Deformed Nuclei Research Articles

Microtubule-induced restriction of nuclear deformability in hypertrophic cardiomyopathy

Abstract Funding Acknowledgements Type of funding sources: Foundation. Main funding source(s): Leducq foundation Background Hypertrophic cardiomyopathy (HCM) is characterized by abnormal thickening of the left ventricular (LV) wall in conjunction with diastolic dysfunction with a prevalence of ~1:200. HCM pathophysiology is incompletely understood. We hypothesized that misregulated mechanotransduction plays an important role in the disease process. Extensive cytoskeletal remodeling has been observed in HCM patients, with a robust increase in tubulin and desmin levels, with a concomitant increase in stabilizing post-translational modifications, which we previously showed contributes to diastolic dysfunction. Microtubules are connected to the nucleus by the LINC complex. Little is known about the interaction of the non-sarcomeric cytoskeleton with the nucleus and the role this may have in the development of HCM. Purpose Relate cytoskeleton changes to nuclear and chromatin morphology in HCM patient myocardium and assess nuclear deformability in contracting cardiomyocytes with and without microtubule destabilizing drugs. Methods Nuclear morphology and chromatin organization was assessed using electron microscopy in cardiac septal tissue from 19 patients with obstructive HCM and compared to samples from 4 non-failing donors (NF). Further nuclear changes were studied using wild type (WT) and homozygous Mybpc3 c.2373InsG mice (Mybpc3c.2373InsG, KI), which have a HCM phenotype. Nuclear morphology was assessed in slices of 6 WT and 6 Mybpc3c.2373InsG paraffin-embedded mouse hearts. To study nuclear deformability during contractions, adult cardiomyocytes were isolated, stained with live cell dyes and imaged live while electrically paced. Lastly, DNA damaged was assessed in 6 WT and 6 Mybpc3c.2373InsG paraffin-embedded mouse hearts. Results Cardiomyocyte nuclei of HCM patients had a significantly higher number of invaginations (0.32±0.09 invaginations/µm in HCM versus 0.18±0.03 invaginations/µm in NF hearts), were more irregular of shape and had altered chromatin organization compared to those from NF hearts. Nuclei of Mybpc3c.2373InsG mice were considerably larger (322±75 µm³ versus 221±24 µm³). While sarcomere shortening is similar (7.0±1.4% in Mybpc3c.2373InsG versus 6.5±1.7% in WT), nuclei from Mybpc3c.2373InsG mice are less deformable than WT nuclei (figure). Addition of microtubule destabilizer nocodazole or detyrosination inhibitor EPO-Y restored nuclear deformability to WT levels, indicating a role of detyrosinated microtubules in nuclear deformability. In addition, nuclei from Mybpc3c.2373InsG have more extensive DNA damage (19.7±3.4 foci in Mybpc3c.2373InsG versus 9.1±3.2 foci in WT). Conclusion Extensive nuclear changes are observed in HCM patients and a HCM mouse model. Cytoskeletal remodeling results in less deformable nuclei that might contribute to chromatin alterations and increased DNA damage. Nuclear deformability can be restored by microtubule modifying drugs, specifically those that decrease microtubule detyrosination.

An oncogenic isoform of septin 9 promotes the formation of juxtanuclear invadopodia by reducing nuclear deformability

Invadopodia are extracellular matrix (ECM) degrading structures, which promote cancer cell invasion. The nucleus is increasingly viewed as a mechanosensory organelle that determines migratory strategies. However, how the nucleus crosstalks with invadopodia is little known. Here, we report that the oncogenic septin 9 isoform 1 (SEPT9_i1) is a component of breast cancer invadopodia. SEPT9_i1 depletion diminishes invadopodium formation and the clustering of the invadopodium precursor components TKS5 and cortactin. This phenotype is characterized by deformed nuclei and nuclear envelopes with folds and grooves. We show that SEPT9_i1 localizes to the nuclear envelope and juxtanuclear invadopodia. Moreover, exogenous lamin A rescues nuclear morphology and juxtanuclear TKS5 clusters. Importantly, SEPT9_i1 is required for the amplification of juxtanuclear invadopodia, which is induced by the epidermal growth factor. We posit that nuclei of low deformability favor the formation of juxtanuclear invadopodia in a SEPT9_i1-dependent manner, which functions as a tunable mechanism for overcoming ECM impenetrability.

Effect of deformation dependence and mirror nucleus corrections energy on multinucleon transfer reaction cross sections

Multinucleon transfer reactions are currently a powerful way to synthesize neutron-rich nuclei. To explore the effect of nucleus deformation and mirror nucleus shell correction energy in the nucleus mass model on the calculation of multinucleon transfer reaction cross sections in the dinuclear system (DNS) model, three macroscopic microscopic mass models are selected and the transfer reaction cross sections are calculated for 136Xe+208Pb and 64Ni+238U by improved DNS model+GEMINI++, respectively. The mirror nucleus shell correction energy does not improve the accuracy of the cross section of the transfer reaction. The introduction of a different dependence of the Coulomb and surface energy on the deformation can improve the calculation of the transfer reaction cross section when the projectile and target nuclei are deformed nuclei.

A mesoscale mechanical model of cellular interactions

Computational models of cell mechanics allow the precise interrogation of cell shape change. These morphological changes are required for cells to survive in diverse tissue environments. Here, we present a mesoscale mechanical model of cell-substrate interactions using the level set method based on experimentally measured parameters. By implementing a viscoelastic mechanical equivalent circuit, we accurately model whole-cell deformations that are important for a variety of cellular processes. To effectively model shape changes as a cell interacts with a substrate, we have included receptor-mediated adhesion, which is governed by catch-slip bond behavior. The effect of adhesion was explored by subjecting cells to a variety of different substrates including flat, curved, and deformable surfaces. Finally, we increased the accuracy of our simulations by including a deformable nucleus in our cells. This model sets the foundation for further exploration into computational analyses of multicellular interactions.

The role of vimentin–nuclear interactions in persistent cell motility through confined spaces

The ability of cells to move through small spaces depends on the mechanical properties of the cellular cytoskeleton and on nuclear deformability. In mammalian cells, the cytoskeleton is composed of three interacting, semi-flexible polymer networks: actin, microtubules, and intermediate filaments (IF). Recent experiments of mouse embryonic fibroblasts with and without vimentin have shown that the IF vimentin plays a role in confined cell motility. Here, we develop a minimal model of a cell moving through a microchannel that incorporates explicit effects of actin and vimentin and implicit effects of microtubules. Specifically, the model consists of a cell with an actomyosin cortex and a deformable cell nucleus and mechanical linkages between the two. By decreasing the amount of vimentin, we find that the cell speed increases for vimentin-null cells compared to cells with vimentin. The loss of vimentin increases nuclear deformation and alters nuclear positioning in the cell. Assuming nuclear positioning is a read-out for cell polarity, we propose a new polarity mechanism which couples cell directional motion with cytoskeletal strength and nuclear positioning and captures the abnormally persistent motion of vimentin-null cells, as observed in experiments. The enhanced persistence indicates that the vimentin-null cells are more controlled by the confinement and so less autonomous, relying more heavily on external cues than their wild-type counterparts. Our modeling results present a quantitative interpretation for recent experiments and have implications for understanding the role of vimentin in the epithelial–mesenchymal transition.

The Neutrophil Nucleus: An Important Influence on Neutrophil Migration and Function.

Neutrophil nuclear morphology has historically been used in haematology for neutrophil identification and characterisation, but its exact role in neutrophil function has remained enigmatic. During maturation, segmentation of the neutrophil nucleus into its mature, multi-lobulated shape is accompanied by distinct changes in nuclear envelope composition, resulting in a unique nucleus that is believed to be imbued with extraordinary nuclear flexibility. As a rate-limiting factor for cell migration, nuclear morphology and biomechanics are particularly important in the context of neutrophil migration during immune responses. Being an extremely plastic and fast migrating cell type, it is to be expected that neutrophils have an especially deformable nucleus. However, many questions still surround the dynamic capacities of the neutrophil nucleus, and which nuclear and cytoskeletal elements determine these dynamics. The biomechanics of the neutrophil nucleus should also be considered for their influences on the production of neutrophil extracellular traps (NETs), given this process sees the release of chromatin “nets” from nucleoplasm to extracellular space. Although past studies have investigated neutrophil nuclear composition and shape, in a new era of more sophisticated biomechanical and genetic techniques, 3D migration studies, and higher resolution microscopy we now have the ability to further investigate and understand neutrophil nuclear plasticity at an unprecedented level. This review addresses what is currently understood about neutrophil nuclear structure and its role in migration and the release of NETs, whilst highlighting open questions surrounding neutrophil nuclear dynamics.

Frontline Science: Elevated nuclear lamin A is permissive for granulocyte transendothelial migration but not for motility through collagen I barriers.

Transendothelial migration (TEM) of lymphocytes and neutrophils is associated with the ability of their deformable nuclei to displace endothelial cytoskeletal barriers. Lamin A is a key intermediate filament component of the nuclear lamina that is downregulated during granulopoiesis. When elevated, lamin A restricts nuclear squeezing through rigid confinements. To determine if the low lamin A expression by leukocyte nuclei is critical for their exceptional squeezing ability through endothelial barriers, we overexpressed this protein in granulocyte-like differentiated HL-60 cells. A 10-fold higher lamin A expression did not interfere with chemokinetic motility of these granulocytes on immobilized CXCL1. Furthermore, these lamin A high leukocytes exhibited normal chemotaxis toward CXCL1 determined in large pore transwell barriers, but poorly squeezed through 3 μm pores toward identical CXCL1 gradients. Strikingly, however, these leukocytes successfully completed paracellular TEM across inflamed endothelial monolayers under shear flow, albeit with a small delay in nuclear squeezing into their sub-endothelial pseudopodia. In contrast, CXCR2 mediated granulocyte motility through collagen I barriers was dramatically delayed by lamin A overexpression due to a failure of lamin A high nuclei to translocate into the pseudopodia of the granulocytes. Collectively, our data predict that leukocytes maintain a low lamin A content in their nuclear lamina in order to optimize squeezing through extracellular collagen barriers but can tolerate high lamin A content when crossing the highly adaptable barriers presented by the endothelial cytoskeleton.

Abstract 1897: The role of nuclear deformation and rupture in breast cancer cell migration

Abstract Invasion of tumor cells into the surrounding tissue is a critical step in the metastatic cascade, which is responsible for the vast majority of cancer-related deaths. Recent findings have begun to demonstrate that the biophysical properties of the cell nucleus play a critical role in this process. During invasion, cancer cells must often pass through interstitial spaces much smaller than the cell nucleus. While the cell cytoplasm easily maneuvers through confined spaces, the deformability of the nucleus, which is the largest and stiffest organelle, ultimately determines how efficiently a cell can pass through a tight space. Furthermore, as the nucleus deforms to move through a confined space, it can exhibit transient loss of nuclear envelope (NE) integrity, where the nuclear membranes rupture and nuclear and cytoplasmic components interchange. We previously showed that chromatin is exposed to the cell cytoplasm during NE rupture, and cells can incur DNA damage. While this work revealed that cancer cell migration requires nuclear deformation and can involve NE rupture, it is currently unknown whether such events correlate with metastatic potential. We used a panel of human breast cancer cells lines, including claudin-low, basal-like, and lumen-like cells. Cells were stably labeled with a green fluorescent protein fused to a nuclear localization sequence (NLS-copGFP) to investigate whether some cell lines were particularly well suited to migrate through tight spaces, and if any were particularly prone to NE rupture. The cells were loaded into microfluidic devices that were designed to mimic interstitial in vivo spacing and monitored by time-lapse microscopy. Devices contained constrictions 5 µm tall and 1, 2, or 15 µm wide. We found that claudin-low cell lines such as BT-549 migrated through confined spaces (1+2 µm wide constrictions) significantly faster and more efficiently than basal-like HCC70 cancer cells. In contrast, the various cell lines displayed similar migration rates in the 15 µm wide constrictions, which do not require nuclear deformation. Thus, the differences observed between the cell lines reflect specific defects in migration through confined spaces, and not general migration defects. We are currently expanding our studies to a larger panel of cancer cell lines and to mouse breast cancer models. If confirmed, these results could indicate that highly invasive cancer cells may benefit from more deformable nuclei that facilitate movement through tight spaces encountered in the tissue microenvironment. Citation Format: Alexandra L. McGregor, Joshua J. Elacqua, Emily S. Bell, Jan Lammerding. The role of nuclear deformation and rupture in breast cancer cell migration [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2017; 2017 Apr 1-5; Washington, DC. Philadelphia (PA): AACR; Cancer Res 2017;77(13 Suppl):Abstract nr 1897. doi:10.1158/1538-7445.AM2017-1897

Nuclear deformability and telomere dynamics are regulated by cell geometric constraints

Forces generated by the cytoskeleton can be transmitted to the nucleus and chromatin via physical links on the nuclear envelope and the lamin meshwork. Although the role of these active forces in modulating prestressed nuclear morphology has been well studied, the effect on nuclear and chromatin dynamics remains to be explored. To understand the regulation of nuclear deformability by these active forces, we created different cytoskeletal states in mouse fibroblasts using micropatterned substrates. We observed that constrained and isotropic cells, which lack long actin stress fibers, have more deformable nuclei than elongated and polarized cells. This nuclear deformability altered in response to actin, myosin, formin perturbations, or a transcriptional down-regulation of lamin A/C levels in the constrained and isotropic geometry. Furthermore, to probe the effect of active cytoskeletal forces on chromatin dynamics, we tracked the spatiotemporal dynamics of heterochromatin foci and telomeres. We observed increased dynamics and decreased correlation of the heterochromatin foci and telomere trajectories in constrained and isotropic cell geometry. The observed enhanced dynamics upon treatment with actin depolymerizing reagents in elongated and polarized geometry were regained once the reagent was washed off, suggesting an inherent structural memory in chromatin organization. We conclude that active forces from the cytoskeleton and rigidity from lamin A/C nucleoskeleton can together regulate nuclear and chromatin dynamics. Because chromatin remodeling is a necessary step in transcription control and its memory, genome integrity, and cellular deformability during migration, our results highlight the importance of cell geometric constraints as critical regulators in cell behavior.

On intrinsic stress fiber contractile forces in semilunar heart valve interstitial cells using a continuum mixture model

Heart valve interstitial cells (VICs) play a critical role in the maintenance and pathophysiology of heart valve tissues. Normally quiescent in the adult, VICs can become activated in periods of growth and disease. When activated, VICs exhibit increased levels of cytokines and extracellular matrix (ECM) synthesis, and upregulated expression and strong contraction of α-smooth muscle actin (α-SMA) fibers. However, it remains unknown how expression and contraction of the α-SMA fibers, which vary among different VIC types, contribute to the overall VIC mechanical responses, including the nucleus and cytoskeleton contributions. In the present study, we developed a novel solid-mixture model for VIC biomechanical behavior that incorporated 1) the underlying cytoskeletal network, 2) the oriented α-SMA stress fibers with passive elastic and active contractile responses, 3) a finite deformable elastic nucleus. We implemented the model in a full 3D finite element simulation of a VIC based on known geometry. Moreover, we examined the respective mechanical responses of aortic and pulmonary VICs (AVICs and PVICs, respectively), which are known to have different levels of α-SMA expression levels and contractile behaviors. To calibrate the model, we simulated the combined mechanical responses of VICs in both micropipette aspiration (MA) and atomic force microscopy (AFM) experiments. These two states were chosen as the VICs were under significantly different mechanical loading conditions and activation states, with the α-SMA fibers inactivated in the MA studies while fully activated in the AFM studies. We also used the AFM to study the mechanical property of the nucleus. Our model predicted that the substantial differences found in stiffening of the AVIC compared to the PVICs was due to a 9 to 16 times stronger intrinsic AVIC α-SMA stress fiber contractile force. Model validation was done by simulating a traction force microscopy experiment to estimate the forces the VICs exert on the underlying substrate, and found good agreement with reported traction force microscopy results. Further, estimated nuclear stiffness for both AVICs and PVICs were similar and comparable to the literature, and were both unaffected by VIC activation level. These results suggest substantial functional differences between AVICs and PVICs at the subcellular level. Moreover, this first VIC computational biomechanical model is but a first step in developing a comprehensive, integrated view of the VIC pathophysiology and interactions with the valve ECM micro-environment based on simulation technologies.

The tethering of chromatin to the nuclear envelope supports nuclear mechanics.

The nuclear lamina is thought to be the primary mechanical defence of the nucleus. However, the lamina is integrated within a network of lipids, proteins and chromatin; the interdependence of this network poses a challenge to defining the individual mechanical contributions of these components. Here, we isolate the role of chromatin in nuclear mechanics by using a system lacking lamins. Using novel imaging analyses, we observe that untethering chromatin from the inner nuclear membrane results in highly deformable nuclei in vivo, particularly in response to cytoskeletal forces. Using optical tweezers, we find that isolated nuclei lacking inner nuclear membrane tethers are less stiff than wild-type nuclei and exhibit increased chromatin flow, particularly in frequency ranges that recapitulate the kinetics of cytoskeletal dynamics. We suggest that modulating chromatin flow can define both transient and long-lived changes in nuclear shape that are biologically important and may be altered in disease.

Mechanical trapping of the nucleus on micropillared surfaces inhibits the proliferation of vascular smooth muscle cells but not cervical cancer HeLa cells

The interaction between cells and the extracellular matrix on a topographically patterned surface can result in changes in cell shape and many cellular functions. In the present study, we demonstrated the mechanical deformation and trapping of the intracellular nucleus using polydimethylsiloxane (PDMS)-based microfabricated substrates with an array of micropillars. We investigated the differential effects of nuclear deformation on the proliferation of healthy vascular smooth muscle cells (SMCs) and cervical cancer HeLa cells. Both types of cell spread normally in the space between micropillars and completely invaded the extracellular microstructures, including parts of their cytoplasm and their nuclei. We found that the proliferation of SMCs but not HeLa cells was dramatically inhibited by cultivation on the micropillar substrates, even though remarkable deformation of nuclei was observed in both types of cells. Mechanical testing with an atomic force microscope and a detailed image analysis with confocal microscopy revealed that SMC nuclei had a thicker nuclear lamina and greater expression of lamin A/C than those of HeLa cells, which consequently increased the elastic modulus of the SMC nuclei and their nuclear mechanical resistance against extracellular microstructures. These results indicate that the inhibition of cell proliferation resulted from deformation of the mature lamin structures, which might be exposed to higher internal stress during nuclear deformation. This nuclear stress-induced inhibition of cell proliferation occurred rarely in cancer cells with deformable nuclei.

Chromatin Association with the Nuclear Envelope Supports Stable Nuclear Mechanics

Although the nuclear lamina is considered to be the primary mechanical defense of the nucleus, lamins are part of an integrated network of lipids, proteins, and chromatin. Here, we isolate the contribution of chromatin to nuclear mechanics by employing fission yeast, which lack a nuclear lamina. We have combined a quantitative imaging platform capable of measuring 3D nuclear contours in vivo with an in vitro optical tweezers assay to probe the mechanical properties of S. pombe nuclei. In live cells, we find that association of chromatin with the inner nuclear membrane (INM) through integral membrane proteins is required for a normal mechanical response to microtubule (MT) forces. Increasing loss of integral INM proteins results in highly deformable nuclei specifically in response to exogenous MT forces. These nuclei also show a decreased capacity to recover from mechanical stress. Using optical tweezers, we find that nuclei lacking integral INM proteins are less stiff than wild type nuclei and have increased chromatin flow, particularly when force is applied at rates that recapitulate the kinetics of MT dynamics in vivo. Wild type mitotic nuclei, in which chromatin is globally released from the INM, are extremely soft and also display increased chromatin flow compared to interphase nuclei. Interestingly, decreasing the chromatin to nuclear volume ratio without altering the association of chromatin with the INM has only a slight effect on stiffness and does not alter chromatin flow. Together, these findings suggest that association of chromatin with the nuclear envelope underlies nuclear stiffness. Further, release of chromatin from the INM allows chromatin to flow into MT-dependent fluctuations of the nuclear envelope, leading to larger, longer-lasting nuclear deformations. Lastly, these results suggest that chromatin association with the lamina may contribute to the mechanical behavior of metazoan nuclei.

Myopathic lamin mutations impair nuclear stability in cells and tissue and disrupt nucleo-cytoskeletal coupling

Lamins are intermediate filament proteins that assemble into a meshwork underneath the inner nuclear membrane, the nuclear lamina. Mutations in the LMNA gene, encoding lamins A and C, cause a variety of diseases collectively called laminopathies. The disease mechanism for these diverse conditions is not well understood. Since lamins A and C are fundamental determinants of nuclear structure and stability, we tested whether defects in nuclear mechanics could contribute to the disease development, especially in laminopathies affecting mechanically stressed tissue such as muscle. Using skin fibroblasts from laminopathy patients and lamin A/C-deficient mouse embryonic fibroblasts stably expressing a broad panel of laminopathic lamin A mutations, we found that several mutations associated with muscular dystrophy and dilated cardiomyopathy resulted in more deformable nuclei; in contrast, lamin mutants responsible for diseases without muscular phenotypes did not alter nuclear deformability. We confirmed our results in intact muscle tissue, demonstrating that nuclei of transgenic Drosophila melanogaster muscle expressing myopathic lamin mutations deformed more under applied strain than controls. In vivo and in vitro studies indicated that the loss of nuclear stiffness resulted from impaired assembly of mutant lamins into the nuclear lamina. Although only a subset of lamin mutations associated with muscular diseases caused increased nuclear deformability, almost all mutations tested had defects in force transmission between the nucleus and cytoskeleton. In conclusion, our results indicate that although defective nuclear stability may play a role in the development of muscle diseases, other factors, such as impaired nucleo-cytoskeletal coupling, likely contribute to the muscle phenotype.

Gamma radiation induced micronuclei and erythrocyte cellular abnormalities in the fish Catla catla

Ionizing radiation induced DNA damage in fishes is a scarcely studied topic and very few studies are available in fishes exposed to ionizing radiation using the erythrocyte micronucleus assay under laboratory conditions. Since radionuclides released accidentally or during a nuclear disaster can contaminate inland water bodies, biomonitoring methods are required for assessing the impacts of high and low levels of radiation that may ultimately result in ionizing radiation exposure to both humans and non-human biota. Fresh water fish, Catla catla were subjected to protracted (0.002Gy/min) and acute (3.2Gy/min) gamma radiation to a total dose of 5Gy. Peripheral blood samples were collected at different intervals (days 3, 6, 12, 18, 30, 45, 90, 135, 202) and analyzed by the erythrocyte micronucleus assay. Nuclear anomalies observed were micronuclei (MN), deformed nuclei (DN), nuclear bud (NBu), nuclear bridge (NBr), vacuolated nucleus (VN), binucleated cell (BNC), apoptotic cells (AC) while cytoplasmic abnormalities detected were vacuolated cytoplasm (VC), anisochromasia (AN), echinocytes (EC) and enucleus (EN). Both exposures caused a statistically significant increase in nuclear and cytoplasmic abnormalities that correlated with micronucleus and other nuclear anomalies. However, the extent of damage is higher after an acute exposure lasting for a longer period leading to apoptosis. Nuclear and cytoplasmic abnormalities are the resultants of gamma radiation induced genotoxicity and cytotoxicity.

An in vitro model for Pelger-Huët anomaly

The principal human blood granulocyte (neutrophil) possesses a lobulated and deformable nucleus, important to facilitate rapid egress from blood vessels as these cells migrate to sites of bacterial or fungal infection. This unusual nuclear shape is a product of elevated levels of an integral membrane protein of the nuclear envelope lamin B receptor (LBR) and of decreased amounts of lamin A/C. In humans, a genetic deficiency of LBR produces Pelger-Huët anomaly, resulting in blood neutrophils that exhibit hypolobulated nuclei with redistributed heterochromatin. Structural changes in nuclear architecture occur during granulopoiesis within bone marrow. The exact mechanisms of this nuclear shape change and of heterochromatin redistribution remain largely unknown. As a tool to facilitate analysis of these mechanisms, a stable LBR knockdown subline of HL-60 cells was established. During in vitro granulopoiesis induced with retinoic acid, the LBR knockdown cells retain an ovoid shaped nucleus with reduced levels of lamin A/C; whereas, the parent cells develop lobulated nuclei. Macrophage forms induced in LBR knockdown cells by in vitro treatment with phorbol ester were indistinguishable from the parent cells, comparing both nuclear shape and attached cell morphology. The capability of differentiation of LBR knockdown HL-60 cells should facilitate a detailed analysis of the molecular relationship between LBR levels, granulocyte nuclear shape and heterochromatin distribution.

QRPA CALCULATIONS FOR SPHERICAL AND DEFORMED NUCLEI WITH THE GOGNY FORCE

Fully consistent axially-symmetric-deformed Quasi-particle Random Phase Approximation (QRPA) calculations have been performed with the D1S Gogny force. Impact of the deformation in giant multipole resonances is discussed. QRPA and 5 Dimensional Collective Hamiltonian results are compared for low lying 2+ states in N = 16 isotones and Ni isotopes. Multipole resonances are also obtained for the heavy nucleus 238 U .

Excited states of deformable odd 157,159Tb nuclei: Nonconservation of the angular momentum of external nucleon

The previously developed rotationally single-particle and vibrational model of the triaxial deformable odd nuclei is extended to the case where the total angular momentum of an external nucleon is not conserved. The calculated ratios of the excitation energies of the 157,159Tb nuclei are compared with the existing experimental data. The ratios of E2-transition probabilities and those of quadrupole moments of the above nuclei are calculated using parameters determined from the spectra of these nuclei.

Relativistic Analysis of Intermediate Energy Proton Inelastic Scatterings from Heavy Deformed Nuclei

A relativistic coupled channel analysis based on the Dirac equation is performed for inelastic scattering of an intermediate energy proton from a heavy, deformed nucleus by using an optical potential model. In order to describe the low-lying excited states of the deformed nucleus, we used a rotational collective model to get the transition optical potentials. The Dirac coupled-channel equations are solved numerically to calculate the di erential cross sections by using the sequential iteration method. Employing Dirac phenomenology, we vary the optical potential parameters and deformation parameters to reproduce the experimental observables. The theoretical results are observed to agree reasonably well with the inelastic scattering experimental data of 800 MeV p+176Yb, and the importance of the multistep process for inelastic scatterings at a deformed nucleus is con rmed. The e ective Schr odinger-equivalent central and spin-orbit potentials are calculated by reducing the Dirac equation to a Schr odinger-like second-order di erential equation and by comparison them with those of a Schr odinger calculation in which the spin-orbit potential is not included, showing the relatively large strength of a real central potential. Surface-peaked phenomena are not observed for e ective central potentials when the heavy, deformed nucleus of 176Yb is considered.

Optimal path of diffusion over the saddle point and fusion of massive nuclei

The diffusion of a particle passing over the saddle point of a two-dimensional quadratic potential is studied via a set of coupled Langevin equations, and the expression for the passing probability is obtained exactly. The passing probability is found to be strongly influenced by the off-diagonal components of inertia and friction tensors. If the system undergoes the optimal path to pass over the saddle point by taking an appropriate direction of initial velocity into account, which departs from the potential valley and has minimum dissipation, the passing probability should be enhanced. Applying this to the fusion of massive nuclei, we show that there exists an optimal injection choice for the deformable target and projectile nuclei, namely, the intermediate deformation between spherical and extremely deformed nuclei, that maximizes the fusion probability.