Cecilia Clementi s research group.

Transcription

1 Cecilia Clementi s research group

2 Proteins don t have a folding problem it s we humans that do! Cartoons by Larry Gonick In principle, the laws of physics completely determine how the linear sequence of amino acids in a protein will fold into a complex three-dimensional structure with useful biochemical properties. In practice, predicting structure from sequence remains a major unsolved problem.

3 Mesoscale Modeling: Blending Theory, Simulation And Experiment This robustness of folding behavior makes the empirical case for some protected behavior of mesoscopic biological matter. [...] Are there organizing principles in mesoscopic systems? The truth is that we do not know one way or the other. The experimental record has not yet spoken. But it is clear that the question is sufficiently important that it cannot be evaded much longer. Whether we want to or not, we are now forced to take a stand Meso Nano

4 In principle, basic Physics and Chemistry are applicable to the process, but in practice. femtosecond picosecond nanosecond microsecond second. protein folding is difficult to characterize! helix coil MD (force field/all-atom) simulations (microscopic) too slow! 16 orders of magnitude Mesoscale description Wet lab Experiments (macroscopic). too fast!. protein folding is difficult to characterize!

5 How do proteins fold? the public is perplexed Proteins fold spontaneously into their Native Structure, in a biologically short time scale (~ secs) the Native Structure is the ground state of the system, the energy gap to the first excited state is >> kt folding of a protein is a chemical reaction, the reaction mechanism is such that the transition state has low free energy. proteins fold or unfold as a response to external stimuli and to perform a biological function

6 Connection between Hydrogen exchange simple folding models and experiments through THE DETECTION OF HETEROGENEITIES IN THE FREE ENERGY LANDSCAPE Free energy TS Homogeneous folding mechanism (all contacts are equally important ) Reaction coordinate Free energy Intermediate State Heterogeneous folding mechanism (order of contact formation matters) Reaction coordinate

7 Inverse methods Free energy Reaction coordinate Statistical Mechanics

8 Reconstructing the landscape Pieces Big picture Experimental measurements Folding landscape How can we reconstruct the whole picture? We need to develop new methodologies

9 Φ value Analysis Φ value is related to the ratio between change in free energy of the transition state and change in total stability for a given mutation kt ln( k Φ = G mut 0 / k k mut folding rate of a given mutant k wt folding rate of the wild type protein wt ) Φ = 1 environment native-like 0 environment unfolded-like

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11 Calculation of Free Energy differences upon mutations Model Hamiltonian for a protein system Sum over all interactions Strength of the interaction Conservative mutation Amino acids with large side chains are replaced by amino acids with smaller side chains (gly, ala) We assume that a mutation removes some interactions between atoms Tryptophan Alanine S.Matysiak & C.Clementi (J.Mol.Biol. 2004, in press)

12 Hamiltonian after mutation of residue k Sum over all the contacts involving residue k Fraction of deleted interactions Perturbation performed on the Hamiltonian With δh we can calculate the variation in Free Energy due to mutation of residue k This average is computed by simulations How can we adjust {ε ij } in order to reproduce exactly the experimental data? We can compare these quantities with the experimental measurements! S.Matysiak & C.Clementi (J.Mol.Biol. 2004)

13 Inverse procedure : outline We have experimental data for free energy differences (for instance) Assume that a set of optimal parameters {ε*} exist such that Assume the 0 th order model parameters are not too far from the optimal ones can be expressed as a function of simple average quantities, easily obtained from simulation System of linear equations gives the optimal parameters! S.Matysiak & C.Clementi (J.Mol.Biol. 2004)

14 For each single mutation we can do a Taylor expansion of G(mut,k) in ε ij We obtain the following equation: experimental data simulation result These averages are computed by simulations Corrections in the energy parameters The above equation reduces to a system of linear equations S.Matysiak & C.Clementi (J.Mol.Biol. 2004)

15 INVERSE PROCEDURE Given a Hamiltonian function Initial guess for the parameters (zero order approximation) Calculation of G j and G 0 for each single mutation Same as in experiments? Optimal values of the parameters First order Taylor expansion of G j and G 0 in ε ij Correct the energy parameters S.Matysiak & C.Clementi (J.Mol.Biol. 2004)

16 Ribosomal protein S6 Homology between the Alzheimer peptide (β- AP) and a 16 residue segment in wild-type S6 Detours on the landscape can be induced either by changing experimental conditions or by mutating a few key residues The Free Energy landscape of S6 Collaboration with Dr. Mikael Oliveberg (Umea University, Sweden) Shaped by natural evolution to avoid dangerous configurations prone to misfolding?

17 STARTING POINT Comparison of free energy of wild-type S6 and circular permutant S6 perm13-14 wild-type S6 Free energy barrier is much higher for WT than p13-14, in agreement with experiments S6 perm13-14 Comparison of Transition State structure from experiments. and from simulations

18 Ribosomial protein S6: experimental data from Oliveberg s group? Most energetic native interactions Longest loops

19 Energetic heterogeneity Starting with the homogeneous distribution of energies and after doing a few iterations with our procedure. WT and p13-14 BLIND TEST!!! We find an effective set of contact energies!

20 Energetic heterogeneity

21 Energetic heterogeneity: effect on the free energy barrier

22 General approach: design minimally frustrated sequences in a coarse-grained (completely non-go ) model 1-bead per residue (C α model) 5-8 aminoacid colors Key to successful design : take into account the fact that native proteins are very compact objects P.Das, S.Matusiak & C.Clementi 2004

23 Design minimally frustrated sequences in a coarse-grained (completely non-go) model In practice: color -dependent parameters Hamiltonian Assigned from distribution of native contact distances, and optimized for high packing Iterative design procedure to select optimal values of {ε} and {δ} for a given amino-acid sequence a(i), i=1,,n P.Das, S.Matusiak & C.Clementi 2004

24 Generate set of non-native structures (decoys) native structure decoy structures Extract sequence, and set of parameters ({ε} and {δ}) by maximizing the energy gap between native and decoys structures Heat & quench simulations of selected sequence(s) parameter subspace 2 native structure parameter subspace 1 NO Fold back to native structure? YES Proceed to thermodynamics and kinetics analysis Iterative procedure converges very nicely for all proteins we have tried so far ( aa)! D.Maxwell & C.Clementi 2004

25 Application to src-sh3 : Free Energy Landscape

26 Application to src-sh3 : Folding Rate 1 2 as predicted by Plotkin Onuchic - PNAS 2000 as predicted by Clementi Plotkin - Protein Science 2004

27 Application to src-sh3 : Comparison with Experimental Data (Phi-values)

28 Energetically Best sequences Unfrustrated from Non-Go (Go) Model can follow not the efficiently folding distinguish mechanisms between of wt-pyp the folding and apo-pyp free energy as reported landscapes of wt-pyp experimentally and apo-pyp wt-pyp apo-pyp rmsd U rmsd U F F Q Intermediate The interactions between chromophore and rest of the protein was tuned to repulsive in the apo-pyp and σ value was fixed at = 4.0 A Q P.Das & C.Clementi, 2004

29 Average displacement from native structure Structural Comparison of the intermediate with NMR data Cross-peak intensity retained for the regions : 32-41,80-94, Cross-peak intensity completely lost for the regions : 6-18,26-29,42-58,69-78, Residue number The results from our simulation exactly reproduces experimental results! P.Das & C.Clementi,2004 Intensity of backbone amide peaks C.Craven et.al (2000)Biochemistry 39, Residue number

30 Cecilia Clementi s research group

31 Dr. Cecilia Clementi Chemistry Department Rice University Anderson Biological Bld

32 Recovery 350 ms pg Photocycle of PYP ps-ns hυ pr Chromophore isomerization Photophysics extend over 14 orders of magnitude in time Protein quake with its epicenter at chromophore takes place during pb formation Short lifespan of pb Interactions between chromophore and protein has been detailed pb pb 250 µs Intramolecular proton transfer Chromophore: p-coumaric acid (pca) linked with cys 69 via a thio-ester pb state linkage. Signaling state 2 ms Global conformational changes Structure????? Partially(30%) unfolded Hydrophobic surface area (N-terminal domain) exposed to solvent In solution, exhibits structural and dynamical disorder

33 Structural Characterization Of The Intermediate G.Rubinstern et.al (1998)Nat.Str.Biol. 5, Entire structure has been affected Domains of major perturbation matches with the NMR result. P.Das & C.Clementi, 2004

34 Why is Protein Folding a problem? Anyone who has ever struggled to fold a roadmap should have an extra measure of respect for protein molecules, which fold up all on their own and practically put themselves away in the glove box - (by Brian Hayes, from a paper published on American Scientist, 1998)

35 Topology and Energetic in Protein Folding Experimental evidence: Generally, proteins that have the same structure show the same folding mechanism Ex: SH3 domains, fibronectin-like modules, cold-shock proteins (Csp),. There is a substantial correlation between the contact order (= a measure of the relative importance of local and non-local contacts in a native structure) and the folding rate for single domain proteins LOW contact order FAST FOLDER From: Plaxco, Simons & Baker J.Mol.Biol. (1998) 277, Biochemistry (2000) 39, HIGH contact order SLOW FOLDER

36 Go-like potential = only native interactions are taken into account (named after a paper by Taketomi, Ueda, Go 1975) 2 2 C.Clementi, H.Nymeyer, J.Onuchic, Topological and energetic factors: what determines the structural details of the transition state ensemble and ``on-route intermediates for protein folding? An investigation for small globular proteins. J.Mol.Biol. 298:937, 2000

37 We can consider a plain Go-like model as a zeroth order approximation for the protein free energy F(Q) F(Q) = F0(Q) + F1(Q) + F2(Q) +. Go-like?? How can we quantify the relative weight in the same protein of the entropic and energetic heterogeneity in the protein free energy F(Q)? How can we quantify the topological (entropic) effects on the folding mechanism ( topological frustration )? How can we quantify the relative weight in different proteins of F 0 (Q) with respect to the further terms in the expansion?

38 Predicting folding rates from topological models : C. Clementi & L. Chavez, submitted to JACS, 2004

39 How can we quantify the topological effects on the folding mechanism ( topological frustration )? routing of folding: R(Q) = (<Qi> - Q ) MQ(1-Q) 2 Qi = { 1 if contact (i) is formed 0 if contact (i) is not formed <Qi>= average of Qi over all configurations Q = Qi fraction of the M native contacts that are formed M if all M contacts have <Qi> = Q R(Q)=0 all contacts are equally likely to be formed if MQ contacts have <Qi> = 1 and M(1-Q) contacts have <Qi> = 1 R(Q)=1 there is a well defined folding pathway C. Clementi & L. Chavez, submitted to JACS, 2004

40 routing of folding: R(Q) = (<Qi> - Q ) MQ(1-Q) 2 C. Clementi & L. Chavez, submitted to JACS, 2004

41 partial contact order : CO(Q) = Li <Qi> MQ C. Clementi & L. Chavez, submitted to JACS, 2004

42 FACTS : (emerging from recent and less-recent results) 1. Protein are minimally frustrated biopolymers 2. Native structures are very compact (high packing) 3. Topology-based models can often qualitatively describe the overall features of protein folding landscapes but are not accurate enough to make quantitative predictions 4. Non-native native interactions and energetic heterogeneity may play an important role in shaping the folding landscape of certain proteins We can use a simplified, minimally frustrated model as a 0 th order approximation for the protein free energy F({x}) MAIN CHALLANGES: F({x}) = F0({x}) + F1({x}) + F2({x}) What are the most important terms to include in the corrections? 2. How do we select the parameters in the higher order terms? 3. Is this strategy robust and general?

43 MAIN CHALLANGES: 1. What are the most important terms to include in the corrections? 2. How do we select the parameters in the higher order terms? 3. Is this strategy robust and general? One possibility: check the usual suspects one by one S.S.Plotkin & C.Clementi 2004 (in progress) More general approach: Effect design of minimally non-native native frustrated interactions sequences? in a coarse-grained (completely non-go) model Effect of explicit side-chain packing? Effect of native heterogeneity? C.Clementi & S.S.Plotkin, 2004 (submitted) C.Clementi et al., JMB 2003

44 Generate set of non-native structures (decoys) native structure decoy structures Extract sequence, and set of parameters ({ε} and {δ}) by maximizing the energy gap between native and decoys structures Heat & quench simulations of selected sequence(s) parameter subspace 2 native structure parameter subspace 1 NO Fold back to native structure? YES Proceed to thermodynamics and kinetics analysis Iterative procedure converges very nicely for all proteins we have tried so far ( aa)! D.Maxwell & C.Clementi 2004

45 Results for SH3 : we obtain ~50 good sequences with strongly reduced frustration exhibiting two-state kinetics P.Das, D.Maxwell & C.Clementi 2004

46 Results for SH3 : comparison with experimental data simulation experiment χ 2 = 1.0 p-value = 10-7 P.Das, D.Maxwell & C.Clementi 2004

47 POLYMER TRANSLOCATION THROUGH A LONG NANOPORE (in collaboration with Tolya Kolomeisky and Matteo Pasquali), submitted to PRL Mesoscale Modeling works GREAT in this instance!! BD COUPLING BOUNDARY CONDITION CHARGE SCREENING BY DFT + IMC BASE-PORE INTERACTION BY MD + IMC BD or DPD CONFINED DRAG BY MD + IMC CHARGE SCREENING BY DFT + IMC Silvina Matysiak, 2004