Topic 2

Question 1

Briefly discuss and compare three different force-fields, using the alcohol octanol as an example.

Answer 1

• All-atom: An all atom/atomistic force-field treats each atom explicitly. At every step, the simulation must input all bonding/non-bonding interactions in a system. In long molecules like octanol, this can lead to many dihedral angles needing to be specified for all differing ~-OH chains. Very precise however, computationally costly.
• United-atom: cheaper way to describe the system that saves computational time, but still expensive. It does this by grouping less chemically involved hydrogen atoms into CH­₂ groups. Good for lipid descriptions
• Coarse graining: 4-5 heavy atoms with their H’s are grouped into a single interaction site, saving large amount of computational effort. Octanol is split into a polar (hydrophilic) and non-polar (hydrophobic) half. Lose a degree of chemical detail as cannot capture hydrogen bonding explicitly. However partial charges assigned to these blocks to describe electrostatic and non-bonding interactions.

Question 2

Using a course-grained forcefield allows simulation of larger … for … timescales than with all-atom forcefields, giving a higher chance of overcoming … …

Answer 2

Using a course-grained forcefield allows simulation of larger systems for longer timescales than with all-atom forcefields, giving a higher chance of overcoming kinetic barriers.

Question 3

What are three ways in which coarse graining allow simualtion on larger systems for longer timescales?

Answer 3

• Decrease in total number of particles N
• Larger time step
• Smoother energy landscape

Question 4

How does a decrease in total number of particles N ‘speed up’ a coarse grain simulation?

Answer 4

• A decrease in total number of particles reduces the number of force calculations required at each step.
• Resulting in less computational time needed to move the system forward one-time step, as less forces and energies must be calculated each step.

Question 5

How does larger time-step ‘speed up’ a coarse grain simulation?

Answer 5

• A ​time step for integration needs to be smaller than the highest frequency motion in a system.
• The verlet algorithm can be used to move an atom through calculation of the force, with respect to all other atoms, to apply in one timestep, which should be constant.
• A time step may be suitable for bond stretch of a low frequency (left), resulting in it being closer to its equilibrium value. However, the same force acting on a higher frequency motion (right) results in a high energy final position, leading to assumption of force being constant over our chosen timestep to be invalid.
• Timesteps should be 10x smaller than highest frequency motion, which are generally bond stretches of light hydrogen atoms.
• By removing bonds involving them, a larger time step can be used, as particles of higher mass oscillate slower. Each time step now propagates us further forward in time.

Question 6

How does a smoother energy landscape ‘speed up’ coarse graining?

Answer 6

• Rugged energy landscape of an atomistic model has many local minima.
• Averaging that occurs through coarse-graining results in a smoother energy landscape with less local trapping/friction and faster dynamics.
• Beads can slide over each other much easier

Question 7

Why must we develop new interaction potentials for coarse grained systems?

Answer 7

• Coarse-grained particles do not interact in the same way that atoms do.
• New coarse-grained potentials must be developed that are unique to each system.
• Parameterising is a large challenge as takes a lot of time to predict the correct output.

Question 8

What are two methods of generating course-grained interaction potentials?

Answer 8

• Use an analytical functional form with associated parameters; like atomistic interaction potentials but with CG beads
• Numerically fitting data from atomistic simulations using tabulated potentials (list of r’s between atoms with corresponding F’s/E’s – useful for complex systems where don’t have analytical function)

Question 9

What is mapping, and why is it essential for developing a CGP? (PPQ)

Answer 9

• The first stage in developing a CG interaction potential (CGP) is to define mapping of the atomistic system in to a CG one.
• Essential for new molecules and there are many ways to assign atomistic structure depending on what interactions are expected to be the focus.

Question 10

What are 2 general rules of mapping?

Answer 10

• Each bead will inherit the mass/charge of its constituents
• Must maintain the overall shape of the molecule (otherwise may not replicate the correct self-assembled structure)

Question 11

Outline how you would produce a CG trajectory from an atomistic simulation using a bottom up approach

Answer 11

• First, run a reference atomistic simulation to use as our benchmark (however does not necessarily equal experimental/ab initio PES)
• Extract effective CG potentials using a trajectory of a system (a series of snapshots over time).
• Each snapshot in the atomistic simulation will have positions for all atoms at each timestep which will be used to find their corresponding Force/Energy.
• A CG pseudo trajectory can be attained by grouping atoms in to beads using the beads centre of mass based on an atomistic average.

Question 12

What is an RDF?

Answer 12

• A radial distribution function g(r) shows the probability of finding a particle at distance r from a reference particle.
• At small distances there is a low probability of finding another atom due to coulombic repulsion (LJP?)
• Shells form around the reference particle as other bands of particles appear, with depletion zones between them.

Question 13

How does an RDF used as a target reference functions help form non-bonded potentials from the trajectory of a system?

Answer 13

• Goal is to form a CGP that reproduces the RDF obtained from atomistic simulations.
• The CG RDF, g(i) is linked to the trajectory of our system CG trajectory,
• Which in turn is linked to an atomistic RDF, g(ref), derived from an atomistic trajectory.

Question 14

What is the potential mean force and how is it related to g(ref)?

Answer 14

• Links the potential of mean force (average force that an atom experiences due to its neighbours) to the radial distribution function at that point.

Question 15

Why can we not use V_PMF as a pair potential in our CG model? (not imp)

Answer 15

• Contains manybody contributions from all particles in the system.
• Want a pairwise interaction potential showing how energy varies with r, the sum of which equals our RDF.

Question 16

How is V_PMF used in Iterative Boltzmann Inversion iteratively?

Answer 16

• V_PMF =k_BTln[g_ref(r)] instead is used as a starting guess for V_CG (intermolecular CG potential)
• V_i+1^CG(r) = V_i^CG(r) + k_BTln[g_i(r) / g_ref(r)] is our improved guess after each iteration
• g_ref(r) is our target probability distribution from atomistic simulation
• g_i(r) is the probability distribution from a CG simulation using the i^th potential
• Difference between the two moves us closer of further to result

Question 17

• How does our improved guess for the intermolecular CG potential [V^CG_i+1(r)] change when g_i(r) = g_ref(r)? – 1 on graph

Answer 17

k_BTln…= 0, no change to interaction potential needed as CG simulation produces same pairwise structure as atomistic

Question 18

• How does our improved guess for the intermolecular CG potential [VCGi+1(r)] change when g_i(r) < g_ref(r)? – 2 on graph

Answer 18

• k_BT… is -ve
• probability of finding particle (correlation between CG beads) at that r underestimated.
• Equation will lower pairwise CG energy at that r, making interaction more favourable

Question 19

• How does our improved guess for the intermolecular CG potential [VCGi+1(r)] change when g_i(r) < g_ref(r)? – 3 on graph

Answer 19

• k_BTln… is +ve
• probability of finding particle (correlation between CG beads) at that r overestimated.
• Equation raises pairwise CG energy at that r, making interaction more appropriately favourable (less than before).

Question 20

• Why does it take so long to produce a CG potential through IBI that is like an atomistic trajectory?

Answer 20

• Must iteratively calculate each pairwise interaction in your system using the IBI method until a full CG tabulated potential that is like the original atomistic trajectory is gained.
• However once this is done, CG allows us to reach much higher simulation times.

Question 21

• What is a problem with the IBI discussed in lectures as well as an example of this being solved?

Answer 21

• It takes only a singular atomistic simulation into account as a reference that will be under certain set conditions. This is a problem if one wanted to study phase transitions, which are dependent temperature changes.
• Moore et al (2016) developed a CGP constructed using many different atomistic simulations at varying temperatures to account for this, known as multi-state IBI.

Question 22

• What is force matching and how does it differ to Iterative Boltzmann inversion?

Answer 22

• IBI tried to match the structure of an atomistic simulation where the RDF is used to reach our target data.
• Force matching aims to match forces on the CG interaction sites with the forces at the atomistic level.

Question 23

• What is an example of a property one may want to look for using force matching?

Answer 23

• Force matching is ideal for looking at thermodynamic properties, for example a partition coefficient.

Question 24

• Explain the process of force matching. (don’t need to know in detail)

Answer 24

• A set of reference forces is collected through running an atomistic simulation
• A reference force F_i^ref on a CG bead = sum of associated atomistic forces on beads constituents f_γ , generating a pseudo CG trajectory acting as our target.
• Match the set of CG forces to the reference forces to minimise (image)
• F_il^p is the Net force on site i in atomistic config l
• F_il^ref is the force determined by the trail force field (similar to V_PMF). Often an existing CGP that is then adapted to fit closer to chosen reference.

Question 25

• What kind of approaches are IBI and force matching and what is the alternative?

Answer 25

• They are both bottom-up approaches, where a reference atomistic simulation is used to construct an effective CGP for our system which takes a long time to do. Inverse Monte Carlo (IMC) is another.
• Alternatively, one can use a top-down approach, which is generally used for investigating thermodynamic properties.

Question 26

• What are some advantages of both bottom-up and top-down approaches?

Answer 26

• Bottom-up: capable of capturing fine detail of interaction as CG interactions are extracted from reference atomistic simulations
• Top-down: provide potentials that are more easily transferable and applicable to experimental data.

Question 27

• What is an example of a top-down approach?

Answer 27

• The MARTINI force field, a CG potential fitted to reproduce experimental target data, using few parameters and standard interaction potentials to maximise transferability.
• A choice of building blocks calibrated against experimental oil/water partition coefficients are available to build a system

Question 28

• What is a disadvantage of the MARTINI force-field?

Answer 28

• No systematic way for developing potentials and introducing new molecules unavailable in building blocks.

Question 29

• Give examples of two systems that require a CG potential

Answer 29

• van Eerden et al – simulation of a large photosynthetic protein complex with membrane bound and water bound parts. Would be very difficult to simulate this complex system for long atomistically.
• Fowler et al – using the MARTINI FF to study the effects of embedded proteins on membrane stiffness using a course grained model.

Question 30

• What are some disadvantages of CG models?

Answer 30

• A model can be too biased, and very untransferable to another system
• A model may only be parameterised for a specific class of molecules, showing a lack of compatibility
• Model may be too coarse to capture desired behaviour

Question 31

• Water must be described accurately in CG models, why is this?

Answer 31

• Present in abundance in many biological systems, showing complex behaviours within those systems. Models generally are split in to three categorise to parameterise water (implicit, explicit, and polarizable)