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Replica Exchange

1. Overview and Usage

Replica Exchange is a method commonly used in the group. This technique is often selected if you desire to see how the system behaves over a range of temperature. For example, it is commonly used to determine the heat capacity as a function of temperature which can then be used to find the melting temperature of a protein or DNA duplex.

2. The Basic Theory

In theory, any thermodynamic property of interest can be calculated from a simulation. However, this can only be done if the phase space is sampled completely. More specifically, the system needs to sample each energy state of the system that are populated at the temperatures of interest. Unfortunately, it is common for systems to become trapped in local energy minima at lower temperatures. Becoming trapped means that it remains in the same state and will not move on to others that are, in reality, populated at the temperature of interest.

Trapping is problematic for many of the systems we care about in the group. For example, if you are trying to explain protein folding (protein stability), the system needs to sample the folded and unfolded configurations many times. However, these two states are often separated by high energy barriers. At lower temperatures, the random fluctuations in the system will not be sufficient to move the system up in energy enough to surmount the barrier. The fluctuations may take the system up in energy a small amount in one instance, and another small amount in the following instance, but eventually the energy will move down rather than up. For small barriers, the probability is high that you have enough consecutive "up" moves to reach the top of the barrier. This probability decreases as the height of the barrier increases.

Figure 1 Qualitative depiction of the inability of traditional simulation techniques to effectively sample systems with complex energy landscapes. The barriers separating different states are larger than the available thermal energy of the system.
The purpose of replica exchange (and many other methods) is to help the system traverse the energy landscape and sample all the relevant regions of phase space. It does so by