Proteins in solution: charge-tuning, cluster formation, liquid-liquid phase separation, and crystallization

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1 HERCULES Specialized Course: Non-atomic resolution scattering in biology and soft matter Grenoble, September 14-19, 2014 Proteins in solution: charge-tuning, cluster formation, liquid-liquid phase separation, and crystallization Tilo Seydel Institut Max von Laue Paul Langevin Outline: (1) Proteins in solution: crowding and salts, biological motivation (2) Charge-tuning and phase diagrams, liquid-liquid phase separation (LLPS) (3) Small-angle scattering (x-rays and neutrons) (4) Interaction potentials (5) Proteins and colloid physics, clusters, [ patchy colloids,] crystallization (6) Complementary methods: Neutron spectroscopy and light scattering (7) Summary and outlook Acknowledgement: Group of Frank Schreiber, Institute of Applied Physics, University of Tübingen

2 (1) Proteins in solution: crowding and salts, biological motivation Macromolecular crowding in living cells Watercolor by David S. Goodsell Proteins as an essential component Figure from: PhD thesis M.Hennig

3 (1) Proteins in solution: crowding and salts, biological motivation BSA in water + YCl3

(2) Charge-tuning and phase diagrams, liquid-liquid phase separation (LLPS) Complex phase diagrams in protein solutions: Solution regime at low salt concentration Precipitate regime involving a

4 (2) Charge-tuning and phase diagrams, liquid-liquid phase separation (LLPS) Complex phase diagrams in protein solutions: Solution regime at low salt concentration Precipitate regime involving a liquid-liquid phase separation at intermediate concentrations Reentrant dissolution at very high salt concentration Rising salt concentration F.Zhang et al., Phys.Rev.Lett. Vol.101, p (2008)

5 (2) Charge-tuning and phase diagrams, liquid-liquid phase separation (LLPS) Salt concentration Schematic of a phase diagram of a protein solution F.Zhang et al., Soft Matter, 2012, 8, Protein concentration D.Soraruf et al., Soft Matter, 2014, 10, 894

6 (2) Charge-tuning and phase diagrams, liquid-liquid phase separation (LLPS) Correlation length increase when approaching c* Static Light Scattering on BSA proteins in water 0.39mM Correlation length 0.38mM 0.33mM YCl3 salt concentration D.Soraruf et al., Soft Matter, 2014, 10, 894 Correlation length obtained from SLS via the Zimm equation from the inverse scattering ratio (details beyond the scope):

7 (2) Charge-tuning and phase diagrams, liquid-liquid phase separation (LLPS) Schematic of a phase diagram of a protein solution (in more detail) F.Zhang et al., Soft Matter, 2012, 8,

8 (2) Charge-tuning and phase diagrams, liquid-liquid phase separation (LLPS) Tuning the protein surface charge is the fundamental mechanism behind the phase diagrams F.Roosen-Runge et al., J.Phys.Chem.B 117, 577 (2013)

9 (3) Small-angle scattering (x-rays and neutrons) In the case of neutrons: Small-angle scattering: The principle Figure from: wikipedia Figure from: wikipedia Figure from: M.Hennig, PhD thesis, University of Tuebingen 2011

(3) Small-angle scattering (x-rays and neutrons) Small-angle scattering: Example data: Bovine Serum Albumin (BSA) in water F.Zhang et al., J. Phys. Chem. B, Vol. 111, No.

10 (3) Small-angle scattering (x-rays and neutrons) Small-angle scattering: Example data: Bovine Serum Albumin (BSA) in water F.Zhang et al., J. Phys. Chem. B, Vol. 111, No. 1, 2007 Dilute solution Obtain the shape (form factor): Polar semiaxis a=1.8+/-0.05nm Equatorial semiaxis: b=4.6+/-0.15nm F.Roosen-Runge et al., PNAS Vol.118, p (2011)

(3) Small-angle scattering (x-rays and neutrons) Small-angle scattering from more complex solutions: Hierarchy of correlation lengths Structural hierarchy of BLG solutions in the re-entrant regime

11 (3) Small-angle scattering (x-rays and neutrons) Small-angle scattering from more complex solutions: Hierarchy of correlation lengths Structural hierarchy of BLG solutions in the re-entrant regime revealed by SAXS. The peak and shoulders in the SAXS curve at q = 2.2, 1.8 and 0.3 nm-1 correspond to the monomer monomer correlation, the form factor of a dimer, and the cluster, respectively. F.Zhang et al., Faraday Discuss., 2012, 159,

12 (3) Small-angle scattering (x-rays and neutrons) Measured intensity in small-angle scattering from protein solutions: Number of protein molecules per unit volume Electron (SAXS) or scattering length density (SANS) difference between protein and solvent Volume of a single protein Form factor Structure factor Dilute solution => form factor Structure factor Fourier transform of the spherically averaged pair correlation function g(r):

13 (3) Small-angle scattering (x-rays and neutrons) Center-to-center distance of BSA molecules in water obtained from SAXS data Low volume fraction Increasing charge screening High volume fraction Protein volume fraction 1 ϕcsp 3 r c c ( ϕ ) 2 a where a=2.8nm and ϕ csp = π F.Roosen-Runge et al., Biochimica et Biophysica Acta 1804 (2010) Gap between two molecules less than diameter

14 (4) Interaction potentials Measured intensity in small-angle scattering from protein solutions: Number of protein molecules per unit volume Electron (SAXS) or scattering length density (SANS) difference between protein and solvent Volume of a single protein Form factor Structure factor Obtain the structure factor using a known form factor Structure factor Fourier transform of the spherically averaged pair correlation function g(r):

15 (4) Interaction potentials Scattering function structure factor interaction potential Structure factor: Radial distribution function indirect part Total correlation function: direct (short-ranged) ( influence of #1 on a third molecule, which in turn affects molecule #2 ) Density Integrate over positions of particle #3 Definition: Ornstein Zernike equation - describes how a correlation between two molecules is calculated (a rigorous derivation is difficult!) Direct correlation function using the mean spherical approximation closure relation : J.B.Hayter, J.Penfold; Molecular Physics 42, 109 (1981) Interaction potential => This is how the interaction potential enters! A set has closure under an operation if performance of that operation on members of the set always produces a member of the same set.

16 (4) Interaction potentials Interaction potential of a pair of protein molecules: Hard sphere screened Coulomb van der Waals attractive F.Zhang et al., J. Phys. Chem. B, Vol. 111, No. 1, 2007 depletion due to excluded volume of salt ions protein self-association

17 (4) Interaction potentials Square-well potential at high salt concentration (high charge screening), net attractive potential: van der Waals interactions excluded volume interactions hydration forces hydrophobic forces with well-depth and well-width given in multiples of the particle diameter (2R) Hard-sphere structure factor at moderate ionic strength predominant hard sphere (excluded volume) interactions In this case, the Percus-Yevick (PY) closure is used to numerically solve the Ornstein-Zernike equation F.Zhang et al., J. Phys. Chem. B, Vol. 111, No. 1, 2007 and references therein

18 (4) Interaction potentials Effect of crowding and salt SAXS on BSA in water F.Zhang et al., J. Phys. Chem. B, Vol. 111, No. 1, 2007

19 (4) Interaction potentials Screened Coulomb vs. cp Square-well Fit to previous slide left Structure factors for BSA + NaCl in water Square-well Screened Coulomb vs. cs F.Zhang et al., J. Phys. Chem. B, Vol. 111, No. 1, 2007 Contribution of hard sphere potential to overall structure factor

20 (4) Interaction potentials - Small-angle scattering and virial expansion Using the virial expansion of the osmotic pressure, one obtains the second viral coefficient B2 as a measure of the integrated strength of the interaction Structure factor in the low-q limit: The effective potential between two proteins separated by a distance r ensembleaveraged over the remaining proteins in solution is described by the potential of mean force, reading Analogously to the second virial coefficient, Bw characterizes the nature of the potential of mean force, in other words: Bw < 0 and Bw > 0 indicate that attraction and repulsion are dominating, respectively. Consequently, S(q-> 0) < 1 indicates that the protein solution is controlled by repulsion, while S(q -> 0) > 1 is a sign that attraction prevails. M.Hennig, PhD thesis, University of Tuebingen, 2011

21 (5) Proteins and colloid physics, clusters, [ patchy colloids,] crystallization Equilibrium clusters or intermediate-range order? Cluster formation in protein solutions Cluster peak SANS T=25oC Monomer peak T=5oC A.Stradner et al., Nature vol.432, p.425 (2004) Lysozyme 169mg/ml (open symbols) and 254 mg/ml (filled symbols) in water No change of the cluster peak position upon increasing concentration from 3 mg/ml to 273 mg/ml, indicating an invariance of the cluster number density and a linear dependence of the protein association number on concentration. A.Stradner et al., Nature vol.432, p.425 (2004)

22 (5) Proteins and colloid physics, clusters, [ patchy colloids,] crystallization Equilibrium clusters or intermediate-range order? Cluster formation in protein solutions Cluster peak SANS T=25oC Monomer peak T=5oC A.Stradner et al., Nature vol.432, p.425 (2004) Lysozyme 169mg/ml (open symbols) and 254 mg/ml (filled symbols) in water Interpretation ambiguous: The results may also be modeled by the form and structure factors of individual lysozyme particles using an interaction potential involving short-range attraction and long-range repulsion, not requiring the assumption of equilibrium clusters. A.Shukla et al., PNAS vol. 105, p.5075 (2008)

23 (5) Proteins and colloid physics, clusters, [ patchy colloids,] crystallization Neutron spin-echo on Lysozyme in aqueous solution The deviation from simple Brownian diffusion corroborates the presence of dynamic clusters. Q 0.08 Å-1, radius Lysozyme 33 Å Y.Liu et al., J. Phys. Chem. B 2011, 115,

(5) Proteins and colloid physics, clusters, [ patchy colloids,] crystallization Crystallization pathways The dashed line corresponds to a tie-line of a pair of solutions after LLPS.

The typical feature of the phase diagram is a metastable liquid liquid coexistence (L+L) below the gas crystal line (G+C). Free energy landscape of classical (a) vs.

24 (5) Proteins and colloid physics, clusters, [ patchy colloids,] crystallization Crystallization pathways The dashed line corresponds to a tie-line of a pair of solutions after LLPS. When the attractive well-width, Δ, is significantly smaller than the diameter of the particle, σ, (Δ/σ < 0.25), the phase behavior can be described by the phase diagram (b). The typical feature of the phase diagram is a metastable liquid liquid coexistence (L+L) below the gas crystal line (G+C). Free energy landscape of classical (a) vs. non-classical pathway (b) of nucleation. ΔGS-I in (b) represents the free energy difference between the intermediate state and the initial supersaturated solution. F.Zhang et al., Pure Appl. Chem. 2014; 86(2):

25 (5) Proteins and colloid physics, clusters, [ patchy colloids,] crystallization SAXS curves at different temperatures during cooling. Crystallization occurs below 25 C. The intensity of the maximum at q = 2.2 nm-1 decreases with lowering temperature, and the low q intensity increases steadily. Bragg peaks appearing in the intermediate q range have been indexed using the crystal structure. The curves are shifted upward for clarity. The inset shows the 2D scattering pattern at 10 C. F.Zhang et al., Faraday Discuss., 2012, 159,

26 (6) Complementary methods: Neutron spectroscopy and light scattering Protein dynamics: Center-of-mass short-time self-diffusion and internal diffusion M.Grimaldo et al., J. Phys. Chem. B 2014, 118,

27 (6) Complementary methods: Neutron spectroscopy and light scattering DLS DLS SLS DLS D.Soraruf et al., Soft Matter, 2014, 10, (a) Diffusion coefficient D1 corresponding to the faster component resulting from the two-exponential fit (symbols). The solid line is a linear fit to the entire dataset. (b) Diffusion coefficient D2 corresponding to the slower component resulting from the two-exponential fit (symbols). The solid line is a fit of a heuristic two-state model to the entire dataset. (c) Normalized inverse scattering intensity (symbols) and linear fit (solid line). (d) Weight ratio of the fast and the sum of both fast and slow components in the fit, measured at Θ = 60O. Vertical dashed lines are guides to the eye. The error bars are the 95% confidence limits from the fits. When not visible, the error bars are smaller than the symbols.

28 (7) Summary and outlook Crowding Complex phase diagrams SAXS/SANS Outlook: Dynamics

Fajun Zhang, Roland Roth, Marcell Wolf, Felix Roosen-Runge, Maximilian W. A. Skoda, Robert M. J. Jacobs, Michael Stzuckie and Frank Schreiber

Soft Matter, 2012, 8, 1313 Fajun Zhang, Roland Roth, Marcell Wolf, Felix Roosen-Runge, Maximilian W. A. Skoda, Robert M. J. Jacobs, Michael Stzuckie and Frank Schreiber Universität Tübingen, Institut für