Week 3: Concepts of mesoscopic forces

Question 1

What are the challenges for calculations with van der Waals forces?

Answer 1

Long range.

Can be attractive and repulsive.

Don’t follow a simple power law
not generally additive.

At large separations relativistic effects occur (retardation).

Quantum mechanical origin.

Question 2

What are the four geometries of the van der Waals force?

Answer 2

Point atoms

Two spheres

Atom/plane

Two planes surfaces

Question 3

How does the force of the van der Waals interaction relate to the energy of the interaction?

Answer 3

F = -dE/dr

Question 4

What are the equations for both the force and the energy of the Van der Waals interaction between two atoms/small molecules?

Answer 4

(13)

Question 5

What are the equations for both the force and the energy of the Van der Waals interaction between two flat surfaces (per unit area)?

Answer 5

(14)

Question 6

What are the equations for both the force and the energy of the Van der Waals interaction between two spheres or macromolecules or radii R1 and R2?

Answer 6

(15)

Question 7

What are the equations for both the force and the energy of the Van der Waals interaction between a sphere/macromolecule of radius R and a flat surface?

Answer 7

(16)

Question 8

What is the equation for Lennard-Jones potential?

Answer 8

(17)

Question 9

What is a typical value for A?

Answer 9

A ~ 10^-19J

Question 10

What are the three relevant electrostatic interactions?

Answer 10

ion-ion
dipole-ion
dipole-dipole

Question 11

Where do electrostatic interactions occur in biology?

Answer 11

In salty solutions.

a) DNA chains
b)Protein/DNA interactions
c)Protein/protein interactions
d)Proteoglycans

Question 12

Sketch the distribution of salt ions around a charged surface. Draw the distribution of the concentration of counterions and coions with distance.

Answer 12

(18)

Question 13

How are screened electrostatic interactions measured?

Answer 13

Debye screening length.

The length scale over which electrostatics can act in physiological salt concentration is about 1nm.

Question 14

What are the formulas for the Bjerrum and Debye screening length?

Answer 14

(19)

Question 15

What is the DVLO potential?

Answer 15

Screened electrostatics + van der Waals interaction.

Question 16

Sketch the total interaction energy with distance.

Answer 16

(20)

Question 17

What are the three types of van der Waals forces?

Answer 17

Hydrogen bonding
Dipole-dipole interactions
London dispersion forces

Question 18

Describe when hydrogen bonding occurs.

Answer 18

Is the strongest type of van der Waals force.

It occurs when hydrogen atoms are covalently bonded to highly electronegative atoms, such as oxygen, nitrogen or fluorine.

Question 19

Describe when dipole-dipole interactions occur.

Answer 19

Occurs when the negative end of a polar molecule is attracted to another polar molecule.

Question 20

Describe when London dispersion forces occur.

Answer 20

A temporary attractive force that occurs when electrons in adjacent atoms create temporary dipoles.

Question 21

Generally, what causes van der Waals forces?

Answer 21

Short-term fluctuations of electron charge distribution in molecules.

These fluctuations create temporary dipoles in molecules, which then interact with each other.

Question 22

How are temporary dipoles created?

Answer 22

When an atom approaches another atom, the electrons in the approaching atom are attracted to the slightly positive end of the other atom.

This creates a temporary dipole in the approaching atom.

Question 23

What role does the domino effect play in a van der Waals force?

Answer 23

The temporary dipole in the approaching atom induces a temporary dipole in the neighbouring atom. This process continues in a domino-like effect.

Question 24

How do the dipole moments in atoms create the van der Waals force?

Answer 24

The temporary dipoles in the neighbouring atoms are attracted/repulsive to each other.

Question 25

Among polar molecules. what are the three components that contribute to the total van der Waals force?

Answer 25

Induction force Orientation force Dispersion force

Question 26

Which component of the total van der Waals force is most important for neutral polar molecules?

Answer 26

The dispersion force.

Question 27

What does the one sixth power of the van der Waals force suggest?

Answer 27

It drops substantially over long distances.

Question 28

How are van der Waals forces computed in a medium?

Answer 28

The solvent material is treated as a continuum. The polarizability and the dielectric permittivity of each particle and molecule, and the dielectric permittivity of the medium are then functions of the absorption frequencies. The expression of the total vdW interaction consists of contributions from zero and non-zero frequency terms. The former includes the contributions from the orientation and induction interaction energies, whereas the latter represents the dispersion interaction energy.

Question 29

What process are the van der Waals forces that act between macroscopic bodies and surfaces in a solvent medium most relevant to?

Answer 29

Protein absorption

Question 30

What suggests the van der Waals component is always negative in protein absorption? What does this imply?

Answer 30

An approximation of energy changes during the protein absorption process suggests that the vdW component is always negative. This implies that attraction always occurs between the protein and the absorbent, however the vdW energy contribution is relatively small.

Question 31

How does the vdW force change in protein absorption with the size of the protein?

Answer 31

Its value becomes more negative if the protein becomes large. This means stronger attraction. It also becomes much less significant when the separation of protein from the surface increases.

Question 32

Explain why it is difficult to derive expressions to estimate van der Waals interactions between biomacromolecules and a cell membrane.

Answer 32

As biocolloidal, nanoparticle or biomolecular systems have different shapes and sizes, interactions between themselves and against a flat surface are complex to compute. i.e. for a protein, it has a rigid 3D structure but because it is hydrated, some of its segments are soft and variable. Furthermore, its hydration, cavity and shape often vary as it approaches a flat membrane surface due to different local interactions. This situation makes it hard to undertake a numerate account of the changes in interfacial structure and interaction.

Question 33

Describe what the hydrophobic effect is.

Answer 33

The hydrophobic effect or hydrophobic interaction refers to a hydrophobic affinity between alkyl or acyl chains in an aqueous environment. Such interaction including pi-pi stacking between aromatic chains is the driving force for self-assembly or co-assembly leading to formation of cell membranes or DNA-protein complexes with different biological functions.

Question 34

What determines surface charges of a cell membrane surface?

Answer 34

Membrane lipids including phospholipids carry charges. In addition, membrane inserted, attached or associated proteins also carry charges. Furthermore, preferential absorption or binding of small ions, organic or inorganic, can lead to changes of net surface charges in a given membrane surface.

Question 35

Describe how a charged double layer is formed on the surface of a cell membrane.

Answer 35

Because of net surface charges bound onto the model surface, the co-ions immediately close to the surface is depleted, but its concentration will gradually rise away from the surface. The counterions will be attracted to the immediate surface region, but their concentration will go down away from the surface. The unequal concentrations of co-ions and counterions at at any given distance away from the surfaces forms a double layer.

Question 36

What is the DVLO theory?

Answer 36

The stability of a pair of colloidal particles in an aqueous solution is affected by the attractive vdW force and repulsive electrostatic force. The balance of the total forces is influenced by the distance between them, in addition to environmental conditions such as T, ion concentrations and surface modifications.

Question 37

How is DVLO theory used to describe protein stability in an aqueous soltution?

Answer 37

For a given system, the pairwise interaction could be developed by modelling the vdW force and electrostatic force as a function of distance and environmental factors. Similar models could be developed to account for absorption of protein onto a given surface or interface.

Question 38

How could charged proteins be stabilised in an aqueous solution when proteins are produced as injectable vaccines?

Answer 38

1) Consider the length of ionic strength to the Debye length. The lower ionic concentration or strength increases Debye length and thus increases electrostatic repulsion between proteins. 2) Ensure the net charges are sufficiently repulsive. Attachment of hydrophilic polymers helps increase hydration, thereby improving stability.