontaneous emission, defines the lifetime of the excited state.

These lifetimes can vary from 10-9 s(ns) for electronic spectra to seconds in NMR spectroscopy.

The lifetime has a profound effect on the shape of a spectral peak, which we can understand from the Heisenberg uncertainty principle.

Lifetimes and Line Width

We can prove a similar relation for the product of the time interval during which the energy of a quantum state is observed (Δt) and the uncertainty in its energy (ΔE).

ΔE Δt ＞1/2 (h/2π) Uncertainties in energy are directly related to

a width of a peak, Δν, by ΔE = h Δν; thus the greater the lifetime, the smaller is the uncertainty in the energy of a transition, and the narrower is the peak. This mechanism is often called lifetime broadening or homogeneous broadening.

Lifetimes and Line Width

If the sample is homogeneous, the fraction decrease in the light intensity is the same across a small interval dx, regardless of the value of x.

The fractional decrease for a solution depends linearly on the concentration of the absorbing substance: -dI/I = αc dx, where dI/I is the fractional change in light intensity, c is the concentration of absorber, and α is a constant of proportionality.

Beer-Lambert Law

If we integrate the equation, -∫dI/I = αc∫dx. ln Io/It = αcl.

It = Ioe-αcl

For measurements made with cuvets of different path lengths, the transmitted intensity Itdecreases exponentially with increasing path length.

A=log Io/It = εcl A= -log T

Beer-Lambert Law

Because absorption depends strongly on wavelength for nearly all compounds, we must specify the wavelength at which measurement is made.

This is usually done using a subscript λ, indicating the particular wavelength, as Aλ or ελ.

For a single substance at a specified wavelength, ελ is a constant, characteristic of the absorbing sample, and is independent of both c and l.

Beer-Lambert Law

The absorbance of a solution of more than one independent species is additive

For two components, M and N, Aλ = AMλ +

ANλ = εM

λl[M] + εNλl[N]

If measurements are made at two wavelengths where the ratios of extinction coefficients differ, the resulting equations, A1

= εM1l[M] + εN

1l[N], A2 = εM2l[M] + εN

2l[N]

Isosbestic wavelength = εMλ = εN

λ = εiso

Beer-Lambert Law

Absorption Spectra of cytochrome c

Most proteins and all nucleic acids are colorless in the visible region of the spectrum; however do exhibit absorption in the near-UV region.

These spectroscopic absorptions contain information relevant to the composition of these complex molecules, as well as about the conformation or three dimensional structure of the molecules in solution.

There is a distinctive absorption maximum at around 280 nm and a much stronger maximum at 190 to 210 nm.

The 280-nm band is assigned to π→π* transitions in the aromatic acids, the 200-nm band to π→π* transitions in the amide group.

Proteins and Nucleic Acids:UV

The spectra of nucleic acids in the same region show different characteristics.

An absorption maximum occurs at 260 nm, and a shoulder is seen near 200 nm on a background rising to shorter wavelengths.

These features are assigned to π→π* transitions and are characteristic of all nucleic acids.

Proteins and Nucleic Acids:UV

UV Absorption Spectra of Proteins and Nucleic Acids

UV spectra of selected amino acids

UV spectra of selected amino acids

The broad absorption centered at 192 nm is characteristic of the amide linkage in poly-L-lysine and increases the absorbance in this region by eightfold over that of the free amino acid.

All proteins have contribution to the absorption spectra in the region around 190 nm from the polypeptide backbone; however, they are accompanied by absorption contributions from certain of the side chains.

Polypeptide Spectra

The secondary structure of a protein describes which residues are in helices or other ordered conformations.

The figure on the right shows the effect on the poly-L-lysine spectrum resulting from raising the pH to induce helix formation and by raising the temperature, which converts the polypeptide to the β-sheet structure.

Secondary Structure

Changes in environment of the amino acids contribute to the spectroscopic changes that occur when a protein undergoes a change in secondary structure.

Most of the effects are electrical in origin because the spectra are sensitive to charge effects on the ground and excited electronic states.Local charge distributionThe dielectric constantBonding interactions, such as H-bondsDynamic coupling between different parts of the

molecule.

Origin of Spectroscopic Changes

By contrast with the amino acid units of proteins, the nucleotides that make up the nucleic acids polymers have similar absorption spectra.

The free base, the nucleoside, the nucleotide, and the denatured polynucleotide all have similar absorptions spectra in this region.

In general, polynucleotides and nucleic acids absorb less per nucleotide than their constituent nucleotides.

Native double-stranded DNA absorb less per nucleotide than denatured DNA strands.

Nucleic Acids

A decrease in absorptivity is called hypochromicity, or hypochromism; an increase in absorptivity is hyperchromicity, or hyperchromism.

For the melting of a double-stranbdedDNA, % hyperchromicity = [A(melted DNA)-A(native DNA)]/A(native DNA) x 100

%hypochromicity = [A (mononucleotide)-A (tetranucleotide)]/A (mononucleotide) x 100

Nucleic Acids

Absorption Properties of Nucleotides

The hypochromicity of the polynucleotides or nucleic acids relative to the nucleotides results primarily from interactions between adjacent bases in their stacked arrangement in the helical polymer.

The change upon denaturation to single strands or upon hydrolysis to the mononucleotides is easily measured and is often used to follow the kinetics or thermodynamics of the denaturation process.

The origin of the hypochromism is electromagnetic in nature.

Nucleic Acids

Chromophores contribute to the absorption spectrum in the visible or near-UV regions.

Rhodopsins consist of a colorless protein, opsin, to which the chromophore retinal is covalently attached.

In mammals the isomer 11-cis-retinal is attached to the ε-amino group of a lysine side of the opsinby a photonated Schiff’s base linkage.

Rhodopsins have intense broad absorption bands with maxima lying between 440 and 565 nm, depending on the specific chromophore and its environment.

Rhodopsin: A ChromophoricProtein

Solid line: purifies rhodopsin; dotted line: illuminated rhodopsin

Absorption spectrum of cow rhodopsin

The long wavelength absorption band (a π→π* transition) of isolated retinal in a variety of organic solvents occurs between 366 and 377 nm, which is the expected region for polyenes of this length.

The spectrum of rhodopsin after it has been photoconverted is very similar to that of retinal, the origin of the shift of this band to 500 nm or even longer wavelengths in unilluminated rhodopsin has been connected to the presence of a negative charge in the opsin near the C-12, C-13, and C-14 atoms in retina.

This indicates which part of the π system of electrons was needed to produce the large shift on binding (opsin shift).

Rhodopsin: A ChromophoricProtein

Most biological molecules have molecular asymmetry, or chirality.

These molecules are not identical to their mirror images.

Chiral molecules have distinctive properties.

Handedness : screw or nuts

Interact with polarized light

Optical Rotatory Dispersion and Circular Dichroism

Proteins in the α-helical conformation wind in a right-handed sense.

The handedness of the helices depends on the stereochemistry of the monomer units: the L amino acid isomer for proteins and the D sugar for nucleic acid.

The overall structure of biologically active proteins depend on additional determinants of tertiary structure that are not easily characterized.

Optical Rotatory Dispersion and Circular Dichroism

These are very important because they serve to make the detailed surface structure of an enzyme or antibody nonsuperimposable with its mirror image.

As a consequence, the active site of these molecules are able to distinguish between mirror-image substrate molecules, much as left-handed nuts will interact with only left-handed bolts.

Optical Rotatory Dispersion and Circular Dichroism

Chiral molecules can be distinguished by polarized light.

The optical properties usually measured are optical rotation, the rotation of linearly polarized light by the sample, and the circular dichroism (CD), the difference in absorption of left- and right-circularly polarized light.

The spectrum of optical rotation is known as optical dispersion (ORD).

Polarized light

Electromagnetic radiation can be described by an electric-field vector that oscillates with a characteristic frequency in time and space.

For unpolarized light, the electric vector may oscillate in any direction perpendicular to the direction of propagation.

For a large number of photons in an unpolarizedbeam, all directions are equally represented.

For plane-polarized light, the electric vector oscillates in a single plane that includes the propagation direction.

Polarized Light

Different types of polarized light

To an observer moving at the photon’s velocity, the electric vector appears to be oscillating back and forth along a line.

For this reason, plane-polarized light propagates so that the tip of its electric vector sweeps out a helix; right-circularly polarized light produces a right-handed helix.

To an observer moving with the photons, the electric vector appears to be moving in a circle, like the hands of a clock.

Polarized Light

The convention is that for left-circularly polarized light the electric vector moves counterclockwise as the light moves away from the observer; for right-circularly polarized light, it moves clockwise.

We can represents the electric vector of light in terms of its components. For light propagating in the z-direction and plane polarized in the x-direction, the x- and y-components of the electric vector for plane-polarized light are:

Polarized Light

Plane-polarized light;

Ex(z, t) = E0 sin2πν (z/c – t) = E0 sin2π/λ (z/c – t)

where c is the speed of light in a vacuum.

The x- and y-components of the oscillating electric vector are Ex(z,t) and Ey(z,t); En is the maximum amplitude of the vector.

Because the oscillating magnetic field is perpendicular to the electric field, its components are the same as the electric components, except that x and y are interchanged.

Polarized Light

If we specify the electric field, we do not have to consider the magnetic field explicitly because Maxwell’s equations characterize the magnetic field. The x- and y-components of the electric vector for circularly polarized light are:

Left-circularly polarized light:

Ex(z, t) = E0 sin2πν(z/λ – ct/λ)

Ey(z, t) = E0 sin2πν(z/λ – ct/λ + 1/4)

Polarized Light

Right-circularly polarized light;Ex(z, t) = E0 sin2πν(z/λ – ct/λ)Ey(z, t) = E0 sin2πν(z/λ – ct/λ + 1/4 ) The y-component of the light is one-fourth of a

cycle ahead of the x-component. The resultant of the components is an electric field

whose magnitude is constant, but which rotates counterclockwise or clockwise as it moves forward in space (along z) and in time.

Polarized lights can be produced through appropriate films (such as Polaroid) or crystals (Nicol prozm).

Polarized Light

Materials that are birefringent toward plane-polarized light must be geometrically anisotropic; they have different properties along different directions.

Linear birefringence occurs because the refractive index, and hence the light propagation velocity, is different for polarization planes oriented along different directions of the material.

In an absorption band of an anisotropic material, linear dichroism occurs, the absorbance is different for different orientation of the plane of polarized light.

Polarized Light

Substances that are optically active (chiral) exhibit circular birefringence, where circular birefringence is nL-nR, the difference between the refractive index for left-circularly polarized and refractive index for right-circularly polarized light.

The circular birefrigence results from an intrinsic property of the material that persists even though the orientations of the molecules are random.

Chiral molecules also show circular dichroism(AL-AR), a difference in absorbance for left- and right-circularly light.

Polarized Light

Optical rotation by chiral results from and is a measure of their circular birefringence.

The term optical rotation comes from the usual experimental measurement procedure.

If a plane-polarized light is propagated through a transparent chiral sample, the emerging beam will also be plane-polarized, but its plane of polarization will be rotated by an angle of φ with respect to the direction of the polarization of the incident light.

Optical Rotation

If the rotation is clockwise as seen by an observer, φ is positive; counterclockwise rotation is assigned a negative value of φ.

Optical Rotation

The origin of optical rotation can be made up of two opposite circularly polarized but in-phase components.

Because the chiral sample is circularly birefringent (nL≠nR), the two circular-polarized component electric vectors will propagate through the sample with different velocities (c/n), and they will have different wavelengths λm in the medium (λm=λ/n).

As a consequence, one of them becomes advanced in phase with respect to the other.

Optical Rotation

The resultant light, which remains plane polarized, becomes rotated progressively upon passage through the sample.

When it emerges from the other side, it has undergone a rotation.

Rotation (rad/cm) = φ = π/λ (nL-nR) It is given per centimeter of pathlength in the sample. The rotation is measured by placing a polarized element

(suitable crystal or Polaroid) called an analyzer in the emergent beam.

By turning the analyzer so that it is crossed to the direction of polarization of the emergent beam, the intensity is extinguished, and the angle of rotation can be measured.

Optical Rotation

Circular dichroism, analogously, results from a different absorption of left- and right-circularly polarized light by a sample that exhibits molecular asymmetry.

A simple expression of the circular dichroismis given by ΔA = AL-AR , where AL and AR are the absorbance of the sample for pure left-and right-circularly polarized light, respectively.

Circular dichroism may be wither positive or negative.

Circular Dichroism

Circular dichroism occurs only in a region of the spectrum where the sample absorb, whereas circular birefringence occurs in all wavelength regions of an optically active substance.

Circular Dichroism

The optical rotation of a nucleic acid or protein is the sum of the individual contribution from the monomeric units and the contribution from their interactions in the polymeric arrangement.

By comparing the circular dichroism (CD) of the native polymer to that of its monomeric units, their separate contributions can be determined experimentally and substracted from the optical activity of the intact polymer.

The difference then gives the contribution from the interactions in the native polymer conformation.

Circular Dichroism of Nucleic Acids and Proteins

CD of double stranded DNA and RNA

compared with their components

The dramatic difference between the solid and dashed curves in the figure in the previous page demonstrate that the principal contribution to the CD of the nucleic acids arises from interactions in the polymer.

The synthetic polynucleotide poly(dG-dC)·poly(dG-dC) is a double stranded helix with a sequence of alternating guanine and cytosine bases on each strand.

Circular Dichroism of Nucleic Acids and Proteins

CD of synthetic polynucleoidpoly(dG-dC)·poly(dG-dC)

At high salt concentration, its unusual CD suggested that the helix could be left-handed.

Because this was the first experimental indication of a left-handed DNA helix, there was much skeptism.

CD is a powerful probe of nucleic acid secondary structure.

Circular Dichroism of Nucleic Acids and Proteins

Several forms of secondary structure are present in native proteins.

They include α-helix, parallel and antiparallel β-pleated sheets, and random coil.

By measuring homopolypeptides under conditions in which the conformation is uniform throughout the polymer, Gratzerprepared plots of ORD and CD spectra in the peptide region that show the range of value encountered for polypeptides of different amino acids.

Circular Dichroism of Nucleic Acids and Proteins

CD and ORD of homopolypeptidesin the random coil.