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Art Advancing Science: Filmmaking Leads to Molecular Insights at the Nanoscale

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Wyss Institute for Biologically Inspired Engineering, Harvard University, Boston, Massachusetts 02115, United States
Vascular Biology Program and Department of Surgery, Boston Children’s Hospital and Harvard Medical School, Boston, Massachusetts 02115, United States
§ John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02139, United States
Cite this: ACS Nano 2017, 11, 12, 12156–12166
Publication Date (Web):October 18, 2017
https://doi.org/10.1021/acsnano.7b05266

Copyright © 2017 American Chemical Society. This publication is licensed under these Terms of Use.

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Abstract

Many have recognized the potential value of facilitating activities that span the art–science interface for the benefit of society; however, there are few examples that demonstrate how pursuit of an artistic agenda can lead to scientific insights. Here, we describe how we set out to produce an entertaining short film depicting the fertilization of the egg by sperm as a parody of a preview for another Star Wars movie to excite the public about science, but ended up developing a simulation tool for multiscale modeling. To produce an aesthetic that communicates mechanical continuity across spatial scales, we developed custom strategies that integrate physics-based animation software from the entertainment industry with molecular dynamics simulation tools, using experimental data from research publications. Using this approach, we were able to depict biological physicality across multiple spatial scales, from how sperm tails move to collective molecular behavior within the axoneme to how the molecular motor, dynein, produces force at the nanometer scale. The dynein simulations, which were validated by replicating results of past simulations and cryo-electron microscopic studies, also predicted a potential mechanism for how ATP hydrolysis drives dynein motion along the microtubule as well as how dynein changes its conformation when it goes through the power stroke. Thus, pursuit of an artistic work led to insights into biology at the nanoscale as well as the development of a highly generalizable modeling and simulation technology that has utility for nanoscience and any other area of scientific investigation that involves analysis of complex multiscale systems.

There has been increasing recognition of the potential value of convergent approaches in basic research, including ones that span the art–science interface, (1-3) as evidenced by the recent National Academies Keck Futures Initiative conference on “Art and Science, Engineering and Medicine Frontier Collaborations”. (4) While there are many examples where collaborations between artists and scientists have led to innovative approaches to education, communication, and the arts, there are few demonstrating how pursuit of an artistic path can lead to insights that advance science at the cellular or molecular scale.
Here, we set out with the primary agenda of producing a work of art in the form of an entertaining cinematic short film (Short) to excite the public about science. We approached this project with the aim of entertaining by blurring the line between science and fiction using animation principles (e.g., exaggeration) particularly in the rendering, in much the same way as television’s The Daily Show has expanded audience appreciation of the intricacies and absurdities of politics and current affairs by the deliberate blurring of the line between news and entertainment. (5) In this way, we hoped to garner increased interest from members of the lay public beyond those who are already interested in science. Thus, by using some of the core principles of this artistic medium, (6) we hoped to pull viewers into the story through the power of entertainment and, at the same time, experience the excitement, drama, and visual beauty of the cellular and molecular world.
For the subject of the Short, we chose a highly recognizable cellular scale biological phenomenon with an inherent narrative: the fertilization of the egg by a sperm. We felt that this “story” with its identifiable “characters” would allow for communication of the drama, suspense and beauty that are present across all biological scales. To further advance the cinematic aspect of the Short and better engage with viewers, we parodied one of the most successful film franchises of all time. The story, entitled “THE BEGINNING”, starts with the viewers believing they are seeing a preview for another Star Wars movie, and it progresses so that they feel that they are racing in a spacecraft toward a distant blue planet, much as Han Solo did in his Millenium Falcon cruiser, with other futuristic spacecraft trying to pass on either side. Eventually, it is revealed that we are in fact one sperm among many racing toward an egg. The story follows the struggle of our “hero” sperm as it outruns the others and fertilizes the egg. We show the sperm hit the egg and how the mechanical force needed to penetrate its surface is achieved based on forces generated by a series of motor proteins found in the axonemal cytoskeleton of the sperm’s tail, all working rhythmically in unison. Our hero beats out its competitors to fulfill its mission of being the only sperm to fertilize the egg, and then we show how this is not the end of the story, but actually the beginning, as life is generated anew with the egg’s first cell division (Figure 1); see the full short film at https://wyss.harvard.edu/the-beginning/.

Figure 1

Figure 1. Storyboard showing an overview of the shots created for the cinematic Short film, “THE BEGINNING” (from start at top left to film end at bottom right).

Another primary goal of the Short was to create a visual aesthetic that paralleled the mechanical complexity of the sperm and its movement with that of a sophisticated futuristic spaceship through the use of cinematography, rendering, and staging. (6) But as scientists we also had an educational goal, which was to convey the process of how the sperm moves with a high degree of physical reality. Physics-based animation software used for games and special effects provides a platform for integration of real and simulated data for an enhanced sense of realism. (7) Thus, in an attempt to anchor the Short in physical reality, we built a computational production pipeline that combines software from the entertainment industry with scientific simulation tools. We employed a procedural animation and design strategy (8, 9) that allows for integration and interpolation of many kinds of data, including molecular dynamics simulation (MDS) and cryo-electron microscopic (cryoEM) data from the scientific literature, to model and animate the characters in the story (e.g., sperm, egg, axoneme cytoskeleton, dynein motors). The interplay between parametric modeling, animation, and simulation involved in our approach to character design ultimately led to us unintentionally tackle one of the fundamental challenges in science today—modeling and integrating hierarchical cellular and molecular motions responsible for biochemical activities that underlie cellular functions across multiple spatial scales.

Results and Discussion

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Simulating Sperm Movement

The first challenge in creating the Short was animating the sperm in a way that would capture its natural directional, but frenetic movement. First, we used the finite element method (FEM) within Houdini special effects software to create a simulated soft body model of a sperm’s tail attached at its proximal end to a rigid object via spring constraints (Figure 2A). By coupling FEM with the inverse kinematics approach used for animation, we were able to rotate the rigid object at a rate consistent with that previously observed in freely swimming mouse sperm. (10) We then explored computationally how the tail moved in response to the rigid object rotation while varying the material properties (stiffness) of the soft body over a broad range and ran the simulations until the model’s waveforms achieved a sinusoidal pattern with an amplitude and periodicity that were consistent with the range of motions seen in these previous studies of swimming sperm. (10) The wide range of movements seen in 3D studies of sperm swimming (10) meant that with subtle variations in simulation parameters, we were able to produce a wide range of movements that are biologically plausible, yet still presented an aesthetic that communicated the natural biological diversity observed in living sperm populations and their range of individual responses to their local microenvironments. When we added a rigid ovular-shaped object representing the bounding volume of a sperm’s head and passively connected its neck region to the proximal end of this computer-generated tail, it produced a depiction of a moving sperm cell (Figure 2B and movie S1). Interestingly, during the simulation, the deformations within the model that allowed for a waveform to emerge produced an effect that is similar to one of the “principles of animation”, (6) where the squashing and stretching of a character’s form while maintaining overall volume can lead to an enhanced sense of realism, particularly when combined with rendering effects such as motion blur. (6, 11)

Figure 2

Figure 2. Modeling a multiscale swimming sperm based on multiple kinds of published experimental data. (A) Each sperm’s axoneme movement was simulated using an inverse kinematic-coupled finite element method (FEM). Here, the long cylindrical FEM model of the axoneme was bound to a rotating rigid structure via spring constraints at its proximal end. As the rigid structure was rotated, the soft axoneme model was deformed, and material properties of the axoneme model were then tuned to achieve a sinusoidal waveform. This generated a dynamic axoneme model that was used as cytoskeletal input during the modeling of sperm ultrastructures. (B) FEM simulations are used to model ultrastructures and rendered using animation software to achieve a realistic depiction of swimming sperm. (C) 3D electron micrographic (EM) density map of a portion of an axoneme based on averaged data from multiple model organisms (obtained from EM Data Bank), which was used to guide the modeling of the sperm axoneme. (D) Schematic showing a cross-section of the axoneme with component parts labeled. (E) Images from a FEM simulation of the sperm tail with internal forces mapped showing that local regions of the microtubule doublets transition between being under tension versus compression during tail motion while the whole multimolecular structure is stabilized through intermolecular attractive (tensile) bonding forces. (F) Molecular trajectories of dynein and tubulin are positioned in the FEM model according to mapped forces and biological periodicity.

Despite the rigor of our simulation and data integration strategy, we were still faced with the limitations of animation rendering when depicting the highly dynamic molecular environment. (11) One such challenge was strobing (11) and the effect this phenomenon has on the perception of movement. At times, with our complex multiscale models moving at such high speeds relative to the camera, a “wagon wheel effect” (12) would occur and result in the appearance of objects moving in the wrong direction when rendered. To address this, we often performed artistic iteration with effects, such as motion blur, during the rendering process of each shot to achieve a balance between depictions of movement while still maintaining atomistic detail. Thus, an artistic strategy was applied in an attempt to communicate physicality with added realism.
The “procedural” approach we took, where dynamic modeling and animation are achieved using defined functions instead of discrete data inputs, lends itself to the incorporation and interpolation of many kinds of data as input parameters. In our study, the outputs of the simulation at one spatial scale provided the boundary constraints or parameter attributes for simulation at another scale. Using this approach of procedural modeling and animation, the spatially and temporally distinct data sets characterizing the movements of the whole sperm tail were combined to generate a dynamic model of the entire multimolecular axoneme that fit within the boundary conditions generated at the larger cellular scale. This approach means that experimental data also can be used where available, to either augment the simulated components or guide how they are integrated into larger scale structures. The use of experimental data to influence simulation parameters in this way is not too dissimilar to other MDS strategies where simulations are initiated using coordinates from crystal structures; for example, in the case of flexible fitting, these data are combined with lower resolution cryoEM data to refine protein conformations. (13) The difference with our approach is that we extended the utility of this general principle through a modular modeling strategy that exploits the periodic, fractal and cyclic nature of biology, and in this specific case, the periodic nature of the axoneme. Our general strategy for combining molecular dynamics and physics-based animation, which allows bridging of spatial and temporal domains that cannot be resolved by a single integrated simulation or experimental approach, is summarized in Figure 3.

Figure 3

Figure 3. Procedural modeling of the multiscale axoneme. (A) A cell-scale model was built using cryoEM data to guide initial geometry for a 9-edged cylindrical representation of an axoneme prior to FEM simulation. (B) Each edge is made up of 24 nm (at rest) subunits that represent the distance between the periodically repeating dynein. As the FEM progresses, the relative subunit lengths fluctuate and based on cryoEM data the bounding volumes of the molecular components can be interpolated for each subunit in the axoneme model. (C) CryoEM data of multiple dynein conformations are used to further refine bounding volume and provide local positional information for atomistic depiction of dynein. (D) MDS provided a trajectory that transitions between the pre- and poststrike cryoEM conformations. (E) Conformations from the MDS are placed within the axoneme model procedurally, based on relative length of subunit, edge normal, and previous time step parameters. The cryoEM data of a section of an axoneme provides bounding volumes for additional “tuning” of the model.

Depicting Movement-Related Conformational Changes in the Axoneme Cytoskeleton

Because we desired to visualize the physical behaviors of how sperm move and drive themselves through the surface of the egg during fertilization, we needed to realistically depict the internal structure of the sperm’s tail and how motive force is generated at the molecular level. Although an artistic goal led us to pursue this path, this challenge provided an ideal model system for understanding hierarchical mechanics at the molecular and cellular scales. Inside the sperm tail, there is a cytoskeleton in the form of a highly conserved, multimolecular, axoneme structure, which contains the macromolecular machinery responsible for sperm locomotion. (14) The axoneme is made up of bundles of microtubule doublets in a 9 + 2 arrangement, where a ring of nine doublets surrounds a central pair, with all microtubules being connected by supporting proteins and protein complexes (Figure 2C,D). Motility is achieved through the actions of a series of dynein motor proteins, each of which anchors to a doublet and exerts force upon it with the consumption of adenosine triphosphate (ATP). The synchronized and periodically repeating dynein motor deformations, in turn, cause adjacent microtubule doublets to slide laterally along each other, which in turn causes the entire axoneme to bend, thereby generating the tail’s characteristic waveforms and forward motion. (14)
To reveal to the viewer how the sperm tail actually moves in the Short, it was necessary to achieve physical continuity across spatial scales in the animation. To accomplish this with the axoneme simulation generated at a larger spatial scale using our integrated simulation pipeline described above (Figure 3), we calculated the deviations from rest length of subregions of each of the outer edges of the 9-edged cylindrical axoneme model. We leveraged the fact that each dynein is known to be separated from its nearest neighbors by 24 nm in a repeating pattern along each microtubule within the multimolecular axoneme cytoskeleton (15) (Figure 4A,B) to simulate how these local regions change their shape, position. and conformation at the scale of the whole axoneme (Figure 2D). As the cellular-scale simulation progressed and the representative waveform of the moving axoneme emerged, we observed that the local relative length (24 nm at rest) of each edge section (which corresponds to the length of the microtubule bundles in that region) fluctuated rhythmically with the same periodicity as the waveform exhibited by the whole simulated sperm cell (movie S2). Thus, this simulation revealed that the lifelike waveform of the swimming sperm tail requires that the length of each of these individual subregions of the axoneme rhythmically shortens and lengthens inside the sperm tail, which would in turn result in local increases in compression and tension, respectively, within these subregions of the multimolecular axoneme cytoskeleton (Figure 2E, Figure S1A,B, and movie S3).

Figure 4

Figure 4. Dynamic model of dynein built using a MD simulation guided by qualitative CryoEM data. (A) 3D depiction of a region of the axoneme based on CryoEM data showing that the periodically repeating dynein proteins are tethered to a microtubule doublet via a multimolecular complex that includes a linker region. (B) Higher magnification of the region of the axoneme shown in A that displays averaged CryoEM tomograms of dynein (16) in the pre- and postpower stroke positions, with the Linker, Hinge, and Dynein ATPases associated with diverse cellular activity (AAA) domains highlighted. (C) Locomotion of the dynein molecule when the hinge point is fixed as in the axoneme visualized in 3D using a custom atomistic MDS strategy. The strategy involves rapidly increasing the vibrational energy of bound ligands by applying a prestress force to an intramolecular bond of the bound ADP prior to carrying out the simulation. Meanwhile, to replicate the effect of the dynein linker, the alpha carbons of amino acid residues in the dynein “hinge” (red) region are fixed. (D) A snapshot image from our simulated trajectory that passes through the two conformations seen in B. (E) Representations of dynein conformations and corresponding microtubule positions during a power stroke.

Local Mechanical Fluctuations Revealed within the Axoneme Molecular Assemblage

Past work has shown that the dynein protein spends more time in its poststrike position during a molecular power stroke when found on microtubules positioned along the longer (extended) edges of an axoneme, whereas it is more frequently in the prestrike conformation when in contact with microtubules in shorter, more compressed regions. (16) This suggests that the dynein may be “reloaded” when the edge of the multimolecular axoneme assemblage is compressed and shortened, before it strikes the complementary opposing edge in a subregion of the axoneme where it is tensed and lengthened. We then quantified local changes in unit shortening (compression) and lengthening (tension) of each edge subregion as sinusoidal movement of the axoneme model progressed in our simulation (Figure S1A,B). With knowledge of how each edge region in the axoneme multimolecular assemblage experienced shortening and extension in our animation, it was possible to use data from the axoneme FEM model described above to map corresponding three-dimensional (3D) molecular representations of both dynein and microtubule doublets to these different axoneme locations as each of the individual 24 nm repeats along the axoneme edge transitioned between being under tension and compression (Figure 2E,F).
The action of the forces generated by dynein and transferred to the microtubules that result in changes in length of the 24 nm edge regions should induce associated changes in shape or position of the individual microtubule subunits at these sites. Past EM studies combined with MDS revealed local conformational changes in microtubule structure when bound to dynein, and the resulting conformational alterations were shown to influence the binding affinity between dynein and the microtubule subunits. (17) To confirm that these local intermolecular conformational shifts influence the length and width of microtubule subunits, we performed our own MDS using the published PDB structure of the microtubule subunits in the region where it binds to dynein. (17) Our MDS confirmed that the individual microtubule subunits are capable of undergoing conformational shifts that influence their length and width in a manner consistent with what we predicted to occur within each 24 nm edge region during axonemal deformations associated with tail movement (movie S4).
Thus, without a hypothesis or even asking an experimental question, these observations revealed that the multimolecular axoneme cytoskeleton stabilizes its 3D shape through an internal force balance between compressive forces exerted in local subregions (Figure 2E and Figure S1) and tensional forces generated by intermolecular attractive (bonding) forces that are distributed globally throughout the structure. This form of structural stabilization is consistent with the use of a tensegrity (tensional integrity) mechanism, (18, 19) which also has been shown to stabilize the form and mechanics of other multimolecular cytoskeletal filament assemblages, such as actin stress fibers, (20) as well as individual molecules (e.g., ubiquitin) (18, 19) and whole living cells (21, 22) in both computational models and experimental studies.

Insight into How Dynein Generates Force That Drives Motion at the Nanometer Scale

Biological phenomena often rely on hierarchical mechanics that span a large spatial and temporal dynamic range, (23, 24) which is a key part of the biological realism that we wanted to convey in our Short. The animation we had created using the FEM simulation captured sperm motility, but at a scale where dynein power strokes were described with single data points corresponding to edge regions of the axoneme experiencing complementary states of compression and tension, and the periodic transition between these states. To communicate to the viewer the mechanical continuity and physicality of the world at the nanometer scale, we wanted to show a series of microtubule-bound dynein motors moving in unison like rowers at an atomic resolution, and to visualize the complex molecular dynamics required in every power stroke. This was achieved with the development of a MDS (25, 26) that generates a power stroke which can be used as the basis of a “walk cycle”, with the walk cycles then being mapped to the FEM-simulated axoneme model. But this required a different simulation approach because conventional all-atom MDS strategies require unrealistic compute times when attempting to achieve the scale of biological motions we required for the aesthetic of the Short. Coarse grain simulations are faster, but they do not display the finer details of molecular mechanics that we believed would convey the beauty of living systems to a lay audience, and which could provide further insight into collective biophysical behavior at the molecular scale.
When simulating the motion of the individual dynein motors, we wanted to depict how each motor protein changes its shape and generates force within the axoneme. In an attempt to mimic the transfer of energy that results from ATP hydrolysis and is known to trigger these molecular conformational changes, we developed an all-atom MDS strategy in which energy is introduced to the simulation within the proximity of the active site where ATP binds to dynein. To achieve this, noncovalently bound ADP (present in the crystal structure used for initial simulation coordinates) was tensionally prestressed by computationally stretching internal bonds within each of the ADP at the 4 different known ATP binding sites of dynein prior to initiating the MDS. As the simulation progressed, force was transferred from the ADP to the atoms of the dynein active site.
Initially, we wanted to begin this film sequence with a close-up view of ADP leaving the dynein binding site (as it would upon the cleavage of ATP), as this is the driving force responsible for subsequent motor movement. We began by computationally exerting a force on every ADP atom in a random direction to induce the ADP to overcome its highly stable dynein-bound position. Unexpectedly, we discovered that the added internal vibrational energy of the ligand was transferred to the surrounding atoms of the bound dynein and then to distant sites, causing the entire molecule to move. As a result of carrying out these simulations, we learned that we could achieve our desired visualization of overall dynein motion by introducing a specific and localized force to a single internal ADP bond. Thus, to more closely mimic the energy generated during ATP hydrolysis, we prestressed the ADP by applying a constant energy of 10 kcal/mol/Å (equivalent to a force of approximately 700 pN) to stretch the bond between the two ADP phosphates and approximate the force that would be generated by dissociation and hydrolysis of ATP to form ADP and Pi based on the standard Gibbs free energy of ATP hydrolysis. (27, 28)
When we initiated these studies, we needed to fix a point on the dynein molecule where it attaches to the microtubule to prevent the whole protein from “wandering” during the simulation. In the axoneme, dynein attaches to the larger and more rigid microtubule structure via a linker protein that binds to dynein’s “hinge” region (Figure 4A,B). Thus, we chose to fix the hinge region at this site because the existence of a hinge constraint is also supported by past experimental work. (15) Interestingly, during our design iterations, we observed that fixing of the hinge position to the linker region of the dynein molecule had a focusing effect on the force introduced via ligand prestressing. Even more surprisingly, the characteristic directional locomotion of dynein relative to microtubules spontaneously emerged during the simulation (Figure 4C–E and movie S5). In contrast, when we introduced energy without the hinge being fixed, the dynein failed to achieve the same motion (movie S6).
An advantage of this strategy is that applying ligand prestressing combined with a fixed point at the hinge does not bias the simulation toward any particular location or conformation, as is the case with other atomistic simulation techniques used to generate and observe large scale structural changes, such as steered-MDS or flexible-fitting-MDS. (13, 27) When MDSs of dynein with and without the hinge constraint were carried out, the root mean squared deviation (RMSD) of atomic positions within the model had a larger and more pronounced periodic variation over the course of the trajectory when the constraint was present (Figure 5A). The amplitude of this periodic cycling was further increased with the introduction of energy to the dynein via the prestressed ligand approach (Figure 5B and movie S7).

Figure 5

Figure 5. Custom simulation designed for the generation of a dynein walk cycle. (A) Graph showing the root mean squared deviation (RMSD) in angstroms of a 5 ns MDS of dynein with (red) or without (blue) a hinge constraint. Note that the reduced degrees of freedom caused by the constraint had a focusing effect and resulted in a more pronounced periodic cycling of dynein conformations. (B) Graph showing the RMSD of a dynein simulation where the ADP ligands have been prestressed with a force equivalent to 10 kcal·mol–1 (red) versus a simulation with no prestress (blue). This increased the conformational variation needed to obtain a walk cycle with a relatively short computational simulation time. (C) Series of dynamic images from the short film depicting multiple dynein motors working in unison to deform the microtubule cytoskeleton of the axoneme. This was produced by integrating dynamic MDS data with FEM data, providing a multiscale and multimolecular depiction of dynamic behaviors with molecular precision across biologically relevant time scales. (D) Using our simulation method, a dynein walk cycle was generated that could be used in the short film. The MDS trajectory transitioned through conformations that correspond to structures previously identified with cryoEM tomographic averaging. (E) Two conformations of the dynein molecule taken from the simulated walk cycle and “fit” to the 3D EM maps, with both conformations obtaining correlation coefficients of greater than 0.9.

To further validate the effect of local and specific introduction of energy via bound ligands and the subsequent transfer of force throughout the molecule, the MDSs were repeated (movie S8). But this time, following equilibration, the total temperature of the system was reduced to absolute zero so that every atom in the system had a zero velocity. Using Langevin dynamics and a coupling coefficient of 1 for ADP and 0 for all other atoms, the temperature was increased every 1000 ps by 1 degree until it reached 310 K. Again, this local, specific, and de novo introduction of energy within the region where energy is naturally released through ATP hydrolysis, resulted in the transfer of strain throughout the molecule and facilitated the emergence of dynein’s characteristic conformational shifts. Importantly, the hinge-based angular movements of the dynein ring and flexible stalk stepping mechanism predicted by our model are consistent with recent experimental observations. (29)
Thus, this multiscale computer visualization strategy revealed that the large-scale motion of dynein emerges as a result of the constrained hinge, and that this reduced range of motion has a focusing effect on energy introduced into the molecule upon ATP hydrolysis. Importantly, this is consistent with experimental studies which show that cytoplasmic dynein requires cargo-binding components in order to achieve its processive unidirectional locomotion. (30, 31) At the same time, by integrating MDS data with procedural animation, we were able to produce a highly effective, exciting, and physically realistic depiction of a series of dynein motors working in unison, like oarsmen in a boat race, to generate the microtubule sliding that drives axoneme movement and forward motion of the sperm during fertilization in the Short (Figure 5C and movie S9), which would be difficult using conventional scientific visualization approaches. More importantly, our MDS trajectory also resulted in changes in dynein shape, position and orientation (Figure 4E) that pass through two characteristic molecular conformations (Figures 4C,D and 5D) similar to those identified in recent studies involving tomographic averaging of cryoEM-determined dynein structures.(Figure 5E) (14, 16, 32, 33) The fidelity of our modeling approach that integrates MDS data with physics-based animation was extremely high as demonstrated by the finding that the molecular conformations of dynein at its pre- and poststrike positions predicted by our simulation fit within the respective density maps of dynein configurations previously generated by cryoEM (16) with correlation coefficients of greater than 0.9.

Alternative View of the Dynein Power Stroke

Past cryoEM studies (13, 14, 29, 30) have postulated that the dynein motor and its linker proteins behave like a winch with grappling hooks that bind to microtubules, instead of previous analogies that suggested an ensemble resembling a walking machine with sturdy legs. Our physics-based animation, combined with these previous studies, suggests instead that the “legs” are more like flexible cables that allow for a wide range of conformations, combined with a flexible region that allows for grappling hook-like behavior. Thus, the entire series of macromolecular shape changes that underlie the dynein force stroke (Figure 5D) are reminiscent of a person swinging by their arms on monkey bars, with the flexible wrist-like joint being essential for binding the microtubule. The fidelity of this simulation also supports earlier theoretical work (23, 24) and MDS studies (19) on the role of internal tensional prestress due to a tensegrity-force balance in determining the structure and function of individual molecules, where internal hydrogen bonding plays a critical role. The inclusion of these internal hydrogen bonds through our atomistic-simulation, instead of coarse-graining, was a key component in the success of our simulation strategy.

Revisiting Dynein’s Chemomechanical Cycle

It is important to clarify that past studies that modeled the chemomechanical cycle of dynein estimated the different molecular conformations that mediate the powerstroke by interpolating between conformational extremes, which were both static and averaged across inherent biological diversity due to the use of cryoEM. (14, 16, 32, 33) The cryoEM data previously used to determine the structural mechanism of the dynein power stroke has a resolution of 30 and 34 Å (EMDB 5757 and 5758, respectively) in the pre- and poststroke conformations. (16) In contrast, we built our model using the highest resolution crystal structure of dynein available, which is also in a prestrike conformation; (34) this structure has a total resolution of 3.8 Å, with an even higher resolution (2.8 Å) in the motor domain (pdb entry 3vkh).
Published models of the chemomechanical cycle of dynein (35) do not consider how the transfer of chemical energy from the cleavage of ATP drives mechanical conformational changes within the dynein protein. They do, however, show a change in strain in the ATP binding domains at the pre- and postpowerstroke time points: the domain is relaxed in the prepowerstroke conformation, whereas it is strained after the powerstroke, as it is in the leg-connecting region. To explore the fidelity of our simulation, we analyzed a region within our simulation of the dynein powerstroke that covers the steepest rise in RMSD relative to the prestroke conformation as highlighted in Figure. 5. We chose this time because this is when the molecule is undergoing the most rapid conformational shift and hence, experiencing the largest transfer of mechanical strain through the different subregions of the protein. When we measured the average speed (distance covered over time) at which the different portions of the dynein molecule were moving in all possible directions, we found that all regions simultaneously begin to move more rapidly at the onset of the powerstroke.(Figure 6) Moreover, when we analyzed how the direction and velocity of different regions of the molecule changes during the full course of the powerstroke, we found that all of the molecular domains were initially relatively mobile and moved in virtually all directions simultaneously when the molecule was in a conformation closest to that of the prepowerstroke position,(Figure 6) which is consistent with the “relaxed configuration” predicted by a past model. (35) Importantly, as the molecule progresses through the course of the powerstroke, the velocities increase and the domains begin moving in a highly coordinated rotational manner in the ATPase regions, and in a linear direction as force propagates toward the leg-connecting region (Figure 6, bottom), which is again consistent with past models that predict both of these regions will experience higher levels of strain in the poststroke configuration. (35) Throughout this simulation—as the dynein moves from fitting the conformation of the prestrike EM density map based on crystal structure, transitions through intermediary conformations, and ends by fitting the poststrike map consistent with cryoEM data—the RMSD varied by no more than 30 Å. Thus, our simulation approach not only supports previous studies of dynein mechanisms based on static low resolution cryoEM data, but also provides potential transition states between these conformations that are derived from a higher resolution crystal structure of the molecule. It is also important to note that we obtained similar results to these past models using an entirely different simulation method in which molecular conformational changes are produced de novo by increasing mechanical strain at the ADP binding site as a result of ATP hydrolysis, which is how this process occurs naturally.

Figure 6

Figure 6. Strain transfer within the dynein during the powerstroke revealed by the simulation. (Top) The graph shows the change in average speed of five different regions (1–5) of the dynein protein analyzed over approximately 0.25 ns during simulation of the dynein powerstroke that covers the steepest rise in RMSD relative to the prestroke conformation, as highlighted in Figure 5B. Region 1 connects directly to the hinge; regions 2 and 3 form one of the ATP binding clefts; regions 4 and 5 connect the ATPase region to the leg region. (Bottom) Visualization of motion of α carbons of dynein during the powerstroke over the time course shown at the top, as determined from the simulation. The length of each line indicates the magnitude of the average velocities at each indicated time step; orientation indicates its direction. All carbons within regions 1–4 moved in a concerted manner with a consistent counterclockwise rotation, which peaked during the most rapid increase in average speed (shown at top) during the powerstroke. Strain also propagated downward through the bottom of regions 4 and 5 toward the leg, which resulted in net downward and lateral motion (the bottom portion of the leg region shown outside of the circle at the left is omitted for clarity in the depictions at the right).

Conclusion

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Taken together, these studies show how pursuit of an artistic agenda can lead to insights into biological mechanisms at the molecular and cellular scale, as well as development of a highly generalizable, animation-based, multiscale, computational modeling approach that may be useful for future scientific investigations down to the nanometer scale. Our convergent approach to character design in the making of our short film involved a combined top-down and bottom-up process, and resulted in the development of integrated modeling, simulation and visualization techniques that provide robust and reproducible depictions of biological behaviors at multiple size scales. Application of these methods to create an entertaining film for the lay public led to the discovery of force-balanced molecular tensegrity mechanisms at two size scales—in the axoneme cytoskeleton and in individual dynein motor proteins—which is consistent with its use at smaller and larger size scales in the hierarchy of life. (23, 24) We also discovered that like in higher order biological structures, the dynamic 3D shape-shifting behavior of dynein that underlies its ability to generate motive force is context-dependent and strongly influenced by its local environment. Most notably, application of energy at the ADP binding site drives conformation changes throughout the molecule, but dynein only undergoes directional processional movement when the hinge region is fixed in space (e.g., via linkage to a more rigid microtubule).
The computational production pipeline we developed that combines physics-based animation software from the entertainment industry with scientific molecular simulation tools, and uses an iterative ‘design for discovery’ approach, may therefore be useful as a robust scientific modeling and analysis tool for the study of any biological process where 3D shape and physicality comes into play, regardless of scale. By leveraging animation, our strategy can go beyond conventional MDS models that are constrained by conformations derived from rigid crystal structures and can integrate many kinds of data to enable the exploration of a much wider range of dynamic conformations of any molecule, as well as how that molecule fits and functions within larger multimolecular structures. For example, the modular design approach we developed that uses an animation pipeline to develop hypotheses, which are then validated through an iterative process of convergence with previously published experimental data, could be used to examine how different local microenvironmental conditions influence locomotion of individual sperm cells in future studies. Also, by introducing random variables for some physical parameters of the sperm structure (e.g., head size, 3D shape, center of mass, flagellum length, thickness variations, etc.), it might be possible to better understand and model phenotypic defects, which could have important implications for clinical diagnosis of infertility. In the specific context of nanoscience, any study that involves molecular specificity and the impact it has on self-assembly could benefit from the utility of combining molecular precision with large scale coarse-grained depiction, guided by experimental data. Furthermore, this modular and hierarchical approach can be generalized to many different scales and used for hypothesis generation as well as data analysis.
More generally, this work provides a clear example of how pursuing an artistic path can indeed lead to scientific insights—in this case, better understanding of how sperm move. Finally, the strategy we developed enabled the depiction of dynamic, physically integrated, multiscale and multimolecular collective biological behaviors. By tackling this fundamental scientific challenge of hierarchical modeling, we were able to show molecular precision at biologically relevant time scales. Thus, our approach should find applications in many areas of scientific research and nano-biotechnology, in addition to being used to produce entertaining animations that convey the physical reality and wondrous beauty of the natural world.

Experimental Methods

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3D Modeling, Animation, and Multiscale Simulation

The overall approach to making the Short film involved a pipeline strategy. This modular process enabled any changes in input data, either experimental or simulated, to be propagated throughout the project (Figure S2), enabling continuous design iteration at every stage of the project. First, models for the various characters and objects were built based on experimental or simulated data. These models were then combined in a central staging environment and procedurally (8) placed with other models to build an animation scene. Simulations were then repeated and refined until the necessary scene was achieved. The main 3D animation software used as a central staging environment for heterogeneous data integration was Houdini (SideFX software). In this same environment, cameras, lighting, and shading strategies were designed, followed by rendering, compositing, and editing.
To model and simulate the sperm, a geometry generated by Chimera (33) was imported and used to guide the generation of a simplified shape of the sperm tail in 3D, where primitives represented the major 24 nm repeating units of dynein and microtubule complexes. This axoneme model was tetrahedralized with preservation of edges using Houdini’s internal operators before being imported into the Houdini-AutoDop environment for finite element method (FEM) simulation. In the AutoDop network, toroidal geometry was introduced to generate a rigid body deformer that could be rotated based on the rate that represented the observations observed experimentally in high speed camera footage of sperm swimming. (10) This toroid was then bound to edges at the head of the axoneme softbody model via spring constraints. Simulations were performed that varied parameters of the FEM. These parameters included shape stiffness or shear modulus (values 0.0001–1.0 Pa), volume stiffness (0.01–10 Pa), damping ratio (values 0.1–0.5), and mass density (mass per cubed length; 500–1100). After scanning the parameter space, parameters were identified that would generate a waveform most similar to that exhibited by free swimming sperm. For a 25 unit long sperm tail, the corresponding Houdini parameter values for shape stiffness, volume stiffness, damping ratio and mass density were 1.68 × 10–5, 8.2 × 10–4, 0.5, and 1000, respectively. A simulation database of “swimming” sperm axonemes was then generated with varying deformer rotation and translation parameters, which generated a repertoire of heterogeneous sperm “swim-cycles”.
To generate a large population of sperm with a “schooling aesthetic”, the swimming geometry of multiple sperm was combined with a particle-based fluid simulation. Each swim cycle from the custom database we created above was positioned on the dynamic points in the fluid simulation. A copy-stamping (https://www.sidefx.com/docs/houdini/copy/stamping) animation strategy was used to select unique swim cycles, create modified surface geometry, and alter the swimming speed and direction for each point within the fluid simulation based on point attributes (ID number, velocity, and position).
To map internal forces being experienced across the different regions of the simulated axoneme, the length of each 24 nm (at rest) repeating unit of each microtubule doublet was measured computationally and the length of these units relative to the rest length was calculated at each time point, which indicated whether it was under tension (lengthened) or compression (shortened). In addition, during the FEM simulation, local energy densities were assigned to vertex attributes on the simulation geometry. The changing relative lengths of adjacent microtubule regions over time were then used to give each point on the simulated geometry a value that could be correlated to a conformation in the dynein walk cycle MDS trajectory. Using copy stamping, dynein could be copied to each point with an appropriate walk cycle position based on point attributes at each frame of the animation.
We exploited the regular periodicity of the 24 nm repeating structure of the axoneme (16) to map atomic structures to the simulated cytoskeleton. The large and small microtubule structures of the doublets were constructed using 13 and 10 protofilaments, respectively. The protofilaments were built using tubulin dimers (pdb 3J2U) arranged in a pseudohelical manner. The pseudohelices were then copied across the entire axoneme based on point normals and position. Dynein pairs were built using the presimulated “walk cycle” and a series of dyneins were assigned to points along the microtubules in the simulated axoneme, with point normals, relative position and microtubule section length dictating the dynein conformation at each point and animation frame. With an animation frame rate of 25 frames per second, these states could only appear at an approximate position and therefore motion blur was used to blend between multiple frames to achieve a dynamic aesthetic.

Molecular Dynamics Simulation

The dynein walk cycle and all other molecular dynamics simulations (MDSs) were performed with NAMD 2.9 (25) with CHARM22 parameters in implicit solvent conditions. The dynein starting structure was generated from the A chain of pdb entry 3VKH (34) and parametrized with the VMD (36) autopsf plugin and swissparam. (26) Hinge constraints were generated by fixing the backbone α carbons of the linker domain. (16) Prestressing of the ADP bound to dynein was accomplished by fixing the phosphorus atom nearest to the 5′ carbon of ADP and applying a constant force to the remaining phosphorus in a direction defined by the vector between the two atoms and then pulling the second atom away from the first.
Simulations using Langevin dynamics to increase temperature within the vicinity of ATP binding utilized a coupling coefficient of 1 for the ADP and 0 for dynein. Where Langevin dynamics (37, 38) was used to control the temperature of the entire system a langevin dampening coefficient of 1 was used. Prior to the production runs, the systems were subjected to energy minimization for 2000 times steps and equilibrated by performing temperature annealing by increasing the temperature by 10° every 100 ps until 300 K and then reducing the temperature by 10 degrees every 100 ps until 0 K. Production runs using the above Langevin parameters were then performed with 1 degree increments every 1000 ps until 310 K was achieved.
The simulation of microtubule subunits bound to dynein was performed using PDB entry 3J1T. (17) Energy minimization and equilibration was performed as described above and simulations run for 8 ns with a fixed Langevin temperature set to 300.
MDS trajectory data were imported to Houdini using the ProDy python module (39) and a custom script. Velocity and speed calculations were made using Houdini’s CHOP network and trail SOP. To visualize velocities within regions of the protein at specific time points, velocity was calculated based on the distance each α carbon moved during 2 ps time steps. The speed and direction of each α carbon was then used to scale the size and direction of lines that were placed on each of the alpha carbons within the protein at each relevant conformation.
To plot the average speed of protein segments during the powerstroke, the α carbon speeds of each protein segment were averaged and normalized.

Molecular Modeling Based on cryoEM Data

All 3DEM maps were obtained from data from multiple model organisms found at the EMDataBank (www.emdatabank.org). The axoneme section containing all nine microtubules was from entry EMD-5302. (40) The dynein pre and postpower stroke maps were from entries EMD-5758 and EMD-5757, respectively, (16) and entries EMD-2131 and EMD-5330 were also used as additional visual guides during modeling. UCSF Chimera (33) was used to generate geometry from these maps for importing into animation and modeling software.
The mapping of conformations in the simulated trajectory of dynein to cryoEM data, was performed using the Fit in Map tool in Chimera. Coordinates from the start and end of the indicated power stroke were mapped to the pre and postpower stroke EMDataBank entries of EMD-5758 and EMD-5757, respectively. (16) The RMSD (root mean squared deviation) trajectory tool (RMSDTT v3.0) of VMD (36) was used to compare trajectories of simulations. In cases without fixed constraints, the trajectories were first aligned to the starting structure.

Rendering

Rendering for the Short film was performed using Mantra with compositing in Nuke Studio, while taking advantage of an AOV and Deep based pipeline. The color pallet chosen and general aesthetic was based on imagery associated with contemporary films set in outer space. This was to ensure the audience begins thinking that what they are watching is at a scale consistent with another Star Wars movie. Color hue and saturation were used to amplify complexity and indicate biological variation. As the perceived complexity is increased, so too is color saturation. The color is at its most prominent and saturated when at the molecular scale. Here, the reduced color pallet is used to exaggerate the periodicity of the molecular structures. High saturation is used to ensure the viewer is aware that they are at the molecular scale and no longer at the cellular level. The hue for the cytoplasm of the sperm remains the same at all scales, with only the saturation changing when we transition from being outside the cell to being inside.

Supporting Information

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The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.7b05266.

  • Videos showing an overview of the filmmaking pipeline (ZIP)

  • Conformation mapping within subregions of the axoneme and accompanying plots, which show relative length changes in ∼24 nm repeating subunits (PDF)

Terms & Conditions

Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.

Author Information

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  • Corresponding Author
    • Donald E. Ingber - Wyss Institute for Biologically Inspired Engineering, Harvard University, Boston, Massachusetts 02115, United StatesVascular Biology Program and Department of Surgery, Boston Children’s Hospital and Harvard Medical School, Boston, Massachusetts 02115, United StatesJohn A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02139, United StatesOrcidhttp://orcid.org/0000-0002-4319-6520 Email: [email protected]
  • Author
  • Notes
    The authors declare no competing financial interest.

Acknowledgment

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This work was supported by the Wyss Institute for Biologically Inspired Engineering at Harvard University. We thank M. Giampaolo for her editing assistance and M. Ingber for his music score in the short film. We also thank B. Culliton for her helpful editorial advice.

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  1. Seán I. O'Donoghue. Grand Challenges in Bioinformatics Data Visualization. Frontiers in Bioinformatics 2021, 1 https://doi.org/10.3389/fbinf.2021.669186
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  • Abstract

    Figure 1

    Figure 1. Storyboard showing an overview of the shots created for the cinematic Short film, “THE BEGINNING” (from start at top left to film end at bottom right).

    Figure 2

    Figure 2. Modeling a multiscale swimming sperm based on multiple kinds of published experimental data. (A) Each sperm’s axoneme movement was simulated using an inverse kinematic-coupled finite element method (FEM). Here, the long cylindrical FEM model of the axoneme was bound to a rotating rigid structure via spring constraints at its proximal end. As the rigid structure was rotated, the soft axoneme model was deformed, and material properties of the axoneme model were then tuned to achieve a sinusoidal waveform. This generated a dynamic axoneme model that was used as cytoskeletal input during the modeling of sperm ultrastructures. (B) FEM simulations are used to model ultrastructures and rendered using animation software to achieve a realistic depiction of swimming sperm. (C) 3D electron micrographic (EM) density map of a portion of an axoneme based on averaged data from multiple model organisms (obtained from EM Data Bank), which was used to guide the modeling of the sperm axoneme. (D) Schematic showing a cross-section of the axoneme with component parts labeled. (E) Images from a FEM simulation of the sperm tail with internal forces mapped showing that local regions of the microtubule doublets transition between being under tension versus compression during tail motion while the whole multimolecular structure is stabilized through intermolecular attractive (tensile) bonding forces. (F) Molecular trajectories of dynein and tubulin are positioned in the FEM model according to mapped forces and biological periodicity.

    Figure 3

    Figure 3. Procedural modeling of the multiscale axoneme. (A) A cell-scale model was built using cryoEM data to guide initial geometry for a 9-edged cylindrical representation of an axoneme prior to FEM simulation. (B) Each edge is made up of 24 nm (at rest) subunits that represent the distance between the periodically repeating dynein. As the FEM progresses, the relative subunit lengths fluctuate and based on cryoEM data the bounding volumes of the molecular components can be interpolated for each subunit in the axoneme model. (C) CryoEM data of multiple dynein conformations are used to further refine bounding volume and provide local positional information for atomistic depiction of dynein. (D) MDS provided a trajectory that transitions between the pre- and poststrike cryoEM conformations. (E) Conformations from the MDS are placed within the axoneme model procedurally, based on relative length of subunit, edge normal, and previous time step parameters. The cryoEM data of a section of an axoneme provides bounding volumes for additional “tuning” of the model.

    Figure 4

    Figure 4. Dynamic model of dynein built using a MD simulation guided by qualitative CryoEM data. (A) 3D depiction of a region of the axoneme based on CryoEM data showing that the periodically repeating dynein proteins are tethered to a microtubule doublet via a multimolecular complex that includes a linker region. (B) Higher magnification of the region of the axoneme shown in A that displays averaged CryoEM tomograms of dynein (16) in the pre- and postpower stroke positions, with the Linker, Hinge, and Dynein ATPases associated with diverse cellular activity (AAA) domains highlighted. (C) Locomotion of the dynein molecule when the hinge point is fixed as in the axoneme visualized in 3D using a custom atomistic MDS strategy. The strategy involves rapidly increasing the vibrational energy of bound ligands by applying a prestress force to an intramolecular bond of the bound ADP prior to carrying out the simulation. Meanwhile, to replicate the effect of the dynein linker, the alpha carbons of amino acid residues in the dynein “hinge” (red) region are fixed. (D) A snapshot image from our simulated trajectory that passes through the two conformations seen in B. (E) Representations of dynein conformations and corresponding microtubule positions during a power stroke.

    Figure 5

    Figure 5. Custom simulation designed for the generation of a dynein walk cycle. (A) Graph showing the root mean squared deviation (RMSD) in angstroms of a 5 ns MDS of dynein with (red) or without (blue) a hinge constraint. Note that the reduced degrees of freedom caused by the constraint had a focusing effect and resulted in a more pronounced periodic cycling of dynein conformations. (B) Graph showing the RMSD of a dynein simulation where the ADP ligands have been prestressed with a force equivalent to 10 kcal·mol–1 (red) versus a simulation with no prestress (blue). This increased the conformational variation needed to obtain a walk cycle with a relatively short computational simulation time. (C) Series of dynamic images from the short film depicting multiple dynein motors working in unison to deform the microtubule cytoskeleton of the axoneme. This was produced by integrating dynamic MDS data with FEM data, providing a multiscale and multimolecular depiction of dynamic behaviors with molecular precision across biologically relevant time scales. (D) Using our simulation method, a dynein walk cycle was generated that could be used in the short film. The MDS trajectory transitioned through conformations that correspond to structures previously identified with cryoEM tomographic averaging. (E) Two conformations of the dynein molecule taken from the simulated walk cycle and “fit” to the 3D EM maps, with both conformations obtaining correlation coefficients of greater than 0.9.

    Figure 6

    Figure 6. Strain transfer within the dynein during the powerstroke revealed by the simulation. (Top) The graph shows the change in average speed of five different regions (1–5) of the dynein protein analyzed over approximately 0.25 ns during simulation of the dynein powerstroke that covers the steepest rise in RMSD relative to the prestroke conformation, as highlighted in Figure 5B. Region 1 connects directly to the hinge; regions 2 and 3 form one of the ATP binding clefts; regions 4 and 5 connect the ATPase region to the leg region. (Bottom) Visualization of motion of α carbons of dynein during the powerstroke over the time course shown at the top, as determined from the simulation. The length of each line indicates the magnitude of the average velocities at each indicated time step; orientation indicates its direction. All carbons within regions 1–4 moved in a concerted manner with a consistent counterclockwise rotation, which peaked during the most rapid increase in average speed (shown at top) during the powerstroke. Strain also propagated downward through the bottom of regions 4 and 5 toward the leg, which resulted in net downward and lateral motion (the bottom portion of the leg region shown outside of the circle at the left is omitted for clarity in the depictions at the right).

  • References

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    This article references 40 other publications.

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