Biochemical Toolkits

Biochemical Toolkits

Apart from small molecules such as water and some metabolites, there are four large

classes of macromolecules in a cell.

Each class is formed by a small number of units that can be combined systematically to produce structures of great complexity.

Interactions

real and entropic

S T

H

G = D - D

D

Intra- and Inter-molecular interactions is what biology is all about

Weak interactions are dynamic

(interactions form, break, re-form constantly)

Weak Interactions are additive

Energy of interactions

Hydrophobic < 40 kJ/mol Electrostatic ~ 20 kJ/mol

Hydrogen bond 12-30 kJ/mol van der Waals 0.4-4 kJ/mol Cation – π interaction 5-80 kJ/mol π – π stacking 0-50 kJ/mol

C-O bond 340kJ / mol 1.43Å

C-C bond 360kJ / mol 1.53Å

C-H bond 430kJ / mol 1.11Å

C=C bond 600kJ / mol 1.33Å

C=O bond 690kJ / mol 1.21Å

The two basic parameters affecting protein interactions

Correspondence between Charge and Precipitation

Equilibria - Soy Protein.

Biomolecular structure is determined by a

combination of covalent and noncovalent bonds.

Covalent bonds are static entities which are little effected by environment – stability.

Noncovalent bonds exist in a dynamic equilibrium - flexibility.

Thermal motion - biomolecules are stable enough to make things work, and yet allow the systems to play around in

order to allow the evolution

B A Û

o

GAB

D

E_a

A B

T k G B

A ^B

o B A

A e K B

D «

-

«

= =

] [

]

At equilibrium

[

kT E_a

e rate

Rate =

´

Probable Improbable

Disorder is Favorable

Entropic „Forces”

Pressure

Tension

To create order work must be done

The entropic forces can create a situation where two molecules will interact strongly, although there is

not a direct “force” between them.

Hydrophobic effect

This is not an intermolecular force, but rather the effect due to the peculiar

solvent – water.

Glucose Aspartate Glicine

Lactate Glycerol

Hydrophilic molecules

Phenylalanine

Phosphatidylcholine

Hydrophobic molecules

Amphiphilic molecules

At the interface between water and a non H-bonding group, there are fewer

opportunities for H-bond exchange.

This leads to longer H-bond lifetime, and creation of ice-like ordered water

clusters at the interface, and consequent loss of entropy.

For n-butane in water at 25

C.

∆G = ∆H - T∆S = + 24.5 kJ/mol

It is enthalpically favorable but it is very entropically unfavorable.

-T∆S = +28.7 kJ/mol

∆H = - 4.3 kJ/mol

Water molecules form cage-like structure to encase hydrophobic

molecule.

q System explores different conformations through diffusion and random thermal motion.

Lipid supension

v Water concentration – 55 M v Lipid concentration < 1 µM

107

5 . 5 ´ molecules »

lipid

molecules water

q The water molecules easily change orientations, or move to new neighboring locations.

q System will stay with the lowest energy conformation it encounters.

Often a small ΔH, but a large, favorable ΔS component.

Hydration of macromolecules

LDW stabilizes hydrophobic effect.

Introduction of a hydrocarbon molecule creates a unfavourable cavities in water.

By clumping together in water hydrophobic molecules can reduce the total surface area of the cavity (ΔS > 0).

Lysozyme in explicit water

When a macromolecule moves, it

displaces many small solvent molecules.

Alcohol dehydrogenase (homodimer)

Dimer

A B

B A

90

Hydrophobic

sidechains coloured yellow

The strength of the hydrophobic interaction is

proportional to the total hydrophobic surface area

buried.

Exterior (hydrophilic)

A subunit

180

Interior (hydrophobic)

A subunit

The solubility in H₂O:

fatty acid > alcohol > alkane

The hydrophobic effect of exposing

one buried

methylene group to bulk water is 0.8

kcal/mol.

Critical micelle concentration (CMC)

÷÷ ø çç ö

è

æ -

»

= CMC kT

X

0 0

1

1

) exp

( µ µ

Δµ = the work required to transfer a monomer from an aggregate into the aqueous phase

Example:

Single-chained surfactant (12-15 carbons): CMC = 10^-2 – 10^-5 M Double-chained lipids: CMC ~ 10^-6 – 10^-12 M

The Micelle structure depends on:

the hydrophobic effect

the head group interaction stearing constrains

Techniques for measuring the CMC

Polydispersity

Osmosis can be thought of as the driving force for particle motions along a gradient.

This is an entropic „force” that tends to make the concentration uniform in any region of space.

Membrane

permeable to both solute molecules and

water

Osmosis

A semi-permeable membrane.

Osmotic pressure: force required to prevent osmosis.

Because diffusion occurs into a space defined by the semipermeable membrane, a pressure will tend to build

up inside due to the influx of solvent.

Osmotically active = solutes which can t diffuse through the semipermeable membrane.

Easy way to measure osmolality:

Each Osm (of any solute) lowers the freezing point of water by ~ 2

C

The osmolarity of a solution is equal to the molarity of the particles dissolved in it.

3.

2.

1.

In a simple solutions the effect is additive.

Reverse osmosis

Reverse Osmosis is Used for Water

Purification

It is a measure of the probability of the molecule crossing the membrane.

σ – selectivity/reflection coefficient

The osmotic pressure P = gRTC

The effective osmotic pressure depends on the reflection

coefficient:

eff

= s P = s gRTC P

non- selective membrane semipermeabl

e membrane

( ^{D - DP} )

= L P s

J _{V P}

Bulk flow

Ø Each of the large objects is surrounded by a depletion zone of thickness equal to the radius a of the small particles.

Ø The depletion zone reduces the volume available to the small particles – eliminating it would increase their entropy and hence lower their free energy.

Entropy driven aggregation

Sphingomielin Sphingosine

O P O O^- O H₂C

CH H₂C O C R₁

O O C

O R₂

X

Phospholipids

PC18 1; 9-cis-octadecenoic PC14 1; 9-cis-tetradecenoic PC16 1; 9-cis-hexadecenoic

PC20 1; 11-cis-eicosenoic PC22 1; 13-cis-docosenoic

Alcyl-chain variations

Polyunsaturated Fatty Acids

Omega-3

Omega

-6

•The omega-6 and omega-3 fatty acids are

metabolically distinct and have opposing physiologic functions.

•The increased omega-6/omega-3 ratio in Western diets most likely contributes to an increased incidence of heart disease and inflammatory disorders.

•Omega-3 PUFAs suppress cell mediated immune responses and reduce inflammation.

Steroid

a molecule having the ring system

Steroid skeleton

A B

C D

Shape: fairly flat and fairly rigid

Example: cholesterol and cholesterol esters

CH3

CH3

H

OH

H3C

H H

hydrophillic

hydrophobic

R O

usually palmitate drawn this way

Cholesterol is biological precursor to all other steroids

In lipid bilayer cholesterol induces ordering of lipid acyl chains but retains the liquid-like structure in

the plane of the bilayer: a new liquid-ordered phase!

The polar regions

A phospholipid is an amphiphilic molecule

The hydrophobic regions

Molecules with a fatty acid chain of 4 carbons or less have reasonable solubility in water.

Above 8 carbons, molecules bind strongly to a membrane or proteins with hydrophobic pockets.

Lipid assembly is a water (entropy)-driven process.

The hydrophobic Effect

Meaning of 'Structure' in Fluid Bilayers.

Kolor kode: water, headgroups, glycerol backbone, CH₂, CH₃, DMPC total density, total electron density.

Electron density profile along the bilayer normal

The lipid bilayer

Free vilume distribution

Region 4: decane

Low tail density –

0-6 Å from the bilayer center

Region 3: soft polymer

High tail density –

6-13 Å from the bilayer center

Region 2: interphase

High headgroup density –

13-20 Å from the bilayer center

Region 1: perturbed water

Low headgroup density –

20-27 Å from the bilayer center

Motions in lipid membranes span a wide range of length and time scales.

König & Sackmann, Curr. Opin. Coll. Int. Sci. 1, 78 (1996)

Thermotropic liquid crystals

– the mesomorphic phase formed is characteristic of the temperature.

Lipid phase behavior

Lyotropic liquid crystals

Acyl Chain Configuration

The distribution of lateral pressure/tension across a

lipid monolayer

Electrostatic repulsion

Steric repulsion

Hydration forces

Hydrogen bonding

van der Waals attraction Hydrophobic effect

Empirical rules

l

a k v

0

=

Lyotropic Phases

DLPC/LA pseudo- binary phase diagram.

Gel, 19˚C, n_w= 12 Liq. Cryst., 50˚C, n_w = 28

1. Tu, Tobias, Blasie & Klein, Biophys. J. 70, 595 (1996) 2. Tristram-Nagle et al., Biophys. J. 64, 97 (1993) 3. Tu, Tobias & Klein, Biophys. J. 69, 2558 (1995) 4. Nagle et al., Biophys. J. 70, 1419 (1996)

X_H

H

Gel Liquid Crystal

Quantity

MD¹ X-ray² MD³ X-ray⁴

A (Ų/lipid) 45.8 47.2 61.8 62.9

D (Å) 65.2 63.4 67.3 67.2

X_HH (Å) 45.6 45.0 37.2 36.4

q(˚) 33.6 32.0

a (Å) 8.6 8.5

b (Å) 5.5 5.6

D

Thermotrophic phase transitions

The main transition temperature as a function of the hydrocarbon chain

double bond position (PC).

circle - 18:1cX/18:1cX PC square - 18:0/18:1cX PC frame - 18:1tX/18:1tX PC X – double bond position Triangle - 18:0r18:0 PC

The effect of number of double bonds per chain in the 18 (PC) – carbon on T_m

18:0/18:0 PC,

18:1c9/18:1c9 PC,

18:2c9,12/18:2c9,12 PC

18:3c9,12,15/18:3c9,12,15 PC.

Surface modifications

The polymers, lipid chains, and head group have repulsive interactions (i.e., positive pressures p(z) > 0).

The water-oil surface tension is the only attractive contribution (i.e., p(z) < 0) that tends to minimize the area per molecule.

The bilayer without the polymers will have an average area per molecule that is smaller than that of the mixed lipid-PEG system.

Planar bilayers formed by mixtures of lipids and lipid-PEO.

Lipid hydration number > 14 1

PEG²⁰⁰⁰ hydration number up to 180 6

High concentration PEG:

Strongly-overlapping and highly hydrated brush regime at

concentration pf PEG-lipid over 20 mol%

Middle concentration:

Weakly-overlapped regime at

concentration of PEG-lipid 5-9 mol%

with dehydrated lipid bilayer.

Low concentration:

Non-overlapped mushroom regime at concentrations of PEG-lipid up to 4 mol%

q DSPE-PEG 2000 is laterally excluded from the protein binding site when proteins bind to the PS membrane surface mediated by the PS head group.

The PS-enriched protein binding microdomain

model

q Compression of the packing area per PEG molecule at the liposome surface from 1000 Ų (at 5 mol% DSPE-PEG 2000) to 330 Ų is proposed to be necessary for accommodating the bound proteins.

Actual velocity Þ Maxwell’s distribution

Thermal motion

2 1

2

3 2 1 2

3

÷ ø ç ö

è

= æ

=

M v kT

v M kT

For T = 300 K

500 Da (ATP) – v = 70 m/s

50 000 Da (protein) – v = 7 m/s

6.25 GDa (200 nm diameter vesicle) – v = 600 µm/s

RT Mv

e RT v

v M

f

2 /

3 ²

4 2 )

( ÷

ø ç ö

è

= æ

p p

The distribution of molecular speeds with temperature and molar mass.

§ The mean-square dosplacement in a one-

dimensional random walk.

( ) ^x

^{= 2 Dt}

( ) ^{r !}

⁼ ( ) ( ) ( ) ^x

^{+ y}

^{+ z}

^{= 6 Dt}

§ 3D diffusion.

§ No net movement occurs.

= 0 x

§ The distribution is symmetrical.

Diffusion

Force dx

potential

J µ d ( ) = -

The random walk of a large number of particles results with deterministic flow of particles.

Diffusion in a gradient

The flux is the number of particles crossing a surface in a given time.

Fick s first law

J = – D dc dz

Instead of the number density N we can express the concentration in molarity c.

The number density N = N_Ac, where N_A is Avagadros number.

D – Diffusion constant (m²/s)

dz

a dN

J = -

The width of the distribution grows with time

c = c

pDt e

The solution to this equation is a Gaussian.

¶c ¶t = D ¶

c

¶z

z t y

x

dz

c d dy

c d dx

c D d

dt

z y x

dc ÷÷

ø çç ö

è

æ + +

=

, ,

)

,

,

(

Diffusive transport in biology

dx D dC J

= -

A concentration penalty – diffusive transport requires a concentration gradient.

The time penalty – diffusive transport time scales as the square of the distance or <X²> = 4Dt

No directional specificity

The size limit

As a cell gets bigger there will come a time when its surface area is insufficient to meet the demands of the cell's volume and the cell

stops growing or it will divide.

Passive transport across the lipid

bilayer

What if there is a barrier ??

Membrane permeability to nonelectrolytes

Steps (any can be rate limiting)

1) enter the membrane (potential barrier) 2) diffusion through the bilayer core

3) exit the membrane (potential barrier)

Benzene

kT E_a

e P

P =

E_a correlates to the number of H-bonds a permeant molecule can form.

Diffusion of non-electrolytes

( ^C

^C

)

D

J = - -

Steady-state flow

Molecules in the aqueous phase are in equilibrium with molecules in the membrane phase.

The chemical potential in the water phase (µ_w) = the chemical potential in the membrane (µ_m):

m o

m m

w o

w

w

= µ + RT ln C = µ = µ + RT ln C µ

The concentration at the surface of

the membrane (C_m) ^÷÷_ø

çç ö è

æ -

= C RT

C

o m o

w w

m

µ exp µ

(

)

o m o

w

C C

RT d

J D ÷÷ -

ø çç ö

è

æ -

-

= µ µ

exp

The permeability coefficient

÷÷ ø çç ö

è

æ -

÷ ø ç ö

è

= æ

RT d

P D

o m o

w

µ

exp µ

÷÷ ø çç ö

è

æ -

=

= C RT

K C

o m o

w eq

m p

µ exp µ

The membrane:water partition coefficient (K_p)

C_m – concentration just inside the hydrophobic core of the bilayer,

C_aq – concentration in the aqueous solution.

d P = DK

Permeability coefficients are a combined property of the solute and

the membrane system.

(

)

p

C C

d K

J = - D -

P in membranes is strongly correlated with K_p for

nonpolar solvent

The lipid bilayer

Free vilume distribution

Region 4: decane

Low tail density –

0-6 Å from the bilayer center Region 3: soft polymer

High tail density –

6-13 Å from the bilayer center Region 2: interphase

High headgroup density –

13-20 Å from the bilayer center Region 1: perturbed water

Low headgroup density –

20-27 Å from the bilayer center

Hydrogen bonds donor acceptor

H

H

H H

O O

O

O H

HH

H

Electrostatic interactions – very strong when the carboxy-group is ionized

Charge-transfer

Hydrophobic residues

Aspirin

2-acetoxybenzoic

acid

Atenolol

N H

O O

O

N H

H H

H

H H H

H H H

H

H H

H H

H H

H H

H

H

2-{4-[2-hydroxy-3-(isopropylamino)propoxy]phenyl}acetamide

Atenolol is less amphiphilic than aspirin

Ion transport across a membrane d

P = DK

the Nernst Equation

i o o

i

c

c zF

RT

] [

] ln [

= - y

y

At equilibrium

Walther Hermann Nernst Nobel Prize 1920

dx uc d

dx D dc

J _{= - -} y

Equilibria of weak acids and weak bases

At neutral pH, weak acids and weak bases are predominantly in their charged forms (A^- and BH⁺).

The charged species do not permeate across the membrane’s hydrophobic barrier.

The charged species are in equilibrium with uncharged species that will permeate the membrane.

The uncharged species (B) will reach the equilibrium (B_o = B_i).

Unprotonated species are in equilibrium

with the protonated form: _i

i i

o o

BH H B

BH H K B

] [

] [

] [ ]

[

] [

] [ ₀

+ + +

+ =

=

Since [B]_o = [B]_i

o i o

i

H H BH

BH

] [

] [

] [

] [

+ + +

+ =

For a weak base

B + H

« BH

For a weak acid.

i o o

i

H H A

A

] [

] [

] [

] [

+ + -

-

=

A H

A

+

« [

[ ]

]

log ^{where, [BH+}] = molar concentration of the salt of the base [B] = molar concentration of the weak base.

Henderson - Hassalbach theory of dissociation

[ ] [ ]

A-

log

where, [A^-] = molar concentration of the salt of the acid [HA] = molar concentration of the weak acid.

Example

What will the % ionization be for a weak acidic drug with a pKa of 3.0;

(a) in the stomach which has a pH of 2.25?

(b) in the blood which has a pH of 7.4?

75 . 0 3

25 . ] 2 [

] log [A

- = - = -

HA 1

1778 .

0 ] [

] [A^- =

HA

[ ]

1 100 1778

. 0 1

1778 .

A^- 0 =

= + x

Percentage of drug ionized in trhe stomach

4 . 4 3 4 . ] 7 [

] log [A

- = - =

HA 1

25119 ]

[ ] [A^- =

HA

Percentage of drug ioznized in the blood

[ ]

1 100 25119

1

25119

A^- =

= + x