The application of the "inverse problem" method for constructing confining potentials that make N-soliton waveforms exact solutions in the Gross-Pitaevskii equation.

In this work, we discuss an application of the "inverse problem" method to find the external trapping potential, which has particular N trapped soliton-like solutions of the Gross-Pitaevskii equation (GPE) also known as the cubic nonlinear Schrödinger equation (NLSE). This inverse method assumes particular forms for the trapped soliton wave function, which then determines the (unique) external (confining) potential. The latter renders these assumed waveforms exact solutions of the GPE (NLSE) for both attractive (g<0) and repulsive (g>0) self-interactions. For both signs of g, we discuss the stability with respect to self-similar deformations and translations. For g<0, a critical mass Mc or equivalently the number of particles for instabilities to arise can often be found analytically. On the other hand, for the case with g>0 corresponding to repulsive self-interactions which is often discussed in the atomic physics realm of Bose-Einstein condensates, the bound solutions are found to be always stable. For g<0, we also determine the critical mass numerically by using linear stability or Bogoliubov-de Gennes analysis, and compare these results with our analytic estimates. Various analytic forms for the trapped N-soliton solutions in one, two, and three spatial dimensions are discussed, including sums of Gaussians or higher-order eigenfunctions of the harmonic oscillator Hamiltonian.

Uniform-density Bose-Einstein condensates of the Gross-Pitaevskii equation found by solving the inverse problem for the confining potential.

In this work, we study the existence and stability of constant density (flat-top) solutions to the Gross-Pitaevskii equation (GPE) in confining potentials. These are constructed by using the "inverse problem" approach which corresponds to the identification of confining potentials that make flat-top waveforms exact solutions to the GPE. In the one-dimensional case, the exact solution is the sum of stationary kink and antikink solutions, and in the overlapping region, the density is constant. In higher spatial dimensions, the exact solutions are generalizations of this wave function. In the absence of self-interactions, the confining potential is similar to a smoothed-out finite square well with minima also at the edges. When self-interactions are added, terms proportional to ±gψ^{*}ψ and ±gM with M representing the mass or number of particles in Bose-Einstein condensates get added to the confining potential and total energy, respectively. In the realm of stability analysis, we find (linearly) stable solutions in the case with repulsive self-interactions which also are stable to self-similar deformations. For attractive interactions, however, the minima at the edges of the potential get deeper and a barrier in the center forms as we increase the norm. This leads to instabilities at a critical value of M. Comparing the stability criteria from Derrick's theorem with Bogoliubov-de Gennes (BdG) analysis stability results, we find that both predict stability for repulsive self-interactions and instability at a critical mass M for attractive interactions. However, the numerical analysis gives a much lower critical mass. This is due to the emergence of symmetry-breaking instabilities that were detected by the BdG analysis and violate the symmetry x→-x assumed by Derrick's theorem.

Actin's C-terminus coordinates actin structural changes and functions.

Actin is essential to eukaryotic cellular processes. Actin's C-terminus appears to play a direct role in modulating actin's structure and properties, facilitating the binding and function of actin-binding proteins (ABPs). The structural and functional characterization of filamentous actin's C-terminus has been impeded by its inherent flexibility, as well as actin's resistance to crystallization for x-ray diffraction and the historical resolution constraints associated with electron microscopy. Many biochemical studies have established that actin's C-terminus must retain its flexibility and structural integrity to modulate actin's structure and functions. For example, C-terminal structural changes are known to affect nucleotide binding and exchange, as well as propagate actin structural changes throughout extensive allosteric networks, facilitating the binding and function of ABPs. Advances in electron microscopy have resulted in high-resolution structures of filamentous actin, providing insights into subtle structural changes that are mediated by actin's C-terminus. Here, we review existing knowledge establishing the importance of actin's C-terminus within actin structural changes and functions and discuss how modern structural characterization techniques provide the tools to understand the role of actin's C-terminus in cellular processes.

Increasing the calcium sensitivity of muscle using trifluoperazine-induced manipulations in silico, in vitro and in vivo systems.

Many therapeutics for cardiomyopathy treat the symptoms of the disease rather than the underlying mechanism. The mechanism of cardiomyopathy onset is believed to include two means: calcium sensitivity changes and myosin activity alteration. Trifluoperazine is a compound that binds troponin, and other components of the calcium pathway, which impacts calcium regulation of contraction. Here, the ability of TFP to shift calcium sensitivity was examined in vitro with purified proteins and the impact of TFP on heart function was assessed in vivo using embryonic zebrafish. The binding of TFP to troponin was modeled in silico and a model of zebrafish troponin was generated. TFP increased regulated cardiac actomyosin activity in vitro and elevated embryonic zebrafish heart rates at effective drug concentrations. Troponin structural changes predicted in silico suggest altered protein interactions within thin filaments that would affect the regulation of heart function.

The Dark Side of Actin: Cardiac actin variants highlight the role of allostery in disease development.

Mutations in the α-cardiac actin ACTC1 gene cause dilated or hypertrophic cardiomyopathy. These diseases are the result of changes in protein interactions between ACTC protein and force-generating ß-myosin or the calcium-dependent cardiac-tropomyosin (cTm) and cardiac troponin (cTn) regulatory complex, altering the overall contractile force. The T126I and S271F ACTC variants possess amino acid substitutions on the other side of actin relative to the myosin or regulatory protein binding sites on what we call the "dark side" of actin. The T126I change results in hyposensitivity to calcium, in accordance with the calcium sensitivity pathway of cardiomyopathy development while the S271F change alters the maximum in vitro motility sliding speed, reflecting a change in maximum force. These results demonstrate the role of actin allostery in the cardiac disease development.

Assembly and Maintenance of Sarcomere Thin Filaments and Associated Diseases.

Sarcomere assembly and maintenance are essential physiological processes required for cardiac and skeletal muscle function and organism mobility. Over decades of research, components of the sarcomere and factors involved in the formation and maintenance of this contractile unit have been identified. Although we have a general understanding of sarcomere assembly and maintenance, much less is known about the development of the thin filaments and associated factors within the sarcomere. In the last decade, advancements in medical intervention and genome sequencing have uncovered patients with novel mutations in sarcomere thin filaments. Pairing this sequencing with reverse genetics and the ability to generate patient avatars in model organisms has begun to deepen our understanding of sarcomere thin filament development. In this review, we provide a summary of recent findings regarding sarcomere assembly, maintenance, and disease with respect to thin filaments, building on the previous knowledge in the field. We highlight debated and unknown areas within these processes to clearly define open research questions.

Homology-Directed Repair in Zebrafish: Witchcraft and Wizardry?

Introducing desired mutations into the genome of model organisms is a priority for all research focusing on protein function and disease modeling. The need to create stable mutant lines has resulted in the rapid advancement of genetic techniques over the last few decades from chemical mutagenesis and zinc finger nucleases to clustered regularly interspaced short palindromic repeats (CRISPR) and homology-directed repair (HDR). However, achieving consistently high success rates for direct mutagenesis in zebrafish remains one of the most sought-after techniques in the field. Several genes have been modified using HDR in zebrafish, but published success rates range widely, suggesting that an optimal protocol is required. In this review, we compare target genes, techniques, and protocols from 50 genes that were successfully modified in zebrafish using HDR to find the statistically best variables for efficient HDR rates.

M-class hypertrophic cardiomyopathy cardiac actin mutations increase calcium sensitivity of regulated thin filaments.

Hypertrophic cardiomyopathy is a commonly occurring cardiovascular disease resulting primarily from changes in proteins participating in muscle contraction in the heart, including the cardiac actin protein. Changes in cardiac actin located exclusively in the myosin binding site are called M-class variants and include the H88Y, R95C, and E99K substitutions and F90Δ deletion. The prevailing hypothesis for these mutations is that hypertrophic cardiomyopathy is the result of increased calcium sensitivity of contraction in the myocardium. To test this hypothesis, we studied the activity of myosin at varying calcium concentrations in the presence of regulated thin filaments containing M-class cardiac actin variants. We found that all M-class cardiac actin variants exhibit increased calcium sensitivity, with the R95C variant also displaying significant decreases in maximal myosin activity. This work represents the first characterization of all M-class variant proteins and suggests that drugs targeting contraction specifically to treat hypertrophic cardiomyopathy must consider the impact on both calcium sensitivity and maximal myosin activity on overall heart health.

A crosslinked and ribosylated actin trimer does not interact productively with myosin.

A purified F-actin-derived actin trimer that interacts with end-binding proteins did not activate or bind the side-binding protein myosin under rigor conditions. Remodeling of the actin trimer by the binding of gelsolin did not rescue myosin binding, nor did the use of different means of inhibiting the polymerization of the trimer. Our results demonstrate that ADP-ribosylation on all actin subunits of an F-actin-derived trimer inhibits myosin binding and that the binding of DNase-I to the pointed end subunits of a crosslinked trimer also remodels the myosin binding site. Taken together, this work highlights the need for a careful balance between modification of actin subunits and maintaining protein-protein interactions to produce a physiologically relevant short F-actin complex.

PI3Kα-regulated gelsolin activity is a critical determinant of cardiac cytoskeletal remodeling and heart disease.

Biomechanical stress and cytoskeletal remodeling are key determinants of cellular homeostasis and tissue responses to mechanical stimuli and injury. Here we document the increased activity of gelsolin, an actin filament severing and capping protein, in failing human hearts. Deletion of gelsolin prevents biomechanical stress-induced adverse cytoskeletal remodeling and heart failure in mice. We show that phosphatidylinositol (3,4,5)-triphosphate (PIP3) lipid suppresses gelsolin actin-severing and capping activities. Accordingly, loss of PI3Kα, the key PIP3-producing enzyme in the heart, increases gelsolin-mediated actin-severing activities in the myocardium in vivo, resulting in dilated cardiomyopathy in response to pressure-overload. Mechanical stretching of adult PI3Kα-deficient cardiomyocytes disrupts the actin cytoskeleton, which is prevented by reconstituting cells with PIP3. The actin severing and capping activities of recombinant gelsolin are effectively suppressed by PIP3. Our data identify the role of gelsolin-driven cytoskeletal remodeling in heart failure in which PI3Kα/PIP3 act as negative regulators of gelsolin activity.

Identification of the actc1c cardiac actin gene in zebrafish.

Zebrafish is rapidly becoming a key model organism for studying a variety of biological processes from molecules to organisms. Interactions involving actin, a contractile protein and part of the cytoskeleton, are regulated by actin binding proteins in the majority of physiological processes in eukaryotic cells. To understand the contribution of actin proteins to the physiological processes of zebrafish, it is important to identify the diverse isoforms of actin encoded by its genome; however, significant sequence identity complicates isoform assignments. Through a combination of human-directed sequence and functional analysis, we have assigned and performed localization of actc1c, a previously undesignated cardiac actin gene, and propose an updated assignment of α-actin protein isoform identities in zebrafish.

Classifying Cardiac Actin Mutations Associated With Hypertrophic Cardiomyopathy.

Mutations in the cardiac actin gene (ACTC1) are associated with the development of hypertrophic cardiomyopathy (HCM). To date, 12 different ACTC1 mutations have been discovered in patients with HCM. Given the high degree of sequence conservation of actin proteins and the range of protein-protein interactions actin participates in, mutations in cardiac actin leading to HCM are particularly interesting. Here, we suggest the classification of ACTC1 mutations based on the location of the resulting amino acid change in actin into three main groups: (1) those affecting only the binding site of the myosin molecular motor, termed M-class mutations, (2) those affecting only the binding site of the tropomyosin (Tm) regulatory protein, designated T-class mutations, and (3) those affecting both the myosin- and Tm-binding sites, called MT-class mutations. To understand the precise pathogenesis of cardiac actin mutations and develop treatments specific to the molecular cause of disease, we need to integrate rapidly growing structural information with studies of regulated actomyosin systems.

Cardiac actin changes in the actomyosin interface have different effects on myosin duty ratio.

Hypertrophic cardiomyopathy (HCM) is an inherited cardiovascular disease (CD) that commonly causes an increased size of cardiomyocytes in the left ventricle. The proteins myosin and actin interact in the myocardium to produce contraction through the actomyosin ATPase cycle. The duty ratio (r) of myosin is the proportion of the actomyosin ATPase cycle that myosin is bound to actin and does work. A common hypothesis is that HCM mutations increase contraction in cardiac sarcomeres; however, the available data are not clear on this connection. Based on previous work with human α-cardiac actin (ACTC), we hypothesize that HCM-linked ACTC variants with alterations near the myosin binding site have an increased r, producing more force. Myosin duty ratios using human ACTC variant proteins were calculated with myosin ATPase activity and in-vitro motility data. We found no consistent changes in the duty ratio of the ACTC variants, suggesting that other factors are involved in the development of HCM when ACTC variants are present.

Do cardiac actin mutations lead to altered actomyosin interactions?

It is currently hypothesized that increased heart muscle contractility leads to hypertrophic cardiomyopathy (HCM), and reduced contractility leads to dilated cardiomyopathy (DCM). To determine if changes in the core interaction between actin and myosin occur due to mutations in the cardiac actin gene (ACTC), we measured the interactions between myosin and 8 ACTC mutant proteins found in patients with HCM or DCM. R312H showed a decreased actin-activated myosin S1 ATPase rate (13.1 ± 0.63 µmol/L/min) compared to WT (15.3 ± 1.6 µmol/L/min), whereas the rate with E99K was significantly higher (20.1 ± 1.5 µmol/L/min). In vitro motility assays with varying ATP concentrations showed that the KM for E99K remains unchanged with a significantly decreased Vmax (1.90 ± 0.37 µm/sec) compared to WT (3.33 ± 0.46 µm/sec). Based on a 5 nm myosin step size, we calculated a duty ratio of approximately 0.04 for WT and the majority of mutant actins; however, the duty ratio for E99K was twice as high. Based on our analysis of 8 ACTC mutants, we infer that mutations in ACTC lead to disease through various molecular mechanisms. While changes in actomyosin interactions with the E99K mutation might cause increased ATP usage and tension leading to HCM, measurable changes in the basic interaction between actin and myosin do not appear to be involved in the mechanisms of disease development for the other ACTC mutants tested.

The immediate effect of HCM causing actin mutants E99K and A230V on actin-Tm-myosin interaction in thin-filament reconstituted myocardium.

Human cardiac actin mutants E99K and A230V were expressed with baculovirus/insect cells and used to reconstitute the thin-filament of bovine cardiac (BVC) muscle fibers, together with tropomyosin (Tm) and troponin (Tn) purified from bovine ventricles. Effects of [Ca(2+)], [ATP], and [phosphate] on tension and its transients were studied at 25°C. In the absence of Tm/Tn, both mutants significantly decreased the tension of actin filament reconstituted fibers (WT: 0.75±0.06 T0, E99K: 0.58±0.04 T0, A230V: 0.58±0.03 T0), where T0 is active tension of native fibers (T0=26.9±1.1kPa, N=41), indicating diminished actin-myosin interactions. However, in the presence of Tm and Tn, WT, E99K, and A230V recovered tension (0.85±0.06 T0, 0.89±0.06 T0, and 0.85±0.05 T0, respectively), demonstrating the compensatory effect of Tm/Tn. Ca(2+) sensitivity (pCa50) increased (5.59±0.02, 5.80±0.03, 5.77±0.03, respectively) and cooperativity (nH) decreased (2.6±0.3, 1.87±0.21, 1.60±0.11, respectively). The kinetic constants of the cross-bridge cycle were deduced using sinusoidal analysis. E99K did not show any significant changes in any of the kinetic constants compared to those of WT. A230V caused a decrease in K1 (ATP association constant), k2 and k-2 (rate constants of the cross-bridge detachment step). The cross-bridge distribution was similar among WT, E99K, and A230V. In conclusion, our experiments demonstrate that the first step of HCM pathogenesis with E99K is increased pCa50 and decreased nH, which result in larger tension during partial activation to cause a diastolic problem. The effect on nH is more severe with A230V. In addition, A230V has a problem of decreased cross-bridge kinetics, which affects the normal functions of the cross-bridge cycle and may contribute to the first step of the HCM pathogenesis.

Using baculovirus/insect cell expressed recombinant actin to study the molecular pathogenesis of HCM caused by actin mutation A331P.

Recombinant WT human cardiac actin (WT actin) was expressed using the baculovirus/insect cell expression system, purified, and used to reconstitute the thin-filament of bovine cardiac muscle fibers, together with bovine cardiac tropomyosin (Tm) and troponin (Tn). Effects of [Ca(2+)], [ATP], [phosphate] and [ADP] on tension and tension transients were studied at 25°C by using sinusoidal analysis, and the results were compared with those of native fibers and fibers reconstituted with purified bovine cardiac actin (BVC actin). In actin filament reconstituted fibers (without Tm/Tn), those reconstituted with WT actin showed exactly the same active tension as those reconstituted with purified BVC actin (WT: 0.75±0.06 T0, N=11; BVC: 0.73±0.07 T0, N=12, where T0 is the tension of original fibers before extraction). After Tm/Tn reconstitution, fibers reconstituted with WT actin generated 0.85±0.06 T0 (N=11) compared to 0.98±0.04 T0 (N=12) recovered by those reconstituted with BVC actin. In the presence of Tm/Tn, WT actin reconstituted fibers showed exactly the same Ca(2+) sensitivity as those of the native fibers and BVC actin reconstituted fibers (pCa50: native fibers: 5.69±0.01, N=10; WT: 5.69±0.02, N=11; BVC: 5.68±0.02, N=12). Sinusoidal analysis showed that the cross-bridge kinetics were the same among native fibers, BVC actin reconstituted fibers and WT actin reconstituted fibers, followed by reconstitution of Tm/Tn. These results demonstrate that baculovirus/insect cell expressed actin has no significant differences from tissue purified actin and can be used for thin-filament reconstitution assays. One hypertrophic cardiomyopathy (HCM) causing actin mutant A331P actin was also expressed and studied similarly, and the results were compared to those of the WT actin. In the reconstituted fibers, A331P significantly decreased the tension both in the absence of Tm/Tn (0.55±0.03 T0, N=13) and in their presence (0.65±0.02 T0, N=13) compared to those of the WT (0.75±0.06 T0 and 0.85±0.06 T0, respectively, N=11). A331P also showed decreased pCa50 (5.57±0.03, N=13) compared to that of WT (5.69±0.02, N=11). The cross-bridge kinetics and its distribution were similar between WT and A331P actin reconstituted fibers, indicating that force/cross-bridge was decreased by A331P. In conclusion, A331P causes a weakened cross-bridge force, which leads to a decreased active tension, reduces left-ventricular ejection fraction, and eventually results in the HCM phenotype.

Altered interactions between cardiac myosin binding protein-C and α-cardiac actin variants associated with cardiomyopathies.

The two genes most commonly associated with mutations linked to hypertrophic or dilated cardiomyopathies are ß-myosin and cardiac myosin binding protein-C (cMyBP-C). Both of these proteins interact with cardiac actin (ACTC). Currently there are 16 ACTC variants that have been found in patients with HCM or DCM. While some of these ACTC variants exhibit protein instability or polymerization-deficiencies that might contribute to the development of disease, other changes could cause changes in protein-protein interactions between sarcomere proteins and ACTC. To test the hypothesis that changes in ACTC disrupt interactions with cMyBP-C, we examined the interactions between seven ACTC variants and the N-terminal C0C2 fragment of cMyBP-C. We found there was a significant decrease in binding affinity (increase in Kd values) for the A331P and Y166C variants of ACTC. These results suggest that a change in the ability of cMyBP-C to bind actin filaments containing these ACTC protein variants might contribute to the development of disease. These results also provide clues regarding the binding site of the C0C2 fragment of cMyBP-C on F-actin.

Subdomain location of mutations in cardiac actin correlate with type of functional change.

Determining the molecular mechanisms that lead to the development of heart failure will help us gain better insight into the most costly health problem in the Western world. To understand the roles that the actin protein plays in the development of heart failure, we have taken a systematic approach toward characterizing human cardiac actin mutants that have been associated with either hypertrophic or dilated cardiomyopathy. Seven known cardiac actin mutants were expressed in a baculovirus system, and their intrinsic properties were studied. In general, the changes to the properties of the actin proteins themselves were subtle. The R312H variant exhibited reduced stability, with a T(m) of 53.6 °C compared to 56.8 °C for WT actin, accompanied with increased polymerization critical concentration and Pi release rate, and a marked increase in nucleotide release rates. Substitution of methionine for leucine at amino acid 305 showed no impact on the stability, nucleotide release rates, or DNase-I inhibition ability of the actin monomer; however, during polymerization, a 2-fold increase in Pi release was observed. Increases to both the T(m) and DNase-I inhibition activity suggested interactions between E99K actin molecules under monomer-promoting conditions. Y166C actin had a higher critical concentration resulting in a lower Pi release rate due to reduced filament-forming potential. The locations of mutations on the ACTC protein correlated with the molecular effects; in general, mutations in subdomain 3 affected the stability of the ACTC protein or affect the polymerization of actin filaments, while mutations in subdomains 1 and 4 more likely affect protein-protein interactions.

Flightless I is a focal adhesion-associated actin-capping protein that regulates cell migration.

The role of adhesion-associated actin-binding proteins in cell migration is not well defined. In mouse fibroblasts we screened for focal adhesion-associated proteins that were isolated with collagen-coated beads and detected by tandem mass spectrometry. We identified flightless I (FliI) as an actin-binding protein in focal adhesion fractions, which was verified by immunoblotting. By confocal microscopy most FliI was distributed throughout the cytosol and in focal adhesions. By sedimentation assays and in vitro binding assays, we found that FliI associates with actin filaments and actin monomers. Assays using purified proteins showed that FliI inhibits actin polymerization and caps but does not sever actin filaments. Cells with FliI knockdown or cells overexpressing FliI migrated more or less rapidly, respectively, than wild-type controls. Compared with controls, cells with FliI knockdown were less adherent than wild-type cells, exhibited reduced numbers of focal adhesions containing activated ß1 integrins and vinculin, and exhibited increased incorporation of actin monomers into nascent filaments at focal adhesions. These data indicate that FliI regulates cell migration through its localization to focal adhesions and its ability to cap actin filaments, which collectively affect focal adhesion maturation.

Evaluation of 10 genes encoding cardiac proteins in Doberman Pinschers with dilated cardiomyopathy.

OBJECTIVE: To identify a causative mutation for dilated cardiomyopathy (DCM) in Doberman Pinschers by sequencing the coding regions of 10 cardiac genes known to be associated with familial DCM in humans. ANIMALS: 5 Doberman Pinschers with DCM and congestive heart failure and 5 control mixed-breed dogs that were euthanized or died. PROCEDURES: RNA was extracted from frozen ventricular myocardial samples from each dog, and first-strand cDNA was synthesized via reverse transcription, followed by PCR amplification with gene-specific primers. Ten cardiac genes were analyzed: cardiac actin, α-actinin, α-tropomyosin, ß-myosin heavy chain, metavinculin, muscle LIM protein, myosinbinding protein C, tafazzin, titin-cap (telethonin), and troponin T. Sequences for DCM-affected and control dogs and the published canine genome were compared. RESULTS: None of the coding sequences yielded a common causative mutation among all Doberman Pinscher samples. However, 3 variants were identified in the α-actinin gene in the DCM-affected Doberman Pinschers. One of these variants, identified in 2 of the 5 Doberman Pinschers, resulted in an amino acid change in the rod-forming triple coiled-coil domain. CONCLUSIONS AND CLINICAL RELEVANCE: Mutations in the coding regions of several genes associated with DCM in humans did not appear to consistently account for DCM in Doberman Pinschers. However, an α-actinin variant was detected in some Doberman Pinschers that may contribute to the development of DCM given its potential effect on the structure of this protein. Investigation of additional candidate gene coding and noncoding regions and further evaluation of the role of α-actinin in development of DCM in Doberman Pinschers are warranted.