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Mathematical Methods for

Structural BiologyMath 801 / Biochem 729

Julie C. Mitchell

George N. Phillips, Jr.

Stephen J. Wright

Fall 2007

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Course Overview

• What is a protein?

• How do we determine protein structures?

• How do proteins fold?

• What is the dynamical behavior of molecules?

• How do proteins interact to perform their functions?

• How do we use mathematics and computer science to

model molecular behavior?

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Prerequisites

• Calculus through vector calc is essential.

• Some programming proficiency is required. Any of Matlab,

perl, C, java, python, etc, should be OK for doing the course

project.

• Linear algebra, ODE’s and PDE’s are helpful but not

essential.

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Software and WWW

• You may use any programming tools you wish for yourclass projects.

• Some generally useful software tools include • Matlab/Octave

• Xcode

• SwissPDB Viewer

• VMD

• A course website has been set up using Learn@UW.• Log in using your wisc.edu login and password at:

http://learnuw.wisc.edu

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Homework and Projects

• Homework will be assigned for each topic. It is due the

Tuesday following the lectures for that subject.

• Homework is worth 40% of your grade.

• Projects are due Dec. 13 and constitute 60% of your grade.

• Each student will choose a project in collaboration with one

of the faculty members or TA.

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And now…

• … let’s learn about proteins

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DNA unravels

and codes RNA

RNA codes

proteins

A protein folds

into a globular

structure

Proteins interact to

perform biological

functions

A Brief Biology Lesson

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http://bioinfo. mbb.yale.ed

u

Important Areas of Research

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What is a protein?

• A protein is a linear sequence of amino acids that folds into

a characteristic three-dimensional shape.

• Proteins consist of a backbone (N-C!-C) and amino acid

sidechain residues (R)

• There are 20 standard amino acids.

• Each amino acid has different biochemical properties.

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Protein Data Bank Files

ATOM 1 N THR 1 -4.965 28.290 7.243 1.00 31.23

ATOM 2 CA THR 1 -5.255 26.833 7.162 1.00 29.04

ATOM 3 C THR 1 -4.253 26.110 8.081 1.00 27.06

ATOM 4 O THR 1 -3.141 26.590 8.274 1.00 27.32

ATOM 5 CB THR 1 -5.101 26.392 5.694 1.00 29.96

ATOM 6 OG1 THR 1 -5.894 27.267 4.898 1.00 35.08

ATOM 7 CG2 THR 1 -5.599 24.978 5.459 1.00 30.72

ATOM 8 N MET 2 -4.688 25.016 8.699 1.00 23.88

ATOM 9 CA MET 2 -3.826 24.080 9.372 1.00 22.38

ATOM 10 C MET 2 -3.254 23.081 8.384 1.00 24.09

ATOM 11 O MET 2 -4.008 22.471 7.646 1.00 25.98

ATOM 12 CB MET 2 -4.600 23.314 10.406 1.00 21.67

ATOM 13 CG MET 2 -5.204 24.189 11.465 1.00 25.77

ATOM 14 SD MET 2 -4.040 25.028 12.518 1.00 28.87

ATOM 15 CE MET 2 -2.980 23.707 13.105 1.00 24.53

ATOM 16 N CYS 3 -1.943 22.867 8.426 1.00 20.90

ATOM 17 CA CYS 3 -1.225 22.144 7.374 1.00 20.54

ATOM 18 C CYS 3 -0.221 21.228 8.054 1.00 18.98

ATOM 19 O CYS 3 0.370 21.581 9.077 1.00 19.50

ATOM 20 CB CYS 3 -0.432 23.102 6.473 1.00 19.92

ATOM 21 SG CYS 3 -1.327 24.485 5.694 1.00 25.34

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PDB Format

COLUMNS DATA TYPE DEFINITION

1 - 6 String Type of entry

7 - 11 Integer Atom serial number

12 (not used)

13 - 16 String Atom name

17 Character Alternate location indicator

18 - 20 Residue name Residue name

21 (not used)

22 Character Chain identifier

23 - 26 Integer Residue sequence number

27 Character Code for insertion of residues.

28 - 30 (not used)

31 - 38 Real(8.3) Orthogonal coordinates for X in Angstroms

39 - 46 Real(8.3) Orthogonal coordinates for Y in Angstroms

47 - 54 Real(8.3) Orthogonal coordinates for Z in Angstroms

55 - 60 Real(6.2) Occupancy

61 - 66 Real(6.2) Temperature factor

67 - 72 (not used)

73 - 76 String(4) Segment identifier, left-justified

77 - 78 String(2) Element symbol, right-justified

79 - 80 String(2) Charge on the atom

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Hydrophobic Amino Acids

• Alanine ala a CH3-CH(NH2)-COOH

• Isoleucine ile i CH3-CH2-CH(CH3)-CH(NH2)-COOH

• Leucine leu l (CH3)2-CH-CH2-CH(NH2)-COOH

• Methionine met m CH3-S-(CH2)2-CH(NH2)-COOH

• Phenylalanine phe f Ph-CH2-CH(NH2)-COOH

• Proline pro p NH-(CH2)3-CH-COOH

|_________|

• Valine val v (CH3)2-CH-CH(NH2)-COOH

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Polar Amino Acids

• Asparagine asn n H2N-CO-CH2-CH(NH2)-COOH

• Cysteine cys c HS-CH2-CH(NH2)-COOH

• Glutamine gln q H2N-CO-(CH2)2-CH(NH2)-COOH

• Histidine his h NH-CH=N-CH=C-CH2-CH(NH2)-COOH

|__________|

• Serine ser s HO-CH2-CH(NH2)-COOH

• Threonine thr t CH3-CH(OH)-CH(NH2)-COOH

• Tryptophan trp w Ph-NH-CH=C-CH2-CH(NH2)-COOH

|_______|

• Tyrosine tyr y HO-p-Ph-CH2-CH(NH2)-COOH

* Charged at pH > 6.1 13

Charged Amino Acids

• Arginine arg r HN=C(NH2)-NH-(CH2)3-CH(NH2)-COOH

• Aspartic acid asp d HOOC-CH2-CH(NH2)-COOH

• Glutamic acid glu e HOOC-(CH2)2-CH(NH2)-COOH

• Lysine lys k H2N-(CH2)4-CH(NH2)-COOH

• Histidine* his h NH-CH=N-CH=C-CH2-CH(NH2)-COOH

|__________|

And … then there’s glycine

• Glycine gly g NH2-CH2-COOH

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ArgininePhenylalanine

CysteineTryptophan

Amino Acid “Tour”

C=gray, H=white, O=red, N=blue, S=yellow

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Primary Secondary

Tertiary Quaternary

Ala Glu Lys Trp

His Cys Gly Ser

His Pro Cys Gln

Ala Met Arg Asn

Ser His Glu Phe

Protein Structure Heirarchy

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Is it that simple? No!

• Protein function relies on more than protein structure.

• Proteins can have different states (e.g., phosphorylated).

• Proteins can have different environments (e.g., pH, temperature,

salt concentration).

• Proteins need small molecules and prosthetic groups (e.g., ATP,

chloryphyl, sugars, water).

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Week 1 Homework

• Go to http://scholar.google.com and enter simple searches

for structural biology topics in this course (eg: “protein

folding” or “molecular dynamics”)

• Choose a high-impact paper and use the glossary to work

your way through the paper as much as possible.

• Turn in the paper, and highlight any words you had to look

up in the glossary.

• Also, complete the tutorials that we will start on Thursday.