Hierarchical structure formation by crystal growth-front instabilities during ice templating.

Directional solidification of aqueous solutions and slurries in a temperature gradient is widely used to produce cellular materials through a phase separation of solutes or suspended particles between growing ice lamellae. While this process has analogies to the directional solidification of metallurgical alloys, it forms very different hierarchical structures. The resulting honeycomb-like porosity of freeze-cast materials consists of regularly spaced, lamellar cell walls which frequently exhibit unilateral surface features of morphological complexity reminiscent of living forms, all of which are unknown in metallurgical structures. While the strong anisotropy of ice-crystal growth has been hypothesized to play a role in shaping those structures, the mechanism by which they form has remained elusive. By directionally freezing binary water mixtures containing small solutes obeying Fickian diffusion, and phase-field modeling of those experiments, we reveal how those structures form. We show that the flat side of lamellae forms because of slow faceted ice-crystal growth along the c-axis, while weakly anisotropic fast growth in other directions, including the basal plane, is responsible for the unilateral features. Diffusion-controlled morphological primary instabilities on the solid-liquid interface form a cellular structure on the atomically rough side of the lamellae, which template regularly spaced "ridges" while secondary instabilities of this structure are responsible for the more complex features. Collating the results, we obtain a scaling law for the lamellar spacing,  [Formula: see text] , where [Formula: see text] and [Formula: see text] are the local growth rate and temperature gradient, respectively.

E3 ubiquitin ligase rififylin has yin and yang effects on rabbit cardiac transient outward potassium currents (Ito) and corresponding channel proteins.

Genome-wide association studies have reported a correlation between a SNP of the RING finger E3 ubiquitin protein ligase rififylin (RFFL) and QT interval variability in humans (Newton-Cheh et al., 2009). Previously, we have shown that RFFL downregulates expression and function of the human-like ether-a-go-go-related gene potassium channel and corresponding rapidly activating delayed rectifier potassium current (IKr) in adult rabbit ventricular cardiomyocytes. Here, we report that RFFL also affects the transient outward current (Ito), but in a peculiar way. RFFL overexpression in adult rabbit ventricular cardiomyocytes significantly decreases the contribution of its fast component (Ito,f) from 35% to 21% and increases the contribution of its slow component (Ito,s) from 65% to 79%. Since Ito,f in rabbits is mainly conducted by Kv4.3, we investigated the effect of RFFL on Kv4.3 expressed in HEK293A cells. We found that RFFL overexpression reduced Kv4.3 expression and corresponding Ito,f in a RING domain-dependent manner in the presence or absence of its accessory subunit Kv channel-interacting protein 2. On the other hand, RFFL overexpression in Kv1.4-expressing HEK cells leads to an increase in both Kv1.4 expression level and Ito,s, similarly in a RING domain-dependent manner. Our physiologically detailed rabbit ventricular myocyte computational model shows that these yin and yang effects of RFFL overexpression on Ito,f, and Ito,s affect phase 1 of the action potential waveform and slightly decrease its duration in addition to suppressing IKr. Thus, RFFL modifies cardiac repolarization reserve via ubiquitination of multiple proteins that differently affect various potassium channels and cardiac action potential duration.

Microstructural Pattern Formation during Far-from-Equilibrium Alloy Solidification.

We introduce a new phase-field formulation of rapid alloy solidification that quantitatively incorporates nonequilibrium effects at the solid-liquid interface over a very wide range of interface velocities. Simulations identify a new dynamical instability of dendrite tip growth driven by solute trapping at velocities approaching the absolute stability limit. They also reproduce the formation of the widely observed banded microstructures, revealing how this instability triggers transitions between dendritic and microsegregation-free solidification. Predicted band spacings agree quantitatively with observations in rapidly solidified Al-Cu thin films.

Ephaptic Coupling as a Resolution to the Paradox of Action Potential Wave Speed and Discordant Alternans Spatial Scales in the Heart.

Previous computer simulations have suggested that existing models of action potential wave propagation in the heart are not consistent with observed wave propagation behavior. Specifically, computer models cannot simultaneously reproduce the rapid wave speeds and small spatial scales of discordant alternans patterns measured experimentally in the same simulation. The discrepancy is important, because discordant alternans can be a key precursor to the development of abnormal and dangerous rapid rhythms in the heart. In this Letter, we show that this paradox can be resolved by allowing so-called ephaptic coupling to play a primary role in wave front propagation in place of conventional gap-junction coupling. With this modification, physiological wave speeds and small discordant alternans spatial scales both occur with gap-junction resistance values that are more in line with those observed in experiments. Our theory thus also provides support to the hypothesis that ephaptic coupling plays an important role in normal wave propagation.

The endosomal trafficking regulator LITAF controls the cardiac Nav1.5 channel via the ubiquitin ligase NEDD4-2.

The QT interval is a recording of cardiac electrical activity. Previous genome-wide association studies identified genetic variants that modify the QT interval upstream of LITAF (lipopolysaccharide-induced tumor necrosis factor-α factor), a protein encoding a regulator of endosomal trafficking. However, it was not clear how LITAF might impact cardiac excitation. We investigated the effect of LITAF on the voltage-gated sodium channel Nav1.5, which is critical for cardiac depolarization. We show that overexpressed LITAF resulted in a significant increase in the density of Nav1.5-generated voltage-gated sodium current INa and Nav1.5 surface protein levels in rabbit cardiomyocytes and in HEK cells stably expressing Nav1.5. Proximity ligation assays showed co-localization of endogenous LITAF and Nav1.5 in cardiomyocytes, whereas co-immunoprecipitations confirmed they are in the same complex when overexpressed in HEK cells. In vitro data suggest that LITAF interacts with the ubiquitin ligase NEDD4-2, a regulator of Nav1.5. LITAF overexpression down-regulated NEDD4-2 in cardiomyocytes and HEK cells. In HEK cells, LITAF increased ubiquitination and proteasomal degradation of co-expressed NEDD4-2 and significantly blunted the negative effect of NEDD4-2 on INa We conclude that LITAF controls cardiac excitability by promoting degradation of NEDD4-2, which is essential for removal of surface Nav1.5. LITAF-knockout zebrafish showed increased variation in and a nonsignificant 15% prolongation of action potential duration. Computer simulations using a rabbit-cardiomyocyte model demonstrated that changes in Ca2+ and Na+ homeostasis are responsible for the surprisingly modest action potential duration shortening. These computational data thus corroborate findings from several genome-wide association studies that associated LITAF with QT interval variation.

Stochastic initiation and termination of calcium-mediated triggered activity in cardiac myocytes.

Cardiac myocytes normally initiate action potentials in response to a current stimulus that depolarizes the membrane above an excitation threshold. Aberrant excitation can also occur due to spontaneous calcium (Ca2+) release (SCR) from intracellular stores after the end of a preceding action potential. SCR drives the Na+/Ca2+ exchange current inducing a "delayed afterdepolarization" that can in turn trigger an action potential if the excitation threshold is reached. This "triggered activity" is known to cause arrhythmias, but how it is initiated and terminated is not understood. Using computer simulations of a ventricular myocyte model, we show that initiation and termination are inherently random events. We determine the probability of those events from statistical measurements of the number of beats before initiation and before termination, respectively, which follow geometric distributions. Moreover, we elucidate the origin of randomness by a statistical analysis of SCR events, which do not follow a Poisson process observed in other eukaryotic cells. Due to synchronization of Ca2+ releases during the action potential upstroke, waiting times of SCR events after the upstroke are narrowly distributed, whereas SCR amplitudes follow a broad normal distribution with a width determined by fluctuations in the number of independent Ca2+ wave foci. This distribution enables us to compute the probabilities of initiation and termination of bursts of triggered activity that are maintained by a positive feedback between the action potential upstroke and SCR. Our results establish a theoretical framework for interpreting complex and varied manifestations of triggered activity relevant to cardiac arrhythmias.

NCX-Mediated Subcellular Ca2+ Dynamics Underlying Early Afterdepolarizations in LQT2 Cardiomyocytes.

Long QT syndrome type 2 (LQT2) is a congenital disease characterized by loss of function mutations in hERG potassium channels (IKr). LQT2 is associated with fatal ventricular arrhythmias promoted by triggered activity in the form of early afterdepolarizations (EADs). We previously demonstrated that intracellular Ca2+ handling is remodeled in LQT2 myocytes. Remodeling leads to aberrant late RyR-mediated Ca2+ releases that drive forward-mode Na+-Ca2+ exchanger (NCX) current and slow repolarization to promote reopening of L-type calcium channels and EADs. Forward-mode NCX was found to be enhanced despite the fact that these late releases do not significantly alter the whole-cell cytosolic calcium concentration during a vulnerable period of phase 2 of the action potential corresponding to the onset of EADs. Here, we use a multiscale ventricular myocyte model to explain this finding. We show that because the local NCX current is a saturating nonlinear function of the local submembrane calcium concentration, a larger number of smaller-amplitude discrete Ca2+ release events can produce a large increase in whole-cell forward-mode NCX current without increasing significantly the whole-cell cytosolic calcium concentration. Furthermore, we develop novel insights, to our knowledge, into how alterations of stochastic RyR activity at the single-channel level cause late aberrant Ca2+ release events. Experimental measurements in transgenic LTQ2 rabbits confirm the critical arrhythmogenic role of NCX and identify this current as a potential target for antiarrhythmic therapies in LQT2.

Universality and Stability Phase Diagram of Two-Dimensional Brittle Fracture.

The two-dimensional oscillatory crack instability, experimentally observed in a class of brittle materials under strongly dynamic conditions, has been recently reproduced by a nonlinear phase-field fracture theory. Here, we highlight the universal character of this instability by showing that it is present in materials exhibiting widely different near crack tip elastic nonlinearity, and by demonstrating that the oscillations wavelength follows a universal master curve in terms of dissipation-related and nonlinear elastic intrinsic length scales. Moreover, we show that upon increasing the driving force for fracture, a high-velocity tip-splitting instability emerges, as experimentally demonstrated. The analysis culminates in a comprehensive stability phase diagram of two-dimensional brittle fracture, whose salient properties and topology are independent of the form of near tip nonlinearity.

Long-Lasting Sparks: Multi-Metastability and Release Competition in the Calcium Release Unit Network.

Calcium (Ca) sparks are elementary events of biological Ca signaling. A normal Ca spark has a brief duration in the range of 10 to 100 ms, but long-lasting sparks with durations of several hundred milliseconds to seconds are also widely observed. Experiments have shown that the transition from normal to long-lasting sparks can occur when ryanodine receptor (RyR) open probability is either increased or decreased. Here, we demonstrate theoretically and computationally that long-lasting sparks emerge as a collective dynamical behavior of the network of diffusively coupled Ca release units (CRUs). We show that normal sparks occur when the CRU network is monostable and excitable, while long-lasting sparks occur when the network dynamics possesses multiple metastable attractors, each attractor corresponding to a different spatial firing pattern of sparks. We further highlight the mechanisms and conditions that produce long-lasting sparks, demonstrating the existence of an optimal range of RyR open probability favoring long-lasting sparks. We find that when CRU firings are sparse and sarcoplasmic reticulum (SR) Ca load is high, increasing RyR open probability promotes long-lasting sparks by potentiating Ca-induced Ca release (CICR). In contrast, when CICR is already strong enough to produce frequent firings, decreasing RyR open probability counter-intuitively promotes long-lasting sparks by decreasing spark frequency. The decrease in spark frequency promotes intra-SR Ca diffusion from neighboring non-firing CRUs to the firing CRUs, which helps to maintain the local SR Ca concentration of the firing CRUs above a critical level to sustain firing. In this setting, decreasing RyR open probability further suppresses long-lasting sparks by weakening CICR. Since a long-lasting spark terminates via the Kramers' escape process over a potential barrier, its duration exhibits an exponential distribution determined by the barrier height and noise strength, which is modulated differently by different ways of altering the Ca release flux strength.

Hyperphosphorylation of RyRs underlies triggered activity in transgenic rabbit model of LQT2 syndrome.

RATIONALE: Loss-of-function mutations in human ether go-go (HERG) potassium channels underlie long QT syndrome type 2 (LQT2) and are associated with fatal ventricular tachyarrhythmia. Previously, most studies focused on plasma membrane-related pathways involved in arrhythmogenesis in long QT syndrome, whereas proarrhythmic changes in intracellular Ca(2+) handling remained unexplored. OBJECTIVE: We investigated the remodeling of Ca(2+) homeostasis in ventricular cardiomyocytes derived from transgenic rabbit model of LQT2 to determine whether these changes contribute to triggered activity in the form of early after depolarizations (EADs). METHODS AND RESULTS: Confocal Ca(2+) imaging revealed decrease in amplitude of Ca(2+) transients and sarcoplasmic reticulum Ca(2+) content in LQT2 myocytes. Experiments using sarcoplasmic reticulum-entrapped Ca(2+) indicator demonstrated enhanced ryanodine receptor (RyR)-mediated sarcoplasmic reticulum Ca(2+) leak in LQT2 cells. Western blot analyses showed increased phosphorylation of RyR in LQT2 myocytes versus controls. Coimmunoprecipitation experiments demonstrated loss of protein phosphatases type 1 and type 2 from the RyR complex. Stimulation of LQT2 cells with ß-adrenergic agonist isoproterenol resulted in prolongation of the plateau of action potentials accompanied by aberrant Ca(2+) releases and EADs, which were abolished by inhibition of Ca(2+)/calmodulin-dependent protein kinase type 2. Computer simulations showed that late aberrant Ca(2+) releases caused by RyR hyperactivity promote EADs and underlie the enhanced triggered activity through increased forward mode of Na(+)/Ca(2+) exchanger type 1. CONCLUSIONS: Hyperactive, hyperphosphorylated RyRs because of reduced local phosphatase activity enhance triggered activity in LQT2 syndrome. EADs are promoted by aberrant RyR-mediated Ca(2+) releases that are present despite a reduction of sarcoplasmic reticulum content. Those releases increase forward mode Na(+)/Ca(2+) exchanger type 1, thereby slowing repolarization and enabling L-type Ca(2+) current reactivation.

Helical crack-front instability in mixed-mode fracture.

Planar crack propagation under pure tension loading (mode I) is generally stable. However, it becomes universally unstable with the superposition of a shear stress parallel to the crack front (mode III). Under this mixed-mode (I + III) loading configuration, an initially flat parent crack segments into an array of daughter cracks that rotate towards a direction of maximum tensile stress. This segmentation produces stepped fracture surfaces with characteristic 'lance-shaped' markings observed in a wide range of engineering and geological materials. The origin of this instability remains poorly understood and a theory with which to predict the surface roughness scale is lacking. Here we perform large-scale simulations of mixed-mode I + III brittle fracture using a continuum phase-field method that describes the complete three-dimensional crack-front evolution. The simulations reveal that planar crack propagation is linearly unstable against helical deformations of the crack front, which evolve nonlinearly into a segmented array of finger-shaped daughter cracks. Furthermore, during their evolution, facets gradually coarsen owing to the growth competition of daughter cracks in striking analogy with the coarsening of finger patterns observed in nonequilibrium growth phenomena. We show that the dynamically preferred unstable wavelength is governed by the balance of the destabilizing effect of far-field stresses and the stabilizing effect of cohesive forces on the process zone scale, and we derive a theoretical estimate for this scale using a new propagation law for curved cracks in three dimensions. The rotation angles of coarsened facets are also compared to theoretical predictions and available experimental data.

Morphological instability of grain boundaries in two-phase coherent solids.

We show both computationally and analytically that grain boundaries that exhibit shear-coupled motion become morphologically unstable in solid alloys that phase separate into coherent domains of distinct chemical compositions. We carry out simulations of continuum models demonstrating that this instability is mediated by long-range elastic interaction between compositional domains and grain boundaries. In addition, we perform a linear stability analysis that predicts the range of unstable wavelengths in good quantitative agreement with simulations. In nonlinear stages, this pattern-forming instability leads to the breakup of low-angle grain boundaries, thereby strongly impacting microstructural evolution in a wide range of phase-separating materials.

Crack Front Segmentation and Facet Coarsening in Mixed-Mode Fracture.

A planar crack generically segments into an array of "daughter cracks" shaped as tilted facets when loaded with both a tensile stress normal to the crack plane (mode I) and a shear stress parallel to the crack front (mode III). We investigate facet propagation and coarsening using in situ microscopy observations of fracture surfaces at different stages of quasistatic mixed-mode crack propagation and phase-field simulations. The results demonstrate that the bifurcation from propagating a planar to segmented crack front is strongly subcritical, reconciling previous theoretical predictions of linear stability analysis with experimental observations. They further show that facet coarsening is a self-similar process driven by a spatial period-doubling instability of facet arrays.

"Good enough solutions" and the genetics of complex diseases.

In this Emerging Science Review, we discuss a systems genetics strategy, which we call gene module association study (GMAS), as a novel approach complementing genome-wide association studies (GWAS), to understand complex diseases by focusing on how genes work together in groups rather than singly. The first step is to characterize phenotypic differences among a genetically diverse population. The second step is to use gene expression microarray (or other high-throughput) data from the population to construct gene coexpression networks. Coexpression analysis typically groups 20 000 genes into 20 to 30 modules containing tens to hundreds of genes, whose aggregate behavior can be represented by the module's "eigengene." The third step is to correlate expression patterns with phenotype, as in GWAS, only applied to eigengenes instead of single nucleotide polymorphisms. The goal of the GMAS approach is to identify groups of coregulated genes that explain complex traits from a systems perspective. From an evolutionary standpoint, we hypothesize that variability in eigengene patterns reflects the "good enough solution" concept, that biological systems are sufficiently complex so that many possible combinations of the same elements (in this case eigengenes) can produce an equivalent output, that is, a "good enough solution" to accomplish normal biological functions. However, when faced with environmental stresses, some "good enough solutions" adapt better than others, explaining individual variability to disease and drug susceptibility. If validated, GMAS may imply that common polygenic diseases are related as much to group interactions between normal genes, as to multiple gene mutations.

Unified theoretical framework for polycrystalline pattern evolution.

The rate of curvature-driven grain growth in polycrystalline materials is well known to be limited by interface dissipation. We show analytically and by simulations that, for systems forming modulated phases or nonequilibrium patterns with crystal ordering, growth is limited by bulk dissipation associated with lattice translation, which dramatically slows down grain coarsening. We also show that bulk dissipation is reduced by thermal noise and that this reduction leads to faster coarsening behavior dominated by interface dissipation for a high Peierls-Nabarro barrier to dislocation motion and high noise. Those results provide a unified theoretical framework for understanding and modeling polycrystalline pattern evolution in diverse systems over a broad range of length and time scales.

Scaling laws for two-dimensional dendritic crystal growth in a narrow channel.

We investigate analytically and computationally the dynamics of two-dimensional needle crystal growth from the melt in a narrow channel. Our analytical theory predicts that, in the low supersaturation limit, the growth velocity V decreases in time t as a power law V∼t^{-2/3}, which we validate by phase-field and dendritic-needle-network simulations. Simulations further reveal that, above a critical channel width Λ≈5l_{D}, where l_{D} is the diffusion length, needle crystals grow with a constant V

Role of ephaptic coupling in discordant alternans domain sizes and action potential propagation in the heart.

Discordant alternans, the spatially out-of-phase alternation of the durations of propagating action potentials in the heart, has been linked to the onset of fibrillation, a major cardiac rhythm disorder. The sizes of the regions, or domains, within which these alternations are synchronized are critical in this link. However, computer models employing standard gap junction-based coupling between cells have been unable to reproduce simultaneously the small domain sizes and rapid action potential propagation speeds seen in experiments. Here we use computational methods to show that rapid wave speeds and small domain sizes are possible when a more detailed model of intercellular coupling that accounts for so-called ephaptic effects is used. We provide evidence that the smaller domain sizes are possible, because different coupling strengths can exist on the wavefronts, for which both ephaptic and gap-junction coupling are involved, in contrast to the wavebacks, where only gap-junction coupling plays an active role. The differences in coupling strength are due to the high density of fast-inward (sodium) channels known to localize on the ends of cardiac cells, which are only active (and thus engage ephaptic coupling) during wavefront propagation. Thus, our results suggest that this distribution of fast-inward channels, as well as other factors responsible for the critical involvement of ephaptic coupling in wave propagation, including intercellular cleft spacing, play important roles in increasing the vulnerability of the heart to life-threatening tachyarrhythmias. Our results, combined with the absence of short-wavelength discordant alternans domains in standard gap-junction-dominated coupling models, also provide evidence that both gap-junction and ephaptic coupling are critical in wavefront propagation and waveback dynamics.

Cell invasion during competitive growth of polycrystalline solidification patterns.

Spatially extended cellular and dendritic array structures forming during solidification processes such as casting, welding, or additive manufacturing are generally polycrystalline. Both the array structure within each grain and the larger scale grain structure determine the performance of many structural alloys. How those two structures coevolve during solidification remains poorly understood. By in situ observations of microgravity alloy solidification experiments onboard the International Space Station, we have discovered that individual cells from one grain can unexpectedly invade a nearby grain of different misorientation, either as a solitary cell or as rows of cells. This invasion process causes grains to interpenetrate each other and hence grain boundaries to adopt highly convoluted shapes. Those observations are reproduced by phase-field simulations further demonstrating that invasion occurs for a wide range of misorientations. Those results fundamentally change the traditional conceptualization of grains as distinct regions embedded in three-dimensional space.

Surface modes of coherent spinodal decomposition.

We use linear stability theory and numerical simulations to show that spontaneous phase separation in elastically coherent solids is fundamentally altered by the presence of free surfaces. Because of misfit stress relaxation near surfaces, phase separation is mediated by unique surface modes of spinodal decomposition that have faster kinetics than bulk modes and are unstable even when spinodal decomposition is suppressed in the bulk. Consequently, in the presence of free surfaces, the limit of metastability of supersaturated solid solutions of crystalline materials is shifted from the coherent to chemical spinodal.