macromolecules. Over the 60 years since the invention of this methodology,
computers have evolved enormously, along with concomitant algorithm development, such that today computer simulation is capable of being a true partner to
experiments.
Amphiphilic polymers have the ability to self-assemble into supramolecular
structures of remarkable complexity [8–11]. To understand the formation of such
structures, knowing the chemical structure of the macromolecules involved is
necessary, but not sufficient. Molecules with similar chemical structure may form
strikingly different structures when immersed in the same environment. The reason
for this complexity has a relatively simple chemical origin: with the exception of a
macromolecule’s own chemical bonds, the cohesive forces between its atoms are
often outmatched by those between its atoms and those of another macromolecule.
As a result, the gap between a simplified “mean field” model and a satisfactory
model is so great as to defeat even the most clever reductionist approaches. More
often than not, a direct simulation is the only efficient route to modeling the selfassembly of amphiphilic polymers into the plethora of novel structures.
Historically, computational molecular scientists have used many methods to
investigate the structures and thermodynamics of polymer assemblies. In recent
years, molecular dynamics (MD) simulations with empirical potential energy
functions (“potentials”) have become, arguably, the preferred approach towards
this goal. Aside from defining the thermodynamic coupling between the microscopic model and the macroscopic environment [12–14], and choosing suitable
potentials [15–19], MD simulations feature little or no approximation in describing
the real motions of polymers during their self-assembly. Therefore, self-assembly
into an organized phase, or transformations between different phases, can be
predicted with surprising accuracy [11].
2 Coarse-Grained Molecular Dynamics Simulations
One of the primary limitations when using MD is ensuring completeness of the
statistical sampling. For model systems of realistic size (up to tens of nanometers of
linear dimensions, or a few hundreds or thousands of macromolecules), the longest
times accessible to simulation are typically between microseconds and milliseconds.
To improve statistical convergence, while retaining the accuracy of the physical
model, many approaches have been developed. For example, approaches based upon
the addition of external constraints (e.g., thermodynamic integration and umbrella
sampling [20, 21]), or the reweighting of high temperature distributions (e.g.,
parallel tempering [22, 23]) have been used successfully. Unfortunately, these
approaches also suffer from limitations specific to the self-assembly phenomenon:
namely, the lack of knowledge of the mechanism hampers the definition of the
“reaction coordinate” [20, 21]. Moreover, the conditions for performing parallel
tempering [22] are difficult to satisfy for increasingly larger systems, when the
relative fluctuation of the total energy, ΔE/E, becomes narrower in the thermodynamic limit.
Computer Simulation of Self-Assembling Macromolecules
95
computers have evolved enormously, along with concomitant algorithm development, such that today computer simulation is capable of being a true partner to
experiments.
Amphiphilic polymers have the ability to self-assemble into supramolecular
structures of remarkable complexity [8–11]. To understand the formation of such
structures, knowing the chemical structure of the macromolecules involved is
necessary, but not sufficient. Molecules with similar chemical structure may form
strikingly different structures when immersed in the same environment. The reason
for this complexity has a relatively simple chemical origin: with the exception of a
macromolecule’s own chemical bonds, the cohesive forces between its atoms are
often outmatched by those between its atoms and those of another macromolecule.
As a result, the gap between a simplified “mean field” model and a satisfactory
model is so great as to defeat even the most clever reductionist approaches. More
often than not, a direct simulation is the only efficient route to modeling the selfassembly of amphiphilic polymers into the plethora of novel structures.
Historically, computational molecular scientists have used many methods to
investigate the structures and thermodynamics of polymer assemblies. In recent
years, molecular dynamics (MD) simulations with empirical potential energy
functions (“potentials”) have become, arguably, the preferred approach towards
this goal. Aside from defining the thermodynamic coupling between the microscopic model and the macroscopic environment [12–14], and choosing suitable
potentials [15–19], MD simulations feature little or no approximation in describing
the real motions of polymers during their self-assembly. Therefore, self-assembly
into an organized phase, or transformations between different phases, can be
predicted with surprising accuracy [11].
2 Coarse-Grained Molecular Dynamics Simulations
One of the primary limitations when using MD is ensuring completeness of the
statistical sampling. For model systems of realistic size (up to tens of nanometers of
linear dimensions, or a few hundreds or thousands of macromolecules), the longest
times accessible to simulation are typically between microseconds and milliseconds.
To improve statistical convergence, while retaining the accuracy of the physical
model, many approaches have been developed. For example, approaches based upon
the addition of external constraints (e.g., thermodynamic integration and umbrella
sampling [20, 21]), or the reweighting of high temperature distributions (e.g.,
parallel tempering [22, 23]) have been used successfully. Unfortunately, these
approaches also suffer from limitations specific to the self-assembly phenomenon:
namely, the lack of knowledge of the mechanism hampers the definition of the
“reaction coordinate” [20, 21]. Moreover, the conditions for performing parallel
tempering [22] are difficult to satisfy for increasingly larger systems, when the
relative fluctuation of the total energy, ΔE/E, becomes narrower in the thermodynamic limit.
Computer Simulation of Self-Assembling Macromolecules
95