Toward accurate coarse-graining approaches for protein and membrane simulations

Michele Cascella and Stefano Vanni

DOI: 10.1039/9781782622703-00001

1 Introduction

From the smallest biological molecules to complex living organisms, the organisation of the living matter follows highly hierarchical organisation. As depicted in Fig. 1, starting from the Ångström dimensionality, we first encounter atoms and molecules, then oligomers and polymer, like short RNAs or single-domain globular proteins; at larger scales, macromolecular assemblies give rise to cellular organelles and cells, that in turns, in superior organisms, form tissues, organs, and finally the whole body. Likewise, different biological phenomena occur at different size and time-scales, and therefore can be understood by employing methods of investigation at the most pertinent level of resolution.

Since the beginning of the informatics revolution in the 50's of the past century, major effort has been put in developing reliable mathematical and physical computational models of complex systems at different resolutions. In bottom-up approaches, the aim is to establish computational models based on fundamental physical principles that are able to predict the behaviour of the system of interest (Fig. 2). At the most fundamental level, quantum mechanics approaches can be used to treat relatively small-sized molecular systems (up to ~103 atoms, and for times of the order of 10-12,-10 s).

Quantum mechanical calculations can nowadays reach up even to millions of atoms for static calculations, also in this case depending on the degree of approximation with respect to the exact theoretical formulation (and according to the complexity of the system of interest).

For larger systems and longer times (~106 atoms, and for routinely times of 10-8,-7 s up to 10-6,-3 s) molecular models employing explicit representation of atoms (all-atom models, AA hereafter) interacting through parameterised mechanical effective potentials are the most commonly used approach. Such potentials can be trained on both accurate quantum-mechanical calculations and on large experimental data set and they can reliably reproduce molecular processes involving non-covalent intermolecular interactions or conformational changes.

Combination of quantum mechanical and classical methods in a hierarchical structure is often used as a way of treating those biochemical phenomena that require quantum mechanical treatment while keeping a direct coupling with the environment. Historically, the first multi-scale model proposed dates back to 1976 by Arieh Warshel and Michael Levitt, where the idea of embedding quantum mechanical treatment of a chemically relevant portion of a biological system (like the active site of an enzyme) into a parameterised description of the environment was proposed. In the past decades, a large family of hybrid quantum mechanics/classical mechanics (QM/MM) methods stemmed from this seminal work, and have established what is today recognised as the standard common practice to treat quantum mechanical phenomena in biological systems. For this fundamental theoretical work Profs. Warshel and Levitt, together with Prof. Martin Karplus, were awarded the Nobel Prize in Chemistry in 2013.

Even though atomistic simulations can now deal with systems as large as tens of millions of atoms, and for simulation times beyond the millisecond, several biological processes involving large macromolecular complexes require description at time and sizes that go beyond even such dimensionalities. In order to overcome these bottlenecks, in the past decades several groups have been working on the development of reliable Coarse-Grained (CG) models. Similarly to AA, effective CG potentials can be derived from higher-resolution AA simulations, or from direct match with specific experimental properties of interest. In such approaches the detailed atomic resolution is lost; nonetheless, some information on the topological structure of the molecular assembly is retained, as described in Fig. 3. These models can e?ciently represent molecular systems composed by several millions of atoms, for effective times that can reach the second scale; therefore, they are in principle well-adapted to investigate the structure and dynamics of large macromolecular assemblies and multi-phase systems. The large number of reviews published on the subject in recent years highlights the strong interest by the scientific community in this topic (for example: ref. 1, 16, 50, 53, 57–67).

Treatment of very large systems, and for very long times, opens up a completely different view on the understanding of biological systems and phenomena. In fact, it is often the case that the complexity of such systems is irreducible to the fundamental properties of individual or relatively few molecules, but it requires the treatment of a large number of particles. Moreover, biochemical/biophysical processes are often not simply driven by simple thermodynamic equilibrium, but several kinetic effects, like for example diffusional barriers, may play a fundamental role.

As a pivotal example of the power of coarse-graining approaches in modern computational investigations, a very recent study by Marrink and co-workers was able to investigate the lipid composition, dynamics and diffusion in a realistic model of the plasma membrane. Biological membranes are extremely complex environments formed by several lipophilic/amphiphilic compounds, which can behave in very different manners according to their specific composition. Building reliable models of such environments necessarily implies the use of large model systems to respect the relative concentration of the different species.

Moreover, properties such as lipid lateral...