Dr.Abel MORENO CARCAMO Instituto de Química, UNAM. address:

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1 Dr.Abel MORENO CARCAMO Instituto de Química, UNAM. address:

2 When? Understanding the macromolecular scale in time for crystal growth phenomena It is typical for crystal growth that many different length scales occur simultaneously: 0.01 ns for molecular conformations, ns for surface structure and defect displacements, µs for surface step displacement, ms for growth on one atomic layer, seconds for hydrodynamic transport, and minutes for homogenous nucleation.

3 Why are DLS & SLS needed? How? For problems of homogeneity, nucleation, protein-protein interactions, precrystallization conditions, and recently to predict the induction time for growing protein crystals. Growth from solutions is usually predicted by hydrodynamic properties using dynamic and static light scattering methods.

4 Dynamic Light Scattering Photon correlation spectroscopy (PCS) also known as dynamic light scattering (DLS) is concerned with the investigation of correlation of photons. The objective of PCS is to find any peculiar properties of the scattered signal which can be used to characterize and describe the seemingly random noise of the signal, and the correlation curve is used to achieve this objective.

5 What is needed from the experimental viewpoint?

6 How does DLS work? In principle, dynamic light scattering (DLS) can be used to study any phenomenon that gives rise to an intensity fluctuation in the light that has been scattered from a scattering source: a) Protein monomers b) Protein aggregates c) Micro-crystals d) Precipitating agents e) Additives f) Even dust particles.

7 Each scattering source will scatter light with a characteristic intensity (static property), which we will give the static light scattering data and a characteristic scattered intensity fluctuation (dynamic property) giving us the dynamic light scattering data.

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9 Light scattering and crystal growth Using dynamic light scattering to screen and improve protein crystal growth procedures, one does not need to employ overly sophisticated data reduction schemes. From the crystal growth point of view, one would like to be able to: a) detect the formation of the small protein aggregates which allows nucleation and growth to be monitored, b) estimate the mean value for the diffusion coefficient and hence the particle size of the protein molecules under various solutions conditions, and c) characterize aggregates as protocrystals or protoprecipitates

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13 What kind of solid phase is obtained? Early in the evolution of a supersaturated solution of macromolecules, monomers assemble to form aggregates, which lead either to crystals or precipitates. In an obvious terminology it is convenient to refer to the former as CRAGGS (crystalline aggregates) and the latter as PRAGGS (precipitating aggregates).

14 DLS & SLS for PROTEINS The reported uses of DLS & SLS for the specific purpose of studying crystallizing protein solutions have generally been for: a) Characterize of the thermodynamic properties of the solutions where aggregates are forming b) Monitoring the nucleation kinetics for control purpose. Reference: W.W. Wilson. Methods: A companion to methods in enzymology, 1, No.1 (1990)

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28 NUCLEATION: THE BIRTH OF CRYSTALS Figure 2: Schematic representation of the different nucleation mechanisms, starting from (a) a supersaturated solution to (b) a crystal. Reprinted with permission from Erdemir et al. 21. Copyright 2009 American Chemical Society.!

29 Crystalliza*on process and nuclea*on Energe&cs of the whole crystalliza&on process: Δµ = µ s - µ c (1) were µ s and µ c are the chemical potentials of a molecule in the solution and in the bulk of the crystal phase, respectively. When Δµ > 0, the solu&on is supersaturated, and only then is nuclea&on and/or crystals growth possible. The solu&on is, respec&vely, saturated or under- saturated when µ s - µ c = 0 or Δµ < 0. Δµ = kt ln β (2) on this equa&on β = C /C e = supersatura&on. where k is the Boltzmann constant, T is the absolute temperature. The β the supersaturation, i.e. the ratio of actual solute concentration (more precisely the activity) divided by the concentration (or activity) at the equilibrium. The work W (J) to form a cluster of n = 1, 2, 3 molecules can be obtained by thermodynamic considera&ons W(n) = - nδµ + Φ(n) (3) Φ (J) represents the effec&ve excess energy of the cluster, while Δµ is given by Equa&on 2

30 According to the classical nuclea&on theory, Φ(n) is merely equal to the cluster total surface energy γa c (n) where γ (J m - 2 ) is the specific surface energy of the cluster/solu&on interface, A c (n) = (36πν o2 ) 1/3 n 2/3 is the area of the cluster surface. In this case, ν o (m 3 ) is the volume occupied by a molecule in the cluster. W(n) = - n k T ln β + (36 π ν o2 ) 1/3 γ n 2/3 (4) γ = Bλ/ν o 2/3 (5) In this equa&on, B is a numerical factor (ranging from 0.2 to 0.6), this value is approximately equal to for spherical clusters, and λ (J) is the molecular heat of dissolu&on. For the case of proteins and other biological macromolecules this value must be adjusted to for quasi- spherical par&cles.

31 This implies that γ is propor&onal to the ln C e and indeed is the case, since λ and the solubility C e are related by C e = (1/ν o )exp(- λ/kt) as described by Moelwyn- Hughes. γ = (B k T / ν o 2/3 ) ln [1 / ν o C e (T)] (6) So that: λ = - kt ln (C e ν o ) (7) Finally for the surface energy, we can get a whole equa&on as follows: γ = B [ - kt ln (C e ν o )]/ν o 2/3 (8) For the crystalliza&on process we have the following equa&on: ΔG = - [(4/3 π r 3 ) / Ω] k T ln β + 4 π r 2 γ (9) The supersatura&on is defined by β = C/C e or α= [(C- C e )/C e ]. In solu&on some parameters and surface energy can be derived from Juarez- Mar&nez and Moreno Equa&on: 2 γ v o / r = k T ln β + A 2 k T M r C e (β- 1)... (10)

32 Substance M r (kda) γ (erg/cm 2 ) H 2 O content (%) Reference DMSO 78 x Benzene 78 x Glycerol 92 x Insulin Lysozyme Chymotrypsinogen Thermolysine Concanavalin A Apo-ferritin STMV * kda in MW is generally used only for proteins Reference: Sanchez-Puig et al. Protein and Peptide Letters. Vol 19, June 2012.

33 The Physicochemical parameters to understand the crystallization process Reference: Sanchez-Puig et al. Protein and Peptide Letters. Vol 19, June 2012.

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