1 / 41

RNA-directed Viral Assembly

I ) Self-Assembly and Free Energy Minimization. RNA-directed Viral Assembly. II) Fundamental Interactions. III ) Self-Assembly Empty Capsids. IV) Condensation of RNA genome molecules. V) Free Energy Landscape Viral Assembly. I ) . (1995, Scientific American). “Mark I” Self-Assembly

lieu
Download Presentation

RNA-directed Viral Assembly

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. I) Self-Assembly and Free Energy Minimization. RNA-directed Viral Assembly II) Fundamental Interactions. III) Self-Assembly Empty Capsids. IV) Condensation of RNA genome molecules. V) Free Energy Landscape Viral Assembly.

  2. I) (1995, Scientific American) “Mark I” Self-Assembly Self-assembling Monolayer

  3. “Thermodynamic Assembly”: assembled and disassembled components in thermal equilibrium. Amphihilic Molecules Variational Principle: Gibbs Free Energy G = U – TS – m N dG = 0 “Hydrophilic” “Hydrophobic” Limited Complexity

  4. Synthetic Chemistry: J-M Lehn, D.Cram circular helical * weak, non-covalent bonds * water soluble “host-guest”

  5. “Mark II” Coded assembly. • DNA encoded assembly program -> protein synthesis-> assembly • Constant free energy consumption. dG ≠ 0 • Complexity: unlimited. • Is viral assembly Mark I or Mark II ? Free energy ?

  6. Genome: II ) Fundamental Interactions. • Cowpea Chlorotic Mottle Virus: CCMV • (J. Johnson et al.) T=3 Capsid 180 identical proteins • In-vitro Self-Assembly

  7. A) Capsid Proteins: Amphiphilic Layer capsid proteins N-terminal tail Water • Layer: Spontaneous Curvature Hydrophobic • Expect reversible, thermodynamic assembly Water

  8. B) • Strength attractive interactions increases with acidity.

  9. C) Electrostatic Interactions • Water-accessible equipotential surfaces. Blue positive; Red negative. • Inside-Outside Voltage Difference (McCammon et al.)

  10. Electrical Charges CCMV Dimers QC(pH=7) = -28 “ core” charges (physiological) Very large ! + + D = 2 nm QT=+20 “tail” charges/dimer

  11. Some “just so” questions about CCMV electrostatics RNA has a total negative charge ≈ -3,000 Positive tail charge ≈ 90 x 20 = + 1,800 • Neutralization promotes viral assembly. 1) Why neutralize only a fraction of RNA charge ? Outer layer charge ≈ - 28 x 90 = -2,520 • 2) What’s the role of the large negative protein charge? • Prevents aggregation of viruses. • Prevents RNA from sticking to capsids.

  12. III) Self-Assembly Empty Capsids Electrostatic Repulsion vs. Hydrophobic Attraction + +

  13. Treat viral assembly as a chemical reaction: Assembled T=3 capsid 90 Free CP Dimers (“subunits”) Thermal Equilibrium Concentrations “Law of Mass Action” Dimer Concentration “Signature” of Thermodynamic Self-Assembly • DG = assembly energy/dimer

  14. Empty capsid assembly experiments * Acidic environment (low pH) Chromatography dG = 0 • DG ≈ 30 kBT/dimer. • Capsid assembly is irreversible!? reversible irreversible

  15. Capsid Van der Waals/Landau Free Energy Ns adsorbed proteins R D QC=28 rs = [Ns / R2] area density “order parameter” Entropic Free Energy 2D ideal solution e: Adsorption energy proteins on sphere. vs: Second “virial coefficient” ws: Third virial coefficient ≈ kBT D4 Thermal equilibrium: Chemical potential proteins

  16. Second Virial Coefficient Qc=-28 • Electrostatics vs Hydrophobicity • vS = vDH - J Qc=-28 - - - - - - - 2D - Capsid Proteins “Bjerrum Length” ≈ nm R ψ “Debye Parameter” ≈ 1/nm Angle-dependent hydrophobic attraction Optimal Angle/ Radius CCMV (pH=5): QC = 20 vDH /kB T = 400 nm2 Measured for empty shells Capsid Radius CP-CP Hydrophobic Attraction

  17. Debye-Hückel Theory of Aqueous Electrostatics Macro ion Charge Density (CPs/RNA) Dielectric Constant Water Debye parameter Electrical Potential - Bjerrum length Electrostatic Free Energy Sheet of charges

  18. Summary • Delicate balance between large repulsive interactions and large attractive interactions • Second virial coefficient depends on the sphere radius R. VS ≈ VDH RC R R*

  19. Free energy “landscape” F(R,Ns) F(R,Ns) R vs> 0 R* vs= 0 Rc vs< 0 Ns Nc =90 “Common-tangent construction” Phase-coexistence: nearly closed shells and nearly bare spheres

  20. IV) Condensation RNA genome molecules • Highly branched, highly charged “polyelectrolyte” Q ≈ - 3,000 L = 300 nm Paired stretches l ≈ 5 bp ≈ 100 nm Neutron scattering R ≈ 11 nm (no “condensing agents”) • Highly compactified ( Knobler et al. ) CCMV RNA 1

  21. Free energy F = U - TS RNA Condensation Condensing Agent “Intermediary” “Native” dG = 0 “Folded Fraction” # condensing agents per RNA θ Gibbs Free Energy G = F – m( [agent])θ Chemical potential condensing agent Condensing agent concentration (polyvalent counterions) • Highly cooperative, first-order phase transition. Koculi E, Lee NK, Thirumalai D, Woodson SA. J Mol Biol. 2004, 341(1):27-36.

  22. Tertiary contacts N state: folded • Ribozyme (Tetrahymena) RNAse • (Cech)

  23. RNA inside T=3 virus: • Highly condensed What are the condensing agents ? CCMV Capsid protein ss RNA PO4- Disordered N-Terminal Tail: + 10 charges RNA Condensing Agent Numerical Simulation: e (tail/RNA)≈ 10-15 kB T Zhang et al. Biopolymers. 2004 November; 75(4): 325–337)

  24. CCMV Dimers Remove Protein Cores QT=+20 tail charges/dimer

  25. Condensation of CCMV RNA R Good Solvent: “fractal” R(N) ≈ N 1/2 l =5bp • Flory-Landau mean-field theory # segments N N=300 segments Entropic Elasticity U Radius gyration of an “ideal” Flory-Stockmayer branched polymer Linear polymers: much larger • V(q): Second Virial Coefficient. q: # tails / segment • W: Third Virial Coefficient ≈ kB T l 6

  26. Condensed Globule Swollen Fractal V V=0 “Theta Solvent” • CCMV RNA genome free in solution • R ≈ 11 nm • l = 0.5 nm • V(q=0)/ kB T = 1-10 nm3 * No phase transition

  27. Second Virial Coefficient Segment charge Tail fraction Bjerrum Length ql = - 10 Maximum concentration Non-electrostatic QT = + 10 (CCMV) Polyvalent Counterion Charge Neutralization Debye parameter (free RNA in solution) RNA/tail association: “unveils” strong RNA self-attraction

  28. RNA Globule 15-20 milli Volt Voltmeter DV qM q “Donnan Potential” Charge neutral

  29. RNA/tail affinity * Minimize with respect to R Chemical potential tails V(q) > 0 Swollen, charged V(q) < 0 Condensed, neutralized q qm= ql /QT • Common-tangent Construction: Phase Coexistence Gel swelling/shrinking Large, reversible first-order phase transition

  30. V) Free Energy Landscape Combine: # Surface-Adsorbed CPs = # Tails

  31. Charged Tail- neutralized Radius R Micro-segregation 60 excess CP dimers # proteins/segment

  32. Is this processes thermodynamic reversible self-assembly? Step 1 Reversible Protein-RNA assembly Same CP chemical potentials Irreversible Step 2 Micro-segregation Lowered CP chemical potential Enhanced RNA self-attraction Irreversible + 60 Step 3 Protein expulsion Lowered CP chemical potential Donnan Potential + Protein Self-repulsion “Michaelis-Menten like”

  33. How are excess proteins expelled? - - Brownian Ratchet: - - - - + Capsid Proteins _ + _ + _ Tails RNA

  34. How good is mean-field theory? Protein-Protein binding sites Toy T=1 Virus Flexible linear polymer genome genome binding sites” * Genome molecule: no branching. * Assembled state: # binding sites = chain length Elrad and Hagen

  35. Protein-genome affinity e > Protein-protein affinity J time * RNA/Protein pre-assembly condensate

  36. A B C D E Problem: Optimal angles visible in A-C A C D • Local correlations. E

  37. Genome-protein affinity e weaker than protein-protein affinity J RNA “glues” capsomers together one-by-one * Heterogeneous nucleation of a shell on a flexible RNA scaffold

  38. “Down the funnel” Partial shells Many possible assembly pathways

  39. “Antenna-Assembly” (Hu and Shklovskii)

  40. “Hamiltonian Cycle” • Graph-theoretic problem • (R.Twarock)

  41. Conclusions Assembly of small ss RNA viruses can be viewed as the combination of reversible RNA condensation + quasi-reversible shell formation. Combination of two simple thermodynamic assembly processes produces a more complex free energy landscape with different possible multi-step Irreversible pathways. 3) Viral assembly appears intermediate between Mark I and Mark II assembly.

More Related