Hopf bifurcation in a gene regulatory network model: Molecular movement causes oscillations

Gene regulatory networks, i.e. DNA segments in a cell which interact with each other indirectly through their RNA and protein products, lie at the heart of many important intracellular signal transduction processes. In this paper we analyse a mathematical model of a canonical gene regulatory network consisting of a single negative feedback loop between a protein and its mRNA (e.g. the Hes1 transcription factor system). The model consists of two partial differential equations describing the spatio-temporal interactions between the protein and its mRNA in a 1-dimensional domain. Such intracellular negative feedback systems are known to exhibit oscillatory behaviour and this is the case for our model, shown initially via computational simulations. In order to investigate this behaviour more deeply, we next solve our system using Greens functions and then undertake a linearized stability analysis of the steady states of the model. Our results show that the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf bifurcation. This shows that the spatial movement of the mRNA and protein molecules alone is sufficient to cause the oscillations. This has implications for transcription factors such as p53, NF-$kappa$B and heat shock proteins which are involved in regulating important cellular processes such as inflammation, meiosis, apoptosis and the heat shock response, and are linked to diseases such as arthritis and cancer

Re-Examination of Possible Bimodality of GALLEX Solar Neutrino Data

The histogram formed from published capture-rate measurements for the GALLEX solar neutrino experiment is bimodal, showing two distinct peaks. On the other hand, the histogram formed from published measurements derived from the similar GNO experiment is unimodal, showing only one peak. However, the two experiments differ in run durations: GALLEX runs are either three weeks or four weeks (approximately) in duration, whereas GNO runs are all about four weeks in duration. When we form 3-week and 4-week subsets of the GALLEX data, we find that the relevant histograms are unimodal. The upper peak arises mainly from the 3-week runs, and the lower peak from the 4-week runs. The 4-week subset of the GALLEX dataset is found to be similar to the GNO dataset. A recent re-analysis of GALLEX data leads to a unimodal histogram.Comment: 14 pages, 8 figure

Review of Methods of Power-Spectrum Analysis as Applied to Super-Kamiokande Solar Neutrino Data

To help understand why different published analyses of the Super-Kamiokande solar neutrino data arrive at different conclusions, we have applied six different methods to a standardized problem. The key difference between the various methods rests in the amount of information that each processes. A Lomb-Scargle analysis that uses the mid times of the time bins and ignores experimental error estimates uses the least information. A likelihood analysis that uses the start times, end times, and mean live times, and takes account of the experimental error estimates, makes the greatest use of the available information. We carry out power-spectrum analyses of the Super-Kamiokande 5-day solar neutrino data, using each method in turn, for a standard search band (0 to 50 yr-1). For each method, we also carry out a fixed number (10,000) of Monte-Carlo simulations for the purpose of estimating the significance of the leading peak in each power spectrum. We find that, with one exception, the results of these calculations are compatible with those of previously published analyses. (We are unable to replicate Koshio's recent results.) We find that the significance of the peaks at 9.43 yr-1 and at 43.72 yr-1 increases progressively as one incorporates more information into the analysis procedure.Comment: 21 pages, 25 figure

Sunspot rotation. I. A consequence of flux emergence

Context. Solar eruptions and high flare activity often accompany the rapid rotation of sunspots. The study of sunspot rotation and the mechanisms driving this motion are therefore key to our understanding of how the solar atmosphere attains the conditions necessary for large energy release. Aims. We aim to demonstrate and investigate the rotation of sunspots in a 3D numerical experiment of the emergence of a magnetic flux tube as it rises through the solar interior and emerges into the atmosphere. Furthermore, we seek to show that the sub-photospheric twist stored in the interior is injected into the solar atmosphere by means of a definitive rotation of the sunspots. Methods. A numerical experiment is performed to solve the 3D resistive magnetohydrodynamic (MHD) equations using a Lagrangian-Remap code. We track the emergence of a toroidal flux tube as it rises through the solar interior and emerges into the atmosphere investigating various quantities related to both the magnetic field and plasma. Results. Through detailed analysis of the numerical experiment, we find clear evidence that the photospheric footprints or sunspots of the flux tube undergo a rotation. Significant vertical vortical motions are found to develop within the two polarity sources after the field emerges. These rotational motions are found to leave the interior portion of the field untwisted and twist up the atmospheric portion of the field. This is shown by our analysis of the relative magnetic helicity as a significant portion of the interior helicity is transported to the atmosphere. In addition, there is a substantial transport of magnetic energy to the atmosphere. Rotation angles are also calculated by tracing selected fieldlines; the fieldlines threading through the sunspot are found to rotate through angles of up to 353 degrees over the course of the experiment

7Be ^7 Be Neutrino Signal Variation in KamLAND

Large Mixing Angle (LMA) neutrino oscillation is the main solution for the long-standing Solar Neutrino Problem (SNP). Whether there is any subdominant effect accompanying the dominant LMA solution can not be ruled out at the moment, but will be settled by the forthcoming data from highly skilled real time experiments targeting essentially the low energy domain of solar neutrinos. Assuming a subdominant effect converting one of the active neutrinos into a sterile partner in the varying solar field with changing sunspot activity, we performed field-profile-independent predictions for $^7 Be$ neutrino signal variation, which might be tested in the KamLAND's future solar neutrino detection program. We found that after a substantial reduction of background and running of KamLAND solar mode through the sunspot maximum period (around 2010 - 2012), when the solar field at the resonance may vary from few $kG$ to $300~kG$, the subdominant time variation effect might be clearly visible (more than $5\sigma$) for $^7 Be$ neutrinos.Comment: 12 pages, 4 figures, typos corrected. To appear in JHE

Kinematic, kinetic and electromyographic response to customized foot orthoses in patients with tibialis posterior tenosynovitis, pes plano valgus and rheumatoid arthritis

Objective. To describe the effect of customized foot orthoses (FOs) on the kinematic, kinetic and EMG features in patients with RA, tibialis posterior (TP) tenosynovitis and associated pes plano valgus.<p></p> Methods. Patients with RA and US-confirmed tenosynovitis of TP underwent gait analysis, including three-dimensional (3D) kinematics, kinetics, intramuscular EMG of TP and surface EMG of tibialis anterior, peroneus longus, soleus and medial gastrocnemius. Findings were compared between barefoot and shod with customized FO conditions.<p></p> Results. Ten patients with RA with a median (range) disease duration of 3 (1–18) years were recruited. Moderate levels of foot pain and foot-related impairment and disability were present with moderately active disease states. Altered timing of the soleus (P = 0.05) and medial gastrocnemius (P = 0.02) and increased magnitude of tibialis anterior (P = 0.03) were noted when barefoot was compared with shod with FO. Trends were noted for reduced TP activity in the contact period (P = 0.09), but this did not achieve statistical significance. Differences in foot motion characteristics were recorded for peak rearfoot eversion (P = 0.01), peak rearfoot plantarflexion (P < 0.001) and peak forefoot abduction (P = 0.02) in the shod with FOs compared with barefoot conditions. No differences in kinetic variables were recorded.<p></p> Conclusion. This study has demonstrated, for the first time, alterations in muscle activation profiles and foot motion characteristics in patients with RA, pes plano valgus and US-confirmed TP tenosynovitis in response to customized FOs. Complex adaptations were evident in this cohort and further work is required to determine whether these functional alterations lead to improvements in patient symptoms.<p></p&gt

Factors associated with the performance and cost-effectiveness of using lymphatic filariasis transmission assessment surveys for monitoring soil-transmitted helminths: a case study in Kenya.

Transmission assessment surveys (TAS) for lymphatic filariasis have been proposed as a platform to assess the impact of mass drug administration (MDA) on soil-transmitted helminths (STHs). This study used computer simulation and field data from pre- and post-MDA settings across Kenya to evaluate the performance and cost-effectiveness of the TAS design for STH assessment compared with alternative survey designs. Variations in the TAS design and different sample sizes and diagnostic methods were also evaluated. The district-level TAS design correctly classified more districts compared with standard STH designs in pre-MDA settings. Aggregating districts into larger evaluation units in a TAS design decreased performance, whereas age group sampled and sample size had minimal impact. The low diagnostic sensitivity of Kato-Katz and mini-FLOTAC methods was found to increase misclassification. We recommend using a district-level TAS among children 8-10 years of age to assess STH but suggest that key consideration is given to evaluation unit size