bio-modeling

introduction molecular biology biotechnology bioMEMS bioinformatics bio-modeling cells and e-cells transcription and regulation cell communication neural networks dna computing fractals and patterns the birds and the bees ….. and ants

course layout

introduction

far and away in the past

Newton’s equations of motions (17th -18th century) Molecular dynamics (MD)

Boltzmann’s statistics (19th century) Monte Carlo (MC)

Schrödinger/Heisenberg’s quantum mechanics (20th century)

birth of simulation in chemistry

1950’s: do it by hand (or mechanical calculator)! Tried to solve Newton’s equation of motion for small systems (e.

g. three-atom system) Didn’t take very long before they saw computers

1970’s: Age of punchcards 1980’s: Better IO devices

Workstations dominated as research platforms

first generation (1980’s – 1990’s)

Gas phase reaction (e.g.) H + H2 H2 + H MD

RA-BRB-C

Liquid simulation (e.g.) Lennard-Jones Fluid MD/MC

first generation (1980’s – 1990’s)

Proteins on lattice MC

first generation (1980’s – 1990’s)

Quantum mechanical structure calculation (semi-empirical, ab initio, …)

first generation (1980’s – 1990’s)

revolution (~ 1995)

Workstation-like PCs 100 hr Cray time 64MB / 150MHz P

entium “Cheap and fast”

Impacts Two directions

1) More accurate methods2) Larger system

Start of bio-simulations

impact on “non-bio” simulations

RA-BRB-C

Better surface Revisions on existing surfaces Dynamics on quantum mechanical s

urfaces Quantum wavepacket dynamics

Time dependent Schrödinger equation instead of Newton’s equation

Totally quantum (can’t be more accurate)

Some people still do this for hydride/proton transfer in enzyme dynamics

Impacts on bio-simulations

Proteins got free from the lattice! Off lattice model (still, each residue as a bead) United atom approach (e.g. CH3 one atom) All atom approach

With water (explicit solvent) Without water (implicit solvent)

What to look at? Kinetics: dynamic characteristics (e.g. folding simulation) Thermodynamics: equilibrium characteristics (e.g. binding affinity of

protein & drug)

Implicit solvent Solvent accessible surface area (SASA) Solvation free energy Cheaper than explicit Discrete nature of solvent not included Different methods for SASA/free-E calculation

Generalized Born model (GB/SA) Poisson-Boltzmann model (PB/SA) Distance dependent dielectric (DD/SA)

solvent models

solvent models

Explicit solvent Water as individual molecules Expensive calculation Periodic boundary conditions usually necessary

Rigid/flexible, polarizable/non-polarizable SPC, TIP3P, TIP4P, TIP5P, …

impacts on bio-simulations

Proteins got free from the lattice! Off lattice model (each residue as a bead) United atom approach (e.g. CH3 one atom) All atom approach

With water (explicit solvent) Without water (implicit solvent)

What to look at? Kinetics: dynamic characteristics (e.g. folding simulation) Thermodynamics: equilibrium characteristics (e.g. binding affinity

of protein & drug) Remember, proteins are still big!

off lattice go model

Developed from lattice model: “funnel concept”

Nature has developed proteins to fold (evolution)

Proteins can be modeled to fold Native contacts energy surface Matches with experimental observatio

ns

united atom/implicit model folding

“Statistical folding” Starts from many independent traj

ectories Lucky trajectories fold

Nfolded / Ntotal = kfold x time

all atom unfolding

Folding inferred from unfolding At high T, unfolding is fast (~ 1 ns) Full atomistic detail from folded state to unfolded state

binding free energy: docking

Molecular modeling” Binding free energy is calculated based on the shape of ligand an

d protein Drug design

binding free energy: more accurate versions

Free energy: Potential + entropy factor P + L PL

Thermodynamic integration (TI) Free energy perturbation (FEP) Jarzinsky’s inequality

Extremely expensive calculationsF

free energy landscape method

Kinetic information is inferred from free energy surface

Rough free energy surface can be obtained faster by parallelization

“Trajectory by intuition”

current limitation

Accuracies of models Force field Solvent models

Speed For small proteins (<50 amino acids):

1 ns ~ 1 day Biologically relevant event timescale > 1 s

Size Many proteins are not just large: they are huge!

responses to the challenges

Accuracy: Blend with quantum mechanical calculation QM/MM, QM-trajectory method (e.g. CPMD)

Speed E.g. Compute on video card

Size E.g. Umbrella sampling

Biological Systems are complex, thus, a combination of experimental and computational approaches are needed.

computational biology

Computational Biology Bioinformatics More than sequences, database searches, statistics or

image analysis.

A part of Computational Science Using mathematical modeling, simulation and

visualization Complementing theory and experiment

computational biology

A B

irreversible, one-molecule reaction examples: all sorts of decay processes, e.g.

radioactive, fluorescence, activated receptor returning to inactive state

any metabolic pathway can be described by a combination of processes of this type (including reversible reactions and, in some respects, multi-molecule reactions)

simplest chemical reaction

A B

various levels of description: homogeneous system, large numbers of molecules =

ordinary differential equations, kinetics small numbers of molecules = probabilistic equations,

stochastics spatial heterogeneity = partial differential equations,

diffusion small number of heterogeneously distributed

molecules = single-molecule tracking (e.g. cytoskeleton modelling)

simplest chemical reaction

Imagine a box containing N molecules.

How many will decay during time t? k N Imagine two boxes containing N/2 molecules

each.

How many decay? k N Imagine two boxes containing N molecules

each.

How many decay? 2k N In general:

)(*)(

tndt

tdn teNtn 0)(

differential equation (ordinary, linear, first-order)

exact solution (in more complex cases replaced by a numerical approximation)

kinetic description

what is bio-modeling?

DNA

RNA

PROTEIN

GAA GTT GAA AAT CAG GCG AAC CCA CGA CTG

GAA GUU GAA AAU CAG GCG AAC CCA CGA CUG

GLU GAL GLU ASN GLN ALA ASN PRO ARG LEU

biological building blocks

GLU GLU ASNVAL LEUARGPROASNALAGLN . . .

GLU VAL

GLU

ASN GLN

ALA

ASN PRO

ARG

LEU

protein folding

some fundamental questions

Question #1:Given a protein or DNA molecule, what is the geometric structure of the molecule?

Question #2:Why and how protein folds to a unique three-dimensional structure?

Question #3:Given a set of distances between pairs of atoms, how can we determine the coordinates of the atoms?

Question #4:Given the magnitudes of the structure factors of a protein, how can we determine the phases of the structure factors?

Question #5:Given two proteins, how can we compare their geometric structures?

Question #6: …

Protein X-ray Crystallography Nuclear Magnetic Resonance Potential Energy Minimization Molecular Dynamics Simulation Homology Modeling Fold Recognition Inverse Protein Folding

methods for structure prediction and determination

empirical structure determination

Two major experimental methods for determining protein structure

X-ray Crystallography Requires growing a crystal of the protein

(impossible for some, never easy) Diffraction pattern can be inverse-Fourier transformed to

characterize electron densities (Phase problem) Nuclear Magnetic Resonance (NMR) imaging

Provides distance constraints, but can be hard to find a corresponding structure

Works only for relatively small proteins

X-ray crystallography

X-rays, since wavelength is near the distance between bonded carbon atoms

Maps electron density, not atoms directly Crystal to get a lot of spatially aligned atoms Have to invert Fourier transform to get structure, but

only have amplitudes, not phases

X-ray crystallography

In X-ray crystallography, protein first needs to be purified and crystallized, which may take months or years to complete, if not failed.

After that, the protein crystal is put into an X-ray equipment to make an X-ray diffraction image. The diffraction image can be used to determine the three-dimensional structure of the protein.

The process is time consuming, and some proteins cannot even be crystallized.

X-ray crystallography computing

X-ray crystallography computing

A mathematical problem, called the phase problem, needs to be solved before every crystal structure can be fully determined from the diffraction data.

80% of the structures in PDB Data Bank were determined by using X-ray crystallography.

NMR structure determination

The NMR approach is based on the fact that nuclei spin and generate magnetic fields. When two nuclei are close their spins interact. The intensity of the interaction depends on the distance between the nuclei. Therefore, the distances between certain pairs of atoms can be estimated by measuring the intensities of the nuclei spin-spin couplings.

The distance data obtained from the NMR experiment can be used to deduce the structural information for the molecule. One way of achieving such a goal is based on molecular distance geometry.

NMR structure determination

Not all distances between pairs of atoms can be detected. In practice, only lower and upper bounds for the distances can be obtained also.

Structure can be determined by solving a distance geometry problem with the distance data from the NMR experiments.

15% of the structures in PDB Data Bank were determined by using NMR spectroscopy.

potential energy minimization

HypothesisProtein native structure has the lowest or almost lowest potential energy. It can therefore be located at the global energy minimum of protein.

potential energy minimization

A reasonably accurate potential energy function needs to be constructed.

Given such a function, a local minimum is easy to find, but a global one is hard, especially if the function has many local minima. No completely satisfactory algorithm has been developed yet for minimizing proteins.

Potential energy minimization has been used successfully for structure refinement though.

molecular dynamics

Folding can be simulated by following the movement of the atoms in protein according to Newton’s second law of motion.

The step size has to be small in femto-second to achieve accuracy.

Current computing technology can make only picoseconds to microseconds of simulation, while protein folding may take seconds or even longer time.

Molecular dynamics simulation has been used successfully for the study of other types of dynamical behavior of protein.

molecular dynamics

limitations of MD simulations

Full atomic representation noise difficulty in discerning the dominant mechanisms of motion need for methods for filtering out the noise, such as Essential Dynamics.

Empirical force fields limited by the accuracy of the potentials.

Time steps constrained by fastest motion (vibrations in bond lengths occur in the femtoseconds (fs) time range and necessitate the use of timesteps of 1-5 fs).

Inefficient sampling of the complete space of conformations. Limited to small proteins (100s of residues) and/or short time

s (subnanoseconds).

Homology ModelingSequence to Sequence

Fold RecognitionStructure to Sequence

Inverse Protein FoldingSequence to Structure

sequence structure alignment

Known Sequences / Structures

Ranking Sequences / Structures

Sequence Structure Alignment

Scoring functions may not be able to distinguish between good and bad matches.

Computing the best alignment is NP-hard in general when gaps are allowed.

The results are not accurate and have only certain level of confidence.

sequence structure alignment

what is biomolecular modeling?

Application of computational models to understand the structure, dynamics, and thermodynamics of biological molecules

The models must be tailored to the question at hand: Schrödinger equation is not the answer to everything! Reductionist view bound to fail!

This implies that biomolecular modeling must be both multidisciplinary and multiscale

an odd remark

"Every attempt to employ mathematical methods in the study of chemical questions must be considered profoundly irrational and contrary to the spirit in chemistry. If mathematical analysis should ever hold a prominent place in chemistry - an aberration which is happily almost impossible - it would occasion a rapid and widespread degeneration of that science."

A. Comte (1830)

1992 Nobel Prize in ChemistryRudolph Marcus (Theory of Electron Transfer)

1998 Nobel Prize in ChemistryJohn Pople (ab initio)Walter Kohn (DFT-density functional theory)

a Nobel remark

growth of biological databases

3D structures growthhttp://www.rcsb.org/pdb/holdings.html

molecular modeling

Predictions:•Structure•Properties

Mathematicalmodel

“First Principles” • •- dE / dri = mi d2ri / dt2(MD)•Folding simulations

H = EQM

Empirical Correlations - {property} = k {Descriptors}

•E = Ebonded + Enonbonded (MM)

• (QSAR)

•Fold recognition

^

log ' ''1 2C k k k

MolecularModel

structure-property relationships

Conformational energy (potential energy)

Evalence = Ebond + Eangle + Etorsion + Eoop bond stretching(Ebond)

valence angle bending (Eangle)

dihedral angle torsion (Etorsion)

out-of-plane interactions (Eoop)

Enonbond = EvdW + ECoulomb + Ehbond

van der Waals (EvdW)

electrostatic (ECoulomb)

hydrogen bond (Ehbond)

F.Melani Molecular Modeling in Chimica Farmaceutica

nonbondvalencetotal EEE

molecular geometry and molecular properties

Force-field

definition by atoms type atomic charges constant of force, equlibrium values energy equations

Σ Force fields

conformational energy

(potential energy)

molecular geometry and molecular properties

F.Melani Molecular Modeling in Chimica Farmaceutica

standard force field

molecular geometry and molecular properties

F.Melani Molecular Modeling in Chimica Farmaceutica

molecular geometry and molecular properties

F.Melani Molecular Modeling in Chimica Farmaceutica

bond-stretching ( Ebond )

Morse quadratic quartic

2)( 01 rrek 20 )( rrk 4

043

032

02 )()()( rrkrrkrrk

Morse quadratic

valence angle bending (Eangle ) 2

0 )( k4

043

032

02 )()()( kkk

quadratic quartic

dihedral angle torsion ( Etorsion )

)cos(1 0 nk

molecular geometry and molecular properties

F.Melani Molecular Modeling in Chimica Farmaceutica

out-of-plane interactions ( Eoop )

H R'

R

O

2k

k

molecular geometry and molecular properties

F.Melani Molecular Modeling in Chimica Farmaceutica

nonbond term (Enonbond )

van der Waals ( EvdW )

601200 2

ij

ij

ij

ij

i jij r

r

r

rE

612

ij

ij

i j ij

ij

r

D

r

C

hydrogen bond ( Ehbond )

1001200 65

ij

ij

ij

ij

i jij r

r

r

rE

1012

ij

ij

i j ij

ij

r

D

r

C

electrostatic ( Ecoulomb )

i j ij

ji

r

qq

molecular geometry and molecular properties

F.Melani Molecular Modeling in Chimica Farmaceutica

Example: H2O (potential energy )

Koh, b0OH, KHOH, and 0

HOH are parameters of the forcefield

b is the current bond length of one O-H b' is the length of the other O-H bond is the H-O-H angle.

22'2 oHOHHOH

oOH

oOHOH KbbbbKE

molecular geometry and molecular properties

F.Melani Molecular Modeling in Chimica Farmaceutica

ij

ji

ij

ij

i j ij

ij

r

qq

r

D

r

CE

612

int

The objective: searching the orientations with low interaction energies.

DOCKING

molecular geometry and molecular properties

F.Melani Molecular Modeling in Chimica Farmaceutica

MEP

drr

r

R

ZpV

rp

nucleus

A Ap

A )(

)(

i pr

i

ir

qpV )(

electronic density

)()()( rrPrionsBasisFunct

molecular geometry and molecular properties

F.Melani Molecular Modeling in Chimica Farmaceutica

molecular vibration

molecular vibration

protein structure

Most proteins will fold spontaneously in water, so amino acid sequence alone should be enough to determine protein structure

However, the physics are daunting: 20,000+ protein atoms, plus equal amounts of water Many non-local interactions Can takes seconds (most chemical reactions take place

~1012 --1,000,000,000,000x faster) Empirical determinations of protein structure are

advancing rapidly.

protein structure

Proteins are polymers of amino acids linked by peptide bonds.

Properties of proteins are determined by both the particular sequence of amino acids and by the conformation (fold) of the protein.

Flexibility in the bonds around C: (phi) (psi) sidechain

protein structure

Protein structure is described in four levels Primary structure: amino acid sequence Secondary structure: local (in sequence) ordering into

()Helices: compressed, corkscrew structures ()Strands: extended, nearly straight

structures ()Sheets: paired strands, reinforced by

hydrogen bonds parallel (same direction) or antiparallel

sheets Coils, Turns & Loops: changes in direction

Tertiary structure: global ordering (all angles/atoms) Quaternary structures: multiple, disconnected amino acid

chains interacting to form a larger structure

protein structure

helices

2 types of sheets

anti-parallel parallel

turns

combining secondary structures to make motifs

DNA-binding helix-turn-helix Calcium-binding motif

24 ways to arrange adjacent hairpins

alpha/beta domains

Triosephosphate isomerase Dehydrogenase

Ramanchandran plot

Ramanchandran plot

always glycine

protein structure cartoons

protein structure representations

protein structure representations

protein structure representations

protein structure representations

protein structure representations

Proteins are created linearly and then assume their tertiary structure by “folding.” Exact mechanism is still unknown

Proteins assume the lowest energy structure Or sometimes an ensemble of low energy structures.

Hydrophobic collapse drives process Local (secondary) structure proclivities Internal stabilizers:

Hydrogen bonds, disulphide bonds, salt bridges.

protein structure

serine-threonine protein kinase

calmodulin regulation

multimer formation

12 subunitswith the catalytic

domains facing out

CaM Kinase II structure

unc-43 --------------------MQLQQINSGAFSVVRRCVHKTTGLEFAAKIINTKKLSARDrCaMKII -------MATITCTRFTEEYQLFEELGKGAFSVVRRCVKVLAGQEYPAKIINTKKLSARDhCaMKI MLGAVEGPRWKQAEDIRDIYDFRDVLGTGAFSEVILAEDKRTQKLVAIKCIAKEALEGKErCaMKI MPGAVEGPRWKQAEDIRDIYDFRDVLGTGAFSEVILAEDKRTQKLVAIKCIAKKALEGKE .. **** * . . * * * .. unc-43 FQKLEREARICRKLQHPNIVRLHDSIQEESFHYLVFDLVTGGELFEDIVAREFYSEADASrCaMKII HQKLEREARICRLLKHPNIVRLHDSISEEGHHYLIFDLVTGGELFEDIVAREYYSEADAShCaMKI GS-MENEIAVLHKIKHPNIVALDDIYESGGHLYLIMQLVSGGELFDRIVEKGFYTERDASrCaMKI GS-MENEIAVLHKIKHPNIVALDDIYESGGHLYLIMQLVSGGELFDRIVEKGFYTERDAS .* * . . ..***** * * **. **.*****. ** . .*.* *** unc-43 HCIQQILESIAYCHSNGIVHRDLKPENLLLASKAKGAAVKLADFGLAIEVN-DSEAWHGFrCaMKII HCIQQILEAVLHCHQMGVVHRDLKPENLLLASKLKGAAVKLADFGLAIEVEGEQQRWFGFhCaMKI RLIFQVLDAVKYLHDLGIVHRDLKPENLLYYSLDEDSKIMISDFGLSKMED-PGSVLSTArCaMKI RLIFQVLDAVKYLHDLGIVHRDLKPENLLYYSLDEDSKIMISDFGLSKMED-PGSVLSTA . * *.*... * *.*********** * . . ..****.  unc-43 AGTPGYLSPEVLKKDPYSKPVDIWACGVILYILLVGYPPFWDEDQHRLYAQIKAGAYDYPrCaMKII AGTPGYLSPEVLRKDPYGKPVDLWACGVILYILLVGYPPFWDEDQHRLYQQIKARAYDFPhCaMKI CGTPGYVAPEVLAQKPYSKAVDCWSIGVIAYILLCGYPPFYDENDAKLFEQILKAEYEFDrCaMKI CGTPGYVAPEVLAQKPYSKAVDCWSIGVIAYILLCGYPPFYDENDAKLFEQILKAEYEFD .*****..**** . ** * ** *. *** **** ***** ** .*. ** *..  unc-43 SPEWDTVTPEAKSLIDSMLTVNPKKRITADQALKVPWICNRERVASAIHRQDTVDCLKKFrCaMKII SPEWDTVTPEAKDLINKMLTINPSKRITAAEALKHPWISHRSTVASCMHRQETVDCLKKFhCaMKI SPYWDDISDSAKDFIRHLMEKDPEKRFTCEQALQHPWIAGDTALDKNIH-QSVSEQIKKNrCaMKI SPYWDDISDSAKDFIRHLMEKDPEKRFTCEQALQHPWIAGDTALDKNIH-QSVSEQIKKN ** ** .. ** * .. * ** *. .**. ***. . .* * . .**  unc-43 NARRKLKGAILTTMIATRNLSSKRSYRLTLGAEKLVISMKNIEYWQVLLNKIFATYKIKMrCaMKII NARRKLKGAILTTMLATRNFSGG-----------------------------------KShCaMKI FAKSKWKQAFNATAVVRHMR----------------------------------------rCaMKI FAKSKWKQAFNATAVVRHMR---------------------------------------- *. * * * .* . .

…continued

sequence comparison

unc-43 SPEWDTVTPEAKSLIDSMLTVNPKKRITADQALKVPWICNRERVASAIHRQDTVDCLKKFrCaMKII SPEWDTVTPEAKDLINKMLTINPSKRITAAEALKHPWISHRSTVASCMHRQETVDCLKKFhCaMKI SPYWDDISDSAKDFIRHLMEKDPEKRFTCEQALQHPWIAGDTALDKNIH-QSVSEQIKKNrCaMKI SPYWDDISDSAKDFIRHLMEKDPEKRFTCEQALQHPWIAGDTALDKNIH-QSVSEQIKKN ** ** .. ** * .. * ** *. .**. ***. . .* * . .**  unc-43 NARRKLKGAILTTMIATRNLSSKRSYRLTLGAEKLVISMKNIEYWQVLLNKIFATYKIKMrCaMKII NARRKLKGAILTTMLATRNFSGG-----------------------------------KShCaMKI FAKSKWKQAFNATAVVRHMR----------------------------------------rCaMKI FAKSKWKQAFNATAVVRHMR---------------------------------------- *. * * * .* . .  unc-43 KQCRNLLNKKEQGPPSTIKESSESS-QTIDDNDSEKGGGQLKHENTVVRADGATGIVSSSrCaMKII G--G---NKKNDG----VKESSESTNTTIEDED--------------------------- ***. * .******. **.*.* unc-43 NSSTASKSSSTNLSAQKQDIVRVTQTLLDAISCKDFETYTRLCDTSMTCFEPEALGNLIErCaMKII ------------TKVRKQEIIKVTEQLIEAISNGDFESYTKMCDPGMTAFEPEALGNLVE **.*..**. *..*** ***.**..** **.*********.* unc-43 GIEFHRFYFD--GNRKNQ-VHTTMLNPNVHIIGEDAACVAYVKLTQFLDRNGEAHTRQSQrCaMKII GLDFHRFYFENLWSRNSKPVHTTILNPHIHLMGDESACIAYIRITQYLDAGGIPRTAQSE *..******. * ****.*** .*..*.. **.**...**.** * * **. unc-43 ESRVWSKKQGRWVCVHVHRSTQPSTNTTVSEFrCaMKII ETRVWHRRDGKWQIVHFHRSGAPSVLPH---- *.*** .. *.* **.*** **

…continued (overlapped)

sequence comparison

Protein structure basicsprotein structure

proteins consist mostly of a-helices, b-sheets, and turns. the a-helices and b-sheets typically form the framework of the

protein. the turns and other atypical structures often play important bin

ding and catalytic roles. the core of the protein is hydrophobic, whereas the surface is

usually polar or charged. most turns and kinks have glycines and prolines

alpha helix

protein structure

three-stranded antiparallel b-sheet

protein structure

three-stranded antiparallel b-sheet, space filled

protein structure

rCaMKII SPEWDTVTPEAKDLINKMLTINPSKRITAAEALKHPWISHRSTVASCMHRQETVDCLKKFrCaMKI SPYWDDISDSAKDFIRHLMEKDPEKRFTCEQALQHPWIAGDTALDKNIH-QSVSEQIKKN 297 ** ** .. *** * .. .* ** *. .**.****. . . .* * . .**   rCaMKII NARRKLKGAILTTMLATRNrCaMKI FAKSKWKQAFNATAVVRHM 316 *. * * *. .* . .

substrate binding cleft

protein structure

red - chargedblue - polargreen - hydrophobic

sliced protein

rCaMKII HQKLEREARICRLLKHPNIVRLHDSISEEGHHYLIFDLVTGGELFEDIVAREYYSEADASrCaMKI GS-MENEIAVLHKIKHPNIVALDDIYESGGHLYLIMQLVSGGELFDRIVEKGFYTERDAS 119 .* * . . .****** * * ** *** .**.*****. ** . .*.* *** rCaMKII HCIQQILEAVLHCHQMGVVHRDLKPENLLLASKLKGAAVKLADFGLAIEVEGEQQRWFGFrCaMKI RLIFQVLDAVKYLHDLGIVHRDLKPENLLYYSLDEDSKIMISDFGLSKMED-PGSVLSTA 178 . * *.*.** * *.*********** * . . ..****. .

protein structure

rCaMKII HQKLEREARICRLLKHPNIVRLHDSISEEGHHYLIFDLVTGGELFEDIVAREYYSEADASrCaMKI GS-MENEIAVLHKIKHPNIVALDDIYESGGHLYLIMQLVSGGELFDRIVEKGFYTERDAS 119 .* * . . .****** * * ** *** .**.*****. ** . .*.* *** rCaMKII HCIQQILEAVLHCHQMGVVHRDLKPENLLLASKLKGAAVKLADFGLAIEVEGEQQRWFGFrCaMKI RLIFQVLDAVKYLHDLGIVHRDLKPENLLYYSLDEDSKIMISDFGLSKMED-PGSVLSTA 178 . * *.*.** * *.*********** * . . ..****. .

protein structure

rCaMKII HCIQQILEAVLHCHQMGVVHRDLKPENLLLASKLKGAAVKLADFGLAIEVEGEQQRWFGFrCaMKI RLIFQVLDAVKYLHDLGIVHRDLKPENLLYYSLDEDSKIMISDFGLSKMED-PGSVLSTA 178 . * *.*.** * *.*********** * . . ..****. .   rCaMKII AGTPGYLSPEVLRKDPYGKPVDLWACGVILYILLVGYPPFWDEDQHRLYQQIKARAYDFPrCaMKI CGTPGYVAPEVLAQKPYSKAVDCWSIGVIAYILLCGYPPFYDENDAKLFEQILKAEYEFD 238 .*****..**** . ** * ** *. *** **** ***** **.. .*..** *.*

protein structure

protein structure

protein structure prediction

protein model

Goodsell, PDB

protein structure prediction

the 3-D structure of proteins is used to understand protein function and design new drugs

Structural Predictions just from raw protein sequence?

1. ggcacgaggc acggctgtgc aggcacgcat gcaggccagc ….2. atctgcacgt ggttatgctg ccggagtttg ggccgccact….

protein structure prediction

protein structure prediction

1 2

KD Hydrophobicity

Surface Prob.

Flexibility

Antigenic Index

CF TurnsCF Alpha Helices

CF Beta Sheets

GOR Alpha HelicesGOR Turns

GOR Beta SheetsGlycosylation Sites

0.8

1.20.0

-1.7

1.7

10-5.0

5.0

50 100

50 100

Particular structural features can be recognised in protein sequences

protein structure prediction

structure prediction

Comparative modeling Modeling the structure of a protein that has a high degree of sequence identi

ty with a protein of known structure Must be >30% identity to have reliable structure

statistical methods

Residue conformational preferences: Glu, Ala, Leu, Met, Gln, Lys, Arg - helix Val, Ile, Tyr, Cys, Trp, Phe, Thr - strand Gly, Asn, Pro, Ser, Asp - turn

Chou-Fasman algorithm: Identification of helix and sheet "nuclei"

helix - 4 out of 6 residues with high helix propensity sheet - 3 out of 5 residues with high sheet propensity

Propagation until termination criteria met

Threading/fold recognition Uses known fold structures to predict folds in primary

sequence.

structure prediction

inverse protein folding

based on the assumption that there is limited number of structural protein classes (folds). One attempts to assign a new protein sequence to one of these classes.

fold recognition/threading

...MLDTNMKTQL KAYLEKLT KPVELIATL DDSAKSAEIKELL...

structure library

...MLDTNMKTQL KAYLEKLT KPVELIATL DDSAKSAEIKELL...

fold recognition/threading

Ab initio Predicting structure from primary sequence data Generate as many conformations as possible, and assign an e

nergy score to each one When the search terminates (usually when resources run out),

the one with the lowest energy score is selected Usually not as robust nor practical, computationally intensive

structure prediction

function prediction

Key problem: predict the function of protein structures based on sequence and structure information

Function is loosely defined, and can be thought of at many levels Atomic or molecular level Pathways level Network level Etc.

Currently, relatively little progress has been made in function prediction, particularly for higher order processes

Experimentation Experimentally determine the function of proteins and

other structures The “gold standard” of function determination Expensive in terms of time and money

current methods

function prediction

Annotation transfer When sequence or structure analysis yields

correspondences between structures, the known properties and function of one is used to extrapolate the properties and function of the other

This method has been extremely successful, but its drawbacks include [Bork et al., 1998]: Similar sequence or structure does not always imply

similar function The annotated information about the “known” protein or

its sequence or structure information in the database may be incomplete or incorrect

Generally, only molecular functions of a protein can be inferred by analogy (i.e. not higher level functions)

From a formal point of view, properties derived in this manner must be verified through experimentation

current methods

function prediction

simulation-based analysis

Simulation-based analysis tests hypotheses with in silico experiments, providing predictions to be tested by in vitro and in vivo studies.

faster and more economical. Example: Folding@Home

Folding@Home

Simulates protein folds Folds dictate the function of the pro

tein Unfolding was discovered by Christi

an Anfinsen When folds do not fold properly, it l

eads to diseases such as Alzheimer’s disease, Mad Cow, Parkinson’s disease

If the fold of the protein is known then it can also be unfolded

Runs on a distributed system Runs as a screensaver Downloadable at:

http://folding.stanford.edu

Folding@Home

drug design

structured-based drug design

Compound databases,

Microbial broths,Plants extracts,Combinatorial

Libraries

3-D ligand Databases

DockingLinking orBinding

Receptor-LigandComplex

Randomscreening synthesis

Lead molecule

3-D QSAR

Target EnzymeOR Receptor

3-D structure by Crystallography,NMR, electron microscopy OR

Homology Modeling

Redesign to improve

affinity, specificity etc.

Testing

structured-based drug design

3D QSAR

quantitative structure activity relationships to calculate and predict charge distribution, solubility, hydrophobicity, lipophilicity

active sites

Glutathione-GR

drug target site

DHFR

drug target site

multiple alignments of DHFRCLUSTAL W (1.81) multiple sequence alignment chabaudi -----------------------E--KAGCFSNKTFKGLGNEGGLPWKCNSVDMKHFSSV 35 vinckei -----------AICACCKVLNSNE--KASCFSNKTFKGLGNAGGLPWKCNSVDMKHFVSV 47 berghei MEDLSETFDIYAICACCKVLNDDE--KVRCFNNKTFKGIGNAGVLPWKCNLIDMKYFSSV 58 yoelii -----------AICACCKVINNNE--KSGSFNNKTFNGLGNAGMLPWKYNLVDMNYFSSV 47 vivax MEDLSDVFDIYAICACCKVAPTSEGTKNEPFSPRTFRGLGNKGTLPWKCNSVDMKYFSSV 60 falciparum -------------------------KKNEVFNNYTFRGLGNKGVLPWKCNSLDMKYFCAV 35 * *. **.*:** * **** * :**::* :* chabaudi TSYVNETNYMRLKWKRDRYMEK---------NNVKLNTDGIPSVDKLQNIVVMGKASWES 86 vinckei TSYVNENNYIRLKWKRDKYIKE---------NNVKVNTDGIPSIDKLQNIVVMGKTSWES 98 berghei TSYINENNYIRLKWKRDKYMEKHNLK-----NNVELNTNIISSTNNLQNIVVMGKKSWES 113 yoelii TSYVNENNYIRLQWKRDKYMGKNNLK-----NNAELNNGELN--NNLQNVVVMGKRNWDS 100 vivax TTYVDESKYEKLKWKRERYLRMEASQGGGDNTSGGDNTHGGDNADKLQNVVVMGRSSWES 120 falciparum TTYVNESKYEKLKYKRCKYLNKET----------VDNVNDMPNSKKLQNVVVMGRTNWES 85 *:*::*.:* :*::** :*: * .:***:****: .*:* chabaudi IPSKFKPLQNRINIILSRTLKKEDLAKEYN------NVIIINSVDDLFPILKCIKYYKCF 140 vinckei IPSKFKPLENRINIILSRTLKKENLAKEYS------NVIIIKSVDELFPILKCIKYYKCF 152 berghei IPKKFKPLQNRINIILSRTLKKEDIVNENN--NENNNVIIIKSVDDLFPILKCTKYYKCF 171 yoelii IPPKFKPLQNRINIILSRTLKKEDIANEDNKNNENGTVMIIKSVDDLFPILKAIKYYKCF 160 vivax IPKQYKPLPNRINVVLSKTLTKEDVK---------EKVFIIDSIDDLLLLLKKLKYYKCF 171 falciparum IPKKFKPLSNRINVILSRTLKKEDFD---------EDVYIINKVEDLIVLLGKLNYYKCF 136 ** ::*** ****::**:**.**:. * **..:::*: :* :***** chabaudi I----------------------------------------------------------- 141 vinckei IIGGASVYKEFLDRNLIKKIYFTRINNAYT------------------------------ 182 berghei IIGGSSVYKEFLDRNLIKKIYFTRINNSYNCDVLFPEINENLFKITSISDVYYSNNTTLD 231 yoelii IIGGSYVYKEFLDRNLIKKIYFTRINNSYN------------------------------ 190 vivax IIGGAQVYRECLSRNLIKQIYFTRINGAYPCDVFFPEFDESQFRVTSVSEVYNSKGTTLD 231 falciparum I----------------------------------------------------------- 137 * chabaudi --------- vinckei --------- berghei FIIYSKTKE 240 yoelii --------- vivax FLVYSKVGG 240 falciparum ---------

In the absence of a structure of target-ligand complex, it is not a trivial exercise to locate the binding site!!!

This is followed by Lead optimization.

binding site analysis

lead optimisation

Lead Lead OptimizationActive site

LIGAND.wat n +PROTEIN.wat n LIGAND.PROTEIN.watp+(n+m-p) wat

HYDROGEN BONDING

HYDROPHOBIC EFFECT

ELECTROSTATIC INTERACTIONS

VAN DER WAALS INTERACTIONS

STRAIN IN THE LIGAND ( BOUND)

STRAIN IN THE PROTEIN

drug design

factors affecting the affinity of a small molecule for a target protein

difference between inhibitor and drug

Selectivity Less Toxicity Bioavailability Slow Clearance Reach The Target Ease Of Synthesis Low Price Slow Or No Development Of Resistance Stability Upon Storage As Tablet Or Solution Pharmacokinetic Parameters No Allergies

Extra requirement of a drug compared to an inhibitor

Proteins that interact with drugs are typically enzymes or receptors. Drug may be classified as: substrates/inhibitors (for enzymes) agonists/antagonists (for receptors) Ligands for receptors normally bind via a non-covalent reversible binding. Enzyme inhibitors have a wide range of modes:non-covalent reversible,covalent revers

ible/irreversible or suicide inhibition. Enzymes prefer to bind transition states (reaction intermediates) and may not optimal

ly bind substrates as part of energy used for catalysis. In contrast, inhibitors are designed to bind with higher affinity: their affi nities often ex

ceed the corresponding substrate affinities by several orders of magnitude! Agonists are analogous to enzyme substrates: part of the binding energy may be use

d for signal transduction, inducing a conformation or aggregation shift.

thermodynamics of receptor-ligand binding

To understand ‘what forces’ are responsible for ligands binding to Receptors/Enzymes,

It is worthwhile considering what forces drive protein folding –they share many common features.

The observed structure of Protein is generally a consequence of the hydrophobic effect!

Secondary amides form much stronger H-bonds to water than to other sec. Amides hydrophobic collapse

Proteins generally bury hydrophobic residues inside the core,while exposing hydrophilic residues to the exterior Salt-bridges inside

Ligand building clefts in proteins often expose hydrophobic residues to solvent and may contain partially desolvated hydrophilic groups that are not paired:

The desolvation penalty is paid for by favourable (hydrophobic) interaction elsewhere in the structure.

thermodynamics of receptor-ligand binding

docking methods

Docking of ligands to proteins is a formidable problem since it entails optimization of the 6 positional degrees of freedom.

Rigid vs Flexible Speed vs Reliability Manual Interactive Docking

GRID based docking methods

Grid Based methods GRID (Goodford, 1985, J. Med. Chem. 28:849) GREEN (Tomioka & Itai, 1994, J. Comp. Aided. Mol. Des.

8:347) MCSS (Mirankar & Karplus, 1991, Proteins, 11:29).

Functional groups are placed at regularly spaced (0.3-0.5A) lattice points in the active site and their interaction energies are evaluated.

automated docking methods

Basic Idea is to fill the active site of the Target protein with a set of spheres.

Match the centre of these spheres as good as possible with the atoms in the database of small molecules with known 3-D structures.

Examples: DOCK, CAVEAT, AUTODOCK, LEGEND, ADAM, LINKOR,

LUDI.

drug binding pocket of L. casei DHFR

prediction & design of new drugs

Prediction of 3-D PfDHFR using bacterial DHFR and homology modeling approach.

Search for the compounds using bifunctional basic groups that could form stable H-bonds in a plane with carboxyl group.

Optimize the structure of small molecules and then dock them on PfDHFR model.

Toyoda et. al. (1997). BBRC 235:515-519 could identify two compounds.

These two compounds a triazinobenzimidazole &a pyridoindole were found to be active with high Ki against recombinant wild type DHFR.

Thus demonstrate use of molecular modeling in malarial drug design.

identifying new leads

physiome project

virtual human

http://www.physiome.org/

virtual human

Simulation of complex models of cells, tissues and organs

“A worldwide effort to define the physiome by developing databases and models which will facilitate the understanding of the integrative functions of cells, organs and organisms.”

defenitionPhysiome is the quantitative and integrated description of the functional behavior of the physiological state of an individual or species.

physiome project

main objective:“… to understand and

describe the human organism, its physiology and pathophysiology quantitatively, and to use this understanding to improve human health.”

physiome project

Specific Objectives:1. To develop a database with observations of

physiological phenomenon and interpret these in terms of mechanism (reductionism).

2. To integrate experimental information into quantitative descriptions of the functioning of humans and other organisms (modern integrative biology glued together via modeling). 

3. To disseminate experimental data and integrative models for teaching and research. 

physiome project

Specific Objectives:4. To foster collaboration amongst investigators

worldwide, in an effort to speed up the discovery of how biological systems work. 

5. To determine the most effective targets (molecules or systems) for therapy, either pharmaceutical or genomic. 

6. To provide information for the design tissue-engineered, biocompatible implants.

physiome project

physiome project

Issues being addressed:1. Markup language

-- development of SBML (in Caltech) for representing biochemical networks and CellML for electrophysiology, mechanics, energetics and general pathway.

2. Mathematical models-- development of models that are “anatomically based” and “biophysically based” to link gene, protein, cell, tissue ,organ and whole body systems physiology.

Issues being addressed:3. Web-accessible databases

-- For easy data exchange, groups at MIT and UCSD are developing standards for this.Example databases: Genomic Databases, Protein Databases, Material Property Databases, Anatomical Model Databases, Clinical Databases

4. Development of new instrumentation5. Development of Modeling tools, GUIs and web-accessible tools

for visualization of complex models.

physiome project

physiome project

http://www.bme.jhu.edu/news/microphys

1. MicrocirculationA common functional system between organs; It provides an important coupling between cells, tissues, and organs.

a b

physiome project

http://www.bioeng.auckland.ac.nz/projects/nerf/skeletal.php

2. Musculo-skeletal systemContinues to extend the database of parameterised bone geometry to individual muscles, ligaments and tendons.

a Anatomically detailed model of Skeleton.

b Rendered finite element mesh for the bones and a subset of the muscles

a b

physiome project

Computational model of the skull and torso.

a The layer of skeletal muscle is highlighted. b The heart and lungs shown within the torso.

physiome project

3. Cardiome ProjectAn attempt to provide an integrated model of the heart, incorporating electrical activation, mechanical contraction, energy supply and utilization, cell signaling and many other biochemical processes.

Heart model with a textured epidermal surface

a b c

physiome project

Fibrous-sheet architecture of the heart. Ribbons are drawn in the plane of the myocardial sheets a on the epicardial surface of the heart, b at midwall, and c on the endocardial surface. Note the large fibre angle changes. These fibre-sheet material axes are needed for computation of both myocardial activation and ventricular mechanics.

heart structure

physiome project

heart structure

The finite element model of the right and left ventricle of the heart showing various anatomical structures. Geometric information is carried at the nodes of the finite element mesh and interpolated with cubic Hermite basis functions.

physiome project

ventricular mechanics

Mechanics of the cardiac cycle, computed by large deformation finite element analysis, at a zero pressure state, b end-diastole, c mid-systole, d end-systole. Note the apex to base shortening and the twisting about the long axis. Also note the six generations of discretely modeled coronary vessels embedded within the myocardial elements which are used to compute coronary flow throughout the cardiac cycle.

a b c d

physiome project

ventricular mechanics

The collagenous structure of the extra-cellular myocardial tissue matrix, as revealed by confocal microscopy. The material axes used for defining mechanical and electrical constitutive laws in the continuum modeling of the myocardium are based on these microstructurally defined axes.

physiome project

myocardial activation

Activation wave front computed on the finite element model using finite difference techniques based on grid points which move with the deforming myocardium. Bi-domain current conservation equations are solved with trans-membrane ionic currents. The stimulus in this case is a point on the left ventricular endocardial surface near the apex. The activation sequence is heavily influenced by the fibrous-sheet architecture of the myocardium.

physiome project

coronary perfusion

Computed flow in the coronary vasculature

Epicardial Fibers – FEM Model Endocardial Fibers – FEM Model

www.ccmb.jhu.edu

physiome project

ventricular fluid flow

physiome project

Human Torsomodel has been developed which includes the heart, lungs and the layers of skeletal muscle, fat and skin. Current flow from the heart into the torso is computed in order to predict the body surface potentials arising from activation of the myocardium.

physiome project

4. LungsDevelopment of models of the integrated function of various physical processes operating in the lung.

5. Bladder and ProstateAn anatomically detailed model of the bladder and prostate is developed.

6. Circulation SystemA model of the circulation system is being developed based on the Visual Human Project dataset (http://www.nlm.nih.gov/research/visible)

future

Development of Precision Models Simulation requires the integration of multiple

hierarchies of models that have different scales and qualitative properties

Some biological processes take place within milliseconds while others may take hours or daysExample: Protein folding vs. Cell Mitosis

Development of Precision Models Biological processes can involve the interaction

of different types of processes (i.e. biochemical networks coupled to protein transport, chromosome dynamics, cell migration or morphological changes in tissues)

future

Development of Precision Models Types of modeling:

Using differential equations and stochastic simulation

Many cell biological phenomena require calculation of structural dynamics

Deformation of elastic bodies Spring-mass models and other physical processes

future

the end