Multi-scale modeling of protein-dna complexes

Transcription

1 Multi-scale modeling of protein-dna complexes Elizabeth Villa Theoretical and Computational Biophysics Group

2 Outline Motivation Test case: the lac repressor-dna complex Multi-scale method Molecular dynamics of protein-dna Elastic rod model of DNA Linkage between two descriptions Results: Sneak peek

3 Motivation Complexes with looped or coiled arise often in nature, e.g., regulation of gene expression. DNA loops yield large MD systems with slow dynamics! Multi-scale method needed for the study of these complexes.

4 Test case: Lac repressor An E. Coli Transcription Regulator Galactose deactivates the lac repressor and stimulates the expression of the proteins required for its digesttion In the absence of galactose, the lac repressor shuts down the genes, which code for the proteins of the galactosedigesting system RNA poly

5 Lac Repressor : A Genetic Switch Repression loop: forms when the lac repressor binds 2 out of 3 recognized DNA sites: Promoter Genes O 3 76 bp O bp O 2 Lac repressor: a tetramer, dimer of dimers, each with a DNA-binding hand

6 Lac Repressor : Open Questions What is the actual structure of the clamped DNA loop? How does the lac repressor structure change under the stress of the looped DNA? What are the principal degrees of freedom of the protein structure?

7 Multi-scale method Combines Full-atom MD of protein bound to short DNA Elastic rod model of DNA to describe DNA loops Coupled by Boundary conditions (MD) Forces (rod)

8 Molecular Dynamics Use conventional MD to describe protein (NAMD2, Charmm22 force field, PBC, NPT, PME) Connected with rod through terminal base pairs (tbp s)

9 Terminal base pairs (tbp s) a. Harmonic constraints to preserve Watson-Crick base pair structure. b. Definition of boundary conditions with a local frame of reference c,d. Application of forces and torques obtained from the elastic rod calculation

10 Lac repressor structure Structure modeled from avaliable crystal and NMR structures ~230,000 atoms (with water and ions) Periodic boundary conditions Full electrostatics (Ewald summation) Constant pressure and temperature Forces from the DNA loop are applied to the tbp s.

11 Elastic Rod Model of DNA The DNA is approximated by an elastic rod (ribbon) The rod consists of its centerline curve (with principal curvatures κ 1 and κ 2 ), and twist ω(s) A local frame is defined at every base pair Forces and torques act at each point of the rod

12 Elastic Rod Model of DNA Force balance Torque balance Inextensibility Torque approximation Sequence Bending Intrinsec dependence anisotropy curvatures & twist We seek solutions that minimize the Energy functional:

13 Elastic Rod Model of DNA 11 non-linear differential equations of 13th order Include the intrinsic curvatures/ twist

14 Boundary Conditions for the Problem ω ψ Ro Obtained from MD: The distance between the ends of the clamped DNA loop (tbp s) The tbp s relative orientation Yield a Boundary Value Problem (BVP)

15 The Boundary Value Problem (BVP) is Solved by a continuation method

16 Other topologies of the loop IO OO II OI Forces of ~10pN NOTE: The experimental value for the energy is ~20kT small electrostatic contribution to energy

17 Full-atom structures The solution to the elastic rod model can serve as a scaffold to build ideal allatom DNA structures CAP protein binding site RNA polymerase binding site Lac operon genes Lac repressor binding site Lac repressor binding site

18 From the solution to the elastic rod model, one can obtain the torques and forces at the end points (s=0,1) Forces and torques is directly obtained from the solution to the system.

19 Multi-Scale Method F F MD provides the rod calculation with boundary conditions every 10 ps The elastic rod instantly adapts to the new conditions and provides forces at the end points Really useful to save in system size and simulation times!

20 Sneak peek: Multi-scale simulation of the lac repressor-dna complex

21 Outlook Simulate multiprotein-dna complexes (e.g., CAP-lac repressor- DNA) with multi-scale method. An all-atom structure of a segment of the loop (e.g., a binding site of a protein) may be studied at all-atom resolution, using a similar multi-scale approach. F left F right