SupraNano_2024_Fundamentals II.pdf

Today Analytical techniques Complexation, equilibrium and basic thermodynamics Fundamental aspects, Experimental characterization of binding techniques and examples Cyclodextr...

Today Analytical techniques Complexation, equilibrium and basic thermodynamics Fundamental aspects, Experimental characterization of binding techniques and examples Cyclodextrin as example Next lecture Model validation Host-guest systems for ionic and neutral species Hydrogen-bond based assemblies 1 2 1  Experimental techniques NMR spectroscopy (most popular) ΔT fast exchange Fast exchange vs ‘Slow exchange’ How to study an equilibrium like this? δHG populations ≈ relative stability δH coalescence O O [Gt] O N H O N H intermediate 𝑘" 𝑇 #∆𝑮∗ N 𝜋𝛿𝑣 H N N H N exchange N N 𝒌𝒄 = =𝜒 𝑒 &' (Eyring) N H O N H O 2 ℎ O O kc = rate of guest exchange at coalescence, s-1 slow exchange δv = resonance frequency seperation (sl. ex.), s-1 χ = transmission coefficient (normally 1) no exchange kb = Bolzmann’s constant = 1.3805 ∙ 10-23 J K-1 T = temperature, K δv (in Hz!) = Δ ppm * fnucleus h = Plack’s constant = 6.6256 ∙ 10-34 J s @ B0 = 11.74 T f1H = 500 MHz ΔG* = activation free energy, J 3 4 2  NMR spectroscopy (most popular) NMR: NOESY – structural information 1 𝑑%&'(# ) 𝑄= For a process that is in ‘fast exchange’: Nuclear Overhauser Effect SpectroscopY 𝑉%&'(# binding curve analysis gives Ka Through space transfer of spin Qualitative: nOe = close proximity = bound ! 1 NMR titration curve Quantitative: how close are two nuclei? 𝑑"#$ = δHG δobs ∫ = [Ht] 𝑉"#$ 𝑄 10.4 - calibrate (Q) against known distance (d/Vcalib) δH 9.9 [Gt] 9.4 d NH 8.9 8.4 Ka = 920 M -1 7.9 O N H O 3D model 7.4 0 2 4 6 8 10 N H N N equiv. B N H O O ACIE, 2016, 55, p3387 6 7 3  NMR: DOSY – structural information NMR: extract thermodynamic data logD(H2O) = -8.65; logD(cage) = -9.75 >>> r(cage) = 17.75 Å 𝑘𝑇 Diffusion Ordered SpectroscopY 𝑟= value measured 6𝜋𝜂𝐷 Unraveling mechanism - Measure D; diffusion coefficient (so 10 ) of binding with Hlg- vs vs - D is related to radius of molecule by the Stokes-Einstein equation H-bonds - Particularly useful for appreciable size difference between H and G 4 (C–I) 6 (N–H) D = diffusion coefficient in m2s-1 What is the radius k = Boltzmann constant = 1.38 · 10-23 N m K-1 of the cage? T = temperature in K 4 (C–I) + anions in water η = viscosity of matrix in N m-2 s r = radius in m Why? H2O (r = 1.41 Å; η = 6.856 ∙10-4) JACS, 2016,138, p13750 Nat. Chem., 2014,6, p1039 8 9 4  NMR: extract thermodynamic data ITC – measure thermodynamic data (assuming Cp = 0) y-axis x-axis Gibbs & van ‘t Hoff Gibbs & van ‘t Hoff lnKa = –DHo/R · 1/T + DSo/R DGo = –RT lnKa (= DHo – TDSo ) slope intercept DGo = –RT lnKa (= DHo – TDSo ) Driven only by enthalpy ΔHº = -34 kJ/mol Isothermal Titration Calorimetry: ΔSº = -52 J/mol - Measures enthalpy changes - Both exo- and endotherm - Applicable to all systems (if measurable ΔH) 4 (C–I) Method: - Reference and sample cells at fixed temperature - Inject Host >>> sample cell warms or cools - How much energy needed to restore temperature? Driven only by entropy 6 (N–H) ΔHº = +13 kJ/mol ΔSº = +76 J/mol Nat. Chem., 2014,6, p1039 10 11 5  ITC – measure thermodynamic data ITC – common to measure substrate binding 1.9 + NBu4+Cl– in Integrate each peak and plot the sum of heat Often no ‘reporter’ in Natural systems: nitromethane at 25 ºC change vs [Gt] ITC is ideal, e.g.: [G]t in mM ‘CAPN’ Σ(ΔH) in µcal DHo is like δHG in NMR Integrate each peak μcal/s >> normal curve fitting DH o negative cooperativity (Dimer) - S-curve not always obtained (low Ka) kcal / mol - Reliable for order log Ka DH o Affinity 1/ K d - Stoichiometry ignores statistical factors! stroichiomery typical data anaysis D Go = –RT lnKa of S-curve DGo = –DHo – TD So At Kd, [H] = [G] = [HG] = Kd (only if [Ht] = [Gt]!) Nat. Struct. Mol. Bol., 2006,13, p831 12 13 6  Optical spectroscopy – UV-Vis Optical spectroscopy – (I)CD Induced circular dichroism - Host or guest is chiral - Host or guest is optically active - [HG] has different interaction with polarized light vs [H] or [G] Dihydrofolate reductase binding to folate Folate Saturated with folate NB: appearing / disappearing bands can be used to directly measure Ka = 3.2 · 105 M -1 [H] (disappearing) and [HG] (appearing) concentrations. NB2: assigning spectral changes can be non-trivial. Nat. Protoc., 2006, 1, p2733 14 15 7  Optical spectroscopy – Fluorescence Optical spectroscopy – Fluorescence fructose - 2 H2O + fructose - 2 H2O + In 2:1 H2O:MeOH Kinetic?! @ pure methanol no fluorescence response: why!? In 2:1 H2O:MeOH @ pure methanol with ITC: Ka ≈ 2,900 M-1 @ pure methanol UV/Vis displacement study: Ka ≈ 3,800 M-1 @ 2:1 H2O:MeOH = binding >>> disaggregation >>> fluorescence @ pure methanol no aggregation… Data fitted to 1:1 with Ka = 1,300 M -1 @ pure methanol no response: why!? JACS, 2017,139, p5568 JACS, 2017,139, p5568 16 17 ΔH° = −0.2 kcal/mol ΔS° = +15.8 cal/(mol·K) 8  Mass spectroscopy Common techniques – summary NMR Typically use soft ionisations like ESI ! - Binding affinity, thermodynamics and structural information - Binding affinity possible to determine in vacuo - Detection limit ~0.1 mM (depending on spectrometer and symmetry) - Conform existence of complex (and its stoichiometry) - Ka range: 101 – 106 M-1 - Isotope distributions and m/z ratio’s ITC - Direct measurement of ΔH Obs. - all thermodynamic parametes from one titrration - Detection limit ~0.01 mM (depends on ΔH) 5+ - Ka range: 101 – 109 M-1 Optical spectroscopy Calc. 6+ 4+ - Needs chromophore / fluorophore (and chirality for ICD) - Detection limit ~0.1 μM (depends on εabs / εem) - Ka range: 101 – 1010 M-1 MS 3+ 0.25 m/z intervals What would you see with - Can provide important gas phase information = 4+ species mass spectroscopy? Ka > range can be addressed by competitive binding studies J. Am. Soc. Mass Spectr., 2003, 14, p442; Science, 2017, 355, p159 18 19 9  Other techniques Potentiometry - Ion selective electrodes (H+ = pH measurement) - Various tailored hosts for anionic and cationic (metallic) guests Conductivity - Total salt concentration (ionisation equilibria) Electrochemistry Complexation and - Redox signal integration; resistance change - Phenomena where oxidation state alters (metal redox) Crystal structures equilibrium of 1:1 complexes - Can elucidate stoichiometry but ≠ in solution! - Only structural information Computational techniques - Molecular mechanics vs semi empirical vs DFT vs ab initio - Explore steric; conformational freedom expensive to explore - Explore electronics; can give fairly reliable estimated of ΔH - Use with caution (very often post factum addition) + whatever can be measured… 20 21 10  Definitions: Complexation Definitions: Kinetics (reversible) formation of aggregates (complexes) of 2 or more components (molecules, metal ions, …) of which the interaction energy is constituted of Kinetics of complexation: non-covalent interactions kc Example: mA + nB [AmBn] A+B AB kd Rate constants: + kc = complexation (association) Aspects: - interaction types kd = decomplexation (dissociation) - kinetics (association and dissociation) - thermodynamics (binding strength, and constituents) K = kc / kd - stoichiometry (m, n) - solvent effects, structure, function thermodynamic stability: ~ ΔG0 kinetic stability: ~ ΔGd‡ Information about [AB] as a function of [Atotal] or [Btotal] 22 23 11  Definitions: Ka vs. Kd, pKa and IC50 Equilibrium constants association constant vs. dissociation constant Ka Kd H+G HG HG H+G association constant [HG] Ka = [H] [G] Ka Ka = Kd = [H] [G] 1 / Kd [HG] H+G HG supramolecular common in [HG] chemistry biology Ka = [H] [G] IC50 ≠ affinity, but can be How to determine Ka? If 50% inhibition = 50% bound, then: [HG] = [H] = 0.5 [Ht] and [G] = [Gt] – [HG] Ka can easily be derived very common in biology, particularly enzymology 24 25 12  Determination of equilibrium constants Determination of equilibrium constants most basic 1:1 complex multiple binding events From observable to Ka (e.g. NMR) H+G HG Ka K a2 H+G HG HG + G HG2 ‘Slow exchange’ ‘Fast exchange’ Equilibrium > sample rate [HG] Ka should be dimensionless but it is [HG2] Ka = K a2 = δobs ∫ = [H t] [H] [G] not if activity effects are ignored (M -1) [HG] [G] ∫ = [HG] δHG δHG δH ∫ = [H] δH [Gt] [Gt] mass balance equations overall binding constant [Ht] = [H] + [HG] [HG2] β2 = = K a · K a2 Direct measurement of Concentrations unknown… [Gt] = [G] + [HG] [H]2 [G] concentrations and thus Ka If concentrations can be measured, Ka easily computed depends on K a, Relationship between [ HG ] [H t] and [G t] But what if we do not know all concentrations? d obs = d H + (d HG -dH ) concentrations and [ H ]t observable is known! unknown? H = Host; G = Guest But how do we derive Ka? HG = Host-Guest complex 26 27 13  Determination of equilibrium constants Determination of equilibrium constants From observable to Ka (e.g. NMR) From observable to Ka (e.g. NMR) Unknowns: δHG & Ka Unknowns: δHG & Ka Known constants: [Ht], δH Known variables: [Gt], δobs Unknowns: δHG and Ka Rewritten equilibrium and mass balance equations: [ H ]t K [G ][ H ]t 𝐾&&$$. species distribution from [H] = [HG] = 1 + K [G ] 1 + K [G ] = 𝑲𝒂 knowns [Ht], [Gt] + Chemical shift unknown K -(1 - K [G ]t + K [ H ]t ) + (1 - K [G ]t + K [ H ]t ) 2 + 4 K [G ]t d obs - d H &-. d + dH HG = &'(. )*+). [G] = 𝛿"#$. − 𝛿"#$. ∆𝛿 𝜮∆𝜹𝟐 → 𝟎 𝛿+, 2K [ HG ] = 𝜹𝑯𝑮 [ H ]t Trick = compute δHG at each %&'%. 𝛿./0. depends on K a, point and take average [H t] and [G t] [Gt] [ HG ] [ HG ] d = d H + (d HG - d H ) d = d H + (d HG -dH ) d obs - d H obs [ H ]t obs [ H ]t d HG = + dH [ HG ] unknown? [ H ]t In-house spreadsheets and programs = ‘full controle’ Others: http://supramolecular.org/ (free) WinEqNMR, HYPERQUAD, HYPNMR, Open Data Fit, etc.. 28 29 14  Determination of equilibrium constants From observable to Ka (e.g. NMR) What higher order complex (e.g. 1:2)? Ka Ka2 [HG] [HG2] H+G HG + G HG2 Ka = Ka2 = [H] [G] [HG] [G] [Ht] = [H] + [HG] + [HG2] [Gt] = [G] + [HG] + 2[HG2] Species distribution solvable, but third order equations! Basic thermodynamics Chemical shift δH (known) [Ht], [Gt], and δobs Fitting 4 unknowns; δHG and δHG2 (unknown) multiple solutions possible Ka and Ka2 [Gt] Unknowns: δHG & Ka 30 31 15  Basic thermodynamic considerations Temperature dependence of stability constants: van ‘t Hoff’s equation DGo = DHo – TDSo = –RT lnKa (T in Kelvin; R = 8.3145 J/K/mol) y-axis x-axis lnKa = –D H /R · 1/T + D S /R o slope o intercept lnKa exotherm endotherm Experimental This ignores a possible temperature dependence of ΔH: ΔCp = (¶ΔH/¶T)p 1/T (ΔCp = heat capacity) characterization If this occurs: van ‘t Hoff plot will not be linear Heat capacities are accessible by: of binding * calorimetry (measuring ΔH as a function of T; most reliable) * from fitting lnK vs. T (reliability depending on T-interval) 33 34 16  Fundamental aspects and techniques Fundamental aspects and techniques H = Host; G = Guest HG = Host-Guest complex Stoichiometry determination: Mathematical (numerical) modeling of experimental data: Assumption: one complex, stoichiometry ABn: For every datapoint known: 0.04 [H]tot, [G]tot, dexp, (dH, dG, dHG) A + nB ABn 0.03 Obs. Unknown: 0.02 K = [ABn]/[A][B]n Ka, [H], [G], [HG], (dH, dG, dHG) 0.01 If [A+B]tot = [A]tot + [B]tot is constant: Start of model: [Gt] 0 0 0.2 0.4 0.6 0.8 1 - make assumption for Ka Job plot: [ABn] vs. fA,tot = [A]tot/[A+B]tot - calculate [H], [G], [HG] (three equations, three unknowns) has a maximum for fA,tot = 1/(1+n) - calculate chemical shifts: dcalc (or other obs., depending on technique) - least squares minimization of dcalc vs. dexp while optimizing Ka, (dH, dG, dHG) 35 36 17  Practical titration experiments Concentration considerations H+G HG * Solubility of [H], [G], [HG]; aggregation phenomena Addition of guest while keeping concentration of host constant * Sensitivity of measurement / detection limit H+G HG * Ka determines concentrations and Vadd - saturation is required (all Ka’s start linear) - enough data points near saturation Ka = 250 M-1 Ka = 25000 M-1 [G]t in M-1 Vinitial = 0.5 mL * Mathematically not required [H]t = 0.5 mM; [G]stock = 0.25 M [G]stock = Vadd = * Eliminates unnecessary complications ad errors Vadd = 0.5 µL and then 2x as large 0.01 M 0.5 µM * But what concentrations?! 37 38 18  Concentration considerations Some other methods H+G HG H+G HG Ka determines concentrations and Vadd Extraction techniques: Too high concentration: saturation Ratios of [H] and [G] to [HG] conditions – little information - [HG] complexation is very strong in an organic solvent (e.g. CHCl3) complex depend on the [Ht] and [Gt] - [H] is very soluble in organic solvent while [G] is not (dissolves in water) Ka = 100 M -1 (Kd = 0.01 M) - Separate organic phase and quantify [Gt] / [Ht] (e.g. NMR integration) [Ht] = [Gt] [H] = [G] [HG] [HG] - Ratio [Gt] / [Ht] is a measure for binding affinity in mM in mM in mM In % 1 0.92 0.08 8% 10 6.2 3.8 38% 100 27 73 73% 1000 95 905 91% At Kd, [H] = [G] = [HG] = Kd (only if [Ht] = [Gt]!) 39 40 19  Extension to surface immobilization Hs + G HGs Equilibria at a surface: - When H is immobilized at a surface, use Langmuir isotherms: Ka = θHG/θH[G] (instead of K a = [HG]/[H][G]) θH : surface coverage of the free host (e.g. in mol/cm 2) More complex scenario’s θHG : surface coverage of the complex [G] : guest concentration in solution above the surface - Try to measure data that can be translated into θHG or θHG/θH 41 42 20  More complex binding events More complex binding events Induced fit model (opposed to lock-key) Conformational changes in host and/or guest upon complexation (to optimize interactions for ‘as strong as possible binding’) Conformational sampling vs Induced fit model protein changes conformation + Protein substrate Initial complex final complex B–N bond N–H···O hydrogen bonds KUPCIH ACIE, 1991, 30, p1472 ACIE, 1991, 30, p1472 Biochemistry 2012, 51, 5894−5902 43 44 21  More complex binding events More complex binding events Positive cooperativity in Nature What if host and guest have more than one binding sites? @ lungs guest vs. t gu es es gu t Hemoglobin @ muscle Chelate effect multivalent binding (4x myoglobin) Cooperative oxygen binding Cooperativity or allosteric effects (positive / negative): High affinity in lung One binding site influences another (specially separated) binding site Low affinity in muscle 45 46 22  More complex binding events More complex binding events Test for cooperativity: statistical factors Examples of cooperativity / allosteric effects Relation of subsequent binding constants of binding of H + G = HG K1 guests to a host with several binding sites H + HG = HG2 K2 𝐾-./ 𝑖(𝑚 − 𝑖) i – number of binding event (not events) = 𝐾- (𝑖 + 1)(𝑚 − 𝑖 + 1) m – number of binding sites For a simple system with binding to two sites 𝐾0 1(2 − 1) 1 = = 𝐾/ = 4𝐾0 independent sites: K2 = K1/4 𝐾/ (1 + 1)(2 − 1 + 1) 4 positive cooperativity: K2 > K1/4 negative cooperativity: K2 < K1/4 K1 K2 ‘off 2x more Other methods: ‘on 2x more likely than off’ likely than on’ Scatchard or Hill plot + or + NB: statistical factors often glossed over in biology and (kinetic argument) instead [H] increased! Chem. Soc. Rev., 2011, 40, p1305 47 48 23  More complex binding events More complex binding events Exampe negative cooperativity Negative cooperativity Two identical binding sites R = O– K1 ~3100 M-1 K2 ~550 M-1 K1 / K2 = 5.6 Why? Why? ACIE, 2016, 55, p9311 Tet. Lett., 1994, 35, p1295 49 50 24  More complex binding events Cyclodextrins as an example Cyclodextrins: a working horse Positive cooperativity by design OH O OH O O OH HO HO O O OH HO OH OH CD = O O OH HO O HO O 1 OH HO HO HO O O OH n OH HO OH O OH O O HO O HO O CD HO G= JACS 1995, 117, p1453 a-CD n = 6 b-CD n = 7 g-CD n = 8 51 52 25  Cyclodextrins as an example Cyclodextrins as an example Applications of cyclodextrins: Inclusion of guests into cyclodextrins: through hydrophobic interactions reduction of hydration shells upon complexation (entropy effect) 1. Industrial (e.g. dye inclusion) 2. Pharmaceutical (drug solubility increase) 3. Food applications (e.g. odor inclusion) 4. Agricultural (pesticide inclusion) Size-fit concept: 5. Chromatography (enantioselective separations) - enthalpy driven complexation for tightly fitting guests (enthalpically favorable Van der Waals interactions between guest and cavity wall) 6. Sensors (mass, optical, electrochemical) - entropy driven complexation for loosely fitting guests Also: possible hydrogen bonding between guests and OH-groups of CDs 53 54 26  Cyclodextrins as an example Cyclodextrins as an example Enthalpy-entropy compensation Cyclodextrins Analytical methods: NMR Geometry of inclusion: Qualitative argument: NOE measurements: If a binding interaction gets stronger (ΔH more favorable), it will give a stronger fixation of the ligand (ΔS less favorable) Example for cyclodextrins: ○ natural cyclodextrins modified cyclodextrins Chem. Biol. 1995, 2, p709; (DGo = DHo – TDSo = –RT lnKa) H.-J. Schneider et al., J. Am. Chem. Soc. 1991, 113, 1996; Chem. Rev. 1998, 98, 1875. V. Ruediger, H.-J. Schneider et al., J. Chem. Soc., Perkin Trans. 2 1996, 2119 55 56 27  Cyclodextrins as an example Cyclodextrins as an example Binding established by fluorescence Binding analyzed by calorimetry Inclusion of a solvatochromic dye: Steroids in a fluorescent cyclodextrin dimer: Time (min) Time (min) 0 50 100 0 50 100 150 200 O O N O S O 0 0 µcal/sec µcal/sec N 1,8-ANS -1 -1 -2 -2 OH 0 0 kcal/mole of injectant kcal/mole of injectant -2 -2 O O -4 OH COOH -4 COOH OH 7 -6 -6 a-e: increasing CD concentration: HO M. R. de Jong, J. F. J. Engbersen, J. Huskens, -8 -8 - blueshift of λmax (more polar excited state) HO HO OH D. N. Reinhoudt, Chem. 0 1 2 3 4 5 0 1 2 3 4 5 6 - intensity increase (reduced quenching) Eur. J. 2000, 6, 4034-40. Molar Ratio Molar Ratio 57 58 28  Cyclodextrins as an example Cucurbituril has similar properties as CD Extension to surfaces Langmuir 2017, 33, 8614−8623 59 60 29  Cucurbituril in action Cucurbituril in action Supramolecular regulation of bioorthogonal catalysis in cells using nanoparticle-embedded Supramolecular regulation of bioorthogonal catalysis in cells using nanoparticle-embedded transition metal catalysts transition metal catalysts 61 62 30  Cucurbituril in action Summary Supramolecular regulation of bioorthogonal catalysis in cells using nanoparticle-embedded transition metal catalysts What information are we after? * Strength of complexation (Ka; ΔG) * Stoichiometry (1:1, 1:2, more complex?) * Driving forces (type of interactions; ΔH vs ΔS) * Structure of the complex (3D) * Kinetics of complexation (ΔGTS) A plethora of techniques at our disposal J 63 64 31  Summary What typical techniques can we use? Classical: information about [HG] as a function of changing [H] or [G] 1. NMR spectroscopy: different δ and/or ∫ for H, G, HG; 2D techniques 2. Calorimetry: measures ΔH of complexation 3. Optical spectroscopy: absorbance, fluorescence; intensity differences 4. Many other techniques: * Mass spectroscopy: stoichiometry of complexes * Potentiometry: pH- or ion-selective electrodes * Conductivity: total salt concentration * Electrochemistry: redox signal integration, resistance change * Extraction: weight change upon phase transfer, or UV signal, etc. * Crystal structures: structural information * Computer models: sterics, electronics, enthalpies Choice depends on the technique’s concentration range 65 32