pairwise-additive: they are not a sum over residue pairs. Specifically,
the GB model assigns to each atom i a “solvation radius” b i , which
depends on the conformation of the whole system [9]. To overcome this, two methods are available. We can adopt a “Native
Environment Approximation” (NEA), where each solvation radius
is computed for the wildtype or native structure, then kept fixed
[38]. Or, we can adopt a modified GB model, which computes
more information and stores it in the energy matrix, then requires
additional operations during the subsequent MC simulations. This
variant is called the Fluctuating Dielectric Boundary method [39].
2.1.5 Monte Carlo
Simulations to Explore
Sequences and Structures
The energy matrix is read by the C module protMC, which explores
the space of sequences and structures. Three exploration methods
are available; only Monte Carlo (MC) is considered here
[40, 41]. MC can use a single “replica”, exploring a single trajectory. Or it can use multiple replicas, usually 4–8, with distinct
temperatures, which occasionally exchange their temperatures.
The method is known as “Replica Exchange” MC, or REMC. All
the methods output multiple “snapshots”, sampled along the MC
trajectory. MC moves correspond to rotamer changes at one or two
positions, mutations at one or two positions, or a rotamer change at
one position and a mutation at another. The REMC temperatures
usually range from about 50 to 1000 K, with the very hot replica
easily moving among local energy minima for effective sampling.
Adaptive MC is also possible, as outlined in the next section.
2.1.6 Proteus Software
Files and Documentation
Proteus 3.0 is freely available to academic and government scientists, from https://proteus.polytechnique.fr. Industrial scientists
should contact the corresponding author. The distribution includes
source code, binaries for Intel processors, extensive test cases, and
detailed documentation.
2.2 Adaptive
Landscape Flattening
to Design PDZ–Peptide
Binding Affinity
2.2.1 General Method
To design ligand binding means optimizing a free energy difference
between bound and unbound states. This is not tractable by most
CPD methods, such as simulated annealing or plain Monte Carlo
(MC). Most studies have used heuristic methods that optimize the
bound state energy, a very different property. Recently, a new
method was proposed, using MC simulations and adaptive importance sampling. The energy landscape in sequence space is flattened
adaptively for the unbound state, over the course of an MC simulation, thanks to a bias potential [22, 42]. The bias B is constructed
such that all sequences reach comparable populations. B is then
essentially the sequence free energy with its sign changed. Next, the
bias is included in a simulation of the complex, where it “subtracts
out” the unbound state. Thus, negative design of the unbound
state is achieved. Remarkably, the result is a Boltzmann distribution
where sequence populations measure their affinities.
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Nicolas Panel et al.
the GB model assigns to each atom i a “solvation radius” b i , which
depends on the conformation of the whole system [9]. To overcome this, two methods are available. We can adopt a “Native
Environment Approximation” (NEA), where each solvation radius
is computed for the wildtype or native structure, then kept fixed
[38]. Or, we can adopt a modified GB model, which computes
more information and stores it in the energy matrix, then requires
additional operations during the subsequent MC simulations. This
variant is called the Fluctuating Dielectric Boundary method [39].
2.1.5 Monte Carlo
Simulations to Explore
Sequences and Structures
The energy matrix is read by the C module protMC, which explores
the space of sequences and structures. Three exploration methods
are available; only Monte Carlo (MC) is considered here
[40, 41]. MC can use a single “replica”, exploring a single trajectory. Or it can use multiple replicas, usually 4–8, with distinct
temperatures, which occasionally exchange their temperatures.
The method is known as “Replica Exchange” MC, or REMC. All
the methods output multiple “snapshots”, sampled along the MC
trajectory. MC moves correspond to rotamer changes at one or two
positions, mutations at one or two positions, or a rotamer change at
one position and a mutation at another. The REMC temperatures
usually range from about 50 to 1000 K, with the very hot replica
easily moving among local energy minima for effective sampling.
Adaptive MC is also possible, as outlined in the next section.
2.1.6 Proteus Software
Files and Documentation
Proteus 3.0 is freely available to academic and government scientists, from https://proteus.polytechnique.fr. Industrial scientists
should contact the corresponding author. The distribution includes
source code, binaries for Intel processors, extensive test cases, and
detailed documentation.
2.2 Adaptive
Landscape Flattening
to Design PDZ–Peptide
Binding Affinity
2.2.1 General Method
To design ligand binding means optimizing a free energy difference
between bound and unbound states. This is not tractable by most
CPD methods, such as simulated annealing or plain Monte Carlo
(MC). Most studies have used heuristic methods that optimize the
bound state energy, a very different property. Recently, a new
method was proposed, using MC simulations and adaptive importance sampling. The energy landscape in sequence space is flattened
adaptively for the unbound state, over the course of an MC simulation, thanks to a bias potential [22, 42]. The bias B is constructed
such that all sequences reach comparable populations. B is then
essentially the sequence free energy with its sign changed. Next, the
bias is included in a simulation of the complex, where it “subtracts
out” the unbound state. Thus, negative design of the unbound
state is achieved. Remarkably, the result is a Boltzmann distribution
where sequence populations measure their affinities.
242
Nicolas Panel et al.