A Mathematical Analysis of the Dynamics of Prion Proliferation

How do the normal prion protein (PrP(C)) and infectious prion protein (PrP(Sc)) populations interact in an infected host? To answer this question, we analyse the behavior of the two populations by studying a system of differential equations. The system is constructed under the assumption that PrP(Sc) proliferates using the mechanism of nucleated polymerization. We prove that with parameter input consistent with experimentally determined values, we obtain the persistence of PrP(Sc). We also prove local stability results for the disease steady state, and a global stability result for the disease free steady state. Finally, we give numerical simulations, which are confirmed by experimental data

Preeclampsia is associated with compromized maternal synthesis of long chain polyunsaturated fatty acids leading to offspring deficiency

Obesity and excessive lipolysis are implicated in preeclampsia (PE). Intrauterine growth restriction is associated with low maternal body mass index and decreased lipolysis. Our aim was to assess how maternal and offspring fatty acid metabolism is altered in mothers in the third trimester of pregnancy with PE (n=62) or intrauterine growth restriction (n=23) compared with healthy pregnancies (n=164). Markers of lipid metabolism and erythrocyte fatty acid concentrations were measured. Maternal adipose tissue fatty acid composition and mRNA expression of adipose tissue fatty acid–metabolizing enzymes and placental fatty acid transporters were compared. Mothers with PE had higher plasma triglyceride (21%, P<0.001) and nonesterified fatty acid (50%, P<0.001) concentrations than controls. Concentrations of major n−6 and n−3 long-chain polyunsaturated fatty acids in erythrocytes were 23% to 60% lower (all P<0.005) in PE and intrauterine growth restriction mothers and offspring compared with controls. Subcutaneous adipose tissue Δ−5 and Δ−6 desaturase and very long-chain fatty acid elongase mRNA expression was lower in PE than controls (respectively, mean [SD] control 3.38 [2.96] versus PE 1.83 [1.91], P=0.030; 3.33 [2.25] versus 1.03 [0.96], P<0.001; 0.40 [0.81] versus 0.00 [0.00], P=0.038 expression relative to control gene [square root]). Low maternal and fetal long-chain polyunsaturated fatty acid concentrations in PE may be the result of decreased maternal synthesis

Effects of General Incidence and Polymer Joining on Nucleated Polymerization in a Model of Prion Proliferation

Two processes are incorporated into a new model for transmissible prion diseases. These are general incidence for the lengthening process of infectious polymers attaching to and converting noninfectious monomers, and the joining of two polymers to form one longer polymer. The model gives rise to a system of three ordinary differential equations, which is shown to exhibit threshold behavior dependent on the value of the parameter combination giving the basic reproduction number R0. For R00 \u3e1, the system is locally asymptotic to a positive disease equilibrium. The effect of both general incidence and joining is to decrease the equilibrium value of infectious polymers and to increase the equilibrium value of normal monomers. Since the onset of disease symptoms appears to be related to the number of infectious polymers, both processes may significantly inhibit the course of the disease. With general incidence, the equilibrium distribution of polymer lengths is obtained and shows a sharp decrease in comparison to the distribution resulting from mass action incidence. Qualitative global results on the disease free and disease equilibria are proved analytically. Numerical simulations using parameter values from experiments on mice (reported in the literature) provide quantitative demonstration of the effects of these two processes

The negatively charged nitrogen-vacancy centre in diamond: the electronic solution

The negatively charged nitrogen-vacancy centre is a unique defect in diamond that possesses properties highly suited to many applications, including quantum information processing, quantum metrology, and biolabelling. Although the unique properties of the centre have been extensively documented and utilised, a detailed understanding of the physics of the centre has not yet been achieved. Indeed there persists a number of points of contention regarding the electronic structure of the centre, such as the ordering of the dark intermediate singlet states. Without a sound model of the centre's electronic structure, the understanding of the system's unique dynamical properties can not effectively progress. In this work, the molecular model of the defect centre is fully developed to provide a self consistent model of the complete electronic structure of the centre. The application of the model to describe the effects of electric, magnetic and strain interactions, as well as the variation of the centre's fine structure with temperature, provides an invaluable tool to those studying the centre and a means to design future empirical and ab initio studies of this important defect.Comment: 24 pages, 6 figures, 10 table

Nonequilibrium dynamics of a simple stochastic model

We investigate the low-temperature dynamics of a simple stochastic model, introduced recently in the context of the physics of glasses. The slowest characteristic time at equilibrium diverges exponentially at low temperature. On smaller time scales, the nonequilibrium dynamics of the system exhibits an aging regime. We present an analytical study of the scaling behaviour of the mean energy, of its local correlation and response functions, and of the associated fluctuation-dissipation ratio throughout the regime of low temperature and long times. This analysis includes the aging regime, the convergence to equilibrium, and the crossover behaviour between them.Comment: 36 pages, plain tex, 7 figures, to be published by Journal of Physics

A study of the dynamics of magnetic disaccommodation in amorphous ferromagnets. I. Experimental results

Systematic room‐temperature measurements of the aftereffect of the ac magnetic permeability have been performed on a Fe81B13.5 Si3.5C2 amorphous ribbon in order to get detailed information about the nature of the atomic ordering processes responsible for the magnetic relaxation. The magnetic aftereffect related to 180° domain‐wall motion has been measured by means of a specific technique allowing periodic domain‐wall displacements to be induced between two fixed, neighboring equilibrium positions by applying a square‐wave field of proper amplitude and frequency. In this way, the average direction of the magnetization vector is cyclically modified in all points where the studied directional ordering processes may occur. As a consequence, the kinetics of ordering is modified in a characteristic way, giving rise to relevant variations in the intensity of the magnetic aftereffect measured between fixed times (t1=2×10−3 s and t2=10−1 s), and in the value of the magnetic induction at the time t2. All measurements have been performed at constant applied field. The degree of reliability of this experimental technique has been analyzed in detail. The magnetic aftereffect, ΔB=B(t1)−B(t2), and the magnetic induction B(t2) have been measured as functions of the number of domain‐wall cycles, and after removing the square‐wave field for a variable time t∗. The results of many independent measurements are reported and discussed

Enumeration of States in a Periodic Glass

We present an analytic enumeration of the metastable states, $N_s$, in a periodic long-range Josephson array frustrated by a transverse field. We find that the configurational entropy, $S_{conf} \equiv \ln N_s$, is extensive and scales with frustration, confirming that the non-random system is glassy. We also find that $S_{conf}$ is different from that of its disordered analogue, despite that fact that the two models share the same dynamical equations

Implicit theories and offender representativeness in judgments about sexual crime

Implicit theories structure the way people understand and respond to various human actions. Typically, people believe attributes are either fixed (entitists) or malleable (incrementalists). The present study aimed to examine: (a) whether attitudes towards sexual offenders differ depending upon one’s implicit theory about human nature and sexual offenders, and (b) whether implicit theories are associated with judgments made about different types of child abuser. A sample of 252 community participants was recruited. Their attitudes, implicit theories, and political orientation were assessed via self-report. One of three vignettes describing an incidence of child sexual abuse was then presented. The cases were identical except the perpetrator was either an adult male, an adult female, or a male juvenile. Participants then made judgments about the offender's deserved sentence and moral character. Entitists (across both domains) held more negative attitudes than incrementalists, although the magnitude of the difference was greatest when examining implicit theories about sexual offenders. Compared to those with an incremental theory of sexual offenders, entity theorists judged sexual offending to be more: (a) indicative of the perpetrator’s moral character, and (b) deserving of punishment. However, scores were greater towards the adult male relative to the adult female and juvenile. The findings suggest that implicit theories about sexual offenders are domain-specific. They also indicate that judgments made by those with an entity theory (about sexual offenders) are affected by whether a case is representative of a stereotypical sexual offender. Implications of the findings are discussed, along with limitations and future research