The effects of Ce6-mediated sono-photodynamic therapy on cell migration,apoptosis and autophagy in mouse mammary 4T1 cell line

Purpose

Sono-Photodynamic therapy (SPDT) is an alternative therapy which claims to enhance the anti-cancer effects by combining sonodynamic therapy (SDT) with photodynamic therapy (PDT). In the present study, we investigated the effects of chlorin e6 (Ce6) mediated SPDT on migration, apoptosis and autophagy in mouse mammary 4T1 cancer cells, and its underlying mechanisms.

Materials

Cell migration was determined by wound healing assay. Apoptosis was analyzed using annexin V-PE/7-ADD staining as well as Hoechst 33342 staining. Changes of mitochondria membrane potential (MMP) was evaluated by flow cytometry. Formation of acidic vesicular organelles (AVOs) during autophagy was observed with fluorescence microscope by MDC staining. Immunofluorescence assays were performed to detect the co-localization of LC3 and Lamp2. Western blotting was employed to analyze the activity of the apoptosis related proteins Caspase-3, PARP, Bax and Bcl-2, as well as the autophagy associated processing of LC3-I to LC3-II and Beclin-1 expression.

Results

Ce6 mediated SPDT further enhanced cell migration inhibition, significantly triggered cell apoptosis, nuclear condensation and MMP drop. Cleaved Caspase-3 and PARP increased dramatically after Ce6-SPDT, accompanied by decreased Bcl-2 expression, while the expression of Bax remained stable. Additionally, AVOs formation, co-localization of LC3 and Lamp2 occurred following Ce6-SPDT and simultaneously accompanied by LC3-II processing and increased Beclin-1 expression.

Conclusions

Ce6-SPDT could enhance cell migration inhibition, and induce mitochondria-dependent apoptosis as well as autophagy in 4T1 cells.     

Does autophagy in the midgut epithelium of centipedes depend on the day/night cycle?

The midgut epithelium of two centipedes, Lithobius forficatus and Scolopendra cingulata, is composed of digestive, secretory and regenerative cells. In L. forficatus, the autophagy occurred only in the cytoplasm of the digestive cells as a sporadic process, while in S. cingulata, it occurred intensively in the digestive, secretory and regenerative cells of the midgut epithelium. In both of the species that were analyzed, this process proceeded in a continuous manner and did not depend on the day/night cycle. Ultrastructural analysis showed that the autophagosomes and autolysosomes were located mainly in the apical and perinuclear cytoplasm of the digestive cells in L. forficatus. However, in S. cingulata, the entire cytoplasm was filled with autophagosomes and autolysosomes. Initially the membranes of phagophores surround organelles during autophagosome formation. Autolysosomes result from the fusion of autophagosomes and lysosomes. Residual bodies which are the last stage of autophagy were released into the midgut lumen due to necrosis. Autophagy in the midgut epithelia that were analyzed was confirmed using acid phosphatase and mono-dansyl-cadaverine stainings.     

Mapping of neurokinin-like immunoreactivity in the human brainstem

Background

Using an indirect immunoperoxidase technique, we have studied the distribution of immunoreactive fibers and cell bodies containing neurokinin in the adult human brainstem with no prior history of neurological or psychiatric disease.

Results

Clusters of immunoreactive cell bodies and high densities of neurokinin-immunoreactive fibers were located in the periaqueductal gray, the dorsal motor nucleus of the vagus and in the reticular formation of the medulla, pons and mesencephalon. Moreover, immunoreactive cell bodies were found in the inferior colliculus, the raphe obscurus, the nucleus prepositus hypoglossi, and in the midline of the anterior medulla oblongata. In general, immunoreactive fibers containing neurokinin were observed throughout the whole brainstem. In addition to the nuclei mentioned above, the highest densities of such immunoreactive fibers were located in the spinal trigeminal nucleus, the lateral reticular nucleus, the nucleus of the solitary tract, the superior colliculus, the substantia nigra, the nucleus ambiguus, the gracile nucleus, the cuneate nucleus, the motor hypoglossal nucleus, the medial and superior vestibular nuclei, the nucleus prepositus hypoglossi and the interpeduncular nucleus.

Conclusion

The widespread distribution of immunoreactive structures containing neurokinin in the human brainstem indicates that neurokinin might be involved in several physiological mechanisms, acting as a neurotransmitter and/or neuromodulator.     

Heme oxygenase-2 gene deletion attenuates oxidative stress in neurons exposed to extracellular hemin

Background

Hemin, the oxidized form of heme, accumulates in intracranial hematomas and is a potent oxidant. Growing evidence suggests that it contributes to delayed injury to surrounding tissue, and that this process is affected by the heme oxygenase enzymes. In a prior study, heme oxygenase-2 gene deletion increased the vulnerability of cultured cortical astrocytes to hemin. The present study tested the effect of HO-2 gene deletion on protein oxidation, reactive oxygen species formation, and cell viability after mixed cortical neuron/astrocyte cultures were incubated with neurotoxic concentrations of hemin.

Results

Continuous exposure of wild-type cultures to 1–10 μM hemin for 14 h produced concentration-dependent neuronal death, as detected by both LDH release and fluorescence intensity after propidium iodide staining, with an EC₅₀ of 1–2 μM; astrocytes were not injured by these low hemin concentrations. Cell death was consistently reduced by at least 60% in knockout cultures. Exposure to hemin for 4 hours, a time point that preceded cell lysis, increased protein oxidation in wild-type cultures, as detected by staining of immunoblots for protein carbonyl groups. At 10 μM hemin, carbonylation was increased 2.3-fold compared with control sister cultures subjected to medium exchanges only; this effect was reduced by about two-thirds in knockout cultures. Cellular reactive oxygen species, detected by fluorescence intensity after dihydrorhodamine 123 (DHR) staining, was markedly increased by hemin in wild-type cultures and was localized to neuronal cell bodies and processes. In contrast, DHR fluorescence intensity in knockout cultures did not differ from that of sham-washed controls. Neuronal death in wild-type cultures was almost completely prevented by the lipid-soluble iron chelator phenanthroline; deferoxamine had a weaker but significant effect.

Conclusions

These results suggest that HO-2 gene deletion protects neurons in mixed neuron-astrocyte cultures from heme-mediated oxidative injury. Selective inhibition of neuronal HO-2 may have a beneficial effect after CNS hemorrhage.     

New highly sensitive rodent and human tests for soluble amyloid precursor protein alpha quantification: preclinical and clinical applications in Alzheimer’s disease

Background

Exposure to ethanol during early development triggers severe neuronal death by activating multiple stress pathways and causes neurological disorders, such as fetal alcohol effects or fetal alcohol syndrome. This study investigated the effect of ethanol on intracellular events that predispose developing neurons for apoptosis via calcium-mediated signaling. Although the underlying molecular mechanisms of ethanol neurotoxicity are not completely determined, mitochondrial dysfunction, altered calcium homeostasis and apoptosis-related proteins have been implicated in ethanol neurotoxicity. The present study was designed to evaluate the neuroprotective mechanisms of metformin (Met) and thymoquinone (TQ) during ethanol toxicity in rat prenatal cortical neurons at gestational day (GD) 17.5.

Results

We found that Met and TQ, separately and synergistically, increased cell viability after ethanol (100 mM) exposure for 12 hours and attenuated the elevation of cytosolic free calcium [Ca²⁺]_c. Furthermore, Met and TQ maintained normal physiological mitochondrial transmembrane potential (????_M), which is typically lowered by ethanol exposure. Increased cytosolic free [Ca²⁺]_c and lowered mitochondrial transmembrane potential after ethanol exposure significantly decreased the expression of a key anti-apoptotic protein (Bcl-2), increased expression of Bax, and stimulated the release of cytochrome-c from mitochondria. Met and TQ treatment inhibited the apoptotic cascade by increasing Bcl-2 expression. These compounds also repressed the activation of caspase-9 and caspase-3 and reduced the cleavage of PARP-1. Morphological conformation of cell death was assessed by TUNEL, Fluoro-Jade-B, and PI staining. These staining methods demonstrated more cell death after ethanol treatment, while Met, TQ or Met plus TQ prevented ethanol-induced apoptotic cell death.

Conclusion

These findings suggested that Met and TQ are strong protective agents against ethanol-induced neuronal apoptosis in primary rat cortical neurons. The collective data demonstrated that Met and TQ have the potential to ameliorate ethanol neurotoxicity and revealed a possible protective target mechanism for the damaging effects of ethanol during early brain development.     

Wallerian-like axonal degeneration in the optic nerve after excitotoxic retinal insult: an ultrastructural study

Background  

Excitotoxicity is involved in the pathogenesis of a number neurodegenerative diseases, and axonopathy is an early feature in several of these disorders. In models of excitotoxicity-associated neurological disease, an excitotoxin delivered to the central nervous system (CNS), could trigger neuronal death not only in the somatodendritic region, but also in the axonal region, via oligodendrocyte N-methyl-D-aspartate (NMDA) receptors. The retina and optic nerve, as approachable regions of the brain, provide a unique anatomical substrate to investigate the "downstream" effect of isolated excitotoxic perikaryal injury on central nervous system (CNS) axons, potentially providing information about the pathogenesis of the axonopathy in clinical neurological disorders.     

Influence of X-ray on the autophagic-lysosomal system in rat pancreatic acini

Lysosomes have an important role in radiation injury of cells and tissues. Activation of autophagy is frequently observed in different types of pathological tissue degeneration. In radiation response it increases in some cases, and lysosomes are responsible for regulated degradation of the autophagic vacuoles. Lysosomes are also involved in ionizing radiation induced cell death. In apoptosis lysosomes degrade content of the phagocytotic vacuoles derived from engulfed apoptotic blebs. On the other hand lysosomal enzymes discharged from disintegrated cells have a key role in induction of necrotic changes. In this work we investigate autophagy and lysosomal protein degradation in the relatively radiation insensitive exocrine pancreatic acini in vivo and in vitro. Type of cell death induced by X-ray was also examined in relation to the changes of the lysosomal processes. In 5h after 16 Gy in vivo whole body irradiation we observed significant increase in the cytoplasmic volume fraction of autophagic vacuoles and in the number of apoptotic cells in vivo. But in the acini isolated from irradiated rats we could not detect a change in the lysosomal degradation of intracellular proteins. Therefore irradiation probably influences the autophagy in an earlier step than lysosomal degradation. Extended necrotic lesions were not observed in vivo as long as 48 h. Isolated pancreatic acini usually contain more autophagic vacuoles than in vivo, but we could not observe additional increase in autophagy after 8 Gy, in vitro irradiation. Lysosomal degradation of intracellular proteins was also unaltered after 8 Gy, in vitro irradiation. Other biochemical functional parameters of the isolated pancreatic acini, like protein synthesis and amylase secretion were not changed either after 8 Gy, in vitro X-ray treatment. These results indicate that pancreatic acinar cells in vitro have a high tolerance to irradiation. The observed in vivo radiation induced changes of the exocrine pancreas are possibly indirectly induced by injuries of more sensitive mechanisms.     

Generation and characterization of high affinity human monoclonal antibodies that neutralize staphylococcal enterotoxin B

Background

Staphylococcal enterotoxins are considered potential biowarfare agents that can be spread through ingestion or inhalation. Staphylococcal enterotoxin B (SEB) is a widely studied superantigen that can directly stimulate T-cells to release a massive amount of proinflammatory cytokines by bridging the MHC II molecules on an antigen presenting cell (APC) and the Vβ chains of the T-cell receptor (TCR). This potentially can lead to toxic, debilitating and lethal effects. Currently, there are no preventative measures for SEB exposure, only supportive therapies.

Methods

To develop a potential therapeutic candidate to combat SEB exposure, we have generated three human B-cell hybridomas that produce human monoclonal antibodies (HuMAbs) to SEB. These HuMAbs were screened for specificity, affinity and the ability to block SEB activity in vitro as well as its lethal effect in vivo.

Results

The high-affinity HuMAbs, as determined by BiaCore analysis, were specific to SEB with minimal crossreactivity to related toxins by ELISA. In an immunoblotting experiment, our HuMAbs bound SEB mixed in a cell lysate and did not bind any of the lysate proteins. In an in vitro cell-based assay, these HuMAbs could inhibit SEB-induced secretion of the proinflammatory cytokines (INF-γ and TNF-α) by primary human lymphocytes with high potency. In an in vivo LPS-potentiated mouse model, our lead antibody, HuMAb-154, was capable of neutralizing up to 100 μg of SEB challenge equivalent to 500 times over the reported LD₅₀ (0.2 μg), protecting mice from death. Extended survival was also observed when HuMAb-154 was administered after SEB challenge.

Conclusion

We have generated high-affinity SEB-specific antibodies capable of neutralizing SEB in vitro as well as in vivo in a mouse model. Taken together, these results suggest that our antibodies hold the potential as passive immunotherapies for both prophylactic and therapeutic countermeasures of SEB exposure.     

Slowly developing depression of N-methyl-D-aspartate receptor mediated responses in young rat hippocampi

Background

Activation of N-methyl-D-aspartate (NMDA) type glutamate receptors is essential in triggering various forms of synaptic plasticity. A critical issue is to what extent such plasticity involves persistent changes of glutamate receptor subtypes and many prior studies have suggested a main role for alpha-amino-3-hydroxy-5-methyl-4-isoxazole propionic acid (AMPA) receptors in mediating the effect. Our previous work in hippocampal slices revealed that, under pharmacological unblocking of NMDA receptors, both AMPA and NMDA receptor mediated responses undergo a slowly developing depression. In the present study we have further adressed this phenomenon, focusing on the contribution via NMDA receptors. Pharmacologically isolated NMDA receptor mediated excitatory postsynaptic potentials (EPSPs) were recorded for two independent synaptic pathways in CA1 area using perfusion with low Mg²⁺ (0.1 mM) to unblock NMDA receptors.

Results

Following unblocking of NMDA receptors, there was a gradual decline of NMDA receptor mediated EPSPs for 2–3 hours towards a stable level of ca. 60–70 % of the maximal size. If such an experimental session was repeated twice in the same pathway with a period of NMDA receptor blockade in between, the depression attained in the first session was still evident in the second one and no further decay occurred. The persistency of the depression was also validated by comparison between pathways. It was found that the responses of a control pathway, unstimulated in the first session of receptor unblocking, behaved as novel responses when tested in association with the depressed pathway under the second session. In similar experiments, but with AP5 present during the first session, there was no subsequent difference between NMDA EPSPs.

Conclusions

Our findings show that merely evoking NMDA receptor mediated responses results in a depression which is input specific, induced via NMDA receptor activation, and is maintained for several hours through periods of receptor blockade. The similarity to key features of long-term depression and long-term potentiation suggests a possible relation to these phenomena. Additionally, a short term potentiation and decay (<5 min) were observed during sudden start of NMDA receptor activation supporting the idea that NMDA receptor mediated responses are highly plastic.

     

Arithmetic mismatch negativity and numerical magnitude processing in number matching

Background

After a prolonged exposure to a paired presentation of different types of signals (e.g., color and motion), one of the signals (color) becomes a driver for the other signal (motion). This phenomenon, which is known as contingent motion aftereffect, indicates that the brain can establish new neural representations even in the adult's brain. However, contingent motion aftereffect has been reported only in visual or auditory domain. Here, we demonstrate that a visual motion aftereffect can be contingent on a specific sound.

Results

Dynamic random dots moving in an alternating right or left direction were presented to the participants. Each direction of motion was accompanied by an auditory tone of a unique and specific frequency. After a 3-minutes exposure, the tones began to exert marked influence on the visual motion perception, and the percentage of dots required to trigger motion perception systematically changed depending on the tones. Furthermore, this effect lasted for at least 2 days.

Conclusions

These results indicate that a new neural representation can be rapidly established between auditory and visual modalities.     

Niche-dependent development of functional neuronal networks from embryonic stem cell-derived neural populations

Background

Minocycline, a second-generation tetracycline with anti-inflammatory and anti-apoptotic properties, has been shown to promote therapeutic benefits in experimental stroke. However, equally compelling evidence demonstrates that the drug exerts variable and even detrimental effects in many neurological disease models. Assessment of the mechanism underlying minocycline neuroprotection should clarify the drug's clinical value in acute stroke setting.

Results

Here, we demonstrate that minocycline attenuates both in vitro (oxygen glucose deprivation) and in vivo (middle cerebral artery occlusion) experimentally induced ischemic deficits by direct inhibition of apoptotic-like neuronal cell death involving the anti-apoptotic Bcl-2/cytochrome c pathway. Such anti-apoptotic effect of minocycline is seen in neurons, but not apparent in astrocytes. Our data further indicate that the neuroprotection is dose-dependent, in that only low dose minocycline inhibits neuronal cell death cascades at the acute stroke phase, whereas the high dose exacerbates the ischemic injury.

Conclusion

The present study advises our community to proceed with caution to use the minimally invasive intravenous delivery of low dose minocycline in order to afford neuroprotection that is safe for stroke.     

A role for the membrane protein M6 in the Drosophila visual system

Background

Members of the proteolipid protein family, including the four-transmembrane glycoprotein M6a, are involved in neuronal plasticity in mammals. Results from our group previously demonstrated that M6, the only proteolipid protein expressed in Drosophila, localizes to the cell membrane in follicle cells. M6 loss triggers female sterility, which suggests a role for M6 in follicular cell remodeling. These results were the basis of the present study, which focused on the function and requirements of M6 in the fly nervous system.

Results

The present study identified two novel, tissue-regulated M6 isoforms with variable N- and C- termini, and showed that M6 is the functional fly ortholog of Gpm6a. In the adult brain, the protein was localized to several neuropils, such as the optic lobe, the central complex, and the mushroom bodies. Interestingly, although reduced M6 levels triggered a mild rough-eye phenotype, hypomorphic M6 mutants exhibited a defective response to light.

Conclusions

Based on its ability to induce filopodium formation we propose that M6 is key in cell remodeling processes underlying visual system function. These results bring further insight into the role of M6/M6a in biological processes involving neuronal plasticity and behavior in flies and mammals.     

Probing compositeness with Higgs Boson decays at the LHC

We study how massive ghost-free gravity \(f(R)\) -modified theories, MGFTs, can be encoded into generic off-diagonal Einstein spaces. Using “auxiliary” connections completely defined by the metric fields and adapted to nonholonomic frames with associated nonlinear connection structure, we decouple and integrate in certain general forms the field equations in MGFT. Imposing additional nonholonomic constraints, we can generate Levi-Civita, LC, configurations and mimic MGFT effects via off-diagonal interactions of effective Einstein and/or Einstein–Cartan gravity with nonholonomically induced torsion. We show that imposing nonholonomic constraints it is possible reproduce very specific models of massive \(f(R)\) gravity studied in Cai et al. (arXiv:1307.7150, 2013), Klusoňet al. (Phys Lett B 726:918, 2013), Nojiri and Odintov (Phys Lett B 716:377, 2012) and Nojiri et al. (JCAP 1305:020, 2013). The cosmological evolution of ghost-free off-diagonal Einstein spaces is investigated. Certain compatibility of MGFT cosmology to small off-diagonal deformations of \(\Lambda \) CDM models is established.     

On the Geodesic Hypothesis in General Relativity

In this paper, we give a rigorous derivation of Einstein’s geodesic hypothesis in general relativity. We use small material bodies ${\phi^\epsilon}$ governed by the nonlinear Klein–Gordon equations to approximate the test particle. Given a vacuum spacetime ${([0, T]\times\mathbb{R}^3, h)}$ , we consider the initial value problem for the Einstein-scalar field system. For all sufficiently small ε and δ ≤ ε ^q , q > 1, where δ, ε are the amplitude and size of the particle, we show the existence of the solution ${([0, T]\times\mathbb{R}^3, g, \phi^\epsilon)}$ to the Einstein-scalar field system with the property that the energy of the particle ${\phi^\epsilon}$ is concentrated along a timelike geodesic. Moreover, the gravitational field produced by ${\phi^\epsilon}$ is negligibly small in C ¹, that is, the spacetime metric g is C ¹ close to the given vacuum metric h. These results generalize those obtained by Stuart in (Ann Sci École Norm Sup (4) 37(2):312–362, 2004, J Math Pures Appl (9) 83(5):541–587, 2004).     

Are women better mindreaders? Sex differences in neural correlates of mentalizing detected with functional MRI

Background

Oxidative stress plays a key role in the neuropathogenesis of Human Immunodeficiency Virus-1 (HIV-1) infection causing apoptosis of astroglia cells and neurons. Recent data have shown that oxidative stress is also responsible for the acceleration of human fibroblast telomere shortening in vitro. In the present study we analyzed the potential relations occurring between free radicals formation and telomere length during HIV-1 mediated astroglial death.

Results

To this end, U373 human astrocytoma cells have been directly exposed to X4-using HIV-1IIIB strain, for 1, 3 or 5 days and treated (where requested) with N-acetylcysteine (NAC), a cysteine donor involved in the synthesis of glutathione (GSH, a cellular antioxidant) and apoptosis has been evaluated by FACS analysis. Quantitative-FISH (Q-FISH) has been employed for studying the telomere length while intracellular reduced/oxidized glutathione (GSH/GSSG) ratio has been determined by High-Performance Liquid Chromatography (HPLC). Incubation of U373 with HIV-1IIIB led to significant induction of cellular apoptosis that was reduced in the presence of 1 mM NAC. Moreover, NAC improved the GSH/GSSG, a sensitive indicator of oxidative stress, that significantly decreased after HIV-1IIIB exposure in U373. Analysis of telomere length in HIV-1 exposed U373 showed a statistically significant telomere shortening, that was completely reverted in NAC-treated U373.

Conclusion

Our results support the role of HIV-1-mediated oxidative stress in astrocytic death and the importance of antioxidant compounds in preventing these cellular damages. Moreover, these data indicate that the telomere structure, target for oxidative damage, could be the key sensor of cell apoptosis induced by oxidative stress after HIV infection.     

Enhanced expression of WD repeat-containing protein 35 (WDR35) stimulated by domoic acid in rat hippocampus: involvement of reactive oxygen species generation and p38 mitogen-activated protein kinase activation

Background

Domoic acid (DA) is an excitatory amino acid analogue of kainic acid (KA) that acts via activation of glutamate receptors to elicit a rapid and potent excitotoxic response, resulting in neuronal cell death. Recently, DA was shown to elicit reactive oxygen species (ROS) production and induce apoptosis accompanied by activation of p38 mitogen-activated protein kinase (MAPK) in vitro. We have reported that WDR35, a WD-repeat protein, may mediate apoptosis in several animal models. In the present study, we administered DA to rats intraperitoneally, then used liquid chromatography/ion trap tandem mass spectrometry (LC-MS/MS) to identify and quantify DA in the brains of the rats and performed histological examinations of the hippocampus. We further investigated the potential involvement of glutamate receptors, ROS, p38 MAPK, and WDR35 in DA-induced toxicity in vivo.

Results

Our results showed that intraperitoneally administered DA was present in the brain and induced neurodegenerative changes including apoptosis in the CA1 region of the hippocampus. DA also increased the expression of WDR35 mRNA and protein in a dose- and time-dependent manner in the hippocampus. In experiments using glutamate receptor antagonists, the AMPA/KA receptor antagonist NBQX significantly attenuated the DA-induced increase in WDR35 protein expression, but the NMDA receptor antagonist MK-801 did not. In addition, the radical scavenger edaravone significantly attenuated the DA-induced increase in WDR35 protein expression. Furthermore, NBQX and edaravone significantly attenuated the DA-induced increase in p38 MAPK phosphorylation.

Conclusion

In summary, our results indicated that DA activated AMPA/KA receptors and induced ROS production and p38 MAPK phosphorylation, resulting in an increase in the expression of WDR35 in vivo.     

Computational framework for the prediction of transcription factor binding sites by multiple data integration

Background

Activation of extracellular signal-regulated protein kinase (ERK), a member of mitogen-activated protein kinase (MAPK) family, has been proposed to mediate neurite outgrowth-promoting effects of several neurotrophic factors in vitro. However, the precise activity of ERK during axonal regeneration in vivo remains unclear. Peripheral axotomy has been shown to activate ERK in the cell bodies of primary afferent neurons and associated satellite cells. Nevertheless, whether ERK is also activated in the axons and surrounded Schwann cells which also play a key role in the regeneration process has not been clarified.

Results

Phosphorylation of ERK in the sciatic nerve in several time-points after crush injury has been examined. Higher phosphorylation of ERK was observed in the proximal and distal nerve stumps compared to the contralateral intact nerve from one day to one month after crush. The activation of ERK was mainly localized in the axons of the proximal segments. In the distal segments, however, active ERK was predominantly found in Schwann cells forming Bungner's bands.

Conclusion

The findings indicate that ERK is activated in both the proximal and distal nerve stumps following nerve injury. The role of activated ERK in Wallerian degeneration and subsequent regeneration in vivo remains to be elucidated.     

Diphoton plus Z production at the ILC at \mathcal{O}(\alpha ^4)

In this paper, we consider a system of gravitating bodies in Kaluza–Klein models with toroidal compactification of the extra dimensions. To simulate the astrophysical objects (e.g., our Sun and pulsars) with energy density much greater than the pressure, we assume that these bodies are pressureless in the external space, i.e., the space we inhabit. At the same time, they may have nonzero parameters $\omega _{({\bar{\alpha }} -3)} \, ({\bar{\alpha }} =4,\ldots , D)$ in the equations of state in the extra dimensions. We construct the Lagrange function of this many-body system for any value of $\Sigma =\sum _{{\bar{\alpha }}} \omega _{({\bar{\alpha }} -3)}$ . Moreover, the gravitational tests (PPN parameters, perihelion and periastron advances) require a negligible deviation from the latent soliton value $\Sigma =-(D-3)/2$ . However, the presence of pressure/tension in the internal space results necessarily in the smearing of the gravitating masses over the internal space and in the absence of KK modes. This looks very unnatural from the point of view of quantum physics.     

Localization in the ground state of the ising model with a random transverse field

We study the zero-temperature behavior of the Ising model in the presence of a random transverse field. The Hamiltonian is given by $$H = - J\sum\limits_{\left\langle {x,y} \right\rangle } {\sigma _3 (x)\sigma _3 (y) - \sum\limits_x {h(x)\sigma _1 (x)} } $$ whereJ>0,x,y∈Z ^d, σ₁, σ₃ are the usual Pauli spin 1/2 matrices, andh={h(x),x∈Z ^d} are independent identically distributed random variables. We consider the ground state correlation function 〈σ₃(x)σ₃(y)〉 and prove:

1. Letd be arbitrary. For anym>0 andJ sufficiently small we have, for almost every choice of the random transverse fieldh and everyx∈Z ^d, that $$\left\langle {\sigma _3 (x)\sigma _3 (y)} \right\rangle \leqq C_{x,h} e^{ - m\left| {x - y} \right|} $$ for ally∈Z ^d withC _{x h} <∞.
2. Letd≧2. IfJ is sufficiently large, then, for almost every choice of the random transverse fieldh, the model exhibits long range order, i.e., $$\mathop {\overline {\lim } }\limits_{\left| y \right| \to \infty } \left\langle {\sigma _3 (x)\sigma _3 (y)} \right\rangle > 0$$ for anyx∈Z ^d.

     

Rigid Body Motion in Special Relativity

We study the acceleration and collisions of rigid bodies in special relativity. After a brief historical review, we give a physical definition of the term ‘rigid body’ in relativistic straight line motion. We show that the definition of ‘rigid body’ in relativity differs from the usual classical definition, so there is no difficulty in dealing with rigid bodies in relativistic motion. We then describe

1. The motion of a rigid body undergoing constant acceleration to a given velocity.
2. The acceleration of a rigid body due to an applied impulse.
3. Collisions between rigid bodies.