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Cardiac tagged MR images allow for deformation fields to be measured in the heart by tracking the motion of tag lines throughout the cardiac cycle. Machine learning (ML) algorithms enable accurate and robust tracking of tag lines. Herein, the use of a massive synthetic physics-driven training dataset with known ground truth was used to train an ML network to enable tracking any number of points at arbitrary positions rather than anchored to the tag lines themselves. The tag tracking and strain calculation methods were investigated in a computational deforming cardiac phantom with known (ground truth) strain values. This enabled both tag tracking and strain accuracy to be characterized for a range of image acquisition and tag tracking parameters. The methods were also tested on in vivo volunteer data. Median tracking error was< 0.26 mm in the computational phantom, and strain measurements were improved in vivo when using the arbitrary point tracking for a standard clinical protocol.

Purpose: Myofiber strain, Eff , is a mechanistically relevant metric of cardiac cell shortening and is expected to be spatially uniform in healthy populations, making it a prime candidate for the evaluation of local cardiomyocyte contractility. In this study, a new, efficient pipeline was proposed to combine microstructural cDTI and functional DENSE data in order to estimate Eff in vivo.Methods: Thirty healthy volunteers were scanned with three long-axis (LA) and three short-axis (SA) DENSE slices using 2D displacement encoding and one SA slice of cDTI. The total acquisition time was 11 minutes ± 3 minutes across volunteers. The pipeline first generates 3D SA displacements from all DENSE slices which are then combined with cDTI data to generate a cine of myofiber orientations and compute Eff . The precision of the post-processing pipeline was assessed using a computational phantom study. Transmural myofiber strain was compared to circumferential strain, Ecc , in healthy volunteers using a Wilcoxon sign rank test.Results: In vivo, computed Eff was found uniform transmurally compared to Ecc (-0.14[-0.15, -0.12] vs -0.18 [-0.20, -0.16], P < .001, -0.14 [-0.16, -0.12] vs -0.16 [-0.17, -0.13], P < .001 and -0.14 [-0.16, -0.12] vs Ecc_C = -0.14 [-0.15, -0.11], P = .002, Eff_C vs Ecc_C in the endo, mid, and epi layers, respectively).Conclusion: We demonstrate that it is possible to measure in vivo myofiber strain in a healthy human population in 10 minutes per subject. Myofiber strain was observed to be spatially uniform in healthy volunteers making it a potential biomarker for the evaluation of local cardiomyocyte contractility in assessing cardiovascular dysfunction.

Purpose Cardiomyocyte organization and performance underlie cardiac function, but the in vivo mobility of these cells during contraction and filling remains difficult to probe. Herein, a novel trigger delay (TD) scout sequence was used to acquire high in-plane resolution (1.6 mm) Spin-Echo (SE) cardiac diffusion tensor imaging (cDTI) at three distinct cardiac phases. The objective was to characterize cardiomyocyte organization and mobility throughout the cardiac cycle in healthy volunteers. Materials and methods Nine healthy volunteers were imaged with cDTI at three distinct cardiac phases (early systole, late systole, and diastasis). The sequence used a free-breathing Spin-Echo (SE) cDTI protocol (b-values = 350s/mm2, twelve diffusion encoding directions, eight repetitions) to acquire high-resolution images (1.6x1.6x8mm3) at 3T in ~7 minutes/cardiac phase. Helix Angle (HA), Helix Angle Range (HAR), E2 angle (E2A), Transverse Angle (TA), Mean Diffusivity (MD), diffusion tensor eigenvalues (λ1-2-3), and Fractional Anisotropy (FA) in the left ventricle (LV) were characterized. Results Images from the patient-specific TD scout sequence demonstrated that SE cDTI acquisition was possible at early systole, late systole, and diastasis in 78%, 100% and 67% of the cases, respectively. At the mid-ventricular level, mobility (reported as median [IQR]) was observed in HAR between early systole and late systole (76.9 [72.6, 80.5]° vs 96.6 [85.9, 100.3]°, p Conclusion We demonstrate that it is possible to probe cardiomyocyte mobility using multi-phase and high resolution cDTI. In healthy volunteers, aggregate cardiomyocytes re-orient themselves more longitudinally during contraction, while cardiomyocyte sheetlets tilt radially during wall thickening. These observations provide new insights into the three-dimensional mobility of myocardial microstructure during systolic contraction.

Computational modeling of the heart requires accurately incorporating both gross anatomical detail and local microstructural information. Together, these provide the necessary data to build 3D meshes for simulation of cardiac mechanics and electrophysiology. Recent MRI advances make it possible to measure detailed heart motion in vivo, but in vivo microstructural imaging of the heart remains challenging. Consequently, the most detailed measurements of microstructural organization and microanatomical infarct details are obtained ex vivo. The objective of this work was to develop and evaluate a new method for restoring ex vivo ventricular geometry to match the in vivo configuration. This approach aids the integration of high-resolution ex vivo microstructural information with in vivo motion measurements. The method uses in vivo cine imaging to generate surface meshes, then creates a 3D printed left ventricular (LV) blood pool cast and a pericardial mold to restore the ex vivo cardiac geometry to a mid-diastasis reference configuration. The method was evaluated in healthy (N = 7) and infarcted (N = 3) swine. Dice similarity coefficients were calculated between in vivo and ex vivo images for the LV cavity (0.93 ± 0.01), right ventricle (RV) cavity (0.80 ± 0.05), and the myocardium (0.72 ± 0.04). The R(2) coefficient between in vivo and ex vivo LV and RV cavity volumes were 0.95 and 0.91, respectively. These results suggest that this method adequately restores ex vivo geometry to match in vivo geometry. This approach permits a more precise incorporation of high-resolution ex vivo anatomical and microstructural data into computational models that use in vivo data for simulation of cardiac mechanics and electrophysiology.

Changes in left ventricular (LV) aggregate cardiomyocyte orientation and deformation underlie cardiac function and dysfunction. As such, in vivo aggregate cardiomyocyte “myofiber” strain ( ${E}_{\text {ff}}$ ) has mechanistic significance, but currently there exists no established technique to measure in vivo ${E}_{\text {ff}}$ . The objective of this work is to describe and validate a pipeline to compute in vivo ${E}_{\text {ff}}$ from magnetic resonance imaging (MRI) data. Our pipeline integrates LV motion from multi-slice Displacement ENcoding with Stimulated Echoes (DENSE) MRI with in vivo LV microstructure from cardiac Diffusion Tensor Imaging (cDTI) data. The proposed pipeline is validated using an analytical deforming heart-like phantom. The phantom is used to evaluate 3D cardiac strains computed from a widely available, open-source DENSE Image Analysis Tool. Phantom evaluation showed that a DENSE MRI signal-to-noise ratio (SNR) ≥20 is required to compute ${E}_{\text {ff}}$ with near-zero median strain bias and within a strain tolerance of 0.06. Circumferential and longitudinal strains are also accurately measured under the same SNR requirements, however, radial strain exhibits a median epicardial bias of −0.10 even in noise-free DENSE data. The validated framework is applied to experimental DENSE MRI and cDTI data acquired in eight ( ${N}={8}$ ) healthy swine. The experimental study demonstrated that ${E}_{\text {ff}}$ has decreased transmural variability compared to radial and circumferential strains. The spatial uniformity and mechanistic significance of in vivo ${E}_{\text {ff}}$ make it a compelling candidate for characterization and early detection of cardiac dysfunction.

In this work we extend the Caspar-Klug construction to the archaeal viruses, which in recent years have captured the attention of many researchers for their ability to thrive in extreme environments. We assume that the shells of archaeal viruses are composed of hexamers and pentamers-as is true for icosahedral viruses-together with heptamers, necessary to introduce negative Gauss curvature. Following the original work of Caspar and Klug, we first construct models capable of reproducing the shape observed in electron microscopy images of archaeal viruses. Next, using the technique of kirigami, we present a systematic way to formulate archaeal virus templates from regular hexagonal lattices. Finally, we utilize the presented techniques to build finite element models of archaeal virus geometries and investigate their shapes as a function of material properties. In particular, using thin-shell elasticity theory, we describe a buckling transition as a function of a modified Föppl-von Kármán number γ^{★} and we show how changes in γ^{★} may initiate the tail formation in the Acidianus two-tailed archaeal virus.

Since heart contraction results from the electrically activated contraction of millions of cardiomyocytes, a measure of cardiomyocyte shortening mechanistically underlies cardiac contraction. In this work we aim to measure preferential aggregate cardiomyocyte (“myofiber”) strains based on Magnetic Resonance Imaging (MRI) data acquired to measure both voxel-wise displacements through systole and myofiber orientation. In order to reduce the effect of experimental noise on the computed myofiber strains, we recast the strains calculation as the solution of a boundary value problem (BVP). This approach does not require a calibrated material model, and consequently is independent of specific myocardial material properties. The solution to this auxiliary BVP is the displacement field corresponding to assigned values of myofiber strains. The actual myofiber strains are then determined by minimizing the difference between computed and measured displacements. The approach is validated using an analytical phantom, for which the ground-truth solution is known. The method is applied to compute myofiber strains using in vivo displacement and myofiber MRI data acquired in a mid-ventricular left ventricle section in N=8 swine subjects. The proposed method shows a more physiological distribution of myofiber strains compared to standard approaches that directly differentiate the displacement field.

We propose a hybrid discrete-continuum model to study the ground state of protein shells. The model allows for shape transformation of the shell and buckling transitions as well as the competition between states with different symmetries that characterize discrete particle models with radial pair potentials. Our main results are as follows. For large Föppl-von Kármán (FvK) numbers the shells have stable isometric ground states. As the FvK number is reduced, shells undergo a buckling transition resembling that of thin-shell elasticity theory. When the width of the pair potential is reduced below a critical value, then buckling coincides with the onset of structural instability triggered by over-stretched pair potentials. Chiral shells are found to be more prone to structural instability than achiral shells. It is argued that the well-width appropriate for protein shells lies below the structural instability threshold. This means that the self-assembly of protein shells with a well-defined, stable structure is possible only if the bending energy of the shell is sufficiently low so that the FvK number of the assembled shell is above the buckling threshold.

Many problems in softmatter and membrane biophysics, such as finding the equilibrium configurations of protein clusters on cell-membranes, the highly defect ridden structure of Gag polyproteins in immature HIV capsids, and the unusual fluid-like state of Archaeal viruses can be understood as systems of interacting particles (typically representing proteins or protein capsomers) on deformable surfaces. The coupled interactions between the particles and the underlying elastic medium to which they are constrained pose significant computational challenges. Existing methods often employ expensive constraints to anchor particles to the surface or artificially restrict the particles movement yielding spurious equilibrium states. In this work, a new method is presented where the particles positions are parameterized in the reference configuration. This pull-back operation allows the particles to move freely on the surface without the need of additional constraints. Furthermore, the mapping necessary to describe the particles positions in a discretized setting, e.g., in a finite element mesh, can be done on the reference undeformed configuration at a reduced computational cost. The proposed method is applied to particles moving on manifolds in one and two dimensions to study its convergence characteristics and error when compared to derived analytical and semi-analytical solutions. Finally, the newly developed method is applied to generalized Tammes problems of packing interacting point particles on a deformable shell.

Computational models of cardiac contraction can provide critical insight into cardiac function and dysfunction. A necessary step before employing these computational models is their validation. Here we propose a series of validation criteria based on left ventricular (LV) global (ejection fraction and twist) and local (strains in a cylindrical coordinate system, aggregate cardiomyocyte shortening, and low myocardial compressibility) MRI measures to characterize LV motion and deformation during contraction. These validation criteria are used to evaluate an LV finite element model built from subject-specific anatomy and aggregate cardiomyocyte orientations reconstructed from diffusion tensor MRI. We emphasize the key role of the simulation boundary conditions in approaching the physiologically correct motion and strains during contraction. We conclude by comparing the global and local validation criteria measures obtained using two different boundary conditions: the first constraining the LV base and the second taking into account the presence of the pericardium, which leads to greatly improved motion and deformation.

Computational modeling of the heart requires accurately incorporating both gross anatomical detail and local microstructural information. Together, these provide the necessary data to build 3D meshes for simulation of cardiac mechanics and electrophysiology. Recent MRI advances make it possible to measure detailed heart motion in vivo, but in vivo microstructural imaging of the heart remains challenging. Consequently, the most detailed measurements of microstructural organization and microanatomical infarct details are obtained ex vivo. The objective of this work was to develop and evaluate a new method for restoring ex vivo ventricular geometry to match the in vivo configuration. This approach aids the integration of high-resolution ex vivo microstructural information with in vivo motion measurements. The method uses in vivo cine imaging to generate surface meshes, then creates a 3D printed left ventricular (LV) blood pool cast and a pericardial mold to restore the ex vivo cardiac geometry to a mid-diastasis reference configuration. The method was evaluated in healthy (N = 7) and infarcted (N = 3) swine. Dice similarity coefficients were calculated between in vivo and ex vivo images for the LV cavity (\(0.93\pm 0.01\)), right ventricle (RV) cavity (\(0.80\pm 0.05\)), and the myocardium (\(0.72\pm 0.04\)). The \(R^2\) coefficient between in vivo and ex vivo LV and RV cavity volumes were 0.95 and 0.91, respectively. These results suggest that this method adequately restores ex vivo geometry to match in vivo geometry. This approach permits a more precise incorporation of high-resolution ex vivo anatomical and microstructural data into computational models that use in vivo data for simulation of cardiac mechanics and electrophysiology.

Author(s): Li, Xinzhou; Perotti, Luigi E; Martinez, Jessica A; Duarte-Vogel, Sandra M; Ennis, Daniel B; Wu, Holden H | Abstract: PURPOSE:Real-time magnetic resonance imaging (MRI) is a promising alternative to X-ray fluoroscopy for guiding cardiovascular catheterization procedures. Major challenges, however, include the lack of guidewires that are compatible with the MRI environment, not susceptible to radiofrequency-induced heating, and reliably visualized. Preclinical evaluation of new guidewire designs has been conducted at 1.5T. Here we further evaluate the safety (device heating), device visualization, and procedural feasibility of 3T MRI-guided cardiovascular catheterization using a novel MRI-visible glass-fiber epoxy-based guidewire in phantoms and porcine models. METHODS:To evaluate device safety, guidewire tip heating (GTH) was measured in phantom experiments with different combinations of catheters and guidewires. In vivo cardiovascular catheterization procedures were performed in both healthy (N = 5) and infarcted (N = 5) porcine models under real-time 3T MRI guidance using a glass-fiber epoxy-based guidewire. The times for each procedural step were recorded separately. Guidewire visualization was assessed by measuring the dimensions of the guidewire-induced signal void and contrast-to-noise ratio (CNR) between the guidewire tip signal void and the blood signal in real-time gradient-echo MRI (specific absorption rate [SAR] = 0.04 W/kg). RESULTS:In the phantom experiments, GTH did not exceed 0.35°C when using the real-time gradient-echo sequence (SAR = 0.04 W/kg), demonstrating the safety of the glass-fiber epoxy-based guidewire at 3T. The catheter was successfully placed in the left ventricle (LV) under real-time MRI for all five healthy subjects and three out of five infarcted subjects. Signal void dimensions and CNR values showed consistent visualization of the glass-fiber epoxy-based guidewire in real-time MRI. The average time (minutes:seconds) for the catheterization procedure in all subjects was 4:32, although the procedure time varied depending on the subject's specific anatomy (standard deviation = 4:41). CONCLUSIONS:Real-time 3T MRI-guided cardiovascular catheterization using a new MRI-visible glass-fiber epoxy-based guidewire is feasible in terms of visualization and guidewire navigation, and safe in terms of radiofrequency-induced guidewire tip heating.

In vivo cardiac microstructure acquired using cardiac diffusion tensor imaging (cDTI) is a critical component of patient-specific models of cardiac electrophysiology and mechanics. In order to limit bulk motion artifacts and acquisition time, cDTI microstructural data is acquired at a single cardiac phase necessitating registration to the reference configuration on which the patient-specific computational models are based. Herein, we propose a method to register subject-specific microstructural data to an arbitrary cardiac phase using measured cardiac displacements. We validate our approach using a subject-specific computational phantom based on data from human subjects. Compared to a geometry-based non-rigid registration method, the displacement-based registration leads to improved accuracy (less than 1° versus 10° average median error in cardiomyocyte angular differences) and tighter confidence interval (3° versus 65° average upper limit of the 95% confidence interval).

In vivo cardiac microstructure acquired using cardiac diffusion tensor imaging (cDTI) is a critical component of patient-specific models of cardiac electrophysiology and mechanics. In order to limit bulk motion artifacts and acquisition time, cDTI microstructural data is acquired at a single cardiac phase necessitating registration to the reference configuration on which the patient-specific computational models are based. Herein, we propose a method to register subject-specific microstructural data to an arbitrary cardiac phase using measured cardiac displacements. We validate our approach using a subject-specific computational phantom based on data from human subjects. Compared to a geometry-based non-rigid registration method, the displacement-based registration leads to improved accuracy (less than 1° versus 10° average median error in cardiomyocyte angular differences) and tighter confidence interval (3° versus 65° average upper limit of the 95% confidence interval).

Metrics of regional myocardial function can detect the onset of cardiovascular disease, evaluate the response to therapy, and provide mechanistic insight into cardiac dysfunction. Knowledge of local myocardial microstructure is necessary to distinguish between isotropic and anisotropic contributions of local deformation and to quantify myofiber kinematics, a microstructurally anchored measure of cardiac function. Using a computational model we combine in vivo cardiac displacement and diffusion tensor data to evaluate pointwise the deformation gradient tensor and isotropic and anisotropic deformation invariants. In discussing the imaging methods and the model construction, we identify potential improvements to increase measurement accuracy. We conclude by demonstrating the applicability of our method to compute myofiber strain in five healthy volunteers.

We develop a mixed finite-element approximation scheme for Kirchhoff plate theory based on the reformulation of Kirchhoff plate theory of Ortiz and Morris [1]. In this reformulation the moment-equilibrium problem for the rotations is in direct analogy to the problem of incompressible two-dimensional elasticity. This analogy in turn opens the way for the application of diamond approximation schemes (Hauret et al. [2]) to Kirchhoff plate theory. We show that a special class of meshes derived from an arbitrary triangulation of the domain, the diamond meshes, results in the automatic satisfaction of the corresponding inf − sup condition for Kirchhoff plate theory. The attendant optimal convergence properties of the diamond approximation scheme are demonstrated by means of the several standard benchmark tests. We also provide a reinterpretation of the diamond approximation scheme for Kirchhoff plate theory within the framework of discrete mechanics. In this interpretation, the discrete moment-equilibrium problem is formally identical to the classical continuous problem, and the two differ only in the choice of differential structures. It also follows that the satisfaction of the inf − sup condition is a property of the cohomology of a certain discrete transverse differential complex. This close connection between the classical inf − sup condition and cohomology evinces the important role that the topology of the discretization plays in determining convergence in mixed problems.

Metrics of regional myocardial function can detect the onset of cardiovascular disease, evaluate the response to therapy, and provide mechanistic insight into cardiac dysfunction. Knowledge of local myocardial microstructure is necessary to distinguish between isotropic and anisotropic contributions of local deformation and to quantify myofiber kinematics, a microstructurally anchored measure of cardiac function. Using a computational model we combine in vivo cardiac displacement and diffusion tensor data to evaluate pointwise the deformation gradient tensor and isotropic and anisotropic deformation invariants. In discussing the imaging methods and the model construction, we identify potential improvements to increase measurement accuracy. We conclude by demonstrating the applicability of our method to compute myofiber strain in five healthy volunteers.

We propose a physical model for the capsids of tailed archaeal viruses as viscoelastic membranes under tension. The fluidity is generated by thermal motion of scarlike structures that are an intrinsic feature of the ground state of large particle arrays covering surfaces with nonzero Gauss curvature. The tension is generated by a combination of the osmotic pressure of the enclosed genome and an extension force generated by filamentous structure formation that drives the formation of the tails. In continuum theory, the capsid has the shape of a surface of constant mean curvature: an unduloid. Particle arrays covering unduloids are shown to exhibit pronounced subdiffusive and diffusive single-particle transport at temperatures that are well below the melting temperature of defect-free particle arrays on a surface with zero Gauss curvature.

Heart failure is a leading cause of death, yet its underlying electrophysiological (EP) mechanisms are not well understood. In this study, we use a multiscale approach to analyze a model of heart failure and connect its results to features of the electrocardiogram (ECG). The heart failure model is derived by modifying a previously validated electrophysiology model for a healthy rabbit heart. Specifically, in accordance with the heart failure literature, we modified the cell EP by changing both membrane currents and calcium handling. At the tissue level, we modeled the increased gap junction lateralization and lower conduction velocity due to downregulation of Connexin 43. At the biventricular level, we reduced the apex-to-base and transmural gradients of action potential duration (APD). The failing cell model was first validated by reproducing the longer action potential, slower and lower calcium transient, and earlier alternans characteristic of heart failure EP. Subsequently, we compared the electrical wave propagation in one dimensional cables of healthy and failing cells. The validated cell model was then used to simulate the EP of heart failure in an anatomically accurate biventricular rabbit model. As pacing cycle length decreases, both the normal and failing heart develop T-wave alternans, but only the failing heart shows QRS alternans (although moderate) at rapid pacing. Moreover, T-wave alternans is significantly more pronounced in the failing heart. At rapid pacing, APD maps show areas of conduction block in the failing heart. Finally, accelerated pacing initiated wave reentry and breakup in the failing heart. Further, the onset of VF was not observed with an upregulation of SERCA, a potential drug therapy, using the same protocol. The changes introduced at the cell and tissue level have increased the failing heart’s susceptibility to dynamic instabilities and arrhythmias under rapid pacing. However, the observed increase in arrhythmogenic potential is not due to a steepening of the restitution curve (not present in our model), but rather to a novel blocking mechanism., Author Summary Ventricular fibrillation (VF) is one of the leading causes of sudden death. During VF, the electrical wave of activation in the heart breaks up chaotically. Consequently, the heart is unable to contract synchronously and pump blood to the rest of the body. In our work we formulate and validate a model of heart failure (HF) that allows us to evaluate the arrhythmogenic potential of individual and combined electrophysiological changes. In diagnostic cardiology, the electrocardiogram (ECG) is one of the most commonly used tools for detecting abnormalities in the heart electrophysiology. One of our goals is to use our numerical model to link changes at the cellular and tissue level in a failing heart to a numerically computed ECG. This allows us to characterize the precursor to and the risk of VF. In order to understand the mechanisms underlying VF in HF, we design a test that simulates a HF patient performing physical exercise. We show that under fast heart rates with changes in pacing, HF patients are more prone to VF due to a new conduction blocking mechanism. In the long term, our mathematical model is suitable for investigating the effect of drug therapies in HF.

Quantitative measurement of the material properties (e.g., stiffness) of biological tissues is poised to become a powerful diagnostic tool. There are currently several methods in the literature to estimating material stiffness and we extend this work by formulating a framework that leads to uniquely identified material properties. We design an approach to work with full field displacement data — i.e., we assume the displacement field due to the applied forces is known both on the boundaries and also within the interior of the body of interest — and seek stiffness parameters that lead to balanced internal and external forces in a model. For in vivo applications, the displacement data can be acquired clinically using magnetic resonance imaging while the forces may be computed from pressure measurements, e.g., through catheterization. We outline a set of conditions under which the least-square force error objective function is convex, yielding uniquely identified material properties. An important component of our framework is a new numerical strategy to formulate polyconvex material energy laws that are linear in the material properties and provide one optimal description of the available experimental data. An outcome of our approach is the analysis of the reliability of the identified material properties, even for material laws that do not admit unique property identification. Lastly, we evaluate our approach using passive myocardium experimental data at the material point and show its application to identifying myocardial stiffness with an in silico experiment modeling the passive filling of the left ventricle.

Local Maximum-Entropy (LME) approximation schemes are meshfree approximation schemes that satisfy consistency conditions of order 1, i.e., they approximate affine functions exactly. In addition, LME approximation schemes converge in the Sobolev space \({W}^{1,p}\), i.e., they are C 0-continuous in the conventional terminology of finite-element interpolation. Here we present a generalization of the Local Max-Ent approximation schemes that are consistent to arbitrary order, i.e., interpolate polynomials of arbitrary degree exactly, and which converge in \({W}^{k,p}\), i.e., they are C k -continuous to arbitrary order k. We refer to these approximation schemes as High Order Local Maximum-Entropy Approximation Schemes (HOLMES). We prove uniform error bounds for the HOLMES approximates and their derivatives up to order k. Moreover, we show that the HOLMES of order k is dense in the Sobolev Space \({W}^{k,p}\), for any \(1 \leq p < \infty \). The good performance of HOLMES relative to other meshfree schemes in selected test cases is also critically appraised.

We present a model to understand quantitatively the role of symmetry breaking in assembly of macromolecular aggregates in general, and the protein shells of viruses in particular. A simple dodecahedral lattice model with a quadrupolar order parameter allows us to demonstrate how symmetry breaking may reduce the probability of assembly errors and, consequently, enhance assembly efficiency. We show that the ground state is characterized by large-scale cooperative zero-energy modes. In analogy with other models, this suggests a general physical principle: the tendency of biological molecules to generate symmetric structures competes with the tendency to break symmetry in order to achieve specific functional goals.

Many viral capsids undergo a series of significant structural changes following assembly, a process known as maturation. The driving mechanisms for maturation usually are chemical reactions taking place inside the proteins that constitute the capsid (“subunits”) that produce structural changes of the subunits. The resulting alterations of the subunits may be directly visible from the capsid structures, as observed by electron microscopy, in the form of a shear shape change and/or a rotation of groups of subunits. The existing thin shell elasticity theory for viral shells does not take account of the internal structure of the subunits and hence cannot describe displacement patterns of the capsid during maturation. Recently, it was proposed for the case of a particular virus (HK97) that thin shell elasticity theory could in fact be generalized to include transformations of the constituent proteins by including such a transformations as a change of the stress-free reference state for the deformation free energy. In this study, we adopt that approach and illustrate its validity in more generality by describing shape changes occurring during maturation across different T-numbers in terms of subunit shearing. Using phase diagrams, we determine the shear directions of the subunits that are most effective to produce capsid shape changes, such as transitions from spherical to facetted capsid shape. We further propose an equivalent stretching mechanism offering a unifying view under which capsid symmetry can be analyzed. We conclude by showing that hexamer shearing not only drives the shape change of the viral capsid during maturation but also is capable of lowering the capsid elastic energy in particular for chiral capsids (e.g., T = 7 ) and give rise to pre-shear patterns. These additional mechanisms may provide a driving force and an organizational principle for virus assembly.