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by: Jaden Stiedemann


Marketplace > Rice University > Biological Sciences > BIOS 481 > MOLECULAR BIOPHYSICS I
Jaden Stiedemann
Rice University
GPA 3.78


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Class Notes
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This 8 page Class Notes was uploaded by Jaden Stiedemann on Monday October 19, 2015. The Class Notes belongs to BIOS 481 at Rice University taught by Staff in Fall. Since its upload, it has received 30 views. For similar materials see /class/225026/bios-481-rice-university in Biological Sciences at Rice University.

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Date Created: 10/19/15
Introduction to Spectroscopy Purpose of Course To provide an introduction to a number of physical techniques that are generally acknowledged to be of value in biological research As biochemists and biophysicists the focus of our interest is broadly de ned as quotHow do living cells carry out their functions quot These functions are usually speci c and detailed some examples How does cytochrome c oxidase couple electron transfer to proton transport How does the interaction of actin and myosin lead to muscle contraction What controls the various conformational states of DNA What are the consequences of a photon impacting a rod or cone in the retina What are the structural consequences of adrenaline binding to its receptor The answers to these and similar questions invariably require a knowledge of the structure of the responsible molecules or supramolecular structures or organelles and thus much 0 Biochemistry can be seen as an investigation of biomolecular structure and the relationship of this structure to biological lnction This is usually called the structurefunction paradigm Unfortunately biosystems have two properties that complicate this undertaking a Limited stability restricts the techniques that can be used We need i a pH near neutrality ii a temperature close to ambient iii and the solvent is limited to water b Most systems of interest are not readily crystallized Xray analysis the method of choice for structure determination requires high quality crystals and the availability of heavy atom derivatives if the structure is of a new protein Thus this technique may not be applicable Modern nmr has the potential to obtain data on protein backbone folding comparable to Xray crystallography ie to about 02 nm resolution particularly if 13C and 15N substituted proteins can be prepared However nmr is currently restricted to proteins of mass lt 20 kDa Moreover to collect the necessary data requires about two weeks of uninterrupted data acquisition many pure proteins denature when maintained at room temperature or above for this length of time It is thus apparent that we need methods that allow us to circumvent the intrinsic limitations of the biological systems methods that can complement xray crystallography and nmr Why Spectroscopy Experience has shown that the most reliable structural and dynamic information on molecules of biological interest on subcellular organelles and on cells is obtained by probing these systems with quotlightquot ie with electromagnetic radiation of a wavelength selected because it reveals the property to be studied Thus quotlightquot provides a window into the properties of matter in this case molecules such as proteins nucleic acids and metabolites and of more complex structures such as membranes In particular this probe is usually able to provide both static e g as from Xray and dynamic insights into biostructures Il In general a particular method provides quotlimited informationquot and will either provide extremely detailed information about a small region of the protein or macromolecule or low resolution data about the molecule as a whole Of particular importance is that these methods allow us to study changes in structures as molecules implement their biological function They often provide the high time resolution necessary for functional studies ie for mechanism of action In favorable cases processes that occur within picoseconds psec 103912 sec can be studied Finally these spectroscopic techniques are nondestructive ie the sample is reusable Traditional ir measurements were not applied to biological samples because the material to be studied was first subjected to procedures which denature proteinsrendering the measurement invalid Thus vibrational spectroscopy of biomolecules has only recently become routine using either the Raman or FTIR approaches See Ch VI which overcome this limitation It should be appreciated that the most desirable circumstance is to have detailed structural information such as that provided by Xray crystallography AND the specific information provided by spectroscopy These two areas of research are by no means mutually exclusive and the most rewarding progress is made when both kinds of information are to hand Which Spectroscopy here is some bias in the selection of techniques for this course as will be apparent from the table of contents Other methods could easily be included were more time available Because the emphasis in these lectures will be on the interaction of light with matter we begin with a brief Review of Electromagnetic Radiation Electromagnetic radiation is conventionally described by the wave model in which the radiation is represented as oscillating electric and magnetic fields Fig 11 Th se waves vary in both space and time as depicted in the figure By convention the wave advances from le toright zdirection in this figure An observer at 2 looking at the wave approaching will see the electric component E oscillating in a single plane conventionally assigned to the vertical XZ plane and the magnetic component H not shown oscillating in phase in the plane perpendicular to E in this case the horizontal yz plane Remember that this is only one such wave normally a light source consists of many waves each with its E and H oriented in an unique direction in the xy planethe beam is unpolarized Note also that the energy content of the E and H components is the same The wave is characterized by several quantities The most familiar is the wavelength 7 the separation in meters between two equivalent points e g between 2 peaks Because many wavelengths of interest are of order 10399 meters a common unit is the nanometer nm visible light falls in the range 400700 nm An older unit still very much in use is the angstrom A 1A 01 nm 10398 cm an atom is roughly 1A in diameter 12 31 05 l0 Fig 1 1 Quantities related to 7 are i The wavenum ber v39 the number of waves cm lMcm this is called the kaiser and has the unit cm39J 1000 cm391 l kK is the kilokaiser The symbol v is often written as v with a bar over it It is very common to interchange nm and cm39l a simple aid for this is the rule No of nmNo of cm39l 107 So 500 nm 20000 cm39l ii the frequency v the number of oscillations per sec c cm sec3917tcm where c is the velocity oflight 3 X 1010 cmsec 500 nm 500 X 10399 m 5 X 10395 cm 6 X 1014 Hz iii the energy of the light E hv hcX hcv39 h Planck39s constant 6623 X 103927 erg sec per photon or 6623 X 103934 J s This energy is the energy per photon the amplitude of the wave is speci ed by the number of photonssec in the beam Thus the amplitude of the beam does not change smoothly but in increments these increments are of course very small and are not apparent on a macroscopic scale A mole of photons is called an einstein Usually when we talk about the energy in a wave of some 7 we implicitly mean the energy in an einstein of that 7 Thus the energy in a given monochromatic beam is given by No of photonsEnergy per photon ak a wavelength Useful numeric relationships are 1000 nm 10000 cm391 286 kcaleinstein 124 eV 197 X 103912 erg photon Radiation that consists of a single wavelength is called monochromatic if it is oriented in only a single plane as in Fig Il it is called linearly or plane polarized A linearly polarized beam is composed of two counterrotating circularly polarized beams see Fig 3 of AppendiX I If all the monochromatic waves pass through their maXima at the same moment ie they have the same phase they are called coherent For simplicity we usually use sketches in which the waves are 13 monochromatic linearly polarized and coherent Waves from most real light sources are only approximately monochromatic usually unpolaiized and almost never coherent An overview of the electromagnetic spectrum 43 55 Visible 71 x1014Hz vacuum nmr epr uv Xy rays a IogvHZ 6 7 8 9 lO 1 12 l3 14 15 16 17 18 19 20 L 3m 3cm 30 um 300 nm 03 nm Visible 700 550 400 nm 14300 18200 25000cm1 g E 8 e E 05 o gt Fig 1 2 1 4 The interaction of light with matter The response to the electromagnetic radiation impinging on a molecule can be divided into 3 common categories scattering absorption and emission This is illustrated for the particular case of the absorption of ultraiviolet or visible light UvVis where the various processes are conveniently summarized in a Jablonski diagram Fig 13 S2 Fig 13 J ablonski Diagram We define G the Groundstate this is the equilibrium state in the absence of any radiation Sn are the n excited singlet states of the molecule nl23 these represent states in which a loosely bound valence electron has adopted a new quotshapequot in response to the light beam without any change in the orientation of its spin The ground and excited states are called stationary states as they are either stable G or metastable S For example in the hydrogen atom the sole electron is in a ls orbital and it can be excited into one of the 2p orbitals the change in shape is obvious In molecules the ground state is usually the highest occupied molecular orbital HOMO and the rst excited state SI is the lowest unoccupied molecular orbital LUMO When exposed to an oscillating electric eld the electron cloud of the molecule distorts rhythmically in response to the oscillations When the energy in the beam is smaller than that needed to drive the molecule from G to one of the Sn ie into an excited state the distortion yields a quotVirtual Statequot a non stationary state that is not described by a single wavefunction but can be 15 described as a linear combination a mixture of initial and nal wave lnctions e g G 1 with the relative proportion of 1 increasing as the distortion gets increasingly large When the energy in a photon is comparable to the energy difference 81 minus G the molecule may be driven into the metastable state represented in this instance by 1 This occurs when allowed by a selection rule a quotspectroscopy specificquot rule that controls whetherornot this transition has a high probability The excited states are called singlet states because the electron that has been promoted maintains its original spin orientation with low probability an electron in S can reverse its spin and pass into a Triplet state In UvVis electronic transitions from G to the various substates of 1 occur in atime comparable to 103915 sec the reciprocal of the frequency of visible light responsible for the transition Immediately following promotion the excited molecule is in the equilibrium nuclear configuration of the ground state FrankCondon principle electron motions are very much more rapid than nuclear motions and over the next picosecond the molecules nuclei change to the equilibrium geometry of the excited state In general we can identify four fates to the excited molecule Fig 13 1 The excited molecule leaves the virtual state or Sn and returns immediately to precisely that state from which it originated The photon that is emitted has exactly the same energy as that which was absorbed though its direction of propagation may well have changed This is elastic or Rayleigh scattering Immediately means synchronous with the frequency of the exciting radiation this is a time shorter than 1 vibrational oscillation If the material is ordered eg a crystal and the wavelength is comparable with the size of an atom then xray crystallography can be conducted7 as is described in the other half of this course 2 During the 103915 sec in either the virtual state or Sn the excited molecule may undergo a vibration this has a low probability e g 001 before or during its return to the ground state so that the emitted photon has an energy that differs slightly either greater or smaller from that which was absorbed the difference being the energy associated with the vibrational transition Again this is an quotimmediatequot event It is the inelastic or Raman or Stokes scattering Typically the emitted light falls within i 3000 cm391 of the energy of the exciting light This shift can be measured by Raman spectroscopy and allows the vibrational spectrum of the molecule to be studied 3 The excited molecule stays in the excited state for a time of the order 1 nsec during this time many vibrational events occur and regardless of the initial excited level 1 2 the molecule finds itself in the lowest vibrational level of 81 before emission occurs Emission is to any vibrational level of G The emitted photon has a significantly smaller energy than the photon that was absorbed originally and light of substantially longer wavelength is emitted This delayed emission is called fluorescence 4 The excited molecule stays in the excited state for l nsec or longer as in 3 but returns to the ground state by processes that do not involve the emission of light These processes are called internal conversion typically arising from collisions with the solvent or quenching from collisions with some solute or intersystem crossing singlet gt triplet conversion and are the principal processes responsible for the UvVis phenomenon The triplet state is relatively longlived msec sec and can itself emit light called phosphorescence or also return to the ground state by internal conversion I6 When the incident light beam is reduced in intensity without any change in direction then we have absorption The frequency dependence of the magnitude of this absorption ie the spectrum is an fundamental experimental quantity Most types of spectroscopy provide data of this form 5 An additional possibility is that the light causes a chemical reaction This is called photochemistry a prime example is photosynthesis Typically light of wavelength lt 1000 nm is needed for photochemistry ie light of energy comparable with the strength of chemical bonds Some people classify all of the first 4 processes just listed as spectroscopy However my preference is to omit Rayleigh scattering from this category though I admit that this is a personal prejudice ie I do not consider Xray crystallography to be spectroscopy although there are versions of the crystallographic technique e g MAD that involve absorption of the radiation In principle the shape of an absorption spectrum should be described by the Lorentz formula the reason for this can be found in the optional background material present in appendix II The Lorentz lineshape Lv is given by Lv iLoii 1 1 1 v v0r2 where Lv is the spectral amplitude at frequency v L0 is the amplitude at the absorption maximum which occurs at frequency v0 and F is the halfwidth of the curve when the amplitude has fallen to onehalf the maximum value at v either greater and smaller than v0 F is called the Half Width at Half Height HWHH As the spectrum is symmetric about v0 the HWHH can be measured on either side of the curve Frequently the observed absorption curve consists of a number of overlapping Lorentzian curves that can not be separated either for fundamental reasons or for limitations in the instrument Then the observed absorption curve approximates a Gaussian lineshape GV Go eKP1112VVo 2 12 One o en sees the ln2 omitted from the Gaussian formula whereupon F is replaced by 12F symbolized as A the width when Gv 037G0 Go e If the G0 is replaced by 21112 then the area under the Gaussian curve is 1 Fig I4 shows the relative shapes of the Lorentz and Gaussian curves small but occasionally important differences will be apparent The curves were adjusted to have the same heightconsequently they have different areas Why the emphasis on Magnetic Resonance in this part of the course 1 Many people believe that this is the single most valuable spectroscopic technique available today for determining structures and that its importance can only increase in the future 2 The connection between result and theory is easy to make and hence structural and dynamic information is readily and reliably obtained without extensive training in quantum mechanics I7 of Solid line is gaussian Broken line is Lorentzian Absorbance I 200 220 240 260 280 300 320 340 360 380 400 Wavelengthmm Fig 1 4 Generic Uses Many experiments are 1 quotJ 39 J r J ofthe r r39 method and can be performed with any of them Thus many exp riments that are carried out using spectroscopic methods do not depend upon a detailed knowledge of the physical principles of the selected method For example an important area of biochemical research involves a characterization of the interaction of two or more molecules eg the binding of enzyme substrate antigen antibody repressor nucleic acid hormone receptor etc To characterize any one of these interactions all one needs is a spectral property of one or other species that changes upon binding of the second species Frequently several methods can be used to monitor these changes and one39s choice of which to use may often be made for relatively trivial reasons It is of course prudent that such measurements be performed under the guidance of someone who is familiar with the principles of the selected method Even apparently simple methods might have limitations or potential artifacts that can undermine the significance of your experiment The CcO example However the emphasis this semester will be the use of spectroscopy to provide more illuminating insights into biomolecules In particular the focus will be on how these methods can provide specialized structural information in the absence of an Xray structure General Texts i Campbell and Dwek Biological Spectroscopy Out of print Selected material has been put on reserve ii Cantor and Schimmel Biophysical Chemistry On reserve Appendices I and II are more extensive discussions on Waves and the Forced Damped Harmonic Oscillator Any material in these appendices that is not covered in class will not be tested 18


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