Goal of kinetic studies is to determine the reaction mechanism, the energetics, and the rates of individual steps to: - Understand the origin of the catalytic power of enzymes - Carry out protein and metabolic engineering - Drug design (most potent inhibitors are transition-state analogs. k 1 k 3 k 5 E + S ES EP E+P k 2 k 4 k 6
Initial velocity measurements under steady-state conditions allow to determine the kinetic parameters V max and K M for the substrates, which depend on the rate constants that govern the individual reaction steps. Kinetic measurements under pre-steady-state conditions allow to determine directly the values of the rate constants that govern the individual reaction steps and to identify intermediates
Initial velocity measurements of the enzyme-catalyzed reaction are carried out under a variety of conditions (T, pH, inhibitors; isotope substituted substrates, solvent viscosity, ionic strength), - to quantify the enzyme - to obtain information on the reaction mechanism, on regulatory mechanisms, which is the active enzyme form, etc. Products Substrates [P], μ M or mM d[S] d[P] v = - = dt dt Time, sec or min
The Michaelis-Menten Equation V max [S] k 1 k 3 v = The Model : E + S ES E+P K m + [S] k 2 The assumptions of the model: - [E tot ] << [S o ] - Measure v (initial velocity) when [P]=0 - v = k 3 *[ES] - [ES] = constant The expression of v : The kinetic parameters V max and K m k 3 [E tot ] * [S] k 2 + k 3 v = V max = k 3 [E t ] k 2 +k 3 K m = k 1 + [S] k 1 k cat = V max / [E tot ]
Use of absorbance and fluorescence methods with natural or synthetic substrates to monitor substrate consumption or product formation under steady-state conditions [P] Products Substrates Δ [P] d[S] d[P] v = - = dt dt Δ t Time (min)
A simple case: Monitor NAD(P)H oxidation (or NAD(P) reduction) in reactions catalyzed by dehydrogenases/reductases Alcohol dehydrogenase (ADH ) Ethanol + NAD + Acetaldehyde + NADH + H + ε 340 = 6.23 mM -1 cm -1
When S or P cannot be observed directly it is possible to couple the reaction of interest with an «indicator reaction» with substrates/products suitable for a spectrophotometric assay. D-amino acid oxidase D-alanine + O 2 Pyruvate + ammonia + H 2 O 2 X LDH HRP NADH + H + L-lactate X ox NAD + H 2 O colored LDH, lactate dehydrogenase; HRP, horse radish peroxidase
For consecutive reactions: A → B → C If v B → C >> v A → B , then v A → C = v A → B
When S or P cannot be observed directly it is possible to use synthetic (non-physiological) substrates suitable for a spectrophotometric assay. H 2 O 2 H 2 O Amplex Red Resorufin ε≈ 50 mM -1 cm -1 λ ex λ em
Use of synthetic substrates to study protease activity C C N + � HIV1 protease N N Ser-Nle-Ala-Glu-pNitro-Phe-Leu-Val-Arg-Ala-Lys-His Substrate Spectra: before and after incubation with HIV ‐ 1 protease HIV 1Protease Activity 0.800 0.34 0.700 ε≈ 0.50 mM -1 cm -1 0.32 0.600 Absorbance, 310 nm 0.500 0.3 0.400 Abs (A.U.) 0.28 0.300 0.26 0.200 0.100 0.24 0.000 0.22 200 250 300 350 400 450 500 ‐ 0.100 0.2 ‐ 0.200 Wavelenght (nm) 0 200 400 600 800 1000 1200 1400 1600 1800 time (sec) Substrate Substrate + HIV ‐ 1 Protease Spectra Difference
Use of synthetic substrates to study protease activity: A FRET-based fluorescent assay for HIV1 protease + N � N N Ser-Nle-Ala-Glu-pNitro-Phe-Leu-Val-Arg-Ala-Lys-His-Abz λ ex , 320 nm; λ em , 420 nm;
Fluorescence resonance energy transfer (FRET) occurs when the emission spectrum of a «Donor» molecule overlaps with the absorption spectrum of the «Acceptor» molecule without emission a photon from the «Donor». Emission of the «Donor» will be quenched by the «Acceptor». - The Acceptor may or may not emit light at a longer wavelength. - The Efficiency of FRET depends on the distance between Donor and Acceptor. Thus, FRET can be used to monitor distances between Donor and Acceptor.
With the absorption-based assay of HIV1 protease we can cover a broader range of substrate concentrations due to the high starting fluorescence of Substrate III Conditions: 100 mM NaAcetate, pH 5.0, 1 mM EDTA, 1 mM DTT, 100 mM NaCl; 25 ° C
Activity assays allow to monitor the dissociation of the HIV-1 protease dimer. D (dimer, active) + 2 M [M] 2 v = k cat * [Dimer] K d = [E tot ] = 2*[D] + [M] [D] 1.8 1.6 1.4 100 mM Na Acetate buffer, pH 5.0, 1 mM EDTA, Buffer STD k cat , s -1 Activity (U/ml) 1.2 1 mM DTT, 100 mM NaCl pH 5 U/mL 1 Buffer 10 mM Na phosphate buffer, pH 6.5, 1 mM EDTA, 0.8 Bachem pH 10% glycerol, 75 mM NaCl; calculated Kd, 215 nM 6.5 0.6 0.4 0.2 0 100 200 300 400 500 600 [E] nM
Determination of equilibrium (or dissociation) constants k f At equilibrium: C + D A + B k r [C ]eq *[D] eq k f K eq = = k r [A] eq *[B] eq Δ G° = - RT ln K eq Δ G° [A] eq *[B] eq K d = C + D [C ]eq *[D] eq
Flavin-dependent enzymes contain FMN or FAD as the coenzyme, a useful intrinsic spectroscopic probe
The flavin cofactor acts as an intermediate electron acceptor between the substrate/product couple . Thus, the reductive and the oxidative half-reactions can be studied separately by absorbance and fluorescence spectroscopies under equilibrium or time resolved conditions for kinetic and mechanistic work.
The flavin absorbance (and fluorescence) spectrum is sensitive to the redox state, chemical modifications of the isoalloxazine ring, the «environment» (hydrophobicity, protonation state of ionizable groups, complexes, ....) Flavin ox (Yellow) Flavin hydroquinone (leuco) Red SQ R R H O O CH 3 N N N N CH 3 NH NH CH 3 N CH 3 N Yellow H O O R R O CH 3 N N O CH 3 N N NH + Blue SQ NH CH 3 N CH 3 N O - O - H R R - O O N N N N CH 3 CH 3 NH NH CH 3 N CH 3 N O O H Neutral semiquinone (Blue) Anionic semiquinone (Red)
Influence of the protein on the absorbance spectrum of bound FAD 0.14 MICAL-His h-MICAL-MO 0.12 MICAL-His + 0.2% SDS 0.10 ε 457 = 8.0 mM -1 cm -1 Absorbance 0.08 0.06 0.04 0.02 0.00 300 400 500 600 700 800 Wavelength, nm 1) The spectrum of the «as isolated» MICAL indicates the presence of a flavin coenzyme, but the spectrum differs from that of authentic flavin, FAD or FMN. 2) Release of the coenzyme by denaturation yields the spectrum of authentic FAD or FMN - A charge-transfer complex between the flavin and Trp400 from X-ray structure - Need to determine if the coenzyme is FAD or FMN - Use the information to determine the stoichiometry and the extinction coefficient of the bound coenzyme
Influence of the protein on the fluorescence of bound FAD 4.0 h-MICAL-MO 3.5 3.0 Fluorescence 2.5 Denatured 2.0 1.5 1.0 0.5 Native 0.0 500 520 540 560 580 600 Wavelength, nm 1)The fluorescence of the bound coenzyme is quenched by the protein
Fluorimetric Indentification of the cofactor bound to MICAL as FAD phosphodiesterase + Mg ++ FMN AMP FAD 40 35 30 Fluorescence 25 20 + PDE 15 10 5 Denatured 0 500 520 540 560 580 600 Wavelength, nm If the coenzyme is FAD, PDE will cause a 10x increase of fluorescence due to conversion into FMN, and removal of internal quenching of fluorescence by the AMP moiety.
Some flavoproteins can form a Flavin-N(5)-sulfite adduct R H - O-S=O O - R H - O-S=O O The formation of the flavin-N(5)-sulfite adduct gives information on the electronic distribution of the bound flavin coenzyme (e.g. Degree of electrophilicity of N(5)).
Use of the study of sulfite reactivity to distinguish between the flavins of glutamate synthase (GltS)
Glutamate synthase (GltS) L-Glutamine + 2-oxoglutarate + NADPH → 2 L-Glutamate + NADP + Fd β α Fd-GltS Bacterial NADPH-GltS Eukaryotic NAD(P)H-GltS 1 x 50 kDa + 1 x 150 kDa 1 x 150 kDa 1 x FAD, 1 FMN, 1 FMN, 1 x [3Fe-4S]; 2 x [4Fe-4S] 1 x [3Fe-4S]; 3Fe4S ADP FeS FAD NAD(P) GAT FMN NADPH-GltS Fd-GltS NADH-GltS
Initial Scheme of bacterial NADPH-GltS reaction NADPH NADP + Site 1 Flavin 1 L-Gln Fe-S Flavin 2 L-Glu NH3 Site 2 2-IG L-Glu 2-OG
The study of the reactivity of the flavin coenzymes of GltS with sulfite allowed us to distinguish between the flavin at the synthase site and the flavin at the NADPH oxidizing site. Sulfite titration of NADPH-GltS Backtitration of the NADPH-GltS/ followed by NADPH addition sulfite complex with 2-oxoglutarate GltS GltS + sulfite 2-OG GltS + sulfite (GltS + sulfite) + NADPH Sulfite reacts with only one of the GltS flavins; 2-OG displaces sulfite from GltS in a Sulfite does not interfere with the reduction of competitive fashion the otehr flavin by NADPH
Conclusions: - Flavin 2, the flavin at the synthase (2-OG) site reacts with sulfite, - 2-OG binds near the sulfite-reacting flavin; - From the backtitration of the GltS-sulfite complex with 2-OG we can calculate the K d of the GltS-2-OG complex - the flavin at the NADPH oxidizing site does not react with sulfite NADP + NADPH Site 1 Flavin 1 L-Gln Fe-S Flavin 2 L-Glu NH3 Site 2 2-IG L-Glu 2-OG - We can use sulfite reactivity to monitor the state of site 2 with respect to flavin environment and 2-OG binding
Production and characterization of the isolated α and β subunits and of the homologous Ferredoxin-dependent GltS L-Glutamine + 2-oxoglutarate + NADPH → 2 L-Glutamate + NADP + Fd β α Fd-GltS Bacterial NADPH-GltS Eukaryotic NAD(P)H-GltS 1 x 50 kDa + 1 x 150 kDa 1 x 150 kDa 1 x FAD, 1 FMN, 1 FMN, 1 x [3Fe-4S]; 2 x [4Fe-4S] 1 x [3Fe-4S]; 3Fe4S ADP FeS FAD NAD(P) GAT FMN NADPH-GltS Fd-GltS NADH-GltS
The FMN coenzyme bound to the isolated α subunit and to the homologous ferredoxin-dependent GltS reacts with sulfite that is displaced by 2-OG 0.30 1.0 1.0 (Ax-Ao)/(Af-Ao) (Ao-Ax)/(Ao-Af) 0.8 0.8 0.24 0.6 0.6 0.4 0.4 0.2 K 2OG = 17.4 μ M 0.2 K S = 10.7 mM 0.18 0.0 0.0 Absorbance 0 0.4 0.8 1.2 0 20 40 60 [2-OG], mM [Sodium sulfite], mM 0.12 0.06 0.00 Fd-GltS -0.06 300 400 500 600 700 800 Wavelength (nm)
Conclusions: - Site 2, the synthase (2-OG) site is on the GltS α subunit and on the homologous Fd-GltS, - The flavin is FMN (also 1 x [3Fe-4S] cluster) - We can use sulfite titrations and backtitrations with 2-OG to study the state of the synthase site in mutants (even inactive mutants). L-Gln L-Glu Glutaminase Site GAT site NH 3 Ammonia tunnel α subunit Synthase site 2-IG NADPH 2-OG Site 2 Site 1 L-Glu NADP + β subunit - The β subunit should contain FAD and the NADPH oxidizing site
The equations for the binding curves M + L ML M tot * L tot High Kd: L free ≈ L tot ML = K d +L tot Tight binding: L free = L tot - ML -(L tot +M tot +K d ) ± [(L tot +M tot +K d ) 2 – 4*M tot L tot )] 1/2 ML = 2
0.30 1.0 1.0 0.24 (Ax-Ao)/(Af-Ao) (Ao-Ax)/(Ao-Af) 0.8 0.8 0.18 Absorbance 0.6 0.6 0.12 0.4 0.4 0.06 0.2 K 2OG = 17.4 μ M 0.2 K S = 10.7 mM 0.00 0.0 0.0 -0.06 300 400 500 600 700 800 0 0.4 0.8 1.2 0 20 40 60 Wavelength (nm) [2-OG], mM [Sodium sulfite], mM (A o – A x ) (A o – A fin ) = [E-sulfite] (A o – A x ) → [E-sulfite] (A o – A fin ) → [E tot ] [E tot ] [ESulfite] [Sulfite] K ⎯ = + ← ⎯ → E Sulfite ESulfite Sulfite + [E ] (K [Sulfite]) tot Sulfite [E - 2OG] [2OG] + ← ⎯ → K ⎯ = E 2OG E - 2OG 2OG + [E ] (K [2OG]) tot 2 OG ⎛ + [S] ⎞ = ⎜ ⎟ K K 1 + ← ⎯ ⎯ → + K ESulfite 2OG E - 2OG Sulfite 2OGapp • 2OG 2OG app K ⎝ ⎠ S
Use of spectrophotometric titrations to study the properties of GltS Site 1, the NADPH oxidising site on NADPH-GltS β subunit NADPH-GltS L-Gln L-Glu GAT site NADPH NH 3 Ammonia tunnel α subunit Synthase site 2-IG NADPH 2-OG NADP + L-Glu NADP + β subunit 3Fe4S ADP FeS FAD NAD(P) GAT FMN NADPH-GltS 1) Express, purify and characterize the GltS β subunit 2) Identify the NADPH-binding site by characterizing the G298A variant
Glutathione reductase (GR) as the model of GltS β subunit on the basis of sequence similarities - The adenylate portions of FAD and NADP bind to Rossmann-folds - The consensus sequence is centered on GX G XXG/A/S motifs - In GR , the G-to-A substitution of the second G of the motif is diagnostic to identify the nucleotide that binds to the site. NADP FAD
Anaerobic NADPH titration of β -GltS and the G298A variant As expected, the FAD coenzyme bound to the isolated β subunit does not react with 1.0 0.3 (Ao - A)/(Ao - Af) 0.8 sulfite. 0.6 0.4 0.2 Absorbance 0.2 Bound FAD is reduced by NADPH with 0.0 formation of a stable FAD red -NADP + charge- 0.0 0.5 1.0 1.5 2.0 0.1 [NADPH ]/[ß subunit] transfer complex ß subunit 0 300 400 500 600 700 800 The substitution of the second G of the nm 0.08 GX G XXA motif of the binding site of the (Ao - Ax)/(Ao - Afin) 0.8 adenylate portion of NADP(H) 0.06 0.4 Absorbance - weakens NADPH binding, 0.04 K d,app = 2.3 µM - prevents the formation of the E red -NADP + 0.0 0 1 2 CT complex. 0.02 [NADPH]/[G298A GltS-ß] 0 300 400 500 600 700 800 Wavelength (nm) E-FAD.NADPH (E-FAD red .NADP + ) CT E-FAD + NADPH E-FAD red .NADP + E-FAD red + NADP +
AADP titration of β -GltS and the G298A variant The absorbance spectrum of β GltS is E-FAD + AADP E-FAD.AADP perturbed by 2-amino pyridine 0.16 dinucleotide phosphate a non- NH 2 0.12 reducible analog of NADP + and a mimic + of NADPH. 0.08 N R 0.04 The G298A substitution in the binding site of the adenylate portion of NADP: 0 ß subunit K d =1.1 µM -weakens also AADP binding, -0.04 -decreases the amplitude of absorbance 300 400 500 600 700 800 changes indicating an altered positioning Wavelength (nm) of the nicotinamide ring 0.08 3 ß (Ao-Ax)/[ß] 0.06 G298A-ß 2 - Use AADP to determine the effect of 1 bound NADPH on the redox potential 0.04 0 without the complication of reduction. 0 50 100 150 0.02 [AADP], µM 0 - Which are the consequences of the G298A-ß K d =10.1 µM G298A mutation on the rate of hydride -0.02 transfer from NADPH to the bound FAD? 300 400 500 600 700 800
Determination of the redox potential of flavin coenzymes
Several important reactions are oxidoreductions A n+ ox + B red A red + B n+ ox The E ° (E m ) of a redox couple indicates the tendency of the species to accept/donate electrons E Aox/Ared = E A ° - (RT/nF) ln(A red /A ox ) E A = E A ° (E m ) when A red = A ox A n+ ox + n e - A red E, V B n+ ox + n e - B red In redox reactions electrons flow from species with lower E m to species with higher E m
The Nernst equation A n+ ox + B red A red + B n+ ox ox + n e - = A red E A = E A ° - (RT/nF) ln(A red /A ox ) A n+ B red = B n+ ox + n e - E B = E B ° - (RT/nF) ln(B red /B ox ) A red *B ox RT ln Δ E = E A – E B = (E A ° – E B ° ) - nF A ox *B red [A red ]*[B ox ] 2.303RT Δ G = n F Δ E Log - Δ E = Δ E° - [A ox ]*[B red ] nF At equilibrium Δ E = 0 E A = E B [B red ] [A red ] 2.303RT 2.303RT Log Log E A ° - = E B ° - [B ox ] [A ox ] n B F n A F n= no. transferred electrons; F = Faraday constant= 96494 JV -1 ; R, 8.341 Jmol -1 K -1 ; T, 20 ° C = 293 K; Log N = 2.303 Ln N; 2.302RT/nF with n = 2 = 0.029 V at 20 ° C
Example: Spectrophotometric determination of the E m of FMN: - reductive titration of FMN under anaerobiosis, in the presence of an indicator dye (known E m ) and a mediator (to ensure equilibrium is reached after each addition of reductant ). - Assume FMN and Dye exchange the same no. of electrons (2) FMN ox + 2 e - = FMN red E FMN =E m,FMN -(RT/n FMN F)ln(FMN red /FMN ox ) Dye ox + 2 e - = Dye red E Dye = E m,Dye - (RT/n Dye F) ln(Dye red /Dye ox ) Δ E = E FMN – E Dye At equilibrium Δ E = 0 FMN red 2.303RT 2.303RT Log Dye red E m,FMN - = E m,Dye - Log FMN ox n FMN F n dye F Dye ox n FMN n FMN F Log Dye ox FMN ox (E m,Dye - Log = E m,FMN )* + Dye red FMN red 2.303RT n dye
Spectrophotometric determination of the E m of FMN : (1) Anaerobic reductive titrations of FMN; Dye; FMN+Dye (2) Determine λ and ε useful to measure FMN ox /FMN red and Dye ox /Dye red 521 nm 408 nm 20 μ M FMN 17 μ M Phenosafranine 20 μ M FMN + 17 μ M PS E ° =-252 mV n dye = 2 Conditions: 2 μ M Benzyl viologen, 1 mM Xanthine, 2.5 mU xanthine oxidase in 25 mM Hepes/KOH, pH 7.0, 10% glycerol. 25 ° C. Record spectra every 5 min
Spectrophotometric determination of the midpoint potential of FMN n FMN n FMN F Log Dye ox FMN ox (E m,Dye - E m,FMN )* Log = + Dye red FMN red 2.303RT n dye (A 408,0 - A 408,x ) [FMN red ] Calculation of [FMN red ]: (A 408,0 - A 408,fin ) = [FMN tot ] [FMN tot ] – [ FMN red ] Calculation of [FMN ox ]: (A 521,0 - A 521,x ) [Dye red ] Calculation of [Dye red ]: (A 521,0 - A 521,fin ) = [Dye tot ] [Dye tot ] – [ Dye red ] Calculation of [Dye ox ]:
Spectrophotometric determination of the midpoint potential of FMN FMN ox Log FMN red Log Dye ox Dye red Slope = 0.9 → 1 : n dye = n FMN = 2 Intercept = -0.99 2.303RT = -29.8 mV = (E m,Dye - E m,FMN ) = -252 mV - E m,FMN -0.99 * nF E m,FMN = -252 mV + 30 mV = -222 mV
Redox potential determination of the GltS ß subunit and of the ß GltS-AADP complex: modulation of the potential to favor reduction by NADPH 0.16 Log([ßox]/[ßred]) 1.0 n = 2, ‐ 340 mV 0.12 E ox + n e - → E red Dye ox 0.0 Absorbance -1.0 E ‐ FAD ox 0.08 ßGltS subunit -2.0 -1.0 0.0 1.0 Log([STox]/[STred]) 0.04 n = 2, -340 mV E ‐ FAD red 0 Dye red 300 400 500 600 700 800 (nm) Log([ßox]/[ßred]) 1.0 0.2 ßGltS-AADP complex 0.0 Absorbance -1.0 n = 2, -307 mV -2.0 -1.0 0.0 1.0 0.1 E ox • AADP + n e - → E red • AADP Log([STox]/[STred]) 0 300 400 500 600 700 800 (nm)
- The protein destabilizes FAD red with respect to free coenzyme - Bound AADP (the substrate analog) favors reduction by NADPH E, mV FAD ox + 2 e - FAD red -220 E ox • AADP + 2 e - E red • AADP -300 NADP + + 2 e - NADPH E ox + 2 e - E red -340
From the Anaerobic NADPH titration of β -GltS and the G298A variant E-FAD + NADPH E-FAD.NADPH (E-FAD red .NADP + ) CT E-FAD red .NADP + E-FAD red + NADP + The G298A substitution in the binding 1.0 0.3 (Ao - A)/(Ao - Af) 0.8 site of the adenylate portion of NADP 0.6 0.4 0.2 weakens NADP binding and alters Absorbance 0.2 0.0 0.0 0.5 1.0 1.5 2.0 0.1 the positioning of the nicotinamide [NADPH ]/[ß subunit] ß subunit ring 0 300 400 500 600 700 800 nm 0.08 (Ao - Ax)/(Ao - Afin) 0.8 0.06 Which are the consequences of the 0.4 Absorbance 0.04 K d,app = 2.3 µM rate of hydride transfer from NADPH 0.0 0 1 2 0.02 [NADPH]/[G298A GltS-ß] to the bound FAD? 0 300 400 500 600 700 800 Wavelength (nm)
Does GltS β subunit contain the fully active NADPH oxidising site of GltS? NADPH-GltS L-Gln L-Glu k cat values: GAT site NH 3 Overall glutamate synthase reaction: 60 s -1 Ammonia tunnel α subunit Synthase site 2-IG NADPH-INT oxidoreductase reaction: 200 s -1 2-OG NADPH L-Glu NADP + β subunit k cat values: NADPH-INT oxidoreductase reaction: 40 s -1 E ox NADPH INT red NADP + + H + E red INT ox INT, iodonitrotetrazolium salt; synthetic electron acceptor , becomes red on reduction
Rapid Reaction Kinetics. k 1 k 3 k 5 E + S ES EP E+P k 2 k 4 k 6
Rapid Reaction Kinetics - Pre-Steady-State Kinetics [E] : µM, mM vs nM, µM for steady-state [S] : µM, mM ( [S]> 10x [E] for pseudo-first order conditions) Measuring Times: msec-sec vs sec-min for steady-state Thus, need: - large amounts of enzyme/protein & substrate/ligand - highly concentrated protein/ligand solutions - rapid mixing device - rapid measuring times (in continuous methods) - rapid data acquisition - software (competence) for data analysis
What can be measured by RR Kinetics? Chemical reactions Folding/Unfolding Protein-protein, Protein-ligand interactions Induced conformational changes
Rapid Mixing device E S Turbulent flow to ensure constant velocity across tubing High flow rate ( e.g.:10 m/s = 1 cm/msec)
Detection Continuous methods: Absorbance, Fluorescence, Circular Dichroism, Fluorescence anisotropy, conductivity, X-ray scattering (?) Discontinuous methods: EPR (freeze-quench) Mossbauer (freeze-quench) HPLC separation of reaction components and chemical analysis (chemical quench)
Stopped-flow set-up for rapid reaction studies and absorbance or fluorescence detection Detector Drive Stop Push, 3 atm syringes syringe Trigger Detector
Single Mixing Double Mixing Stopped-flow Stopped-flow
The upper limit of measured rates is set by Dead-time, Time- constant (Time Resolution), Sensitivity of detector Dead-time Time-constant (Resolution) td 2 msec td 2 msec 1.0 1.0 0.8 0.8 Absorbance Absorbance 0.6 0.6 1000/s 50/s 0.4 0.4 50/s 0.2 0.2 100/s 250/s 500/s 1000/s500/s 2000/s 0.0 0.0 0.000 0.020 0.000 0.020 0.040 Time (sec) Time (sec) Detector Push, 3 atm Detector
To directly measure the rates of formation/decay of the various species we need to identify suitable wavelengths k 2 k 1 C A B A = A o e -k1t I λ ,A = [A]* ε λ, A B = A o k 1 /(k 2 -k 1 )(e -k1t - e -k2t ) I λ B = [B]* ε λ, B C = A o [1 + 1/(k 1 - k 2 )(k 2 e -k1t - k 1 e -k2t ) I λ C = [C]* ε λ, C ε A + B + C 120 A 100 C Absorbance B C 80 60 B 40 20 A 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 λ Time (sec) Green : At a given wavelength A, B, C have the same extinction coefficient At different wavelengths: we can distinguish A from B from C
Diode array set-up vs PMT mode
First order reaction k 1 A = A o *e -k1*t A B Pseudo-First order reaction B o >>A o k 1 A + B C A = A o *e -k1obs*t k 1 , obs = f(B) Conditions for a simple sf experiment A o >>E o k 3 k 5 k 1 [A] E = E o *e -k1obs*t E EP EA E k 2 k 6 [P] k 4 k 1 ,obs = f(A) = (k1 * A)/(K d + A)
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