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1 (c) M Gerstein, 2006, Yale, gersteinlab.org Seq. Alignment, Struc. Alignment, Threading Cor e

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Seq. Alignment, Struc. Alignment, Threading. Core. Mail Servers and Web Forms. Extra. Illustration Credits: D Frishman handout. Additional Features of DNA sequences in Genomes. Gene finding. genome. mRNA. composition of codons, nts Splice site finding. Genetic Code. Extra. CAI. - PowerPoint PPT Presentation

TRANSCRIPT

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Seq. Alignment, Struc. Alignment, Threading

Core

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Mail Servers and Web Forms

Method URL Institution

Source code Availability

ANTHE-PROT http://www.ibcp.fr/antheprot.html (currently unreachable)

Institute of Biology and Chemistry of Proteins (Lion) YES

PSSP http://dot.imgen.bcm.tmc.edu:9331/pssprediction/pssp.html Baylor College of Medicine (Houston) NO

DSC http://bonsai.lif.icnet.uk/bmm/dsc/dsc_form_align.html

Imperial Cancer Research Center (London) YES

GOR http://molbiol.soton.ac.uk/compute/GOR.html University of Southampton NO

nnPredict http://www.cmpharm.ucsf.edu/~nomi/nnpredict.html University of California (San Francisco) NO

Predict-Protein http://www.embl-heidelberg.de/predictprotein/predictprotein.html EMBL (Heidelberg) NO

PRED-ATOR http://www.embl-heidelberg.de/argos/predator/predator_form.html EMBL (Heidelberg) YES

PSA http://bmerc-www.bu.edu/psa/

BioMolecular Engineering Research Center, Boston NO

SSPRED http://www.embl-heidelberg.de/sspred/sspred_info.html EMBL (Heidelberg) NO

GOR and DSC http://genome.imb-jena.de/cgi-bin/GDEWWW/menu.cgi IMB (Jena) NO

GOR http://absalpha.dcrt.nih.gov:8008/gor.html DCRT/NIH (Washington) NO

GOR ftp://ftp.virginia.edu/pub/fasta University of Virginia YES

Mult-Predict http://kestrel.ludwig.ucl.ac.uk/zpred.html

Ludwig Institute for Cancer Research (London) NO

Illustration Credits: D Frishman handout

Extra

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Additional Features of DNA sequences in Genomes

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Gene finding

• composition of codons, nts

• Splice site finding

genome

mRNA

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Genetic Code

•Codons with second position pyrimidines encode mostly hydrophobic amino acids (tan), while those with second position purines encode mostly polar amino acids (blue, red, and purple)

• The genetic code is nonambiguous. Each codon encodes a single amino acid. The only exception is GUG which in some mRNAs is used as a start codon to encode Met

•The genetic code includes three stop codons, UAG, UAA, and UGA which are termed amber, ochre, and opal codons

•The genetic code is nearly but not absolutely universal. The genetic code in mitochondria and some ciliates use a slightly modified version of the code

•The genetic code is highly degenerate (64 codons to encode 20 amino acids)

• Three amino acids (Arg, Leu, Ser) are each specified by six codons, and many of the other amino acids are specified by two or four codons

•The arrangement of the codons within the genetic code is not random

•In most cases mutation of the third nucleotide in the codon would either cause no change in the amino acid (Arg, Val or Leu for example) or would create a fairly conservative change (Phe to Leu or Asp to Glu)

(Page adapted from S Strobel, Biochemistry Lecture Notes)

CAI Extra

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Splicing

•Splicing must be done accurately. Missplicing by even one nucleotide would result in a frameshift mutation throughout the remainder of the message

•The splice sites are defined largely by sequences within the intron

•The intron begins with the sequence GU and ends with AG and is part of a larger consensus sequence at both the5’ and 3’ splice sites (see figure)

•30-50 nucleotides upstream of the 3’ splice site is the branch site which includes an A that serves as the nucleophile in the reaction

(Page adapted from S Strobel, Biochemistry Lecture Notes)

Extra

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Alternative Splicing: Multiple Proteins from One Gene

•A single transcript can be processed to include or not include specific exons within the gene. This is termed alternative splicing

•This makes it possible to generate multiple proteins from a single gene

•For example a single rate gene encodes seven tissue-specific variants of the muscle protein a-tropomyosin through the process of alternative splicing

•Sex determination in Drosophila is largely controlled by a series of alternative splicing events

(Page adapted from S Strobel, Biochemistry Lecture Notes)

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Promotors•The RNA polymerase recognizes a promoter sequence within the DNA

•The consensus promoter includes two six base pair regions upstream of the transcription start site (defined as nucleotide +1)

•The Pribnow box (consensus sequence of TATAAT) is 10 nt upstream

•There is second element 35 nt upstream (consensus sequence TTGACA)

•The rates at which genes are transcribed vary directly with the rate that their promoters from stable initiation complexes with the holoenzyme

•The -10 and -35 regions of the promoter sequence are recognized by the sigma subunit of the RNA polymerase holoenzyme (which also includes two and two subunits

•Without the sigma subunit the RNA polymerase has no affinity for the DNA

•After entering the elongation phase of transcription, the sigma factor is removed from the polymerase complex

•Expression of different sigma factors makes it possible for a bacteria to efficiently respond to external stimuli (turn on sporulation genes, heat shock genes, etc.)

(Page adapted from S Strobel, Biochemistry Lecture Notes)

Extra

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ReferencesArgos P. (1976) Prediction of the secondary structure of mouse nerve growth factor and its comparison with insulin. Biochemical and Biophysical Research Communications 3:805-811.

Bairoch A and Apweiler R. (1996) The SWISS-PROT protein sequence data bank and its new supplement TREMBL. Nucleic Acids Res 24:21-25.

Barton GJ. (1995) Protein secondary structure prediction. Curr Opinion Struct Biol 5:372-376.

Benner SA, Gerloff DL, and Jenny TF. (1994) Predicting protein crystal structures. Science 265:1642-1644.

Benner SA. (1995) Predicting the conformation of proteins from sequences. Progress and future progress. J Mol Recogn 8:9-28.

Boyd, D., Schierle, C. & Beckwith, J. (1998). How many membrane proteins are there? Prot. Sci. 7, 201-205.

Crawford IP, Niermann T, and Kirschner K. (1987) Prediction of secondary structure by evolutionary comparison: application to the alpha subunit of thryptophan synthase. Proteins: Struct Func Genet 2:118-129.

Deleage G and Roux B. (1987) An algorithm for protein secondary structure prediction based on class prediction. Protein Engineering 4:289-294.

Eigenbrot C, Randal M, and Kossiakoff AA. (1992) Structural Effects Induced by Mutagenesis Affected by Crystal Packing Factors: the Structure of a 30-51 Disulfide Mutant of Basic Pancreatic Trypsin Inhibitor. Proteins 14:75.

Fasman, G. D. & Gilbert, W. A. (1990). The prediction of transmembrane protein sequences and their conformation: an evaluation. Trends Biochem Sci 15, 89-92.

Frishman D, and Argos P. (1995) Knowledge-Base Protein Secondary Structure Assignment. Proteins: Structure, Function, and Genetics 23:566-79.

Frishman D, and Argos P. (1996) Incorporation of Non-Local Interactions in Protein Secondary Structure Prediction From the Amino Acid Sequence. Protein Engineering 2:in the press.

Frishman D, and Argos P. (1997) The Future of Protein Secondary Structure Prediction Accuracy. Folding & Design 2:159-62.

Frishman, D, and P Argos. (1996) 75% Accuracy in Protein Secondary Structure Prediction. Proteins 1997 Mar;27(3):329-335 .

Garnier J and Levin JM. (1991) The protein structure code: what is its present status. Comput Appl Biosci 7:133-142.

Garnier, J. (1990). Protein structure prediction. Biochimie 72, 513-24.

Garnier, J., Gibrat, J. F. & Robson, B. (1996a). GOR method for predicting protein secondary structure from amino acid sequence. Meth. Enz. 266, 540-553.

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ReferencesGarnier, J., Gibrat, J. F. & Robson, B. (1996b). GOR method for predicting protein secondary structure from amino acid sequence. Methods Enzymol 266, 540-53.

Garnier, J., Osguthorpe, D. & Robson, B. (1978). Analysis of the accuracy and implications of simple methods for predicting the secondary structure of globular proteins. J. Mol. Biol. 120, 97-120.

Geourjon C, and Deléage G. (1995) SOPMA: Significant Improvements in Protein Secondary Structure Prediction by Consensus Prediction From Multiple Sequences. Comput Appl Biosci 11:681-84.

Gibrat, J., Garnier, J. & Robson, B. (1987). Further developments of protein secondary structure prediction using information theory. J. Mol. Biol. 198, 425-443.

Gilbert RJ. (1992) Protein structure prediction from predicted residue prperties utilizing a digital encoding algorithm. J Mol Graph 10:112-119.

Holley LH, and Karplus M. (1989) Protein Secondary Structure Prediction With a Neural Network. Proc Natl Acad Sci USA 86:152-56.

Hunt NG, Gregoret LM, and Cohen FE. (1994) The origins of protein secondary structure. Effects of packing density and hydrogen bonding studied by a fast conformational search. J Mol Biol 241:214-225.

Kabsch W and Sander C. (1984) On the use of sequence homologies to predict protein structure. Identical pentapeptides can have completely different conformation. Proc Natl Acad Sci USA 81:1075-1078.

Kabsch W, and Sander C. (1983) Dictionary of Protein Secondary Structure: Pattern Recognition of Hydrogen-Bonded and Geometrical Features. Biopolymers 22:2577-637.

Kendrew JC, Klyne W, Lifson S, Miyazawa T, Nemethy G, Phillips DC, Ramachandran GN, and Sheraga HA. (1970). Biochemistry 9:3471-79.

King, R. D. & Sternberg, M. J. E. (1996). Identification and application of the concepts important for accurate and reliable protein secondary structure prediction. Prot. Sci. 5, 2298-2310.

King, R. D., Saqi, M., Sayle, R. & Sternberg, M. J. (1997). DSC: public domain protein secondary structure predication. Comput Appl Biosci 13, 473-4.

Levin J, Pascarella S, Argos P, and Garnier J. (1993) Quantification of secondary structure prediction improvement using multiple alignments. Protein Engineering 6:849-854.

Levin JM, Robson B, and Garnier J. (1986) An algorithm for secondary structure determination in proteins based on sequence similarity. FEBS Lett 205:303-308.

Levitt M, and Greer J. (1977) Automatic Identification of Secondary Structure in Globular Proteins. J Mol Biol 114:181-239.

Lim VI. (1974) Algorithms for prediction of alpha-helical and beta-structural regions in globular proteins. J Mol Biol 88:873-894.

Livingstone CD, Barton GJ (1996). Identification of functional residues and secondary structure from protein multiple sequence alignment. Methods Enzymol 266:497-512

Lupas A, Koster AJ, Walz J, and Baumeister W. (1994) Predicted secondary structure of the 20 S proteasome and model structure of the putative peptide channel. FEBS Lett 354:45-49.

Matthews B. (1975) Comparison of the predicted and observed secondary structure of T4 phage lysozyme. Biochem Biophys Acta 405:442-451.

Mehta PK, Heringa J, and Argos P. (1995) A simple and fast approach to prediction of protein secondary structure from multiply aligned sequences with accuracy above 70%. Protein Science 4:2517-2525.

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ReferencesMuggleton S, King RD, and Sternberg MJE. (1992) Protein Secondary Structure Prediction Using Logic-Based Machine Learning. Protein Engineering 5:647-57.

Nishikawa K, and Ooi T. (1986) Amino Acid Sequence Homology Applied to the Prediction of Protein Secondary Structures, and Joint Prediction With Existing Methods. Biochimica Et Biophysica Acta 871:45-54.

Pauling L, Corey RB, and Branson HR. (1951) The structure of proteins: two hydrogen-bonded helical configurations of the polypeptide chain. Proc Natl Acad Sci USA 37:205-211.

Persson, B. & Argos, P. (1997). Prediction of membrane protein topology utilizing multiple sequence alignments. J Protein Chem 16, 453-7.

Presnell SR, Cohen BI, and Cohen FE. (1992) A segment-based approach to protein secondary structure prediction. Biochemistry 31:983-993.

Ptitsyn OB and Finkelstein AV. (1983) Theory of protein secondary structure and algorithm of its prediction. Biopolymers 22:15-25.

Qian N, and Sejnowski TJ. (1988) Predicting the Secondary Structure of Globular Proteins Using Neural Network Models. J Mol Biol 202:865-84.

Rackovsky S. (1993) On the nature of the protein folding code. Proc Natl Acad Sci U S A 90:644-648.

Ramakrishnan C, and Soman KV. (1982) Identification of Secondary Structures in Globular Proteins - a New Algorithm. Int J Pept Protein Res 20:218-37.

Rao S, Zhu Q-L, Vaida S, and Smith T. (1993) The local information content of the protein structural database. FEBS Lett 2:143-146.

Rice CM, Fuchs R, Higgins DG, Stoehr PJ, and Cameron G N. (1993) The EMBL data library. Nucleic Acids Res 21:2967-2971.

Richards FM, and Kundrot CE. (1988) Identification of Structural Motifs From Protein Coordinate Data: Secondary Structure and First-Level Supersecondary Structure. Proteins: Struct Func Genet 3:71-84.

Robson B, and Garnier J. (1993) Protein Structure Prediction. Nature 361:506.

Rost B, and Sander C. (1993) Prediction of Protein Secondary Structure at Better Than 70% Accuracy. J Mol Biol 232:584-99.

Rost B, Sander C, and Schneider R. (1994) Redefining the goals of protein secondary structure prediction. J Mol Biol 235:13-26.

Rost B, Sander C. (1993) Improved prediction of protein secondary structure by use of sequence profiles and neural networks. Proc Natl Acad Sci USA 90:7558-7562

Rost, B., Schneider, R. & Sander, C. (1993). Progress in protein structure prediction? Trends Biochem Sci 18, 120-3.

Rumelhart DE, Hinton GE, and Williams R. (1986) Learning representations by back-propagating errors. Nature 323:533-536.

Salamov AA, and Solovyev VV. (1995) Prediction of Protein Secondary Structure by Combining Nearest-Meighbour Akgorithms Amd Multiple Sequence Alignments. J Mol Biol 247:11-15.

Salamov AA, and Solovyev VV. (1997) Protein Secondary Structure Prediction Using Local Alignments. Journal of Molecular Biology 268:31-36.

Sayle RA, and Milner-White EJ. (1995) RASMOL: Biomolecular Graphics for All. Trends in Biochemical Sciences 20:374-76.

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ReferencesSayle RA, and Milner-White EJ. (1995) RASMOL: Biomolecular Graphics for All. Trends in Biochemical Sciences 20:374-76.

Sklenar H, Etchebest C, and Lavery R. (1989) Describing Protein Structure: a General Algorithm Yielding Complete Helicoidal Parameters and a Unique Overall Axis. Proteins: Struct Func Genet 6:46-60.

Solovyev VV and Salamov AA. (1994) Predicting alpha-helix and beta-strand segments of globular proteins. Comput Appl Biosci 10:661-669.

Stolorz P, Lapedes A, and Xia Y. (1992) Predicting Protein Secondary Structure Using Neural Net and Statistical Methods. J Mol Biol 225:363-77.

Sumpter BG, Getino C, and Noid DW. (1994) Theory and applications of neural computing in chemical science. Ann Rev phys Chem 45:439-481.

Sumpter BG, Getino C, and Noid DW. (19949 Theory and applications of neural computing in chemical science. Ann Rev phys Chem 45:439-481.

Taylor WR and Thornton JM. (1984) Recognition of super-secondary structure in proteins. J Mol Biol 173:487-5141984.

Thompson JD, Higgins DG, and Gibson TJ. (1994) CLUSTAL W: improving the sensitivity of progressive multiple sequence alignment through sequence weighting, position-specific gap penalties and weight matrix choice. Nucleic Acids Res 22:4673-4680.

Thornton JM, Flores TP, Jones DT, and Swindells MB. (1991) Prediction of progress at last. Nature 354:105-106.

von Heijne, G. (1992). Membrane protein structure prediction. Hydrophobicity analysis and the positive-inside rule. J Mol Biol 225, 487-94.

Wasserman PD. (1989) Neural Computing. Theory and Practice. New York.

Zhang X, Mesirov JP, and Waltz DL. (1992) Hybrid System for Protein Secondary Structure Prediction. J Mol Biol 225:1049-63.

Zvelebil MJ, Barton GJ, Taylor WR, and Sternberg MJ. (1987) Prediction of Protein Secondary Structure and Active Sites Using the Alignment of Homologous Sequences. J Mol Biol 195:957-61.

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Main Points

• Sec struc prediction• Computing propensities, generalizing this to a more

elaborate stat model (GOR)• How you evaluate prediction, testing and training• Parametric v heuristic• Protein features: conservation pattern, near termini • Threading and how its related to dynamic

programming

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AB

CD

E0.5

0.5

0.1

0.3

0.2

0.8

0.4MM

Markov ModelsMarkov Models

Path: Path: A D B CA D B C

Probability = Init(A)*0.5*0.3*0.4Probability = Init(A)*0.5*0.3*0.4

Extra

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More HMMs

R: 0.1

G: 0.2

B: 0.7

R: 0.1

G: 0.1

B: 0.8

R: 0.4

G: 0.4

B: 0.2

0.93

0.01

0.50.2

Probability of a given sequence = Sum probability over ALL paths giving that sequence

e.g. observed: e.g. observed: RRRRRR

Extra

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Example: simple fully interconnected model (N=3)

13

2

0.13

0.120.23

0.31

0.32

0.37

0.21

Extra

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Scoring by Brute Force method: Extra

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End of class 2005,04.04

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Over-training

• Cross Validation: Leave one out, seven-fold

Credits: Munson, 1995; Garnier et al., 1996

4-fold

Training Set (determine parms)Testing Set (see how it does) Validation SetPredictions from actual run

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Multiple Sequence Methods

• Average GOR over multiple seq. Alignment

• The GOR method only uses single sequence information and because of this achieves lower accuracy (65 versus >71 %) than the current "state-of-the-art" methods that incorporate multiple sequence information (e.g. King & Sternberg, 1996; Rost, 1996; Rost & Sander, 1993).

Illustration Credits: Livingston & Barton, 1996

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Multiple Structure Alignment

• Building up a Fold Library (structure clusters)

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Analysis: What can beCalculated from Simulation?

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Average over simulation

• Deceptive Instantaneous Snapshots(almost anything can happen)

• Simple thermodynamic averages Average potential energy <U> T ~ < Kinetic Energy > = ½ m < v2 >

• Some quantities fixed, some fluctuate in different ensembles NVE protein MD (“microcanonical”) NVT liquid MC (“canonical”) NPT more like the real world

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Energy and Entropy• Energy

At each point i (with coordinates xi) on the pot. energy surface there is a well-defined “energy” U(xi)

• Probability of occurrence Pi = exp(-Ui/kT)/Q

The boltzmann distribution Q = Sum over all Pi , to normalize

probabilities to 1

xi

A B

U(x

)

in Ain B

• Entropy S(A) = k (Pi ln Pi),

where the sum is over points i in A

• Free Energy G(A) = U(A) - TS(A)

• Entropy and Free Energy are only defined for distinctly diff. “states” -- e.g. A (“unfolded”)and B (“folded”) State B has a lower U and its

minimum is more probable than State A

However, state A has a broader minimum that can be occupied in more ways

• Relative Prob P(A)/P(B) =

exp(-G(A)/kT) ------------------exp (G(B)/kT)

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Number Density

= Number of atoms per unit volume averaged over simulation divided by the number you expect to have in the same volume of an ideal “gas”

Spatially average over all directions gives

1D RDF =

[ Avg. Num. Neighbors at r ] [Expected Num. Neighbors at r ]

“at r” means contained in a thin shell of thickness dr and radius r.

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Number Density (cont)• Advantages: Intuitive,

Relates to scattering expts• D/A: Not applicable to real

proteins 1D RDF not structural 2D proj. only useful with "toy"

systems

• Number densities measure spatial correlations, not packing Low value does not imply

cavities Complicated by asymmetric

molecules How things pack and fit is

property of instantaneous structure - not average

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Measurement of Dynamic Quantities I

• The time-course of a relevant variable is characterized by

(1) Amplitude (or magnitude), usually characterized by an RMS value R = sqrt[ < (a(t) - <a(t)>)2 > ]R = sqrt[ < a(t)2 - 2a(t)<a(t)> +<a(t)>2 > ]R = sqrt[ < a(t)2> - <a(t)>2 ]

• similar to SD• fluctuation

• Relevant variables include bond length, solvent molecule position, H-bond angle, torsion angle

Illustration from M Levitt, Stanford University

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Measurement of Dynamic Quantities II

• The time-course of a relevant variable is characterized by

(2) Rate or time-constant Time Correlation function CA(t) = <A(s)A(t+s)> = <A(0)A(t)> [ averaging over all s ]

Correlation usually exponentially decays with time t decay constant is given by the integral of C(t) from t=0 to t=infinity

• Relevant variables include bond length, solvent molecule position, H-bond angle, torsion angle

Illustration from M Levitt, Stanford University

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D & RMS

• Diffusion constant Measures average rate of

increase in variance of position of the particles

Suitable for liquids, not really for proteins

D r 2

6t

RMS(t ) di (t )

i 1

NN

di (t ) R(xi (t ) T) xi (0)

• RMS more suitable to proteins

di = Difference in position of protein atom at t from the initial position, after structures have been optimally rotated translated to minimize RMS(t)

Solution of optimal rotation has been solved a number of ways (Kabsch, SVD)

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Other Things to Calculate

• Fraction of Native Contacts

• Percent Helix• Radius of

Gyration

Illustration and Caption from Duan & Kollman (1998)

Caption: Time evolution of (A) fractional native helical content, (B) fractional native contacts, (C) R and the main chain rmsd from the native structure, and

(D) SFE of the protein. The helical content and the native contacts are plotted on a logarithmic time scale. The helical content was measured by the

main chain - angle

(60° ± 30°, 40° ± 30°). The native contacts were measured as the number of neighboring residues present in 80% of the last 50 ns of the native

simulation. Residues are taken to be in contact if any of the atom pairs are closer than 2.8 Å, excluding residues i and i+1, which always have the

contacts through main chain atoms. The SFE was calculated as described by Eisenberg and McLachlan (31) using their parameters (0.0163, 0.00637, 0.02114, 0.02376, and 0.05041, in kcal mol Å2, for the surface areas of

nonpolar, polar, sulfur, charged oxygen, and charged nitrogen, respectively). The straight line represents the SFE of the native structure.

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Timescales

Motion length time

(Å) (fs)

bond vibration 0.1 10

water hindered rotation 0.5 1000

surface sidechain rotation 5 105

water diffusive motion 4 105

buried sidechain libration 0.5 105

hinge bending of chain 3 106

buried sidechain rotation 5 1013

allosteric transition 3 1013

local denaturation 7 1014

Values from McCammon &

Harvey (1987) and Eisenberg & Kauzmann

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Simplified Solvent

Figures from Smit et al. (1990)

• Smit et al. (1990) Surfactant simulation

• Three types of particles, o, w and s s consists of

w-w-o-o-o-o s has additional springs

• all particles interact through L-J potential o-w interaction truncated so purely

repulsive

• Above sufficient to give rise to the formation of micelles, membranes, &c

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NMA formalism and implementation:

2(0) (0)( )ij ij ijU r k r R R

1...N

N ij i ji j

U U

R R R R

Hinsen (1998): 2

2( ) exp

o

rk r c

r

Minimize pot. energy

Then diagonalize the 2nd derivative of the potential

energy

Simplified potential

Solve:

0 . .

Q ΛQ

(0)ijk R

ijR

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Normal Mode Analysis

• Examine vibrational motions For a system of N particles:

• Total number of displacement = 3N

• Total number of vibrational modes = 3N-6

• Mode frequency indicates the type of motion: Low frequency: Collective motion High frequency: Localized motion

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What is “NMA”?

sink

v A tm

+

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Normal (Natural) Modes for MOLA

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Adiabatic mapping

• Interpolate then minimize Gives apx. energy

(H) landscape through a barrier

can sort of estimate transition raterate = (kT/h) exp (-dG/kT)

Used for ring flips, hinge motions

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Molecular Dynamics

• Give each atoms a velocity. If no forces, new position of atom

(at t + dt) would be determined only by velocityx(t+dt) = x(t) + v dt

• Forces change the velocity, complicating things immensely F = dp/dt = m dv/dt

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Molecular Dynamics (cont)

• On computer make very small steps so force is nearly constant and velocity change can be calculated (uniform a)

[Avg. v over t] = (v + v/2)

• Trivial to update positions:

• Step must be very small t ~ 1fs

(atom moves 1/500 of its diameter)

This is why you need fast computers

• Actual integration schemes slightly more complicated Verlet (explicit half-step) Beeman, Gear

(higher order terms than acceleration)

v F

mt

x(t t ) x(t ) (v v2

)t

x(t ) vt F

2mt 2

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MC vs/+ MD

• MD usually used for proteins. Difficult to make moves with complicated chain.

• MC often used for liquids. Can be made into a very efficient sampler.

• Hybrid approaches (Brownian dynamics)• Simulated Annealing. Heat simulation up to high T

then gradually cool and minimize to find global minimum.

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Typical Systems:

DNA + Water

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Typical Systems: Protein + Water

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Practical Aspects: simulation cycle I• Divide atoms into types (e.g.

alpha carbon except for Gly, carbonyl oxygen)

• Initially Associate each atom with a mass and

a point charge Give each atom an initial velocity

• Calculate Potential• Calculating non-bonded

interactions take up all the time Electrostatics hardest since longest

ranged Neighbor lists

Illustration Credit: McCammon & Harvey (1987)

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Practical Aspects: simulation cycle II• Update Positions with MD

equations, then recalculate potential and continue

• Momentum conservation• Energy Conserved in NVE

ensemble• Hydrophobic interaction

naturally arises from water behavior

Illustration Credit: McCammon & Harvey (1987)

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Periodic Boundary Conditions

• Make simulation system seem larger than it is

• Ewald Summation for electrostatics(Fourier transform)

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End of class M8 [2006,11.27]

Start of class M9 [2006,11.29]