Digital files -genes Transformation of informationTransformation of energyTransformation of structure Text files -proteins Electromotive forceProton-motive forceATPMolecular machineHydrophobic-hydrophilic balanceAggregationSpacio/temporal organization Hom

Digital files - genes

Transformation of information

Transformation of energy

Transformation of structure

Text files - proteins

Homeostasis

Electromotive force

Proton-motive force

Molecular ATP machine

Hydrophobic- hydrophilic

balance

Aggregation

Spacio/temporal

organization

Biological space -

aqueous phase

Water as a reactant

C₆H₁₂O₆ + 6O₂ Þ 6H₂O + 6CO₂ + energy ATP+H₂O Þ ADP + H₃PO₄ + energy

Polimerization,

condensation, hydrolysis

Perception of

water

The water molecule

OH distance = 0.958 Å HOH angle = 104.5^o

Oxygen is electronegative it draws the electrons in the

bonds it shares with the hydrogen atoms towards it.

This results in the water molecule having a large dipole moment.

Dipole moment = 1.85 Debye = 6x10

Cm

Strength of an H-bond is related to - the D-H---A distance

- the D-H-A angle.

A hydrogen bond consists of a hydrogen atom lying between two small, strongly electronegative atoms with

lone pairs of electrons.

Hydrogen

bonds

Distance Van der Waals radius of

H: 1.1Å, O 1.5 Å.

Intermediate between VdW distance and typical O-H covalent

bond of 0.96Å.

In hydrogen bond separation is about 1 Å less!

It is 1.77 Å.

The closest VdW approach should be 2.6 Å.

The covalent bond between H and O in water (about 492 kJ mol^-1).

The van der Waals interaction (about 5.5 kJ mol^-1).

The hydrogen bond is

• part electrostatic (90%)

• and part covalent (10%)

The hydrogen bonds is in the range of 0.5 - 100 kJ mol^-1.

The hydrogen bond is stronger than typical electrostatic interactions between partial charges, but it is easily disassociated by heat or by

interaction with other atoms.

The strength

Hydrogen bond is directional

( q )

q ' ' 1 cos

cos

6

12

÷ -

ø ç ö

è

æ -

÷ + ø ç ö

è

æ -

= r

B r

A r

B r

U A

Hydrogen bond potential energy

can hold two H-bonded molecules or groups in a specific

geometric arrangement

The hydrogen bonds define secondary structure of proteins.

They are

between the backbone oxygens and

amide hydrogens.

Hydrogen bonds define protein binding

specificity

Solid phase - ice

4 neighbors per molecule

lower density than liquid water H-bonding network

Only 42% of the volume is filled by the van der Waals volumes of the atoms, compared to

74% for spherical close packing.

Solid Ice vs. Solid Benzene

Liquid phase - water

The H-bonding

propensity of the water together with the tetrahedral geometry, leads to a higher entropy

in the bulk phase.

Cooperativity in hydrogen bond formation.

Hydrogen bonds half life = 10

– 10

sec.

The number of nearest neighbors in water is 4.4 (4 in ice).

Upon breakage of one hydrogen bond,

another hydrogen bond forms, with the

same partner or a new one, within 0.1 ps

High viscosity (0.89 cP, at 25 ° _C)

Selected properties of water

High surface tension (72.75 mJ/m

, at 20 ° _C)

High specific heat capacity (C

=4.18 J g

K

at 25 ° _C) The dielectric constant is high (78.4 at 25 ° _C)

Conductivity of protons is anomalously high

A low thermal expansivity (0.00021/ ° _{C at 20} ° _C)

High boiling point

Dissociation

[H₂O] ~ 55M and ionization is very weak, then [H₂O] ~ constant.

For pure water K_W=[H₃O⁺][OH^-] = 10^-14

[H⁺] = [H₃O⁺] = [OH^-] = 10^-7M In a neutral solution

[H

O

] = 10

M; [OH

] = 10

M

That is only 1 H

for every

560,000,000 water molecules!

O H

OH O

K H

OH O

H O

H O

H

eq

2 3

3 2

2

] ][

[

- +

=

+

«

+

Acid-base chemistry is centered on water

The acidity of a solution is defined by the concentration of H⁺ ions.

pH = - log

[H

]

For pure water [H⁺] = 10^-7 moles/L

Acid precipitation refers to rain, snow, or fog with

a pH lower than 5.6

The Acid Precipitation

Ocean acidification impacts shell formation of planktonic organisms

Definition of pK

( )

e

H

1

p

1

= + q

Titration curve:

One state transition

The pK_a of a titrating site is defined as the pH for which the site is 50% occupied,

HA + H

O Û A

+ H

O

Deprotonation reaction

+ +

+ = = -

= _{H O H O}

HA A HA

O H A

3 3

3 -

- 1

a a a

a a

a K_a a

q

q

number of bound protons as a function of pH

% 11 90

1 = 10 » +

= pKa fA-

pH

% 9

1 »

-

= pKa fA-

pH

% 9 . 0

2 »

-

= pKa fA-

pH

pK_a = 4.0

18

Different pathways of viral entry

Protomer

Pentamer

Capsid

(contains RNA genome)

FMDV Assembly

Acid sensitivity of Foot-and-Mouth Disease Virus (FMDV)

Histidine is a prime suspect

+ 0

Virus Capsid

Inter-pentamer interface

+ +

pH 7.0 pH 3.0

+

Proton transport in bulk water

The diffusion coefficient of each is similar to that of hydrated ion such

as Na

Perception of

water

Water in

biological systems

• Intracellular water very close to any membrane or organelle (sometimes called vicinal water).

• The density of bound water is 10% higher and it has a 15%

greater heat capacity suggesting

much reduced molecular motion.

The whole cell water (70–80% of the total mass) is distributed into

only two to three

hydration layers around

macromolecules.

Representation of the first layer of interfacial water at

the surface of a protein.

Its highly heterogeneous structure reflects the

heterogeneity of the macromolecule surface.

Bound water ’ _in

biological systems

Water molecules connecting the haem groups and protein residues of the two

identical subunits of Scapharca inaequivalvis haemoglobin. Note the symmetry of the two pentameric rings. On binding oxygen, the water molecules transfer

information between the subunits before the water cluster is disrupted .

Some surface water is well ordered

Royer et al. Proc. Natl Acad. Sci. USA 93, 14526 (1996).

A single water molecule in the ligand-binding site of concanavalin A functions as a link between Asp₁₄, Asn₁₆ and Arg₂₂₈ of the protein and the 2'-OH hydroxyl group of the trimannoside ligand.

Some water is required for structure (function)

Li & Lazaridis, J. Phys. Chem. B 109, 662 (2005).

Retinal

LYS₂₁₆

ASP₈₅

ASP₂₁₂

TYR₅₇

THR₂₀₅

TYR₇₉ ARG⁸²

GLU₂₀₄

GLU₁₉₄

Water molecules in bacteriorhodopsin; photoisomerization of all-trans-retinal (pKa 13) to 13-cis-retinal (pKa 8.45), drives a proton from its Lys₂₁₆-Schiff base to Asp₈₅

releasing the pentagonal hydrogen-bonded ring, flipping the Arg₈₂ towards the

(arrowed) protonated water molecule, releasing a proton through a water wire) to the extracellular space. The Schiff base is reprotonated from the cytoplasm through

another associated water wire.

Some water is required for proton transfer

Garczarek & Gerwert, Nature 439, 109 (2005).

Rapid electron transfer between two molecules of bovine liver cytochrome b5. The electrostatic interactions of the water molecules provide a large donor-to-acceptor coupling that produces a smooth distance dependency for the electron-transfer rate.

Only the water cluster and the cytochromes are shown, and the protein residues are hidden.

Some water is required for electron transfer

Lin et al. Science 310, 1311 (2005).

Solubility in water

Water structure is different around the solute molecules:

DG = DH - TDS

Formation of ordered structure

hydrogen bonds

DG < 0 Soluble compound DG > 0 Hydrophobic/ insoluble compound

Water is a polar solvent: dissolves charged or polar compounds by replacing solute-solute H-bonds with solute-water H-bonds.

Non-polar molecules such as lipids and side chains of some amino acids

are hydrophobic

Amphipathic molecules have polar or charged regions, as well as non-polar regions.

Compounds that dissolve easily in water are hydrophilic.

Entropy increases as crystalline substances dissolve

Water interacts

electrostatically with charged solutes

Argon

Hydrophobic and hydrophilic hydration

33

Types of ions

Ion Surface charge

density Intra-cellular Extra-cellular Water preference

Ca²⁺ 2.11 10 nM 2.5 mM High density

Na⁺ 1.00 10 mM 150 mM High density

K⁺ 0.56 159 mM 4 mM Low density

• Structure-breaking ion 'chaotrope' (disorder-maker) (Na

)

• structure-forming ion 'kosmotrope' (order-maker) (K

)

• Kosmotropes shift the local equilibrium to the right.

• Chaotropes shift it to the left.

more dense water « less dense water

Moisture Sorption Isotherm

a_w

Moisture content (d.w.b.)

Zone 3 Bulk water Zone 2

Loosely bound water Zone 1 Tightly bound water

- Activity – “effective concentration”

- Ion-ion and ion-H

O interactions (hydration shell) cause number of ions available to react chemically ("free" ions) to be less than the number present

- Concentration can be related to activity using the activity coefficient g, where [a] = g (c)

The value of g depends on:

- Concentration of ions - Charge of the ion

- Diameter of the ion

Hydrophobic effect is crytical for biological systems

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

Arrangement of water molecules is barely disturbed

5

Polar molecule dissolved in water

Non-polar

molecule dissolved in water

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).

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

There is no “ hydrophobic force ” _!!!

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.

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

Amphipatic

compounds in

aqueous solution

The hydrophobic effect can be used for creating well- defined supramolecular assemblies.

Spherical Micelle

(zero-dimensional ensemble)

Cylindrical Micelle (one-dimensional ensemble)

Vesicle

(two-dimensional ensemble)

Spherical micelles of PS-PAA amphiphile

Cylindrical micelles of PS-PAA amphiphile

Perception of

water

Diffusion

Thermal fluctuations Low Reynold’s number

The radius of a water molecule is about 0.1 nm.

Protein radius is in the range 2 - 10 nm.

Fluid can be considered as a continuum

A system is not in equilibrium when the macroscopic parameters (T, P, etc.) are not constant throughout the system.

To approach equilibrium, these non-uniformities have to be dissipated through the transport of energy, momentum, and mass.

The mechanism of transport is molecular movement.

Transport Phenomena

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

Molecular speed

Actual velocity Þ Maxwell ^’ s distribution

RT Mv

e RT v

v M

f

2 /

3 ²

4 2 )

( ÷

ø ç ö

è

= æ

p p

Macroscopic theory of diffusion:

x

Assumptions:

1. conservation of mater

2. the relation between gradient and flux is linear

0

dx

Adolf Eugen Fick (1829-1901)

x D C

t C

2 2

¶

= ¶

¶

¶

J_x in J_x out

x D C J_x

¶ - ¶

=

Fick’s 1^st law:

x J t

C

¶ - ¶

¶ =

From the ¶

conservation of mater: ^{Fick’s 2nd law:}

In thermodynamic terms, we're watching the increase in entropy within a small, isolated system without an input of

energy.

Units m

s

The solution which corresponds to an initial condition that all particles are at x =0 at t =0:

n x, t

( )

Dt exp − x² 4Dt

"

#$ %

&

'

k is a normalization factor

The rms displacement of particles:

Dt x

»

dc(x, y, z)

dt _x,y,z = D d²C

dx² + d²C

dy² + d²C dz²

!

"

# $

%&

t

C t D

and C C

D

J = Ñ

¶ Ñ ¶

-

! =

In three dimensions:

= 0 x

The random walk of a large number of particles results with

deterministic flow of particles.

Diffusive transport in biology

dx D dC J

= -

A concentration penalty

The time penalty ^{– <X2> = 4Dt}

No directional specificity D ~ 10 ^-5 for most small molecules in water

Perception of

water

Forces acting on a particle due to the solvent:

(i) Stochastic thermal (Langevin) force:

Averageing over a large number of particles

The Langevin approach – dissipative force

changes direction and magnitude averages to zero over time

0 )

( t =

x

(ii) a viscous drag force that always slows the motions.

v

f = - z

viscosity

Stokes law

ph R

z = ⁶

The thermal forces

nN f » 4 . 5

The gravitational force

F

» 10

nN << f

Newton’s law for the protein motion in a one-dimensional domain of length L, x(t):

L t

x t

f dt v

m dv dt v

dx

B

£ £

+ -

=

= , z ( ) 0 ( )

) ) (

( 2

) (

2

2 2 2

2 2

t dt xf

x mv d

dt x d

m

+

-

=

- z

The average over a large number of proteins

) 2 (

2

2 2

2 2 2

t dt xf

x mv d

dt x m d

+

-

=

- z

Integrating twice between t = (0, t) with x(0) = 0:

[ ^{( 1 )} ]

), 2 1

2 (

2

t

t

t

z z

B t

B t

k T t e

x T e

k dt

x

d

- -

= -

=

where t = m/z.

The protein behaves as a ballistic particle moving with a velocity v = (k_BT/m)^1/2. For a protein with m = 10^-21 kg, v = 2 m/s.

In a fluid the protein moves at this velocity only for a time t ~ m/z = 10 ^-13 sec – shorter than any motion of interest in a molecular motor.

During this time the protein travels a distance v · t ~ 0.01 nm before it collides with another molecule.

For

t << t

order:

)

2

(

2

= t t << t

m T x k

[ ^{( 1 )} ]

2

2 t

z

B

T t e

x = k - -

) 2 (

2

t

z ^>>

= k T t t

x

When

t >> t

For protein typically D ~ 10^-11 m²/sec.

Because <x²> = 2Dt (Einstein relation – 1905):

z

T

D = k

Friction is quantitatively related to diffusion

[ ^{( 1 )} ]

2

2 t

z

B

T t e

x = k - -

Brownian motion

Brown (1827): observed irregular movement of pollens in water under microscope.

Major contribution of Brown: made sure non-organic particles also have Brownian motion, confirmed that Brownian motion is not a manifestation of life.

Robert Brown

The random impulses from the water molecules are uncorrelated with position.

0 )

( )

( t × f t =

x _B

Einstein, Brownian motion, and atomic hypothesis

Albert Einstein published 4 papers in the Annalen der Physik in 1905.

– Photoelectric effect – Brownian motion

– Special theory of relativity

Albert Einstein, 1905

• Drag force: f = gv

• Diffusion due to random walk: d

= 6Dt

• To reach equilibrium: Dg = kT

• Random collisions (random walk) are related to the

dissipation of kinetic energy to solvent molecules.

External forces acting on macromolecules

) ) (

,

( f t

t t x dt

dx

+ B

¶ - ¶

= f

z

Langevin equation

The inertial term is neglected.

) ( )

,

( x t f t dt F

dx

+

=

z ×

Forces acting on proteins can be characterized by a potential

x t t x

x

F ¶

- ¶

= ( , ) )

,

( j

Perception of

water

(1) Fluids have density ( r ), and thus moving fluids have momentum (requires a force to start or stop them).

(2) Fluids have viscosity

(1) Viscosity changes with temperature and salinity (2) When fluids contact a solid, there is a thin layer

that sticks very tightly to the solid surface. = “No- slip condition”.

Characteristics of Fluids

Momentum Transfer, Viscosity

v_x

Drag – transfer of the momentum in Dz

the direction perpendicular to velocity.

Laminar flow between two surfaces moving with respect to each other.

Δ p_x

Δ t ≡ F_x ∝ A ⋅ v

(

)

Δ z

z u d A

F

= h D

Shear viscosity h is the proportionality between the velocity

gradient and the force required, per area, to keep the plates moving at constant velocity.

h(kg/m•sec at 20^o C)

Water 10^-3

Olive oil 0.084

Glycerine 1.34

Glucose 10¹³

Dimensionless constant

The Reynolds Number

10⁸ 1000

10³ years 10⁹

10 m Whale

10^-5 10^-3

1 msec 10^-12

1 µm Bacterium

Reynolds number Swimming

speed [cm/s]

Diffusion time Mass

[g]

When the Reynolds number ‘_R’ is small the viscous forces dominate.

Shark skin delays transition to turbulence

Low Reynolds Number = Laminar Flow