Waves. λ = c / f ω = 2π f = 2π / T. E = hf = ω E mole = N A. E X ray. ~ ~ J / mol! Wilhelm Röntgen

Transcription

1 Waves An X-ray picture (radiograph), taken by Wilhelm Röntgen in 1896, of Albert von Kölliker's hand. Wilhelm Röntgen λ c / f ω 2π f 2π / T E hf ω E mole N A ω E X ray ~ ~ J / mol!

2 Two and five slit diffrac2on In a crystal millions of planes in direchon lead to coherent rays in the Bragg direchons d λ/2 Minimum λ maximum 2-slit and 5-slit diffrachon

3 Diffrac2on: Bragg s Law The path difference is 2dsinθ The diffrachon condihon for a crystal 2d sinθ nλ λ is the wavelength of gamma-rays ( ~ 1.5A ) d is the distance between planes, θ is the angle of diffrachon and n is an integer known as the order of the diffracted beam In 1915, William Henry Bragg and William Lawrence Bragg were awarded the Nobel Prize for their contribuhons to crystal structure analysis. They were the first and (so far) the only father-son team to have jointly won the prize. Coherence will only be achieved for certain values of θ for each set of planes

4 Diffrac2on from a single crystal Each spot corresponds to a set of parallel planes 2d sinθ nλ

5 Single Crystal Only one crystal is mounted for X-ray crystallography In this crystal all unit cells are oriented the same way

6 Waves An X-ray picture (radiograph), taken by Wilhelm Röntgen in 1896, of Albert von Kölliker's hand. Wilhelm Röntgen Waves and diffrachon X-rays: single crystals to 3D electron density Bragg s condihon (2dsinθnλ ) Unit cell, asymmetric unit, non-crys. symmetry

7 The phase problem Each spot needs: 3 coordinates, h,k,l, intensity and phase, F hkl, A hkl To get the electron density map the Fourier transformahon is used We need spot intensihes and phases, but we only have intensihes. Yet another limitahon of quality Direct methods Anomalous diffrachon (MAD) molecular replacement

8 Drug Targets in PDB Uniprot contains ~20,250 human proteins, with the mean length of 550 and median of 400 amino acids PDB contains structures of some DOMAINS of only of 2600 of those proteins (12 % protein coverage). Many drug targets (around 500 human proteins are among the PDB domains however)

9 Review The chemical potenhal of component J: Gas Liquid mixture ΔG and entropy of mixing. The chemical equilibrium K via concentrahons and reachon stoichiometry From K, to ΔG o From K at T 1 and T 2, to ΔH o, Van t Hoff K µ ln K g µ 0 + i i µ P c µ 0 + i i Δ r G RT P RT ln( i P c RT ln i c a i is molar fraction x i or concentration c i or activity depending on the standard state and ideality n [ A B ν ai i, e. g. K i 1 [ A][ B o ΔrH ln K RT o ΔrS + R o K ln K 2 ΔH R 0 0 ] ] 1 T1 T o )

10 Review Chemical potenhal of the same molecule in different phases or compartments (osmosis) must be equal Chemical potenhal of water is lower (beper) in soluhon If x solutes is small: OsmoHc pressure: P osm MRT, where M is molarity corrected by dissociahon, i, MiM 0 Osmosis: semi permeable membranes. Osmolarity and Tonicity: counhng solutes that can not cross the membrane and taking dissociahon into account ( i, van t Hoff s factor). Boiling point elevahon Freezing point depression (K f does not depend on solutes!). K f K kg/mol Water pressure reduchon: Raoult s law Gas dissoluhon in water: Henry s law The effects are entropic and to the first approximahon do not depend on the nature of solutes (colligahve properhes) µ w _ in _ solution µ w _ pure + RT ln(x w ) Δµ w RT ln(1 x solutes ) RTx solutes ΔS w Rx solutes P osm Δn sol V ΔT boiling K b x solutes ΔT freezing K f x solutes RT iδmrt P w _ vap _ solution P w _ vap _ pure x water P solute_in _ gas K solute Henry x solute_in _ water

11 Review of Energy Contribu2ons to the non-covalent Binding Energy q-q: Coulomb: (+) or (-), strong in non-polar medium and weak in water. Long range (r -1 ). C332 (kcal/mol)å(eu) -2 q-water: Ion and dipole SolvaHon. Large (-):. D-H..A: Hbonds. Medium, short range. A-A: Van der Waals interachon Weak (-0.2 km), but many. Short range (r -6 ). Apolar-Apolar Hydrophobic energy, water entropy contribuhon E el E solv w m C Cq 2r q q 1 ε E hb f (r HA,α ALP HD) E vw A r 12 B r 6 E hp σ Area q 2 1 ε r 2 w 1 ε m

12 H.H.: a quan2ta2ve picture Most drugs are weak acids or weak bases It is not all or nothing, there are always several species at different concentrahons [ A ] log HA [ ] [ B] log [ BH + ] ph ph pka pka K a pka + [H ][Base], [Acid] log( K ph log([ H a + ) ]) Drug SoluHons (acidic and basic) ph pk log c a ph pk a logc

13 LogD depends on LogP of the neutral form O OH and ph-pk a pka 4.2; LogD (ph7.2) water octanol O OH [ AH ] log P log [ AH ] oct wat O O log D [ AH ] log [ AH ] oct wat + [ A + [ A ] ] oct wat O O LogD is apparent LogP logd logp - log( ph-pk a) for acids logp (ph pka) (for ph> pka+1, charged form dominates) logd logp - log( (ph-pk a)) for bases logp + (ph pka) (for ph < pka-1, charged form dominates)

14 Binding Reac2on PL P + L; K d [P][L]/[PL] ; K a 1/K d x [PL]; (P 0 -x)(l 0 -x) x K d x ½ ( P 0 + L 0 + K 0 - ( (P 0 + L 0 + K 0 ) 2-4P 0 L 0 ) ½ ) P 0 << K d : [PL]/[P] L 0 /K d (50% L 0 K d ) Target FracHon: [PL]/[P 0 ]L 0 /(K d + L 0 ) [PL] << P 0 (protein in excess) : [PL]/[L] P 0 /K d, frachon_drug_bound P 0 / (P 0 +K d )

15 Kine2cs and Diffusion k Ae G activation RT [A] [A] o kt J D dc dx ΔC [Drug] Flux(J) Area(A) Time K eq [B] [A] k f k r [A] [A] o e kt 1 [ A] 1 A [ ] 0 k 2 t K bind [PL] [P][L] k on k off K d [P][L] [PL] k off k on

16 Methods Braggs Law of DiffracHon The diffrachon condihon for a crystal 2d sinθ nλ λ is the wavelength of gamma-rays ( ~ 1.5A ) d is the distance between planes, θ is the angle of diffrachon and n is an integer known as the order of the diffracted beam B v E a B v E F + + ) / ( ) ( q m q Lorenz force B q m R B q R m v v v 2