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In classical molecular dynamics simulations of complex molecular systems, the force field (FF) contains information about bonded (bonds, angles, dihedrals and impropers) and non-bonded parameters. It is well known that energies of bonded interactions vary with temperature, with higher energies progressively shifting the molecule to higher vibrational states. However, we predominantly consider temperature-independent FFs and use them to be run over a range of temperatures, for eg. 300 to 400 K in bio-molecular systems or even a larger range of temperatures in systems ionic liquids or deep eutectic solvents.

My question is, how much information are we losing by considering a temperature-independent FF in such systems?

Moreover, why do temperature-independent FFs work so well for systems that involve conformational transitions (like lipid bilayer melting etc.), when these transitions are strongly dependent on the temperature induced changes in the interaction of the system?

Are there examples that provide instances of failure of these temperature-independent FFs?

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The answer to

how much information are we losing by considering a temperature-independent forcefield in such systems?

is, to a first approximation, none. The reason is that the statement

transitions are strongly dependent on the temperature induced changes in the interaction of the system

is actually exactly backwards.

Temperature-induced phase transitions happen because a system's internal interaction energies do not change with temperature. Now, in the canonical ensemble, the probability difference between microstates is inversely exponential in the energy divided by the temperature. Thus, because interaction energies do not change with temperature, as temperature increases, the probability difference between lower- and higher-energy microstates decreases, so that less ordered phases become entropy-preferred relative to more ordered phases.


To make this concrete, consider lipid bilayer melting. A lipid bilayer is held in place because interactions between all of the lipids' tails, and interactions between the lipids' heads and water, stabilize the system, and the bilayer arrangement is an easy enough way to accommodate everyone's preferences.

But let's say we take a thermal sledgehammer to the system and heat it up to 1000 K. Well, then, every molecule's (on average) got the kinetic energy to bounce from its pot right to the roof and back. Who cares about alkane dispersion interactions and water dipoles and any of that jazz any more? Mind you, the interaction energies haven't changed -- but the thermal energies have rendered them irrelevant. You know as well as I do that we end up with a cloud of vapour, whether in real life or in a (proper) simulation.


Now, when you ask

Are there examples that provide instances of failure of these temperature-independent forcefields?

of course they fail. SPC/E water freezes at -58 °C and boils at 123 °C, which are clearly not the correct freezing point and boiling point. However, it does freeze, and it does boil, and nobody set out to say "hey let's make a model of water that freezes and boils" or inserted special switches at those temperatures to suddenly change the interactions involved.

Instead, the reason molecular dynamics models fail to predict the correct transition points of everyday substances is that the potentials used simply cannot be accurate enough. Molecular dynamics atoms are balls on sticks with point charges and two-term equations for forces. Real life atoms are infinitely more complicated. So the exact temperatures at which the interatomic forces lose to entropy will be "wrong" if the interatomic forces themselves are "wrong" in the first place. But when the interatomic forces have the correct qualitative features, then applying temperature correctly in a molecular dynamics simulation must yield qualitatively correct phase transitions. This whole matter of correct thermostatting is an entire field in itself, but it is almost never done by meddling with the force field parameters in an arbitrary way.

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    $\begingroup$ +1 for the answer. But I disagree with "but it is almost never done by meddling with the force field parameters in an arbitrary way." You might want to look into TIP-3P, TIP-4P, TIP-5P and TIP-4P-ICE water models. They were parameterized specifically to reproduce certain modes of interactions. $\endgroup$ Jul 28, 2023 at 7:49
  • $\begingroup$ You're right, I should adjust my answer to discuss temperature-specific parametrisations. What I meant (which I didn't communicate clearly) is that we don't usually have parameters that change continuously as a function of in-simulation temperature. $\endgroup$ Jul 28, 2023 at 8:02
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    $\begingroup$ That's also wrong technically. There is a type of coarse-graining where you do change the descriptions based on how far or close to an interacting partner are you at that frame. $\endgroup$ Jul 28, 2023 at 8:05
  • $\begingroup$ Not sure I've seen that one before. Do you mean adaptive resolution coarse graining? $\endgroup$ Jul 28, 2023 at 9:35
  • $\begingroup$ I do not remember the exact name, It was mentioned during one of the workshops that I attended. $\endgroup$ Jul 28, 2023 at 9:40
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I have reasonable experience with the parameterization and MD simulations of molecules with CHARMM FF, which is one of the temperature-agnostic FF. I will try to answer the questions, but please note that my answers would be strictly based on how CHARMM FF works, but the basic reasoning should carry over to other FFs.

  1. How much information are we losing by considering a temperature-independent forcefield in such systems?

Ans: None, because when you perform a classical MD simulation, the first approximation is that you are looking at temperatures that are much lower than the ones that are required to break bonds. For eg: the bond-dissociation energy of a C-H bond in CH$_4$ molecule would never be reached in a classical MD simulation, and you are guaranteed to stay in the harmonic approximation regime. However, if you are interested in such high energies, then temperature-agnostic FFs might not be suitable for your use case.

  1. Moreover, why do temperature-independent FFs work so well for systems that involve conformational transitions (like lipid bilayer melting etc.), when these transitions are strongly dependent on the temperature induced changes in the interaction of the system?

Ans: The conformational dynamics of these systems are largely based on the dihedral and torsional parameters, and they are generally much more accessible (due to the lower spring constants associated with them). This means that a simulation at 298K would be able to sufficiently sample the conformational space available to the system, without any problems.

  1. Are there examples that provide instances of failure of these temperature-independent FFs?

Ans: There are many. For example, the famous TIP-3P water model will never freeze, even if you lower the temperature. This lead to the creation of a TIP-4P water model which was aimed at introducing the directional nature of the Hbonding in the ice formation. This was subsequently revised to TIP-5P where explicit lone pairs were introduced to further improve the directional nature of the Hbonding in water. You may also refer to TIP-4P-ICE model, which was specifically parameterized to reproduce the ice-structure.

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