A d. Par$cle size and the rate of dissolu$on. Consider the surface of the fixed amount of compound as the func$on of linear microcrystal

Transcription

1 Par$cle size and the rate of dissolu$on Consider the surface of the fixed amount of compound as the func$on of linear microcrystal size, d, and the total volume V For non-cubic shapes, calculate the Area as a func$on of total volume and shape. A d For simple cubic shape the total area of microcrystal surface is inversely propor$onal to the crystal size = V 6d 2 = d 3 6V d

2 Review The chemical poten$al of component J: Gas Liquid mixture ΔG and entropy of mixing. The chemical equilibrium K via concentra$ons and reac$on 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 )

3 Review Chemical poten$al of the same molecule in different phases or compartments (osmosis) must be equal Chemical poten$al of water is lower (beser) in solu$on If x solutes is small: Osmo$c pressure: P osm =MRT, where M is molarity corrected by dissocia$on, i, M=iM 0 Osmosis: semi permeable membranes. Osmolarity and Tonicity: coun$ng solutes that can not cross the membrane and taking dissocia$on into account ( i, van t Hoff s factor). Boiling point eleva$on Freezing point depression (K f does not depend on solutes!). K f = K kg/mol Water pressure reduc$on: Raoult s law Gas dissolu$on in water: Henry s law The effects are entropic and to the first approxima$on do not depend on the nature of solutes (colliga$ve proper$es) 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 RT = imrt V ΔT boiling = K b x solutes ΔT freezing = K f x solutes P w _ vap _ solution = P w _ vap _ pure x water P solute_in _ gas = K solute Henry x solute_in _ water

4 Review of Energy Contribu5ons to the non-covalent Binding Energy q-q: Coulomb: (+) or (-), strong in non-polar medium and weak in water. Long range (r -1 ). C=332 (kcal/mol)å(eu) -2 q-water: Ion and dipole Solva$on. Large (-):. D-H..A: Hbonds. Medium, short range. A-A: Van der Waals interac$on Weak (-0.2 km), but many. Short range (r -6 ). Apolar-Apolar Hydrophobic energy, water entropy contribu$on 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

5 H.H.: a quan5ta5ve picture Most drugs are weak acids or weak bases It is not all or nothing, there are always several species at different concentra$ons [ A ] log HA [ ] [ B] log [ BH + ] = ph = ph pka pka K a pka + [H ][Base] =, [Acid] = log( K ph = log([ H a + ) ]) Drug Solu$ons (acidic and basic) ph = pk log c a ph = pk a logc

6 LogD depends on LogP of the neutral form O OH and ph-pk a pka = 4.2; LogD (ph=7.2) = 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)

7 Binding Reac5on 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 ) [PL] << P 0 (protein in excess) : [PL]/[L] P 0 /K d, frac$on_drug_bound P 0 / (P 0 +K d )

8 Kine5cs 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

9 Braggs Law of Diffrac$on Methods The diffrac$on condi$on for a crystal 2d sinθ = nλ λ is the wavelength of gamma-rays ( ~ 1.5A ) d is the distance between planes, θ is the angle of diffrac$on and n is an integer known as the order of the diffracted beam F = q( E + v B) ( m / q) a = E + v ν = γb B Lorenz force mv R R = 2 = m q qvb v B

10 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!

11 Two and five slit diffrac5on In a crystal millions of planes in direc$on lead to coherent rays in the Bragg direc$ons d λ/2 Minimum λ maximum 2-slit and 5-slit diffrac$on

12 Diffrac5on: Bragg s Law The path difference is 2dsinθ The diffrac$on condi$on 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 diffrac$on and n is an integer known as the order of the diffracted beam In 1915, William Henry Bragg and William Lawrence Bragg were awarded the Nobel Prize for their contribu$ons 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

13 Diffrac5on from a single crystal Each spot corresponds to a set of parallel planes 2d sinθ = nλ

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

15 Waves An X-ray picture (radiograph), taken by Wilhelm Röntgen in 1896, of Albert von Kölliker's hand. Wilhelm Röntgen Waves and diffrac$on X-rays: single crystals to 3D electron density Bragg s condi$on (2dsinθ=nλ ) Unit cell, asymmetric unit, non-crys. symmetry

16 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 transforma$on is used We need spot intensi$es and phases, but we only have intensi$es. Yet another limita$on of quality Direct methods Anomalous diffrac$on (MAD) molecular replacement

17 Mass Spectrometry Analy$cal tool measuring molecular weight of molecules in chemistry, biology and pharmacology Only picomolar concentra$ons required Within 5 ppm for small organic molecules For a 40 kda protein, there is a 4Da error MS can detect amino acid subs$tu$ons, posttransla$onal modifica$ons

18 From mass to compound iden5ty MS iden$fies a mass, but does not tell you what the compound is. Many molecules will have the same mass Interpreta$on of fragmenta$on paserns may help if you choose from a small set Proteins: with a fixed human genome, it may be possible

19 Physics behind MS An ion moves in a magne$c field A neutral molecule CAN NOT BE measured with MS Magne$c field bends the trajectories according to the ra$o m/q

20 Electric (E) and Magne5c (B) Fields Field = Force on a probe charge q=1 Current (I) flowing through a wire produces a magne$c field, B [tesla] E Coulomb = C q r source 2

21 Lorenz Force When charged molecules move in electric and magne$c fields In electric fields they accelerate. F el = qe In magne$c fields their trajectories bend F mg = qvb F = q( E + v B) ( m / q) a = E + v B

22 Radius of ion trajectory The a force is perpendicular to V it causes circular mo$on with accelera$on v 2 /R If magne$c field B is perpendicular to V, then ma = qv B mv R 2 = m R = q qvb v B

23 Mass-to-charge ra5o m/q, or m/e, or m/z, z is the electronic charge of a molecular ion or fragment. If z=+1,m = m/z Mass: isotopes are detected. E.g. 12 C, 13 C, 79 Br : 81 Br, intensity 1:1 and 35 Cl : 37 Cl, intensity 3:1 Charge: in an electron impact mass spectrometer, a high energy beam of electrons displaces an electron from the organic molecule to form a radical ca5on known as the molecular ion. If the molecular ion is too unstable then it can fragment to give other smaller ions.

24 Spectrum of 2-chloropropane Loss of Cl gives the main peak.

25 Separa5on of mixtures Chromotography, (greek, color- wri$ng) Chromatography exploits par$$on between a mobile phase and a sta$onary phase to separate the components in a mixture. Molecules interact with the sta$onary phase based on charge, rela$ve solubility or adsorp$on Gas, thin layer, paper, Column (liquid) ion-exchange (charge) size-exclusion (size) Affinity FPLC (proteins) and HPLC (pressure) Mikhail Semenovich Tsvet, , a Russian botanist. He used liquid - adsorp$on column chromatography Thin layer chromatography is used to separate components of chlorophyll

26 Chromatography terms Prepara5ve chromatography is used to nondestruc$vely purify sufficient quan$$es of a substance for further use, rather than analysis. Large HPLC columns. Analy5cal chromatography is used to determine the iden$ty and concentra$on of molecules in a mixture. Quan$ta$ve. Mid-size HPLC columns LC of LCMS. Small HPLC columns. The analyte is the substance which is to be purified A chromatogram is the visual output of the chromatograph. Different peaks -> different molecules The mobile phase is the analyte and solvent mixture which travels through the sta$onary phase The reten5on 5me is the characteris$c $me it takes for a par$cular molecule to pass through the system Sta5onary phase: Examples include the silica layer, or columns

27 HPLC High-performance (high pressure) LC

28 Shopping in Factory outlets The elu$on $me depends on the number and dura$on of stops

29 Approaching the Finals Friday: Next Friday: 8am, Review (IK), Exam