Dual-topology

Figure 3 Mutation of a ligand Asp into Asn in solution and bound to a protein, (a) Thermodynamic cycle, (b) Dual topology description a hybrid ligand with two side chains. Blocks are used to define the hybrid energy function [Eq. (14)]. Only the ligand is shown the environment is either solvent or the solvated protein, (c) Single-topology description.

In sharp contrast with the single-topology paradigm, the topologies of the reference, 0, and the target, 1, states coexist in the dual-topology scheme throughout the... 

In this section, we present a pseudocode for an FEP alchemical transformation based on the dual-topology paradigm. The steps followed in this algorithm, specifically (c)-(f), may be implemented independently of the core of the program that generates an ensemble of configurations at a given A state - either Monte Carlo or molecular dynamics. This is probably the simplest scheme, which may be improved in several ways, as will be discussed in Sect. 2.9. 

Figure 3 Dual-topology definition for ZMP (1) and AMP (2). Dashed structures incorporate dummy atoms (D).

Rodriguez et al. [52] determined the association free energy of DPPS in a DPPC bilayer, both in the presence and in the absence of calcium ions. They used a dual topology technique with a PC-PS hybrid, and used both thermodynamic integration and free energy perturbation to determine the free energy of DPPS association in a DPPC bilayer. They found that PS-PS association is only favorable in the presence of calcium, which has direct implications for blood coagulation. 

Of the three QM-FEP methods which will be outlined here the QM implementation of the dual topology method is the most similar to the techniques which are used with MM systems. However, as opposed to a dual-topology classical force field calculation in which the interactions are pairwise additive such that only a limited subset of terms needs to be recalculated, a QM method requires two full SCF calculations. This method is readily understood by considering basic FEP theory. In the equation below we give the basic master equations for the FEP method. 

Figure 1 Thermodynamic Cycle for Single and Dual Topology Methods.

Hu, H., Yang, W.T. Dual-topology/dual-coordinate free-energy simulation using QM/MM force field. J. Chem. Phys. 2005,123, 041102. 

However, proteins in mammalian cells manage to escape from quality control in the ER to adopt alternative or dual topology in different intracellular membrane compartments. There are an increasing number of examples of proteins that are expressed in different topological forms with different functions. For example, ductin was found in two different orientations in cellular membranes, one of which serves as the subunit of the vacuolar H -ATPase and the other serves as a component of the microsomal connexin channel of gap... 

Gouffi, K., Gerard, F., Santini, C.L. and Wu, L.F., Dual topology of the Escherichia coli TatA protein, J Biol Chem 279 (2004) 11608-11615. 

Lambert, C. and Prange, R., Dual topology of the hepatitis B virus large envelope protein determinants influencing post-translational pre-S translocation, J Biol Chem 276 (2001) 22265-22272. 

The alternative to the single-topology representation is the dual-topology method. Here, both the molecular topologies are maintained during the entire simulation, such that both species exist (in a topological sense) but do not interact with each other. The Hamiltonian that describes the interaction between these groups and the environment can be described in a number of ways, the simplest of which is the linear relationship ... 

The creation or annihilation of atoms in a molecular system (e.g., in the dual topology description just discussed) is frequently applied in free energy difference calculations. Although such a process is conceptually identical to other mutations, in practice the treatment of dummy atoms in a free energy difference calculation necessitates further approximations, which cause additional problems. 

When large conformational differences are expected between initial and final states of the system, a dual topology file description of the mutation may be useful. When a dual set of coordinates is present, the conformation of the final structure is not determined by the conformation of the initial structure. 

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