CPU time / memory

Development of Complex Curricula for Molecular Bionics and Infobionics Programs within a consortial* framework**

Consortium leader

PETER PAZMANY CATHOLIC UNIVERSITY

Consortium members

SEMMELWEIS UNIVERSITY, DIALOG CAMPUS PUBLISHER

The Project has been realised with the support of the European Union and has been co-financed by the European Social Fund ***

**Molekuláris bionika és Infobionika Szakok tananyagának komplex fejlesztése konzorciumi keretben

***A projekt az Európai Unió támogatásával, az Európai Szociális Alap társfinanszírozásával valósul meg.

PETER PAZMANY CATHOLIC UNIVERSITY SEMMELWEIS

UNIVERSITY

WORLD OF MOLECULES

Computational chemistry methods

semmelweis-egyetem.hu

(Molekulák Világa )

(Számítógépes kémiai módszerek)

Compiled by dr. Péter Mátyus

with contribution by dr. Gábor Krajsovszky

Formatted by dr. Balázs Balogh

Table of Contents

World of Molecules: Computational chemistry

semmelweis-egyetem.hu

1. Introduction 4 – 7

2. ‘Classical’ Mechanics methods 8 – 9

3. Quantum Mechanics (QM) methods 10 – 12

4. Basic sets 13 – 15

5. Basics 16 – 21

6. Examples 22 – 53

I. Introduction

World of Molecules: Computational chemistry

Computational chemistry, molecular modelling, etc.

a branch of chemistry that uses principles of computer science to assist in solving chemical problems

Examples for calculations:

• structure (i.e. the expected positions of the constituent atoms)

• energies

• electronic charge distributions

• dipoles moments

• vibrational frequencies

• reactivity

• spectroscopic quantities

Computational chemistry

World of Molecules: Computational chemistry

Experimental vs. Computational chemistry

Experimental definition of the Computational problem

Design of the experiment assemble the installation

Choose method build up the system

Carry out the experiment Run the calculations Evaluation

of the results

?

World of Molecules: Computational chemistry

1. ‘Classical’ Mechanics (Newton) methods

Molecular Mechanics based on Force Field Methods

• MM3

• Sybyl

• Amber

2. Quantum Mechanics (QM) methods

Schrödinger equation with approximations

• Semi-empirical models

• Ab Initio models

• Density Functional Theory (DFT) models

Teoretical models

World of Molecules: Computational chemistry

Molecular Mechanics (MM) based on Force Field Methods

• Hooke's law,

• van der Waals interactions

• electrostatics

Molecules are considered as a collection of balls (atoms) and springs

(bonds) structures and energies are determined by employing Newtonian physics

Calculations cannot be performed without knowing some parameters from experimental results (force constants, bond lengths and angles, torsions angles, etc.)

‘force field’ is the collection of equations and parameters

‘Classical’ Mechanics methods

World of Molecules: Computational chemistry

Molecular Mechanics methods

E = E _covalent + E noncovalent

E _bond + E _angle + E _torsion E electrostatic + E van der Waals

q₂

- q₂

+

electrostatic van der Waals

Distance distortion

Angle distortion

Dihedral distortion

Hook’s law: F = - k x

x – displacement of the end of the spring F – force exerted by the spring

k – spring constant (force constant)

Coulomb’s law:

F – magnitude of the electrostatic force q1 and q2 – charges

r – distance between the two charges

K_e– proportionality constant (Coulomb force constant)

22 1

r q k q F = _e

World of Molecules: Computational chemistry

Schrödinger equation, describes how the quantum state of a physical

system changes in time. It is as central to quantum mechanics (as Newton's laws are to classical mechanics).

Quantum Mechanics (QM) methods

Total energy

Wavefunction Kinetic energy

Potential energy

If we could find an exact solution for the Schrödinger equation of a

molecular system, we would know everything there is to know about that system. But we can’t. At least, not exactly… → approximations

World of Molecules: Computational chemistry

( ^{x, y, z} ) ^{Ψ(x, y, z) E Ψ(x, y, z)}

m V 8π

h

2

2

⎟⎟ =

⎠

⎜⎜ ⎞

⎝

⎛ − ∇ +

Schrödinger Equation

Nuclei don't move

Electronic Schrödinger equation

Guess how electrons affect each other from idealized problem

parameterization

Density Functional Theory models Electrons move independently

Molecular "solutions" written in terms of atomic solutions

Hartree-Fock

Molecular orbital methods

Semi-empirical models

MOLLER-PLESSET models

Ab initio Hartree-fock

models

Mix in excited states to account for electron correlation

HΨ = EΨ Born-Oppenheimer approximation

Hartree-Fock approximation

LCAO

approximation

Atomic orbitals don't interact + Parameterization

World of Molecules: Computational chemistry

Quantum Mechanics (QM) methods

Semi-empirical methods: (MNDO, AM1, PM3 etc.)

based on the Hartree–Fock formalism makes many approximations

obtains some parameters from empirical data

Ab Initio models: Hartree–Fock (HF)

solve the molecular Schrödinger equation associated with the molecular Hamiltonian do not include any experimental data, being derived directly from theoretical principles solution is an exact one; they are all approximate quantum mechanical calculations

Density Functional Theory (DFT) models:

often considered as ab initio method, although uses parameters derived from empirical data (or from more complex calculations)

total energy is expressed in terms of the total one-electron density rather than the wave function can be very accurate for little computational cost

Quantum Mechanics (QM) methods

World of Molecules: Computational chemistry

Basis Sets

Basis Sets used by Semi-Empirical models:

Slater type functions (combinations of Gaussian functions) Considers only valence electrons (+ parameterized)

• AM1: upper main group elements + Zn

• PM3: main group elements + transition metals

• MNDO: many main group elements + Zn

Basis sets are a set of functions used to create the molecular orbitals expanded as a linear combination of such functions with the weights or coefficients to be determined. These functions are:

• atomic orbitals (centered on atoms)

• centered on bonds or lone pairs

• functions centered in the two lobes of a p orbital

World of Molecules: Computational chemistry

Basis Sets

Basis Sets used by Ab Initio (HF) models: (Non–empiric!)

Based on the Hartree-Fock self-consistent field (HF-SCF) method using Gaussian functions and includes all electrons with minimal approximation.

Large collection of methods and levels of theory for electron correlation and basis functions

• STO-3G Minimal basis set – unreliable energetics

• 3-21G(*) Split-valence / Double Zeta – excellent results

• 6-31G* Polarized basis set – highly accurate

• 6-311+G** Extended basis set – highly accurate Basis Sets used by DFT models:

Based on electron density and includes electron correlation

World of Molecules: Computational chemistry

Which computational method should I choose?

“Choose your method wisely, and interpret your results with care”

Molecule size (number of atoms)

CPU time / memory

Correlated methods

conformational analysis, starting geometries for other calculations, basic questions of structure and shape basic description of structure and bonding, vibrational spectra, starting geometries for higher level calculations

more accurate prediction of structure and properties, NMR spectra, relative

energies of isomers, qualitative description of transition states and reactions

excited states, UV spectra, transition state energies, structures with unusual bonding schemes, most accurate

predictions of structure and properties

Ab initio models

Semi-empirical models Molecule mechanics

World of Molecules: Computational chemistry

II. Basics

World of Molecules: Computational chemistry

Atom coloring conventions in SPARTAN-ban

*van der Waals radii of atoms is shown in „preferences”

World of Molecules: Computational chemistry

*

wire / ball & wire

Molecule display methods in SPARTAN

tube / ball & sticks

Space Filling (CPK) World of Molecules: Computational chemistry

Calculation methods in SPARTAN

Equilibrium Geometry

specifies that the nearest energy minimum will be located Transition State Geometry

the nearest first-order saddle point (energy maximum in one dimension and energy minima in all other dimensions or commonly known as a transition state) will be located

Equilibrium Conformer/ Conformer Distribution / Conformer Library characterizes the conformers available to a molecule based on different criteria Energy Profile

steps along a user-defined coordinate Similarity

quantifies the likeness among molecules based either on

• structure

• chemical functionality

• between molecules and a template (e.g. pharmacophore)

World of Molecules: Computational chemistry

Atoms (and molecules) are made up of nuclei surrounded by a electron cloud. The size and shape of the electron cloud that defines the size and shape of the molecule. The size and shape of an electron cloud is described by the electron density (the number of electrons per unit volume).

Consider a graph of electron density in the hydrogen atom as a function of distance from the nucleus.

Electron Density Surfaces

distance from nuclei

electron density

Electron cloud lacks a clear boundary.

While electron density decays rapidly with distance from the nucleus, it is never falls to zero. If atoms and molecules ‘rub up against each other’, their electron clouds overlap and merge to a small extent.

World of Molecules: Computational chemistry

A surface formed by a set of interpreting spheres (atoms) with specific van der Waals radii, and which is intended to represent overall molecular size and shape. If Space Filling (left) display model is selected the van der Waals radii of atoms are shown. The size of spheres in ‘Ball and wire’

models (right) is correlated with the van der Waals radii, but not equal!

van der Waals Surface

World of Molecules: Computational chemistry

III. Examples

World of Molecules: Computational chemistry

Example 1: rotamers of n-butane

Each point of the energy diagram represents a certain conformational

isomer of the n-butane. The energy of these isomers can be calculated and plotted as a function of the dihedral angle. Those are on the bottom of the energy valleys are low energy conformers.

60° 120° 180° 240° 300° 360°

H H

H CH₃ H

CH₃ H H

H CH₃ CHH₃

CH₃ H

H CH₃ HH

H CH₃

H CH₃ H

H

C H₃ H

H CH₃ HH

H H

H CH₃ H C H₃

H H

H CH₃ CHH₃

0.7 2.9 5.8 rel. E (kcal)

0° dihedral angle

World of Molecules: Computational chemistry

Example 1: rotamers of n-butane

World of Molecules: Computational chemistry

Example 2: Claisen rearrangement of allyl vinyl ether

CH₂ CH₂

O O

C H₂ O

Allyl vinyl ether undergoes Claisen rearrangement. The mechanism of this reaction presumes a chair arrangement of the reactant.

Is this chair arrangement the lowest-energy conformer (global minimum) or is additional energy required to properly orient the molecule this way? To find out, all the conformers of allyl vinyl ether must be identified and its energy to be evaluated. The energy of best chair-like structure and that of the actual global minimum must be compared.

World of Molecules: Computational chemistry

Conformer 001 is the lowest energy conformer (global minimum) but in this structure the distance of key atoms are to far to form a new bond. No arrangement is possible starting from this conformer.

Conformer 005 (a local minimum) has the shortest distance between the key atoms. The energy of this structure is higher than conformer 001, but the rearrangement may be possible.

This indicates some energy is required to the formation of the transition state geometry.

5,31 Å 3,70 Å

Molecule001 Molecule002

C C dist. E (MM) difference E (ab-initio) difference Molecule001 5.31 Å 69.9645177 ~ 8.4 kcal/mol -705715.538 ~ 6.1 kcal/mol

Molecule005 3.70 Å 78.4275912 -705709.437

Example 2: Claisen rearrangement of allyl vinyl ether

World of Molecules: Computational chemistry

Example 3a: π-electron system of butadiene

HOMO – highest occupied molecular orbital LUMO – lowest unoccupied molecular orbital E

AO

1 2

3 4

ψ₁ ψ₂ ψ3

ψ₄

π∗

π π∗

π E₁

E₂ HOMO

LUMO

HOMO-1 LUMO+1

bonding MOsnon-bonding MOs

World of Molecules: Computational chemistry

Example 3a: π-electron system of butadiene

World of Molecules: Computational chemistry

Ψ

Ψ

Ψ

Ψ

∗ Ψ

∗

Ψ

∗

Example 3b: π-electron system of benzene

World of Molecules: Computational chemistry

Example 3b: π-electron system of benzene

World of Molecules: Computational chemistry

Example 4: hydrogenation of benzene

benzene 1,3-cyclohexadiene cyclohexene cyclohexane

H₂ H₂ H₂

Compound E (kJ/mol)

benzene (bnz) -602341

1,3-cyclohexadiene (chd) -605282

cyclohexene (che) -608405

cyclohexane (cha) -611524

hydrogen molecule (H) -2948

E_bnz + E_H = -605290 E_chd = -605282

ΔE ≈ 7 kJ/mol

E_chd + E_H = -608231 E_che = -608405

ΔE ≈ -175 kJ/mol

E_che + E_H = -611354 E_cha = -611524

ΔE ≈ -170 kJ/mol E_bnz + E_H < E_chd E_chd + E_H >> E_che E_che + E_H >> E_cha

benzene 1,3-cyclohexadiene cyclohexene cyclohexane

>> > >

World of Molecules: Computational chemistry

Example 4: hydrogenation of benzene

World of Molecules: Computational chemistry

Example 5: addition vs. substitution

cyclohexene

+Br₂ Br

Br

Br

+

vs.

1-bromocyclohexene trans-1,2-dibromo-

cyclohexane

Br

Br

Br

+

vs.

bromobenzene trans-5,6-dibromo-

cyclohexa-1,3-diene benzene

+Br₂

Label E (kJ/mol)

trans-1,2-dibromo-cyclohexane (chp1) -14052494

1-bromocyclohexene(chp2) -7328885

trans-5,6-dibromo-cyclohexa-1,3-diene (bzp1) -14046251

bromobenzene (bzp1) -7322809

hydrogen bromide (HBr) -6723497

E_chp1 = -14052494 < E_chp2 + E_HBr= -14052382

E_bzp1 = -14046251 > E_bzp2 + E_HBr = -14046306

alkenes → addition arenes → substitution World of Molecules: Computational chemistry

Example 5: addition vs. substitution

World of Molecules: Computational chemistry

Example 6: Electrophylic aromatic substitution (S

Ar)

W = Wheland intermediate arenium ion σ-complex

W E

r Y H CH₃

CH₃ H

CH₃

δH+ δ+

δ+

δ+

Y

Y Y

CH₃

Y

Y H CH₃ Y

H CH₃

Y H CH₃

Y H CH₃ + CH₃⁺

- H⁺ slow

fast Y Y = CH₃, OCH₃

Hammond's Postulate!

Alkylation (methylation)

CH₃

toluene

OMe

anisol

Y

CH₃ H

Y

CH₃ H

Y

CH₃H

o-intermediate m-intermediate p-intermediate

World of Molecules: Computational chemistry

Example 6: Electrophylic aromatic substitution (S

Ar)

World of Molecules: Computational chemistry

The electrostatic potential map projects the value of the electrostatic potential to the electron density surface. According to the conventional coloring, red represents the negative potential, while blue represents the positive potential. Colors in between (such as orange, yellow, green) represent the intermediate values of the potential.

Example 7: Electrostatic potential map

The main advantages of this presentation are its clarity and its compactness. The main disadvantage is that it provides only information about the contact surface and does not reveal how deep electron-rich and electron-poor areas extend beyond the surface.

World of Molecules: Computational chemistry

Electrostatic potential map for p-tert-butylphenol shows oxygen to be red, its attached (acidic) hydrogen to be blue, the π faces of benzene to be orange or yellow and the tert-butyl group to be green.

Example 7: Electrostatic potential map

World of Molecules: Computational chemistry

Example 7: Acidities of Carboxylic Acids

O

OH Cl

H H

chloracetic acid pK_a = 2.85

O

OH Cl

H Cl

dichloracetic acid pK_a = 1.48

O

OH Cl

Cl Cl

trichloracetic acid pK_a = 0.7 O

OH H

formic acid pK_a = 3.75 O

OH C

H₃

acetic acid pK_a = 4.75 O

OH benzoic acid

pK_a = 4.19

O

OH CH₃

CH₃ C

H₃

pivalic acid pK_a = 5.03

Sareant, E.P., Dempsey, B., Ionization constants of Organic Acids in Aqueous Solution, IUPAC no. 23, Permagon Press, 1979.

World of Molecules: Computational chemistry

Example 7: Acidities of Carboxylic Acids

World of Molecules: Computational chemistry

The LUMO map projects the absolute value of the lowest-unoccupied molecular orbital (the LUMO) onto an electron density surface. According to the conventional coloring, blue indicates the high concentration of the LUMO, while red indicates the low concentration. For example, given that the LUMO designates space available for a pair of electrons, a LUMO map indicates where nucleophilic attack would likely occur.

Example 8: LUMO map

World of Molecules: Computational chemistry

LUMO map for cyclohexenone shows concentration in two regions:

• over the carbonyl carbon (1)

• over the β carbon (2)

These areas ara consistent with both a possible carbonyl addition and Michael (conjugate) addition.

Example 8: LUMO map

World of Molecules: Computational chemistry

1.

2.

Michael addition is a nucleophylic addition of a carbanion or another nucleophyle to an α,β unsaturated carbonyl compound. Electron-

withdrawing substituents on the nucleophyle (groups such as acyl and cyano) leads to asymmetric Michael additions.

C C EWG H H

H

HY

base Y CH₂ CH₂ EWG

H

H H

N

Acrylonitrile

H

H H

N O

O

Nitroethane

H

H H

NH₂ O

Acrylamide

H

H H

Styrene

Example 8: LUMO map

World of Molecules: Computational chemistry

Example 8: LUMO map

World of Molecules: Computational chemistry

Example 9: S

2 reaction of bromide and methyl chloride

The S_N2 reaction goes through a transition state with trigonal bipyramid geometry, in which the entering and leaving groups are colinear. The energy and the structure of the intermediate steps can be modelled, the changes in electrostatic charges and in bondlenghts can be plotted.

intermediate

reaction coordinate E

S_N2

S_N1

World of Molecules: Computational chemistry

Br^-

+

H

H

H ^{Br C}

+

H

H H

C Cl

H

H H

Br

Example 9: S

2 reaction of bromide and methyl chloride

World of Molecules: Computational chemistry

Example 10: estimating reaction speed by LUMO energy

CH₂ ED

+

CH₂ EA

ED

EA

ED (electron donor) = R, OR

EA (electron acceptor) = CN, CHO, CO₂H diene dienophil

HOMO

LUMO

Energy

diene dienophil

better electron acceptors better electron donors

In a Diels-alder reaction an ‘elctron rich’ diene reacts with an ‘electron deficient’ dienophile. The better π-electron donor the substituent of the diene is or the better π-electron acceptor the

substituent of the dienophil is the higher the reaction rate will be (the faster the reaction will be).

World of Molecules: Computational chemistry

CH₂ N

acrylonitrile

CH₂ N N

1,1-dicyanoethylene

N N

cis-1,2-dicyanoethylene

N

N

transz-1,2-dicyanoethylene

N N N

tricyanoethylene

N N N

N

tetracyanoethylene log₁₀ = 0 log₁₀ = 4.64 log₁₀ = 1.94

log₁₀ = 7.61 log₁₀ = 5.66

log₁₀ = 1.89

Example 10: estimating reaction speed by LUMO energy

World of Molecules: Computational chemistry

Example 10: estimating reaction speed by LUMO energy

World of Molecules: Computational chemistry

Example 11: Thermodynamic vs. kinetic control

+

O

O

O

H H

O O

O

H H

O O

+

The yield of different products in chemical reactions is depended on the conditions under which they are carried out. High temperatures and long reaction times favor the most stable (thermodynamic) products. Low temperatures and short reaction times favor the most easily formed (kinetic) products. For example, in Diels-Alder cycloaddition the kinetic product is the endo adduct, whereas it seems likely that the less-crowded exo adduct is the thermodynamic product.

„endo” product „exo” product

World of Molecules: Computational chemistry

E E_max E_min E_act E_rctn

endo -202.064243 -117.005624 -349.503866 85.058619 147.439623

exo -202.355946 -116.373315 -356.166563 85.982631 153.810617

„endo” product „exo” product

E_act E_act

E_rctn E_rctn

Example 11: Thermodynamic vs. kinetic control

World of Molecules: Computational chemistry

Example 12: IR spectra simulation

Molecules have different vibrations, such as stretch, bend or twist. These vibrations persist even if the molecule is cooled to absolute zero. These vibrations are the basis of infrared (IR) spectroscopy. If the frequency of the light which irradiates the compound matches the frequency of a

particular molecular motion, the light will be absorbed. IR spectroscopy is important for identifying molecules as different functional groups vibrate at noticeably different and characteristic frequencies, especially in the so called ‘fingerprint region’.

The Spectra dialog of SPARTAN lists 45 vibrational frequencies for cyclohexanone. The motions of these vibrations can be displayed on the model of the molecule. The frequency at 1700 1/cm is corresponding to the CO (carbonyl) stretch. The experimental IR spectrum can be downloaded from a database and can be compared with the calculated spectrum.

World of Molecules: Computational chemistry

experimental calculated

World of Molecules: Computational chemistry

Example 12: IR spectra simulation

NH NH COOH

H₂N-CH₂-COOH Glycine (Gly) G

Proline (Pro) P

CH₃ ^CH3

CH₃

CH₃ CH₃

CH₃

CH₃ Alanine (Ala) A Valine (Val) V Leucine (Leu) L Isoleucine (Ile) I

S CH₃ SH

Methionine (Met) M Cystei (Cys) C OH

Tyrosine (Tyr) Y Tryptophane (Trp) W Phenylalanine (Phe) F

Alifás

Aromás R =

Hidrophobic

Kéntartalmú Polar

R H

H₂N COOH World of Molecules: Computational chemistry

R =

NH N

NH₂ O

Histidine (His) H

Asparagine (Asn) N

NH₂ O

OH

O OH

O

Glutamine (Gln) Q

Aspartic acid (Asp) D Glutamic acid (Glu) E Lysine (Lys) K Arginine (Arg) R

OH Serine (Ser) S

CH₃ OH Threonine(Thr) T Positive

Negative

Polar NH NH₂

NH₂ N

World of Molecules: Computational chemistry

Chirality of amino acids

non chiral!

L = S

D = R L = R

D = S

exception!

Cysteine

Alanine Glycine Serine

World of Molecules: Computational chemistry

Peptide bond, disulfide bond

disulfide bond

Ala Gly

Ser

Cys

peptide bond

World of Molecules: Computational chemistry

Ser

ω dihedral: Cα

– C’

– N

– Cα

ψ dihedral: N

– Cα

– C’

– N

Φ dihedral: C’

– N

– Cα

C’

ALA_i+1

Cα_i+1

↓

↑ C’_i+1

↑ N_i+1

ALA_i-1

Cα_i-1

↓ ↑

C’_i-1

↑ N_i-1

ALA_i

↑ Cα_i

C’_i

↓

N_i

↓

Peptide dihedrals

World of Molecules: Computational chemistry

A Ramachandran plot

Gopalasamudram Narayana Iyer Ramachandran, or G.N. Ramachandran, (8 October 1922 - 7 April 2001) is widely acknowledged as one of the most important Indian scientists of the 20th century, best known for his work that led to his creation of the Ramachandran plot for understanding peptide structure. He was the first to propose a triple-helical model for the structure of collagen. He also made other major contributions in biology and physics.

World of Molecules: Computational chemistry

Intramolecular hydrogen bonds in α-helix

Hydrogen bonds ~ 5 - 30 kJ/mol ~ 3 Å

World of Molecules: Computational chemistry

Intramolecular hydrogen bonds in β-sheets

World of Molecules: Computational chemistry

Humán monoamine-oxidase B (MAO-B) enzime UNIPROT database (www.uniprot.org) under the code P27338

Member of the flavine monoamin oxidase family contains 520 aminoacids (in homo sapiens)

may exists as a homdimer or either heterodimer form shows enzime activity only in monomer form

Function in living organism is the oxidative

deamination of both biogen amins and xenobiotics

MAO-B enzime

World of Molecules: Computational chemistry

World of Molecules: Computational chemistry

Cofactor: flavine-adenozine diphosphate (FAD)

RCH₂NHR' + H₂O + O₂ = RCHO + R'NH₂ + H₂O₂.

Located mostly in the cytoplasm, anchored to the membrane of the mitokondria

UNIPROT database:

MAO-B enzime

World of Molecules: Computational chemistry

location the surroundings of the binding site

MAO-B enzime

World of Molecules: Computational chemistry

G-protein-coupled receptors (GPCRS)

ECL = extra cellular loop

ICL = intra cellular loop TM = transmembrane domain

NT =

N-terminal

CT =

C-terminal

World of Molecules: Computational chemistry

Cherezov V. és munkatársai. High-resolution crystal structure of an engineered human beta2-adrenergic G protein-coupled receptor.

Science2007, 318, 1258-1265.

Okada, T.. és munkatársai. The retinal conformation and its environment in rhodopsin in light of a new 2.2 A crystal structure.

J. Mol Biol.2004, 342, 571-583.

PDB ID 1U19 2RH1

Year of publication: 2004 2007

Species: bovine human (+ enterobcteria phageT4)

Protein: rodopsin β₂-adrenoceptor (+ antitest)

Resolution: 2.2 Å 2.4 Å

GPCRs deposited in the Uniprot database

World of Molecules: Computational chemistry

volume: 619 ų volume: 482 ų volume: 584 ų

α_2A model α_2B model α_2C model

α

-adrenoceptor binding sites comparison

World of Molecules: Computational chemistry

α

-adrenoceptor binding sites comparison

subtype A

subtype B

subtype C

ligand: noradrenaline

World of Molecules: Computational chemistry