Achievement of Target Gain Larger than Unity in an Inertial Fusion Experiment

On December 5, 2022, an indirect drive fusion implosion on the National Ignition Facility (NIF) achieved a target gain G_{target} of 1.5. This is the first laboratory demonstration of exceeding "scientific breakeven" (or G_{target}>1) where 2.05 MJ of 351 nm laser light produced 3.1 MJ of total fusion yield, a result which significantly exceeds the Lawson criterion for fusion ignition as reported in a previous NIF implosion [H. Abu-Shawareb et al. (Indirect Drive ICF Collaboration), Phys. Rev. Lett. 129, 075001 (2022)PRLTAO0031-900710.1103/PhysRevLett.129.075001]. This achievement is the culmination of more than five decades of research and gives proof that laboratory fusion, based on fundamental physics principles, is possible. This Letter reports on the target, laser, design, and experimental advancements that led to this result.

Demonstration of improved laser preheat with a cryogenically cooled magnetized liner inertial fusion platform

We report on progress implementing and testing cryogenically cooled platforms for Magnetized Liner Inertial Fusion (MagLIF) experiments. Two cryogenically cooled experimental platforms were developed: an integrated platform fielded on the Z pulsed power generator that combines magnetization, laser preheat, and pulsed-power-driven fuel compression and a laser-only platform in a separate chamber that enables measurements of the laser preheat energy using shadowgraphy measurements. The laser-only experiments suggest that ∼89% ± 10% of the incident energy is coupled to the fuel in cooled targets across the energy range tested, significantly higher than previous warm experiments that achieved at most 67% coupling and in line with simulation predictions. The laser preheat configuration was applied to a cryogenically cooled integrated experiment that used a novel cryostat configuration that cooled the MagLIF liner from both ends. The integrated experiment, z3576, coupled 2.32 ± 0.25 kJ preheat energy to the fuel, the highest to-date, demonstrated excellent temperature control and nominal current delivery, and produced one of the highest pressure stagnations as determined by a Bayesian analysis of the data.

Lawson Criterion for Ignition Exceeded in an Inertial Fusion Experiment

For more than half a century, researchers around the world have been engaged in attempts to achieve fusion ignition as a proof of principle of various fusion concepts. Following the Lawson criterion, an ignited plasma is one where the fusion heating power is high enough to overcome all the physical processes that cool the fusion plasma, creating a positive thermodynamic feedback loop with rapidly increasing temperature. In inertially confined fusion, ignition is a state where the fusion plasma can begin "burn propagation" into surrounding cold fuel, enabling the possibility of high energy gain. While "scientific breakeven" (i.e., unity target gain) has not yet been achieved (here target gain is 0.72, 1.37 MJ of fusion for 1.92 MJ of laser energy), this Letter reports the first controlled fusion experiment, using laser indirect drive, on the National Ignition Facility to produce capsule gain (here 5.8) and reach ignition by nine different formulations of the Lawson criterion.

The role of interventions in the cancer evolution-an evolutionary games approach

We propose to endow evolutionary gamemodels with changes of the phenotypes adjustment during the transient generations performed by the parameters in the payoff matrix which determine the fitness resulting from different interactions between players. These changes represent an alteration of access to external resources which, in turn, may reflect anticancer treatment. In the case of spatial games, these functions are represented by an additional lattice where another and parallel game based on cellular automata is performed. The main assumption of the spatial games is that each cell on the lattice is represented by a player following only one strategy. We propose to consider cells on the spatial lattice as heterogeneous (instead of homogeneous), so that each particular player may contain mixed phenotypes. Spatial games of the type, proposed by us, are called multidimensional spatial evolutionary games (MSEG). It may happen that within the population, all of the players have diverse phenotypes (which probably better describes biological phenomena). The additional lattice representing the evolution of resources increases only the dimension of the lattice in the MSEG.

Renal complications of cancer therapies

Cancer patients often exhibit preexisting renal impairment and are simultaneously at risk for developing further kidney injury due to direct or indirect complications of oncological therapies. The nature of kidney injury is highly dependent on the therapy regimen used, and the spectrum of possible kidney stressors has widened as a result of the development of new therapeutic modalities such as molecular therapy or immunotherapy. Indirect renal complications are often due to volume depletion or other therapy-related side effects. Direct toxicity from "classic" chemotherapy treatments such as cisplatin usually leads to acute tubular necrosis, whereas treatment with protein kinase inhibitors is more likely to cause disorders such as thrombotic microangiopathy. Immunotherapy often affects kidneys through the development of acute interstitial nephritis. Because of the high risk of nephrological complications in oncological patients, close monitoring of renal function and the early involvement of a nephrologist are strongly recommended.

Self-generated surface magnetic fields inhibit laser-driven sheath acceleration of high-energy protons

High-intensity lasers interacting with solid foils produce copious numbers of relativistic electrons, which in turn create strong sheath electric fields around the target. The proton beams accelerated in such fields have remarkable properties, enabling ultrafast radiography of plasma phenomena or isochoric heating of dense materials. In view of longer-term multidisciplinary purposes (e.g., spallation neutron sources or cancer therapy), the current challenge is to achieve proton energies well in excess of 100 MeV, which is commonly thought to be possible by raising the on-target laser intensity. Here we present experimental and numerical results demonstrating that magnetostatic fields self-generated on the target surface may pose a fundamental limit to sheath-driven ion acceleration for high enough laser intensities. Those fields can be strong enough (~10⁵ T at laser intensities ~10²¹ W cm^–2) to magnetize the sheath electrons and deflect protons off the accelerating region, hence degrading the maximum energy the latter can acquire.

Laser-generated ion acceleration has received increasing attention due to recent progress in super-intense lasers. Here the authors demonstrate the role of the self-generated magnetic field on the ion acceleration and limitations on the energy scaling with laser intensity.

Obstetric and gynecologic problems associated with eating disorders

OBJECTIVE

This article summarizes the literature on obstetric and gynecologic complications associated with eating disorders.

METHOD

We performed a comprehensive search of the current literature on obstetric and gynecologic complications associated with eating disorders using PubMed. More recent randomized-controlled trials and larger data sets received priority. We also chose those that we felt would be the most relevant to providers.

RESULTS

Common obstetric and gynecologic complications for women with eating disorders include infertility, unplanned pregnancy, miscarriage, poor nutrition during pregnancy, having a baby with small head circumference, postpartum depression and anxiety, sexual dysfunction and complications in the treatment for gynecologic cancers. There are also unique associations by eating disorder diagnosis, such as earlier cessation of breastfeeding in anorexia nervosa; increased polycystic ovarian syndrome in bulimia nervosa; and complications of obesity as a result of binge eating disorder.

DISCUSSION

We focus on possible biological and psychosocial factors underpinning risk for poor obstetric and gynecological outcomes in eating disorders. Understanding these factors may improve both our understanding of the reproductive needs of women with eating disorders and their medical outcomes. We also highlight the importance of building multidisciplinary teams to provide comprehensive care to women with eating disorders during the reproductive years.

A typical Wegeners granulomatosis -- but not pauci-immune!

We present a the case of 58-year old man who was admitted to hospital with typical clinical features (bloody nasal discharge, arthralgia, acute kidney injury with a nephritic syndrome) consisting with Wegeners granulomatosis (WG). CT-scan showed pulmonary nodules and antineutrophil cytoplasmatic antibodies (ANCA) were elevated. A kidney biopsy showed a crescentic glomerulonephritis, but not pauci-immune-immune with a histopathological staining of a mesangioproliferative IgA-glomerulonephritis. The patient was put on prednisolone and i.v. cyclophosphamid (CYCLOPS-protocol (1). The anti-proteinase-3 antibody titer decreased and the CT-scan showed decreased activity of Wegener's granulomatosis (BVAS 26 dropped to 2) and the patient`s serum creatinine level was stable. The exact nosological relation of mesangial IgA-nephropathy to WG is still unclear. This case underlines that knowledge of renal histology is essential in the management of patients with renal disease, especially in patients with hematuria and/or proeinuria with positive ANCA.

[Hypertension due to aortic coarctation--a missed clinical diagnosis]

HISTORY AND FINDINGS

A 30-year-old woman presented to our emergency department with severe headaches, dizziness and uncontrolled hypertension. She had arterial hypertension and a known heart murmur since adolescence. Previous medical work up did not reveal any cause for secondary hypertension. Recently her blood pressure had been difficult to control. A systolic murmur as well as absent inguinal and feet pulses were notable at the physical examination.

INVESTIGATIONS

When performing doppler ultrasound the closing pressures of the dorsalis pedis arteries were only 70 mm Hg compared to a blood pressure reading of 160 mm Hg on the upper arms. Thoracic magnetic resonance imaging showed subtotal aortic coarctation causing the differences in blood pressures. Echocardiography and cardiac catheterization additionally revealed a moderately stenosed bicuspid aortic valve, the pressure gradient across the coarctation was 30 mm Hg.

THERAPY AND COURSE

Despite the severity of the coarctation an interventional approach was favoured instead of a classical operative therapy. Balloon dilatation with stent implantation was performed without complications. Since the intervention blood pressure have remained normotensive, the coarctation gradient being markedly reduced.

CONCLUSIONS

In young patients with arterial hypertension, as well as in cases of severe and refractory hypertension, causes of secondary hypertension must be looked for and excluded. Especially when hypertension occurs in adolescence, aortic coarctation should be taken into account, in addition to renal or endocrine causes. A thorough physical examination with cardiac auscultation and checking of all peripheral pulses is the crucial step to the diagnosis.

[Salt appetite, cramps and palpitations in a 21-year old medical secretary]

Hypokalemia is a common finding. The clinical presentation can be paralyses and cardiac arrhythmias. We present a normotensive young woman with salt appetite, cramps and palpitations. In our case report the patient shows a positive family history for hypopotassemia, a metabolic alkalosis with hypotension, and hypocalciuria with an increased urinary potassium loss. The levels of renin and aldosterone were elevated. After a negative testing for metabolites of diuretics, we obtained a positive result of the suspected SLC12A3 genetic test. This mutation leads to a failure of the thiazide-sensitive sodium-2-chloride-cotransporter, the so called Gitelman syndrome, which presents similar to a chronic thiazide therapy. The Gitelman syndrome is a rare disease with renal potassium loss and hypotension. Especially in young patients around the age of twenty or in patients with chronic intractable hypopotassemia a Gitelman syndrome should be considered.

Fibrogenic growth factors in encapsulating peritoneal sclerosis

BACKGROUND

Increased local levels of fibrogenic growth hormones contribute substantially to the process of encapsulating peritoneal sclerosis (EPS) in animal models.

METHODS

We analyzed probes from patients with normal kidney function (n = 10), with normal kidney function and inflammation (n = 10), on PD without (n = 10) and with EPS (n = 9). We investigated the degree of fibrosis and the number of vessels and vasculopathy. Additionally, we investigated the expression of NFkappaB, TGFbeta1, TGFbeta1 receptor, TGFbeta2, TGFbeta2 receptor, FGF-BP, CTGF and VEGF by immunohistochemistry.

RESULTS

In EPS, we found an exclusive upregulation of VEGF (normal 0, appendicitis 1.0 +/- 1.2, PD 1.7 +/- 1.8 and EPS 5.7 +/- 4.4; p < 0.0001), whereas in PD, CTGF was significantly increased (normal 6.0 +/- 2.8, appendicitis 7.3 +/- 2.5, PD 10.0 +/- 1.8 and EPS 7.3 +/- 2.1; p = 0.0059). The results for the TGFbeta system and NFkappaB were not uniform, in EPS no increases were demonstrable. Vasculopathy was significantly more pronounced in EPS (normal 0.4 +/- 0.5, appendicitis 0.2 +/- 0.3, PD 1.0 +/- 0.7 and EPS 1.6 +/- 1.2; p < 0.0001) than in PD or inflammation (normal 30 +/- 16, appendicitis 82 +/- 48, PD 1,936 +/- 952 and EPS 2,613 +/- 1,209; p < 0.0001), whereas the density of vessels were decreased (normal 125 +/- 114, appendicitis 817 +/- 347, PD 81 +/- 57 and EPS 36 +/- 33; p < 0.0001).

CONCLUSIONS

The process of EPS was associated with increased VEGF in the peritoneum. The reduced density of vessels compared with marked fibrosis could point to hypoxia as an inducer.

Controlled transport and focusing of laser-accelerated protons with miniature magnetic devices

This Letter demonstrates the transporting and focusing of laser-accelerated 14 MeV protons by permanent magnet miniature quadrupole lenses providing field gradients of up to 500 T/m. The approach is highly reproducible and predictable, leading to a focal spot of (286 x 173) microm full width at half maximum 50 cm behind the source. It decouples the relativistic laser-proton acceleration from the beam transport, paving the way to optimize both separately. The collimation and the subsequent energy selection obtained are perfectly applicable for upcoming high-energy, high-repetition rate laser systems.

Robust association of the APOE epsilon4 allele with premature myocardial infarction especially in patients without hypercholesterolaemia: the Aachen study

BACKGROUND

Genetic influence on the manifestation of coronary artery disease (CAD) and myocardial infarction (MI) has been shown previously. From many candidate genes the APOE (apolipoprotein E) with the major alleles epsilon2/epsilon3/epsilon4 is in the focus of interest.

MATERIALS AND METHODS

In 1817 patients admitted for their first left heart catheterization at a premature age (males < 55 and females < 65) the association of APOE alleles with MI was analysed. Genotyping was done by 5' exonuclease assay (TaqMan). RESULTS APOE was significantly associated with hypercholesterolaemia (epsilon4 72% vs. epsilon3 66% vs. epsilon2 51%; P < 0.0001), and premature MI (epsilon4 57% vs. epsilon3 50% vs. epsilon2 41%; P < 0.0001; hazard ratio 1.41, 95%CI 1.14-1.75). In patients without hypercholesterolaemia, the APOE allele epsilon4 was highly predictive for the presence of premature MI (epsilon4 55% vs. epsilon3 45% vs. epsilon2 28%; P < 0.0001; hazard ratio 1.75, 95%CI 1.19-2.57).

CONCLUSION

The APOEepsilon4 allele shows a robust association with premature MI independent of hypercholesterolaemia.

APOE alleles are not associated with calcific aortic stenosis

OBJECTIVES

To analyse the association of APOE alleles with aortic stenosis (AS) in a large study population.

METHODS

Patients with AS (n = 538) and a control group of the same age without heart disease (n = 536) were recruited. Left heart catheterisation was performed and mean gradient, aortic valve area, presence of stenotic coronary artery disease (CAD) and cardiovascular risk factors (hypercholesterolaemia, hypertension, smoking, diabetes mellitus and family history of CAD) were assessed. The frequency of the APOE major alleles e2, e3 and e4 was assessed by genotyping the polymorphisms APOE334 and APOE472 with a 5' exonuclease assay (TaqMan).

RESULTS

Mean gradient across the aortic valve in cases was 50 (SD 20) mm Hg corresponding to a mean aortic valve area of 0.84 (SD 0.34) cm(2). 270 patients with AS had stenotic CAD. Among patients with AS, the prevalence of hypercholesterolaemia (64% v 40%, p < 0.001), smoking (43% v 27%, p < 0.001), diabetes (27% v 17%, p < 0.01), family history of CAD (30% v 21%, p </= 0.05), and male sex (65% v 44%, p < 0.001) was higher in those with than in those without CAD. The frequency of the major alleles was not different between cases and controls (APOE e2: 104 (19.3%) v 94 (17.5%); APOE e3: 319 (59.3%) v 332 (61.9%); APOE e4: 115 (21.3%) v 110 (20.5%); all p > 0.10).

CONCLUSION

APOE e4 is not associated with AS, reflecting the different genetic backgrounds of CAD and AS.

New Explicit Expressions for Relative Frequencies of Single-Nucleotide Polymorphisms With Application to Statistical Inference on Population Growth

We present new methodology for calculating sampling distributions of single-nucleotide polymorphism (SNP) frequencies in populations with time-varying size. Our approach is based on deriving analytical expressions for frequencies of SNPs. Analytical expressions allow for computations that are faster and more accurate than Monte Carlo simulations. In contrast to other articles showing analytical formulas for frequencies of SNPs, we derive expressions that contain coefficients that do not explode when the genealogy size increases. We also provide analytical formulas to describe the way in which the ascertainment procedure modifies SNP distributions. Using our methods, we study the power to test the hypothesis of exponential population expansion vs. the hypothesis of evolution with constant population size. We also analyze some of the available SNP data and we compare our results of demographic parameters estimation to those obtained in previous studies in population genetics. The analyzed data seem consistent with the hypothesis of past population growth of modern humans. The analysis of the data also shows a very strong sensitivity of estimated demographic parameters to changes of the model of the ascertainment procedure.

A note on distributions of times to coalescence, under time-dependent population size

Expressions for marginal distributions of times in the time-varying coalescence process are derived. The proposed method allows also for computation of joint probability distribution for pairs, triples, etc. of coalescence times. The expressions derived are useful for (1) extending several statistics from time constant to time-varying case, (2) increasing efficiency and accuracy of simulations in time-varying evolution, and (3) debugging coalescence simulation software.

An application of a general branching process in the study of the genetics of aging

A general branching process model is developed to analyse familial dependence in longevity data. A general formula for the survival function of a randomly chosen sibling of an individual of a specified age is derived. The branching process model takes into account that siblings' ages may be censored. This is applied to a data set consisting of lifelengths of siblings of centenarians. Age distributions used in the branching process model are estimated from US Census data from the relevant period. It is demonstrated that there is a marked difference in the survival function according to the formula assuming no familial effect and the empirical survival function estimated from the data; thus, indicating a strong familial component.

DNA dinucleotide evolution in humans: fitting theory to facts

We examine length distributions of approximately 6000 human dinucleotide microsatellite loci, representing chromosomes 1-22, from the GDB database. Under the stepwise mutation model, results from theory and simulation are compared with the empirical data. In both constant and expanding population scenarios, a simple single-step model with parameters chosen to account for the observed variance of microsatellite lengths produces results inconsistent with the observed heterozygosity and the dispersion of length skewness. Complicating the model by allowing a variable mutation rate accounts for the homozygosity, and introducing a small probability of a large mutation step accounts for the dispersion in skewnesses. We discuss these results in light of the long-term evolution of microsatellites.

Modeling of long-term screening for lung carcinoma

BACKGROUND

Results from the Mayo Lung Project (MLP), a randomized clinical trial for the early detection of lung carcinoma, were interpreted as proof that the early detection of lung carcinoma by chest X-ray does not reduce the mortality from this disease. Recent analysis of extended follow-up data from the MLP subjects found that after approximately 20 years there still was no apparent difference in lung carcinoma mortality between a study group and a control group.

METHODS

To view this result within context, the authors utilized a previously published simulation model of the MLP, with parametric values that were estimated at the time of the original publication based on the data collected by the MLP.

RESULTS

The model produced predictions of the extended follow-up statistics that were found to be consistent with the data published in the prior study. The authors believe this provides long-term validation for the model. Conversely, the same model demonstrated that had the study subjects been screened annually for the extended follow-up period, the difference in mortality would be noticeable, even with the low sensitivity of chest X-ray detection.

CONCLUSIONS

The results of current study strongly suggest that long-term screening with chest X-ray results in a reduction in lung carcinoma mortality. The limited extent of this benefit is the result of the low sensitivity of chest X-ray as a screening tool.

Ultrashort-laser-pulse measurement using swept beams

We demonstrate a frequency-resolved optical gating (FROG) device that uses a sweepshot geometry that combines the advantages of multishot and single-shot pulse-measurement devices, has only one moving part, a galvanometer, and requires no computer control. Like a multishot device, it focuses the beam to a small spot (rather than a line focus) and has a high intensity in the nonlinear medium. Like single-shot devices, it makes measurements quickly, generating an entire FROG trace on a single camera screen (rather than requiring many camera downloads).

Highly simplified device for ultrashort-pulse measurement

We show that a frequency-resolved optical gating device using (1) a thick nonlinear crystal to replace the usual thin crystal and spectrometer and (2) a Fresnel biprism to replace the beam splitter and delay line yields a remarkably simple single-shot ultrashort-pulse intensity-and-phase measurement device with no sensitive alignment parameters and significantly greater sensitivity.

A power analysis of microsatellite-based statistics for inferring past population growth

We present results concerning the power to detect past population growth using three microsatellite-based statistics available in the current literature: (1) that based on between-locus variability, (2) that based on the shape of allele size distribution, and (3) that based on the imbalance between variance and heterozygosity at a locus. The analysis is based on the single-step stepwise mutation model. The power of the statistics is evaluated for constant, as well as variable, mutation rates across loci. The latter case is important, since it is a standard procedure to pool data collected at a number of loci, and mutation rates at microsatellite loci are known to be different. Our analysis indicates that the statistic based on the imbalance between allele size variance and heterozygosity at a locus has the highest power for detection of population growth, particularly when mutation rates vary across loci.

Increased-bandwidth in ultrashort-pulse measurement using an angle-dithered nonlinear-optical crystal

We show that the usual phase-matching-bandwidth constraint in ultrashort-laser-pulse measurement techniques is overly restrictive. Specifically, the phase-matching bandwidth need not exceed the pulse bandwidth on every pulse. Instead, only the phase-matching bandwidth integrated over the measurement period need exceed the pulse bandwidth. We show that angle-dithering a second-harmonic-generation crystal that is otherwise too narrowband (that is, too thick) can yield sufficient phase-matching bandwidth and an accurate pulse measurement. We apply this technique to frequency-resolved optical gating (FROG) and show that accurate pulse measurements can be made using a comparatively very thick and hence narrowband crystal. An additional advantage of using a thick crystal is increased signal strength.

Rate and directionality of mutations and effects of allele size constraints at anonymous, gene-associated, and disease-causing trinucleotide loci

We studied the patterns of within- and between-population variation at 29 trinucleotide loci in a random sample of 200 healthy individuals from four diverse populations: Germans, Nigerians, Chinese, and New Guinea highlanders. The loci were grouped as disease-causing (seven loci with CAG repeats), gene-associated (seven loci with CAG/CCG repeats and eight loci with AAT repeats), or anonymous (seven loci with AAT repeats). We used heterozygosity and variance of allele size (expressed in units of repeat counts) as measures of within-population variability and GST (based on heterozygosity as well as on allele size variance) as the measure of genetic differentiation between populations. Our observations are: (1) locus type is the major significant factor for differences in within-population genetic variability; (2) the disease-causing CAG repeats (in the nondisease range of repeat counts) have the highest within-population variation, followed by the AAT-repeat anonymous loci, the AAT-repeat gene-associated loci, and the CAG/CTG-repeat gene-associated loci; (3) an imbalance index beta, the ratio of the estimates of the product of effective population size and mutation rate based on allele size variance and heterozygosity, is the largest for disease-causing loci, followed by AAT- and CAG/CCG-repeat gene-associated loci and AAT-repeat anonymous loci; (4) mean allele size correlates positively with allele size variance for AAT- and CAG/CCG-repeat gene-associated loci and negatively for anonymous loci; and (5) GST is highest for the disease-causing loci. These observations are explained by specific differences of rates and patterns of mutations in these four groups of trinucleotide loci, taking into consideration the effects of the past demographic history of the modern human population.

Stochastic models of telomere shortening

Shortening of chromosome ends, known as telomeres, is one of the supposed mechanisms of cellular aging and death. We provide a probabilistic analysis of the process of loss of telomere ends. The first work concerned with that issue is the paper by Levy et al. [J. Molec. Biol. 225 (1992) 951-960]. Their deterministic model reproduced the observed frequencies of viable cells in the in vitro experiments. Arino et al. [J. Theor. Biol. 177 (1995) 45-57] reformulated the model of Levy et al. (1992) in the terms of branching processes with denumerable type space. In the present paper, the mathematical results of Arino et al. (1995) are extended to the case in which cell death is present, in cells with telomeres above and below the critical threshold of length, generally with differing probabilities. Both exact and asymptotic results are provided, as well as a discussion of biological relevance of the results.

Quantitation of minimal residual disease in acute myelogenous leukemia and myelodysplastic syndromes in complete remission by molecular cytogenetics of progenitor cells

Detection of karyotypic clonal abnormalities are prognostically useful in patients with acute myelogenous leukemia (AML) and myelodysplastic syndromes (MDS), but cytogenetic methods are not sensitive enough to detect low numbers of residual leukemic cells in patients who have achieved complete remission (CR). Fluorescence in situ hybridization (FISH) and fluorescence activated cell sorting (FACS) were used to investigate the frequency and presence of minimal residual disease (MRD) in AML and MDS patients (n = 28) with monosomy of chromosomes 7, 17 and 18 and trisomy of chromosomes 6, 8, 9 and 10 in CR. MRD was detected in all patients with monosomy 7 (n = 10) and followed by relapse in eight patients after 4.8 +/- 3.1 months. In contrast, persistent leukemic cells occurred in 11/12 patients with trisomy 8, but only three of them relapsed after 7.7 +/- 4.0 months. Cox regression analysis showed that cytogenetic class and levels of clonal cells at CR were related to time to relapse (P = 0.001). The level of MRD identified patients at high and low risk of relapse. High absolute levels of proliferating residual leukemic cells correlated with monosomy 7 and high risk of relapse.

Application of a time-dependent coalescence process for inferring the history of population size changes from DNA sequence data

Distribution of pairwise differences of nucleotides from data on a sample of DNA sequences from a given segment of the genome has been used in the past to draw inferences about the past history of population size changes. However, all earlier methods assume a given model of population size changes (such as sudden expansion), parameters of which (e.g., time and amplitude of expansion) are fitted to the observed distributions of nucleotide differences among pairwise comparisons of all DNA sequences in the sample. Our theory indicates that for any time-dependent population size, N(tau) (in which time tau is counted backward from present), a time-dependent coalescence process yields the distribution, p(tau), of the time of coalescence between two DNA sequences randomly drawn from the population. Prediction of p(tau) and N(tau) requires the use of a reverse Laplace transform known to be unstable. Nevertheless, simulated data obtained from three models of monotone population change (stepwise, exponential, and logistic) indicate that the pattern of a past population size change leaves its signature on the pattern of DNA polymorphism. Application of the theory to the published mtDNA sequences indicates that the current mtDNA sequence variation is not inconsistent with a logistic growth of the human population.

Signatures of population expansion in microsatellite repeat data

To examine the signature of population expansion on genetic variability at microsatellite loci, we consider a population that evolves according to the time-continuous Moran model, with growing population size and mutations that follow a general asymmetric stepwise mutation model. We present calculations of expected allele-size variance and homozygosity at a locus in such a model for several variants of growth, including stepwise, exponential, and logistic growth. These calculations in particular prove that population bottleneck followed by growth in size causes an imbalance between allele size variance and heterozygosity, characterized by the variance being transiently higher than expected under equilibrium conditions. This effect is, in a sense, analogous to that demonstrated before for the infinite allele model, where the number of alleles transiently increases after a stepwise growth of population. We analyze a set of data on tetranucleotide repeats that reveals the imbalance expected under the assumption of bottleneck followed by population growth in two out of three major racial groups. The imbalance is strongest in Asians, intermediate in Europeans, and absent in Africans. This finding is consistent with previous findings by others concerning the population expansion of modern humans, with the bottleneck event being most ancient in Africans, most recent in Asians, and intermediate in Europeans. Nevertheless, the imbalance index alone cannot reliably estimate the time of initiation of population expansion.

Dynamic balance of segregation distortion and selection maintains normal allele sizes at the myotonic dystrophy locus

Myotonic dystrophy (DM), an autosomal dominant neurological disorder, is caused by CTG-repeat expansions at the DMPK locus, with affected individuals having > or = 50 repeats of this trinucleotide. Reduced reproductive fitness of affected individuals and decreased viability of congenital DM have been noted. Expanded CTG-repeat alleles are highly unstable, predominantly yielding even higher repeat sizes. Preferential transmission of longer alleles from heterozygous mothers within the normal size range of alleles also is observed. In view of these observations, it is worth examining how DM has been maintained in human populations for hundreds of generations. We present an analysis of the dynamic properties of a model of joint effects of segregation distortion and selection (intensity of which increases with allele sizes of an individual's genotype). Our mathematical formulation and numerical analyses demonstrate that a weak segregation distortion during female meiosis, together with selection of comparable intensity (within the normal allele size range), can maintain an equilibrium distribution of allele frequencies. Genetic drift, acting in conjunction with the occasional contraction of alleles by mutation, can contribute to the balance of segregation distortion and mutation, in the sense that even weaker selection can explain the observed allele frequencies. The model is applied to CTG-repeat size distributions at the DMPK locus, observed in normal individuals from world populations.

Minimal residual disease in acute myelogenous leukaemia and myelodysplastic syndromes: a follow-up of patients in clinical remission

The majority of patients with acute myelogenous leukaemia (AML) and myelodysplastic syndromes (MDS) relapse, especially those with unfavourable cytogenetics. This study was designed to investigate the presence and frequency of minimal residual disease (MRD) in patients with AML or MDS (n=35) and numerical abnormalities of chromosomes 6, 7, 8, 9, 10, 17 and 18 in clinical remission by using a combination of fluorescence activated cell sorting (FACS), fluorescence in-situ hybridization (FISH) and labelling with bromodeoxyuridine (BUdR). The technique enables the detection of as few as three leukaemic cells in 10(5) normal cells. MRD was detected in 33/35 patients in complete remission (CR). 16 patients relapsed (8/11 with monosomy 7, 4/17 with trisomy 8, and 4/7 with other cytogenetic abnormalities) after a median of 4.8 months (range 3-13). Levels of MRD (P=0.007) and proliferation index (P=0.011) were significantly higher in patients with monosomy 7 than in patients with trisomy 8 or other cytogenetic abnormalities. The percentage of cells in S-phase, the number of abnormal cells and cytogenetic class were related to time to relapse (P=0.001) with S-phase being the single most important prognostic factor (P=0.0001). We conclude that the combination of FACS/FISH/BUdR, which determines the number, phenotype and proliferation rate of very rare leukaemic cells in patients with AML or MDS in clinical remission, provides information that is useful in the identification of patients with high and low likelihood of relapse.

Computer simulation of expansions of DNA triplet repeats in the fragile X syndrome and Huntington's disease

The expansion of DNA triplet repeats has been shown to be responsible for about a dozen hereditary diseases. In this paper we are concerned with a computer model of such expansion, applied to the fragile X syndrome and Huntington's disease, for which enough quantitative data have been collected. The nucleotide sequence associated with the fragile X consists of CGG repeats and is located inside the FMR1 gene. In normal individuals there is a variable number of triplet repeats less than 60; in asymptomatic carriers the number of repeats is 60-200 (premutation). From the premutation range, the number of triplet repeats can increase within one generation to more than 200 producing affected individuals. In Huntington's disease the CAG repeats are located inside the HD gene. In normal individuals the number of repeats varies from around 11, up to 34. In the intermediate range (34-37 repeats), the mutability is increased, frequently leading to alleles of more than 37 repeats, and the disease phenotype. The rapid increase of the number of triplet repeats in affected individuals has been proposed to be due to the formation of folded DNA structures (hairpins) and their repair or misrepair. In order to determine if this proposed mechanism is adequate to account for the rapid increase of repeats and the large number of repeats in affected individuals we developed a mathematical model that includes the known mechanisms of hairpin formation, and strand synthesis and repair. Simulations based on the model using realistic probabilities of hairpin formation produced results that corresponded with the observed range of repeats and transition probabilities from normal to affected individuals. Similar modelling has been published for the Huntington's disease data. However, in this paper we demonstrate that a uniform approach works for fragile X and Huntington's disease, although the detailed assumptions of the model have to be different. These difference provide insight into the mechanisms of expansion in both cases. Among these insights is that an apparent threshold in the number of repeats for rapid expansion, and the preference for expansion over contraction, may be accounted for by relative probabilities of hairpin formation, replication, slippage and repair.

Estimating clonal heterogeneity and interexperiment variability with the bifurcating autoregressive model for cell lineage data

We utilize an extension of the variance-components models for cell lineage data in Huggins and Staudte (R.M. Huggins and R.G. Staudte, Variance components models for dependent cell populations. J. Am. Stat. Assoc. 89:19-29 (1994) to analyze NIH3T3 cells grown in two different media. This modeling approach has the advantage of a simple built-in correlation structure between familial members and allows for estimating experimental effects, rather than treating them as random effects. In addition, this methodology gives robust estimates of model parameters together with standard errors required for statistical inference. The importance of clonal heterogeneity and interexperiment variability in modeling eukaryotic cell cycles was previously pointed out by Kuczek and Axelrod (T. Kuczek and D.E. Axelrod, The importance of clonal heterogeneity and interexperimental variability in modeling the eukaryotic cell cycle. Math. Biosci. 79:87-96 (1986). This analysis confirms significantly positive sister-sister correlation when cells are grown in rich or poor medium and negative mother-daughter correlation when cells are grown in poor medium. However, for cells grown in rich medium, Kuczek and Axelrod's analysis gives negative mother-daughter correlations, whereas this analysis gives significant positive mother-daughter correlations.

Linkage analyses in type I diabetes mellitus using CASPAR, a software and statistical program for conditional analysis of polygenic diseases

We have developed software and statistical tools for linkage analysis of polygenic diseases. We use type I diabetes mellitus (insulin-dependent diabetes mellitus, IDDM) as our model system. Two susceptibility loci (IDDM1 on 6p21 and IDDM2 on 11p15) are well established, and recent genome searches suggest the existence of other susceptibility loci. We have implemented CASPAR, a software tool that makes it possible to test for linkage quickly and efficiently using multiple polymorphic DNA markers simultaneously in nuclear families consisting of two unaffected parents and a pair of affected siblings (ASP). We use a simulation-based method to determine whether lod scores from a collection of ASP tests are significant. We test our new software and statistical tools to assess linkage of IDDM5 and IDDM7 conditioned on analyses with 1 or 2 other unlinked type I diabetes susceptibility loci. The results from the CASPAR analysis suggest that conditioning of IDDM5 on IDDM1 and IDDM4, and of IDDM7 on IDDM1 and IDDM2 provides significant benefits for the genetic analysis of polygenic loci.

Relative mutation rates at di-, tri-, and tetranucleotide microsatellite loci

Using the generalized stepwise mutation model, we propose a method of estimating the relative mutation rates of microsatellite loci, grouped by the repeat motif. Applying ANOVA to the distributions of the allele sizes at microsatellite loci from a set of populations, grouped by repeat motif types, we estimated the effect of population size differences and mutation rate differences among loci. This provides an estimate of motif-type-specific mutation rates up to a multiplicative constant. Applications to four different sets of di-, tri-, and tetranucleotide loci from a number of human populations reveal that, on average, the non-disease-causing microsatellite loci have mutation rates inversely related to their motif sizes. The dinucleotides appear to have mutation rates 1.5-2 times higher than the tetranucleotides, and the non-disease-causing trinucleotides have mutation rates intermediate between the di- and tetranucleotides. In contrast, the disease-causing trinucleotides have mutation rates 3.9-6.9 times larger than the tetranucleotides. Comparison of these estimates with the direct observations of mutation rates at microsatellites indicates that the earlier suggestion of higher mutation rates of tetranucleotides in comparison with the dinucleotides may stem from a nonrandom sampling of tetranucleotide loci in direct mutation assays.