Commentary pubs.acs.org/accounts
A Multiscale Description of Biomolecular Active Matter: The Chemistry Underlying Many Life Processes Published as part of the Accounts of Chemical Research special issue “Holy Grails in Chemistry”. Gregory A. Voth* Department of Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, 5735 South Ellis Avenue, Chicago, Illinois 60637, United States ABSTRACT: This Commentary will describe the goal of developing and implementing novel, powerful, and integrated multiscale computer simulation methodology capable of accessing the large length and long time scales inherent in the behavior of biomolecular, multiprotein “active matter” complexes within the context of cellular biology. Examples include those involved in the actin-based cytoskeleton and its mechanochemistry. The primary objective is to connect detailed molecular and chemical properties with the key mesoscopic features manifest at the scales of cellular biology through a transformative theoretical and computer simulation approach, based on real physical and chemical interactions. This multiscale computational work would also make critical contact with rapidly developing experimental techniques such as super-resolution optical imaging, single molecule spectroscopy, and cryo-electron tomography, which are providing remarkable insight into the internal mesoscale self-organization and dynamics of cells.
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INTRODUCTION The concept of chemistry-driven, biomolecular “active matter” underlies a multitude of behaviors that are seen in cellular biology. One key set of examples includes the mechanochemical processes that utilize the chemical hydrolysis of bound nucleotides (e.g., nucleoside triphosphates such as ATP or GTP) to, in turn, drive critical molecular motions. For example, cells spatially and temporally regulate the formation and maintenance of multiple cytoskeleton networks within the same crowded cytoplasm. The cytoskeleton (the “bones of the cell”) facilitates a range of diverse processes, including division, polarization, and motility.1,2 Distinct actin polymer networks, which have different actin filament organization and dynamics, are assembled through the coordinated action of numerous regulatory proteins with synergistic properties. Similarly, microtubules exhibit remarkable, protein regulated assembly and dynamics. Both of these processes in turn rely critically on the chemistry of hydrolysis. Thus, the problem of biomolecular active matter, by its very nature, presents an ideal “holy grail” target for far-reaching research in chemistry and related fields− not only to help better understand the many complex cellular phenomena but also to provide a basis for bold new physicalbased multiscale theory and simulation concepts and methods. Before going into specific detail, it is valuable to first highlight a “big picture”context for the holy grail challenge described here. Consider that on February 11th, 2016, the detection of gravitational waves due to the ancient collision of two black holes was announced by LIGO, a remarkable observation coming 100 years after its prediction by Einstein from the general theory of relativity. This outcome was a result of © 2017 American Chemical Society
modern physics, along with many others like it that compose a list too long to write down here. This physics (i.e., physical science) was practiced in the way that has served civilization well for so many years: a fundamental theory for general (in this case universal) physical phenomena is developed, a prediction is made from that theory, and the prediction is then confirmed by experiment, often with the support of computation. However, it is noteworthy that approximately four months earlier in the journal Science, Kirk et al.3 published an article entitled “Systems biology (un)certainties: How can modelers restore confidence in systems and computational biology?” The authors proclaim early on in their article that “Although biology is, of course, subject to the same fundamental physical laws−for example, conservation of mass, energy, and momentum−as the other sciences, these laws often do not provide a good starting point for understanding how biological organisms and systems work”. The holy grail research challenge described in this Commentary is focused on a possible way to overcome this point of view. More specifically, the development and application of novel, systematic, and transformative “physics-based” multiscale theory and simulation to describe complex biomolecular phenomena from the “bottom-up” will be described. One outcome of this effort would be to help explain the behavior of key biomolecular active matter targets within the eukaryotic cellular cytoskeleton in order to answer central scientific questions regarding their Received: November 13, 2016 Published: March 21, 2017 594
DOI: 10.1021/acs.accounts.6b00572 Acc. Chem. Res. 2017, 50, 594−598
Commentary
Accounts of Chemical Research
Figure 1. An illustration of the scales of biomolecular systems relevant to cellular biology: (a) molecular scale (actin monomer); (b) multiprotein complexes (actin filament); (c) coarse-grained (CG) model of actin filament; (d) actin filament network that forms a primary component of the cellular cytoskeleton.
behavior. Of course, there would be many other important outcomes. In order to address this holy grail challenge, new physicalbased concepts to connect molecular-scale behavior with phenomena occurring at significantly larger length and time scales in complex biomolecular systems will be required, as well as increasingly accurate representations of the fundamental molecular scale interactions (i.e., “force fields”). Indeed, despite great advances in the field of molecular theory and computer simulation, the impact of that work on areas such as cellularscale biology and mesoscopic materials science remains relatively limited. As recognized as one aspect of the 2013 Nobel Prize in Chemistry, molecular dynamics (MD) simulation, in which Newton’s equations of motion are integrated in time for an atomistic model of a system of interest, can now be routinely carried out for systems having hundreds of thousands of atoms and for trajectories lasting up to microseconds. MD simulations of millions of atoms up to milliseconds seem within reach. However, at the scales relevant to cellular biology such calculations provide only a small part of the overall picture. As now being revealed by pioneering experimental techniques such as super-resolution imaging and cryo-electron microscopy, many real biological systems at the cellular level are far more complicated in their behavior across the scales, so new multiscale theory and computational approaches are critically needed to explain them. As an example (e.g., see also ref 1), a depiction of some of the key components of the eukaryotic cellular cytoskeleton are shown in Figure 1. This spatial-temporal coupling occurs in many important active matter systems: in the field of cellular biology examples include multiprotein complexes, membranes, and nucleic acids, as well as the interactions between them. A key feature of the multiscale connection depicted in Figure 1 is the systematic bridging of the molecular-scale model (images a and b) onto a more simplified and much more computationally efficient coarse-grained (CG) actin filament representation (image c), which can in turn be used to access features of the actin network depicted at the mesoscopic scale (image d). This is, in effect, a systematic process of “renormalization” of the scales and interactions. However, the most physically realistic multiscale descriptions should begin at the level of the biomolecules and their interactions, including their chemical features.
The underlying scientific goal of this holy grail challenge would be, in essence, to transform the current status of multiscale theory and simulation into one based on new concepts that are also firmly based on strong theoretical foundations, that is, those derived from equilibrium and nonequilibrium statistical mechanics and dynamics. A quantum leap in the quantitative descriptive capabilities of multiscale theory for active biomolecular matter is needed, and one based largely on “bottom-up” physical principles.
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TWO GOOD EXAMPLES OF BIOMOLECULAR ACTIVE MATTER AT THE CELLULAR SCALE
Actin Networks
Actin is a highly conserved protein found in almost all eukaryotic cells1 (cf. Figure 1). It is important for cell motility, cell division, cytokinesis, muscle contraction, and a variety of other cellular functions. Actin polymerization into filaments (Factin) powers many eukaryotic cell movements and provides cells with mechanical strength and structural integrity.1 Actin filaments also serve as tracks along which myosin motor proteins generate forces that drive muscle contraction, cell division, and long-range, intracellular cargo transport. Fundamental questions remain about how the dynamics of actin filaments are regulated in the cell, how ATP hydrolysis in the actin nucleoside triphosphate cleft is coupled to polymerization and other properties, and how actin-binding proteins influence actin network topology. ATP hydrolysis and subsequent release of the cleaved inorganic phosphate appear to act as molecular timers, regulating actin filament dynamics and polarity of growth. ADP-actin filaments are less rigid than ATP filaments, and accessory proteins bind to actin in a nucleoside triphosphate state-dependent manner. The state of the bound nucleoside triphosphate in G-actin (monomeric actin) regulates how quickly it polymerizes, and the polymerization of actin affects the rate of hydrolysis. The ATP hydrolysis rate is accelerated by more than a factor of 104 in F-actin.4,5 Actin network dynamics are further regulated by a variety of actin binding proteins.1 These proteins modulate the actin network structure by blocking filament elongation (capping proteins), regulating elongation and nucleation of new filaments (profilin and formins), creating branched filaments (Arp2/3), and destabilizing old filaments (cofilin).1 Models for F-actin (filamentous actin) have been proposed based on X-ray fiber diffraction and cryo-EM imaging,6−8 including evidence from 595
DOI: 10.1021/acs.accounts.6b00572 Acc. Chem. Res. 2017, 50, 594−598
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Figure 2. (left panel) Illustration of a mapping from atomistic to coarse-grained (CG) at a “high resolution” CG level. (right panel) A very highly coarse-grained, ultra-coarse-grained (UCG) model of an actin monomer. The gold CG “bead” in the middle represents the bound nucleoside triphosphate.
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THE CHALLENGE FOR MULTISCALE THEORY AND SIMULATION In general, the multiscale problem is undeniably one of the most important challenges in all of science, and this challenge is amplified several times over for the problem of biomolecular active matter. In that regard, the need continues to be very great for rigorous, bottom-up theoretical and algorithmic foundations to be established and implemented for multiscale simulation of both soft and hard matter. The notion of “coarsegraining”, creatively defined and quantitatively implemented in new ways, must be at the heart of this effort for addressing the problem of biomolecular active matter. Over the past 15 years or so, CG modeling and simulation has already grown rapidly as a means to interrogate the properties of complex biomolecular systems (e.g., see ref 16 for a general review). However, the effort is by no means complete and still inadequate to treat biomolecular active matter in its full complexity at the cellular scale. Research to establish fundamental bottom-up connections of coarse-graining to statistical mechanics has been carried out (e.g., see refs 17−19). This theoretical and simulation effort is to be contrasted with the more popular ad hoc parameterization and computer modeling approach to CG studies (e.g., see ref 20). The latter approach is often of preference to some computational researchers given its ease of implementation through readily downloaded and executed computer programs for this kind of CG MD modeling. On the other hand, within the context of rigorous equilibrium statistical mechanics, coarse-graining may instead be cast as follows: First we define the set of coordinates for CG particles or “beads”, given by RN = {R1, R2, ..., RN}, with N < n (where n is the full set of atomistic coordinates). Each RI is a function of the positions of some set of atoms in the same molecule: RI = MR,I(rn), where MR,I(rn) are mapping function such as a center-of-mass coordinate (see Figure 2, left panel). This bottom-up theory has shown that the CG effective potential, U(RN), appropriate for the CG coordinates (beads), is exactly related to a constrained Boltzmann average with the atomistic potential energy f unction u(rn) over the product of the mapping
cryo-EM and CG simulation that multiple structural states exist in the filament.9,10 Microtubules
Likewise, microtubules are also present in the eukaryotic cellular cytoskeleton. These biopolymers and their networks have been the target of many experimental studies in the area of biomolecular active matter (e.g., see ref 2), and they have served as inspiration for the development of completely new biomimetic systems (e.g., see ref 11). The microtubules are rigid cylindrical filaments assembled from αβ-tubulin heterodimers, which make up protofilaments, which in turn make up the tubular biopolymers. These heteropolymers form one of the key components of the cytoskeleton and are involved in trafficking, structural support, and cytokinesis. Their functionality is closely linked to the complex polymerization dynamics at the microtubule plus end (with the β-tubulin exposed) that switches between phases of growth and rapid disassembly. This latter behavior, the remarkable so-called “dynamic instability”, is controlled by the hydrolysis of GTP in β-tubulin upon polymerization. Though vitally important in the cell, the underlying molecular mechanism leading to the dynamic instability is not well understood. For example, caps of GTPbound tubulin stabilizing the microtubule plus end have been observed experimentally both in vitro and in vivo. When these caps are hydrolyzed, the rapid depolymerization appears to take place. Various structural12 and phenomenological13 models for the causes of the dynamic instability exist, but there is by far no accepted bottom-up molecular-scale model in existence (with support from multiscale simulations). It was once thought the tubulin heterodimers become bent upon GTP hydrolysis and this leads to high strain in the tubulin lattice, thus leading to the instability. However, subsequent work has shown that both GTP and GDP bound protofilaments are intrinsically bent,14 and that hydrolysis likely leads to more subtle, but collective, changes in lattice contacts.15 The latter result has been supported and expanded upon experimentally through high resolution cryo-electron microscopy.12 596
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Figure 3. UCG methodology is depicted in this image. An F-actin filament is shown, with monomers colored in different shades of green and blue. Superimposed on three of the monomers is a 12-site UCG model of actin. The red and orange insets show the all-atom “folded” and “unfolded” conformations of the DB-loop that “live” as internal states within the UCG beads (see Figure 2). The blue inset shows the nucleoside triphosphate (ATP, ADP-Pi, or ADP; see also Figure 2 where the gold UCG “bead” represents the bound nucleoside triphosphate).
operators. This process of interaction “renormalization” shows that the exact CG effective potential can be defined in terms of the equilibrium distribution function of the CG coordinates. Moreover, it reveals that ad hoc CG parametrizations are not well founded in terms of statistical mechanics. Greatly extending and generalizing the bottom-up coarse-graining concepts as discussed below, including into the nonequilibrium regime, will be required to make substantial progress on the problem of biomolecular active matter. To address this problem, it seems clear that very highly coarsegrained models will be required (see Figure 2, right panel) in order to empower simulation to access the length and time scales of relevance to cellular biology while avoiding prohibitively large computational cost. As one such approach, the emerging concept of ultra-coarse-graining (UCG),21−23 in which many atoms (e.g., amino acid residues) are mapped into a single CG site (see right panel of Figure 2 and Figure 3). This low resolution CG mapping also means that the molecular features “inside” the UCG sites can have possible quantum-like “states” that represent various discrete molecular conformations, protonation states, nucleotide states, etc., within the CG sites. These internal CG states will in turn modulate the interactions between the CG beads at the larger scales, while the interactions between the CG beads will affect the behavior of the internal states. In terms of coupling the CG scale to the atomistic scale, one very important goal must also be to even couple the CG scale to the quantum mechanical (QM) level. For example, in F-actin ATP hydrolysis influences filament dynamics, and hydrolysis is much slower in G-actin compared
to F-actin. Results via a CG-constrained QM/MM dynamics approach5 have revealed a significantly lower free energy barrier for ATP hydrolysis in filamentous (F-actin) than in monomeric (G-actin) actin, as well as its molecular scale origins, in good agreement with experiment. The gold CG site shown in the right panel of Figure 2 must have this hydrolysis behavior implicitly described “within” it. The underlying molecular-level free energy landscape must not only be used to derive and validate the CG models (using novel sampling methods, e.g., see refs 24 and 25), but it should also be possible to directly couple such simulations to the CG models in order to focus and help further accelerate the molecular sampling. In addition to the development of highly or “ultra” CG models to sample configurations of complex biomolecular systems, there is a critical need for these CG models to describe “real time” and nonequilibrium dynamics, that is, not just their quasi-equilibrium properties. The degrees of freedom that are not explicitly included among the CG variables should influence the CG dynamics in a way that, as a first approximation, is analogous to the theory of Brownian motion. These missing degrees of freedom in reality generate frictional forces and random fluctuating forces whose net effect is to slow down the motion of CG degrees of freedom.26 An approach for relatively simple CG systems has already been explored,27 as well as more recent algorithmic developments related to the bottom-up theory of coarse-graining.28 However, new theory must still be developed that will allow the dynamics of the highly CG or UCG models to be consistent with the underlying nonequilibrium atomistic dynamics of the system. For the UCG 597
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(11) Boekhoven, J.; Hendriksen, W. E.; Koper, G. J.; Eelkema, R.; van Esch, J. H. Transient Assembly of Active Materials Fueled by a Chemical Reaction. Science 2015, 349 (6252), 1075−1079. (12) Alushin, G. M.; Lander, G. C.; Kellogg, E. H.; Zhang, R.; Baker, D.; Nogales, E. High-Resolution Microtubule Structures Reveal the Structural Transitions in αβ-Tubulin upon GTP Hydrolysis. Cell 2014, 157 (5), 1117−1129. (13) Zakharov, P.; Gudimchuk, N.; Voevodin, V.; Tikhonravov, A.; Ataullakhanov, F. I.; Grishchuk, E. L. Molecular and Mechanical Causes of Microtubule Catastrophe and Aging. Biophys. J. 2015, 109 (12), 2574−91. (14) Grafmüller, A.; Voth, G. A. Intrinsic Bending of Microtubule Protofilaments. Structure 2011, 19 (3), 409−17. (15) Grafmüller, A.; Noya, E. G.; Voth, G. A. Nucleotide-Dependent Lateral and Longitudinal Interactions in Microtubules. J. Mol. Biol. 2013, 425 (12), 2232−2246. (16) Saunders, M. G.; Voth, G. A. Coarse-graining methods for computational biology. Annu. Rev. Biophys. 2013, 42, 73−93. (17) Izvekov, S.; Voth, G. A. A Multiscale Coarse-Graining Method for Biomolecular Systems. J. Phys. Chem. B 2005, 109 (7), 2469−2473. (18) Noid, W. G.; Chu, J. W.; Ayton, G. S.; Krishna, V.; Izvekov, S.; Voth, G. A.; Das, A.; Andersen, H. C. The Multiscale Coarse-Graining Method. I. A Rigorous Bridge between Atomistic and Coarse-Grained Models. J. Chem. Phys. 2008, 128 (24), 244114. (19) Shell, M. S. The Relative Entropy is Fundamental to Multiscale and Inverse Thermodynamic Problems. J. Chem. Phys. 2008, 129 (14), 144108. (20) Marrink, S. J.; Risselada, H. J.; Yefimov, S.; Tieleman, D. P.; de Vries, A. H. The MARTINI Force Field: Coarse Grained Model for Biomolecular Simulations. J. Phys. Chem. B 2007, 111 (27), 7812− 7824. (21) Dama, J. F.; Sinitskiy, A. V.; McCullagh, M.; Weare, J.; Roux, B.; Dinner, A. R.; Voth, G. A. The Theory of Ultra-Coarse-Graining. 1. General Principles. J. Chem. Theory Comput. 2013, 9 (5), 2466−2480. (22) Grime, J. M.; Voth, G. A. Highly Scalable and Memory Efficient Ultra-Coarse-Grained Molecular Dynamics Simulations. J. Chem. Theory Comput. 2014, 10 (1), 423−431. (23) Davtyan, A.; Dama, J. F.; Sinitskiy, A. V.; Voth, G. A. The Theory of Ultra-Coarse-Graining. 2. Numerical Implementation. J. Chem. Theory Comput. 2014, 10 (12), 5265−75. (24) Laio, A.; Parrinello, M. Escaping Free-Energy Minima. Proc. Natl. Acad. Sci. U. S. A. 2002, 99 (20), 12562−6. (25) Dama, J. F.; Parrinello, M.; Voth, G. A. Well-Tempered Metadynamics Converges Asymptotically. Phys. Rev. Lett. 2014, 112 (24), 240602. (26) Zwanzig, R. Ensemble Method in the Theory of Irreversibility. J. Chem. Phys. 1960, 33 (5), 1338−1341. (27) Izvekov, S.; Voth, G. A. Modeling Real Dynamics in the CoarseGrained Representation of Condensed Phase Systems. J. Chem. Phys. 2006, 125 (15), 151101. (28) Hijon, C.; Espanol, P.; Vanden-Eijnden, E.; Delgado-Buscalioni, R. Mori-Zwanzig Formalism as a Practical Computational Tool. Faraday Discuss. 2010, 144, 301−322. (29) Bowman, G. R.; Pande, V. S.; Noe, F. An Introduction to Markov State Models and Their Application to Long Timescale Molecular Simulation; Springer: Dordrecht, the Netherlands, 2014; Vol. 797. (30) Grime, J. M. A.; Dama, J. F.; Ganser-Pornillos, B. K.; Woodward, C. L.; Jensen, G. J.; Yeager, M.; Voth, G. A. CoarseGrained Simulation Reveals Key Features of HIV-1 Capsid SelfAssembly. Nat. Commun. 2016, 7, 11568.
systems, including the internal states of CG sites and their transitions will need to utilize embedded kinetic states29 at subCG resolution acting “within” the CG sites to modulate their effective interactions and dynamics. It is to be noted that such a UCG approach in prototype form has led to a multiscale model for the dynamic self-assembly of the many-protein HIV virial capsid.30 To conclude this Commentary, I emphasize that new and ground-breaking theory and simulation will be required to achieve a physical-based, bottom-up multiscale computational approach to study and understand the remarkable dynamical collection of proteins and other biomolecules that constitute living cells. Even more importantly, such a breakthrough must be able to make key computational predictions that can then be confirmed experimentally (e.g., from mutagenesis, imaging, etc.). Overall, this is a grand challenge of the greatest magnitude−a true “holy grail” if you will−and one that involves chemistry and physical science at its very core.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Gregory A. Voth: 0000-0002-3267-6748 Notes
The author declares no competing financial interest.
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ACKNOWLEDGMENTS Aspects of the research described in this Commentary have been supported by the National Science Foundation. However, the long-range research goals articulated here, which would require a commitment of significant resources across multiple collaborating investigators, have not yet been supported.
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REFERENCES
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