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by: Marjorie Hahn


Marjorie Hahn

GPA 3.95

C. Bustamante

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C. Bustamante
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This 89 page Class Notes was uploaded by Marjorie Hahn on Thursday October 22, 2015. The Class Notes belongs to PHYSICS 177 at University of California - Berkeley taught by C. Bustamante in Fall. Since its upload, it has received 19 views. For similar materials see /class/226693/physics-177-university-of-california-berkeley in Physics 2 at University of California - Berkeley.

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Date Created: 10/22/15
Single Molecule Manipulation Methods Methods of Single Molecule Manipulation 1873 The Dutch scientist JD van der Waals proposes his theory of continuity between the gas and liquid states of matter All properties of matter depend on the strength and the direction of the forces that molecules exert on each other 1889 Svante Arrhenius suggests that the rate ofa chemical reaction is determined by the rate of attainment of a strained high energy state or transition state along its reaction coordinate Bulk Methods vs Single Molecule Methods Bulk Methods Robust but afford little control to investigate forces developed in the course of a chemical reaction Measured properties are time and population averages Smooth varying Fluctuations are mostly cancelled out Picture An idealized molecule with welldefined dynamics Population is assumed to be homogeneous unimodal distrib Bulk Methods vs Single Molecule Methods Single Molecule Methods Molecules display a fast instantaneous dynamics Behavior appear random and stochastic Fluctuations are predominant Molecules are seen to coexist in various states Populations are multimodal Molecules can be found in states far from the mean of the population extreme states Why single Molecule Methods The microscopic view matters in describing the cell interior Many cellular processes such as Chromosome replication and segregation DNA transcription recombination and RNA translation Are often carried out by a few molecules Far from displaying smooth dynamics these process are stochastic in nature Why single Molecule Methods One molecule in an E coli cell about 1 um3 in volume is at a concentration of 16 nM Why single Molecule Methods The advent of methods of single molecule manipulation has made it possible for the first time to Measure the forces that maintain the 3D structure of macromolecules Characterize the stressstrain relationships of molecules Measure the forces generated in chemical amp biochemical reactions Investigate timeaveraged and timedependent fluctuations Characterize the dynamics of molecular motors Exert External forces and torques to alter the extent and fate of chem Rxns Single Molecule Manipulation Experiments Two features distinguish single molecule manipulation experiments From their bulk counterparts 1 The unique role played by forces or torques as direct observables of the experiment 2 The importance of fluctuations Together this area of research can be called Mechanochemistry In Biochemistry Mechanochemical processes often involve the formation or breaking of covalent bonds but also of a large number of highly stereo specific weak interactions Processes as diverse as Protein folding DNA elasticity Proteininduced bending of DNA The stressinduced catalysis of enzymes The dynamics of molecular motors Inducedfit molecular recongnition involve all the generation of stresses and strains along their reaction coordinates Technical Requirements I Methods to locate molecules a microscope that works in qu39g Optical Fluorescence labelling Particle ta ging b Probe Microscopes STM SFM AFM SN M II Means of manipulating or acting on single molecules a Mechanical transducers soft cantilevers bendable micropipettes movable rigid micropipettes etc b External Fields Electric magnetic and photon fields lll Methods of spatial detection a diffractionlimited displacement centroid displacement b optical lever detection c optical interference Methods Capabilities and Applications Table i i Overview of singlemolecule manipulation methods Cantilevers ii i 0397 10 0001100 F39roteil39ripolysaccharidesm High spatial resolution 0nd strengthFm Commercially available B Fiuw eid39 iii39iMU39g 1CquotE rial DNA dynamics RNA polymerases5 Photon ileld iD39W i 0quot 1Cquot5 lO i 04 Protein motors Speci c manipulau39on Protein unfolding High lorce resolution um Iii mm limil if lurrr ranm X i r i mum rim i Difficults Inherent to Single Molecule Work Are all molecules identical Molecular behavior depends a initial conditions b effect of boundaries restricted config space if Eint kT trapping effects if Eimgtgt kT conf changes Consequences Date tends to segregate into classes of similar behavior gonvenient to omogen ous 9 reduce the of classes by using more initial conditions and minimizing boundary effects a Laser I a I Lens Q Canmever ngm Applications b g 4 Postuonrsemsmve deeclor aw mmpax SFM m y w A 55 200 pN 20 nm that electric scanner 1 m sta e 2X1emoecue he canmeverv Further r I mm the SFM 1 15m 5 Applications Bendable mlcloneedl Myos n Actln lament molecules Flgure 2 Using a microneedle to measure the force of myosin acting on a A ehdable microneedle coated in myosln heads not shown catches an actin lament ans lament is brought into Contact with a glass coversllp coated in myosin molecules In the presence of ATP the myosin drags tne acun lament across the coverslrp and generates a force on the mlcroneedle which is observable by videor uorescence mlcroscopy A Iications chvoneedle Magnetic bead Romung magnenc new Evanescent eld Magnetic bead DNA Dwganudig connector Biounavidm Conneclor Biotxnravtdm Conneclols 39 39 39 The motion of x mmonaed e25 mannenr for e 39 V is quot M The Applications Laser light 5 39 RNAPF y p I A AhM lt hmm wima primEE u FAsme DNAP n 5 am A m Adm m the movement ofthe enzyme over the template Timelength and Force Scales of Experiments Time Scale The time scale in single molecule exps ss typically submsec Thus cyclic process on the third level can be resolved but elementary and intermediate processes are averaged out Events in single molecule manipulation experiments result form a large number of stochastic steps that are not directly observable but that influence the microscopic dynamics of the overall process As a result all processes can be described as random walks or diffusions in the parameter space of the system Length Scale The length scale is set by the type of process and the size of the molecules under study Range Angstroms Small motions in a protein Nanometers Most processes Microns Stretching of a long DNA Single molecule manipulation instruments must be able to make and or measure displacements of nanometers or better Force Scale Forces can be Inertial Dissipative frictional Related to a potential of some sort On single molecule experiments inertial forces are usually negligible compared to frictional forces The low Reynolds number regime JZLE Expl For a 1 micron silica bead in water taCC is 107 s 5 well below the time res of m 7 W 7 most instruments y fric coeff and m sphere s mass Range of Forces Typica forces are in the picoNewtons regime 4 Finer e 111 1994 h Svoboda ML1993J C Yin 21111995 d Chilkori e 111 1995 C Smith 2121 1992 f Smith ecaL 19 E Radmacher 2 111 1994a h Svobuda and Block 1994b Force required to stall motion distance stretched or compressed to generam the listed force Means of Manipulating Single Molecules External Fields Electric Magnetic flow and photon fields can be used effectively to exert forces on molecules Choice depends on magnitude of the force desired degree of control of force needed Fields make it possible to act on molecules at a distance Can be an advantage or a disadvantage lts possible to manipulate many molecules simultaneously but their lack of locality makes them less selective Electric Fields Most macromolecules are charged in solution they can be acted on by electric fields Typical design driver electrodes probe electrodes connected to a high impedence voltmeter and separated by a M7 a known distance V Migration DNA Molecules During Gel Electrophoresis QuickTimeTM and a Sorenson Video decompressor are needed to see this picture T4 DNA Difficulties Current may cause Heating of the buffer Polarization of the electrodes due to localized ion build up Electroendosmosis EEO near charged surfaces like glass Glass bubbles at the electrodes Arbitrary fields can be used as long as the electrodes are placed close enough that the potential difference remains below 1 volt the dissociation potential for H20 Difficulties Current may cause Heating of the buffer Polarization of the electrodes due to localized ion bUIld up I Electroendosmosis EEO near charged surfaces like g ass Glass bubbles at the electrodes Arbitrary fields can be used as long as the electrodes are placed close enough that the potential difference remains below 1 volt the dissociation potential for H20 Efields are easy to control and measure But the forces exerted on molecules are not so easily determined Ex DNA in solution Nonhomogeneous Efields Dielectric objects immersed in liquid will develop an induced dipole moment P in an external field E If the field is inhomogeneous they will be attracted to the field with a force FVEOP8VEOE s is the dielectric polarizability of the object relative to the fluid EleCtFO39mtat39On As E rotates w ang freq 0 P will lag by an angle 03 amp E atorque MPxE s E2 Sin 03 will be generated Electrorotation cont For 0 in MHz the applied torque is independent of orientation since it is averaged out over all configurations Method used by S Bacterium Washizu etal IEEE Trans lnd Applications 29 286 1993 and Berg and Turner Biphys J 65 2201 1993 to rotate bacterial cells attached by a single flagella to a glass surface Applied known torques to follow the performance by a single flagellum aiding or opposing this rotation Magnetic Fields Magnetic fields are easy to generate and to control Are ideal to produce small forces fN Method tether molecules to magnetic beads commercially available with a ferrite Fe203 core expose them to an inhomogeneous magnetic field The magnetic force acting on the object is F V01 B Typical force ranges are between 10 fN to 10 pN with commercial beads and permanent magnets DNA Assembly Using a DNA Fishing Line QuickTimeTM and a Sorenson Video decompressor are needed to see this picture DNA Elasticity A sme View Smith et al Science 1992 a and Posmans from Mag o Beads Pngtlllns frnm Mag DNA Elasticity Magnetic beads often contain a preferred magnetization axis These beds lock at a fixed angle with the field This property can be used to supercoil by over or undertwisting a single molecule of DNA Strick et al 1996 Flow Fields Controlled flows can also be used to exert forces on molecules or on molecules tethered to beads Often the force acting on a molecule can be directly calculated from the Stoke s force acting on the bead F 6mrv where is the viscosity of the fluid r the radius of the bead and v the flow velocity This form is often modified by the hydrodynamic coupling between the bead and the surfaces of the microchamber 2x9r F26 1 lI ml 16d JV Lorenz Handbuch der Physik 1907 1 9r8d Experimental Test 22 I o be I in 4 iv 39o 20 4o 60 80 13900 Chamber depth um Smith et al Science 1992 O Reversible Pulling of P5ab Handle behavior is wellpredicted by QuickTimeTM and a Animation decompressor Force are needed to see this picture kT 1 x 1 P 4 x2 Z7 ssds e L Busfarnan39fe at al Science 39 1599 1994 ssds Extension nm Bistable Length with ConstantForceFeedback length QuickTimeTM and a Motion JPEG A decompressor are needed to see this picture QuickTimeTM and a Motion JPEG A decompressor are needed to see this picture QuickTimeTM and a Motion JPEG A decompressor are needed to see this picture time Directly observe k1 k1 and Keq as a function offorce underexp conditions Mechanical Transducers Cantilevers and bendable micropipettes can be used to exert and measure forces on molecules The magnitude of the forces can be readily obtained from the deflection of the mecanical transducers if their force constants are known Typical cantilvers have force constant in the range of 1 001 nNnm while soft bendable micropipettes are about typically 100 to 1000 times softer Mechanical Transducers Advantages Mechanical transducers act locally and are ideal to manipulate macromolecules on the small side of the spectrum Because of their dimensions cantilevers have better time response than optical tweezers or soft bendable micropipettes as indicated by their rather high corner frequencies me Ky where K is the force constant of the cantilever and y its friction coefficient see below Disadvantages Dificult to calibrate Balancing Signal Noise and Time Resolution At temperature T a linear system such as a cantilever experiences a mean square displacement noise ltAx2gt given by the Equipartition Theorem ltAx2gt K Where K is the force constant of the cantilever and k is Boltzmann s constant Correspondingly its mean quadratic force fluctuation will be AF2gt KkT Balancing Signal Noise and Time Resolution Note that a sort of Uncertainty Thermal Relation applies for such systems since the product of the root mean square fluctuations in position and force is equal to the thermal energy ltAF2gtU2 ltAx2gt12 Thus the stiffer the mechanical transducer the smaller its position noise and viceversa Fluctuations are not spread uniformly over all frequencies however The spectrum of fluctuations is determined by the proportionality that exists between the ability of the linear system to absorb thermal energy and its ability to dissipate it by friction Balancing Signal Noise and Time Resolution This result is embodied in the socalled Fluctuation Dissipation Theorem The mean quadratic displacement of a linear device per unit frequency at frequency w is H 2 2kT Axwgt ywfw2 where as before y and DC are the friction coefficient and the corner frequency of the device A 1 um diameter bead in a typical optical trap has a me 1000 Hz whereas that of a 100 um long 10 um wide cantilever is 6000 Hz Balancing Signal Noise and Time Resolution Thus a transducer with higher corner frequency makes it possible to take more data in the same amount of time Moreover since ltAx2gt IltAx2wdw Kidwz 062 332 K Signa39 Thus for the same K the total area under N the power AreakBTm h spectrum is B lch litmplitude2 H24 CJ2 Frequemzjr the same Balancing Signal Noise and Time Resolution Measurements are often performed in a narrow band bandwidth B around the frequency of the signal Suppose that the signal to be measured is a force developed b a molecular motor The signaltonoise in that measurement for B ltlt 0 is B Thus for the same K and the same B the signalnoise ratio of the means will be higher for the transducer having 5 mm ma Frequency EEqEEEF comer Amplitude Hz Balancing Signal Noise and Time Resolution that is for the one having the smaller friction coefficient or for the one possessing the smallest dimensions This is the rationale for the development of minicantilevers whose stiffness are comparable to regular cantilevers but whose y S are significantly smaller and their corner frequencies correspondingly larger F 1Wm Notice also that the SN ratio is independent of the stiffness of the transducer as K decreases the noise increases exactly as fast as the signal Thus a softertransducer does not provide higher Sn than a stiffer one Balancing Signal Noise and Time Resolution Finally the SN can be increased by reducing the bandwidth and therefore the timeresolution of the measurement but this approach is ultimately limited by the frequency of the biological process F 127kTB ArealtBTncJ Amplitude2 H 1 R Areakglm h I B mm m z Frequencyr Physics 177 Biophysics Professor Carlos Bustamante prams J8 vaupnwsacchavme s fs thmsnme VJ 1 4 V u wwmm 77 Pemmag ycan FxguvsiE omsssemm Layman aaaimanymman I An Mamalian Cell eenmmes 9mg apparams Free r 1 nbmmes r an39 A 139 V sxgwl Emmam w vsncumm Lysosame CeH membmne Rough en np asmlc mucumm mum mmmcnawmammu m SMMWMW mm mm PMHMNL Cnnvm mm W 39mndsww wquot m m nacmm wmmmmwwmm s m 1 rawmwmmu wwwmms s unumwa mwmm cNHwhm R m me mv ammo Amnws hw mm mud Biological Systems and Biochemistry Complexity The parts that carry out these functions in biological systems are there for a reason All biological systems must Extract store and transform energy Selfreplicate store and preserve the information from one generation to the next Must be highly structured complex macromolecular assemblies Adapt to changing conditions control of function and evolution The strategy of biochemical studies is 6 g wyf m o we Take things apart and put them back together to determine What are the parts How these parts t together How do they work Hierarchy of Complexity Animals and Plants as Organisms Specialized Organs Specialized Tissues Organelles Macromolecular Assemblies Macromolecules q Simplest Molecular Building Blocks Components of a Living Cell How many components are needed to build a living cell The genome project has started to provide answers to what is the minimal complexity compatible with the living state The simplest cell By comparison Mycoplasma genitalium E coli Eubacterium 468 genes only 4289 genes 39 Intercellular parasite Yeast Saccharomyces cerevisiae Can be cultivated in enriched medium N 6300 genes Humans Estimates 30000 35000 genes 10000 are purely regulatory CompleXity grows exponentially with the number of parts in machinery Pratsimz J Mechanisms Metabolism Biophysics We seek a quantitative description of biological processes and phenomena A description founded on fundamental physical laws Molecular Biophysics Cellular Biophysics Organismal or Systems Biophysics Biophysics at Berkeley Thermodynamics Review l Formalism to keep track accounting of energies 2 Predict if a process is spontaneous or not 3 How much useful energy can be obtained from a chemical rxn as it proceeds from Initial Conditions Equilibrium The laws Thermodynamics Energy conservation Internal energy E Total energy content of a system It can be changed by exchanging heat or work with the system Heatup the system Cooloff the system Do work on the system Extract work from the system WI AB 2 q W PAV W Thermodynamics A use concept is ENTHALPY H H E PV 0 0 At constant AHZqP39 VXBAltIV pressure AE Only PV work involved w39 0 as in most biological systems So At constant pressure the enthalpy change in a process is equal to amount of heat exchanged in the process by the system T Thermodynamics Wehave HEPV 0 0 in biological AP O AH AEBKGy systems AVNO AH E AE at AP O and since AV z 0 Q How is this energy stored in the system A 1 As kinetic energy of the molecules In isothermal AT O processes this kinetic energy does not change 2 As energy stored in chemical bonds and interactions This potential energy could be released or increased in chemical reactions Thermodynamics Entropy and Disorder Energy conservation is not a criterion to decide if a process will occur or not Examples THot TCold gt T q AB AH O This rxn occurs in one direction and not in the opposite 0 O l 00L39LI O these processes occur because the nal state with T T amp P P are the most probable states of these systems Let us study a simpler case tossing 4 coins Thermodynamics All permutations of tossing 4 coins Micro co ie states Macroscoplc states S p 1 way to obtain 4 heads 3 4 ways to obtain 3 heads 1 tail 39 I HTHT 4 6 ways to obtam 2 heads 2 talls gt 6 I THHT pg 4 ways to obtain 1 head 3 talls T T H H 1 way to obtain 4 tails T H T H 6 The most probable 4 4 state is also the 2 H 2 T most disordered 1 3 H 1 T 1 H 3 T 1 I 4 H 0 T 0 H 4 T I Thermodynamics In this case we see that AH O ie there is not exchange of heat between the system and its surroundings the system is isolated yet there is an unequivocal answer as to which is the most probable result of the experiment The most probable state of the system is also the most disordered ie ability to predict the microscopic outcome is the poorest Thermodynamics A measure of how disordered is the nal state is also a measure of how probable it is 6 2H2T E Entropy provides that measure For Avogadro number s Boltzmann of molecules S E kB 1n W Number Of S VIAvogadr0kB In W microscopic ways in which MOIeCUIar Bolt mam a particular R gas 0011513311113 Z Entropy outcome Therefore the most probable conStant macroscopic outcome maX1m1zes entropy state can be attained of 1solated systems AS gt O spontaneous Criterion for Spontaneity AS lt 0 n0nsp0maneou5 Thermodynamics Entropy of Dilution AH O 0 39 39 39 39 39 39 39 39 no interaction among 39 39 o o o sucrose molecules to l M Sucrose 01 M Sucrose begin With For 1 M sucrose water 55M For 01 M sucrose 54 water 55O water 55 slots 550 slots 1 sucrose 1 sucrose W of ways to arrange 1 slot W of ways to arrange 1 slot among possible 55 slots 55 among possible 550 slots 550 Thermodynamics In general 1 We Cone l l Asdilution Sfinal 39 Sinitial 2R1 39 R1 Cfinal C initial Asdilution R final For the previous sucrose example ASHO1 R In 10 z 457 0 01 OK i Thermodynamics The macroscopic thermodynamic de nition of entropy d8 dqreVT ie for a system undergoing a change from an initial state Ato a nal state B the change in entropy is calculated using the heat exchanged by the system between these two states when the process is carried out reversibly fi I dig AS r Carried through a reversible path initial fi 1 C AS in PdT If process occurs at contant pressure initial fi 1 C AS in VdT If process occurs at constant volume initial Spontaneity Criteria 7 In these equations the equal sign applies for reversible processes The inequalities apply for irreversible spontaneous processes i ASsystem AS surroundings Z O ASis0lated system 2 O Thermodynamics Freeenergy Provides a way to determine spontaneity Whether system is isolated or not Combining enthalpic and entropic changes AG E AH T AS Gibbs free energy What are the criteria for spontaneity Take the case of AH 0 AG 2 TAS lt10 gt10 AG gt 0 gt nonspontaneous process AG lt O gt spontaneous process AG O gt process at equilibrium Thennodynan cs Free energy and chemical equilibrium Consider this rxn A B gt C D Suppose we miX arbitrary concentrations of products and reactants These are not equilibrium concentrations Reaction will proceed in search of equilibrium What is the AG is associated with this search and finding MD A B ie AG when A B AG AG RT In C D are mixed in AGquot is the Standard Free Energy of reaction their standard state 1 1 Biochemistry 1M O x 25 C H 70 AGanAG RT1nj p X AGanAGO i Thermodynamics Now Suppose we start with equilibrium concentrations Reaction will not proceed forward or backward AGRXH 0 Then C D AG 0AG RT1n eq Lq K6 6 RT A eqBeq 00 q j C D K 6 RT AGO RT In M g q ALQ Beq 92 AH0 ASO are AGquot RT1nKeq i Thermodynamics raph mksww 7 ane AH AS q RT R Van t Hoff Plot In K Slope Summary in chemical processes AHO 1 Change in potential energy stored in bonds and interactions 2 Accounts for Tdependenc of K601 3 Re ects type and quality of bonds 4 If AHO lt 0 TT gt Keqt If AHO gt 0 TT gt KeqT i Thermodynamics ASquot 1 Measure of disorder S R In of microscopic ways of macroscopic states can be attained 2 Tindependent contribution to K601 3 Re ects orderdisorder in bonding conformational exibility solvation 4 AsoT gt Keqt Rxn is favored Thermodynamics Examples Cons1der the Reactlon A B minim 1M Z 5 Free energy change BLIitial 10 M when products and Keq 1000 reactants are present at AGO RT 1n Keq standard conditions AGquot 2 198 c a1298 Kln 1000 molK AGO 476 ELSE 4 Spontaneous rxn How about AGRXH B G 2 G0 RTln A Rxn A 5 AGRXH 4076 198 gtlt10393 X298K1n10 M Even more s ontaneous AGRXH 109 m p Thermodynamics Another question What are Aeq and Beq AHH1105z1h1 A 1 B Z 1th sq An 21000 13Lq 1000 1 Beq 1001Beq 1000 Be w 0999M z 1M q 1001 Aeq 0001M Thermodynamics Another Example Acetic Acid Dissociation AHO 0 CH3 COOH H20 CH3 COO39 H3O Creation of charges gt Requires ion solvation gt Organizes H20 around ions At 1M concentration this is entropically unfavorable Keq 10395 2 CH3 COO39H3O 105 eq CH3 COOH 1r CH3 COOHtotal 105 gt 50 ionized Percent ionization is concentration dependent We can favor the forward rxn ionization by diluting the mixture If CH3 COOHtota1 108 gt 90 ionized Thermodynamics CH3 COOH H20 2 CH3 COO39 H3O CHq COO39H 20 2 K6 2 CH3 COO H3O 2 CH3 C00HT q CH3 COOH CH3 COOHT CH3 C00 2 CH3 C00HT a2CH3 C00HT CH3 coo39 K with 052 eq 1 05 CH3 C00HT Keq JKzeq 4CH3 C00HT Keq and a 2CH3 COOHT CH3 COOH total Kc al mol 10 Keq w mt famle Backbone Conformational Flexibility CDRLP H l r c N N C HH H O For the process folded unfolded native denatured W ASEackbone conf R 111 M folded How many ways to form the unfolded state Backbone Conformational Flexibility lt1 degrees of freedom 2 lt L11 Assume 2 possible values for each degree of freedom Then Total of 4 conformational isomery residue For 100 amino acids 4100 1060 conformations These results do not take into account excluded volume effects When these effects are considered the number of accessible configurations for the chain is quite a bit smaller Wunfolded 1016 conformations Backbone Conformational Flexibility Thermodynamic considerations Rlnio16 El987gtlt16gtlt2303 73c a1 mol K ASO backbone conf AGEackbone em TASO 22 M at 25 C mol In addition other degrees of freedom may be quite important for example R 0 1 C N We will see this N C later in more detail l H II Ionization of Water Water is the silent most important component in the cell lts properties in uence the behavior and properties of all other components in the cell Here we concern ourselves with its ionization properties H20 H20 2 H3O OH39 H30OH39 eq H20 Since in the cell H20 55M and ionization is very weak then H20 constant so se can de ne the ionic KW H3OOH product Of water Ionization of Water From the previous equation KW H3OOH39 KW 21039 For pure water H H3O OH 210397M ie in a neutral soln H3O 10397M OH39 210397M The overall acidity of the medium greatly affects many biochemical reactions because most biological components can function either as bases or acids A measure of acidity is given by the pH scale defined as 1 H210 lo HO p g10H3O g 3 So in fact for pH 10g 10 L 7 7 pure water 10 Weak Acids and Bases All biological acids and bases belong to this category Consider acetic acid AH A39HJr The Dissociation Constant HA39 a AH A39 AH rearrange PH 2 PKa 10 Where pKa logKa Henderson Hasselbalch equation Weak Acids and Bases Fraction of deprotonated acid is N 2 fA AAH Also fAH 1 f So we can rewrite the fA HendersonHasselbalch pH pKa log 1 equation A ie pKa is the pH at fA 05 which the acid is pKa 50 ionized 0 pH Weak Acids and Bases Based on the previous page mipK1a 10 90 11 If pHpKa1 y9 pH pKalog f 1f A pH pKa 2 fA z 09 etc Morever the lower the pKa the stronger the acid stronger acid 10 fAi 05 weaker acid pH Weak Acids and Bases Some use relationships AH IHI fAH fAH A AH Ka H Multiple Acid Base Equilibria Consider Alanine CH3 NH r COOH Titrate a solution of ala using a gas electrode pH meter and a buret to add a strong base of known concentration a 05 E 4 Please correct in your g 393 notes H 3 2 CH 3 Macroscoplc O g a experlment shows 39 39 2 in ection oints PKi pKz pH p 2 sz Multiple Acid Base Equilibria As we vary the pH of the solution from low to high H CH3 H CH3 H CH3 H N CH COOH 2 H Nt CH COO 2 N CH COO H H H Cation Zwitterion Anion So in fact the two in ection points seen correspond to the deprotonation of the carboxylic group at low pH and then to the deprotonation of the amine group at high pH So How can we estimate the fraction of these different species in solution If we assume that the ionization of a given group is independent of the state of ionization of the others then Multiple Acid Base Equilibria HAH fCOOH XfNH3 H H Km H K32 H K31 H fHA7 fCOO X fNH x fAH COOH fNHz K31 H K212 H K K X a1 37 fA fCOO fNHz Km HKa2 Hj fHAH fHA fAHfA 1


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