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The problem of performing model-based process design and optimization in the pharmaceutical industry is an important and challenging one both computationally and in choice of solution implementation. In this work, a framework is presented to directly utilize a process simulator via callbacks during derivative-based optimization. The framework allows users with little experience in translating mechanistic ODEs and PDEs to robust, fully discretized algebraic formulations, required for executing simultaneous equation-oriented optimization, to obtain mathematically guaranteed optima at a competitive solution time when compared with existing derivative-free and derivative-based frameworks. The effectiveness of the framework in accuracy of optimal solution as well as computational efficiency is analyzed on on two case studies: (i) an integrated 2-unit reaction synthesis train used for the synthesis of an anti-cancer active pharmaceutical ingredient, and (ii) a more complex flowsheet representing a common synthesis-purification-isolation train of a pharmaceutical manufacturing processes.

Drinking water systems commonly use manual or grab sampling to monitor water quality, identify or confirm issues, and verify that corrective or emergency response actions have been effective. In this paper, the effectiveness of regulatory sampling locations for emergency response is explored. An optimization formulation based on the literature was used to identify manual sampling locations to maximize overall nodal coverage of the system. Results showed that sampling locations could be effective in confirming incidents for which they were not designed. When evaluating sampling locations optimized for emergency response against regulatory scenarios, the average performance was reduced by 3%-4%, while using optimized regulatory sampling locations for emergency response reduced performance by 7%-10%. Secondary constraints were also included in the formulation to ensure geographical and water age diversity with minimal impact on the performance. This work highlighted that regulatory sampling locations provide value in responding to an emergency for these networks.

Non-pharmaceutical interventions (NPIs) remain the only widely available tool for controlling the ongoing SARS-CoV-2 pandemic. We estimated weekly values of the effective basic reproductive number (R eff ) using a mechanistic metapopulation model and associated these with county-level characteristics and NPIs in the United States (US). Interventions that included school and leisure activities closure and nursing home visiting bans were all associated with a median R eff below 1 when combined with either stay at home orders (median R eff 0.97, 95% confidence interval (CI) 0.58-1.39) or face masks (median R eff 0.97, 95% CI 0.58-1.39). While direct causal effects of interventions remain unclear, our results suggest that relaxation of some NPIs will need to be counterbalanced by continuation and/or implementation of others.

In storing and transmitting epigenetic information, organisms must balance the need to maintain information about past conditions with the capacity to respond to information in their current and future environments. Some of this information is encoded by DNA methylation, which can be transmitted with variable fidelity from parent to daughter strand. High fidelity confers strong pattern matching between the strands of individual DNA molecules and thus pattern stability over rounds of DNA replication; lower fidelity confers reduced pattern matching, and thus greater flexibility. Here, we present a new conceptual framework, Ratio of Concordance Preference (RCP), that uses double-stranded methylation data to quantify the flexibility and stability of the system that gave rise to a given set of patterns. We find that differentiated mammalian cells operate with high DNA methylation stability, consistent with earlier reports. Stem cells in culture and in embryos, in contrast, operate with reduced, albeit significant, methylation stability. We conclude that preference for concordant DNA methylation is a consistent mode of information transfer, and thus provides epigenetic stability across cell divisions, even in stem cells and those undergoing developmental transitions. Broader application of our RCP framework will permit comparison of epigenetic-information systems across cells, developmental stages, and organisms whose methylation machineries differ substantially or are not yet well understood.

Adult hippocampal neurogenesis has been linked to the effects of anti-depressant drugs on behavior in rodent models of depression. To explore this link further, we tested whether the serotonin-norepinephrine reuptake inhibitor (SNRI) venlafaxine impacted adult hippocampal neurogenesis differently than its primary active SNRI metabolite desvenlafaxine. Adult male Long Evans rats (n = 5-6 per group) were fed vehicle, venlafaxine (0.5 or 5 mg) or desvenlafaxine (0.5 or 5 mg) twice daily for 16 days. Beginning the third day of drug treatment, the rats were given a daily bromodeoxyuridine (BrdU; 50 mg/kg) injection for 5 days to label dividing cells and then perfused 2 weeks after the first BrdU injection to confirm total new hippocampal cell numbers and their phenotypes. The high desvenlafaxine dose increased total new BrdU+ cell number and appeared to accelerate neuronal maturation because fewer BrdU+ cells expressed maturing neuronal phenotypes and more expressed mature neuronal phenotypes in the dentate gyri of these versus vehicle-treated rats. While net neurogenesis was not increased in the dentate gyri of rats treated with the high desvenlafaxine dose, significantly more mature neurons were detected. Our data expand the body of literature showing that antidepressants impact adult neurogenesis by stimulating NPC proliferation and perhaps the survival of neuronal progeny and by showing that a high dose of the SNRI antidepressant desvenlafaxine, but neither a high nor low venlafaxine dose, may also accelerate neuronal maturation in the adult rat hippocampus. These data support the hypothesis that hippocampal neurogenesis may indeed serve as a biomarker of depression and the effects of antidepressant treatment, and may be informative for developing novel fast-acting antidepressant strategies.

Infectious diseases remain a significant health concern around the world. Mathematical modeling of these diseases can help us understand their dynamics and develop more effective control strategies. In this work, we show the capabilities of interior-point methods and nonlinear programming (NLP) formulations to efficiently estimate parameters in multiple discrete-time disease models using measles case count data from three cities. These models include multiplicative measurement noise and incorporate seasonality into multiple model parameters. Our results show that nearly identical patterns are estimated even when assuming seasonality in different model parameters, and that these patterns show strong correlation to school term holidays across very different social settings and holiday schedules. We show that interior-point methods provide a fast and flexible approach to parameterizing models that can be an alternative to more computationally intensive methods.

Asian and non-Asian populations have been reported to differ substantially in the distribution of fragile X alleles into the normal (< 55 CGG repeats), premutation (55-199 CGG repeats), and full-mutation (> 199 CGG repeats) size classes. Our statistical analyses of data from published general-population studies confirm that Asian populations have markedly lower frequencies of premutation alleles, reminiscent of earlier findings for expanded alleles at the Huntington's Disease locus. To examine historical and contemporary factors that may have shaped and now sustain allele-frequency differences at the fragile X locus, we develop a population-genetic/epigenetic model, and apply it to these published data. We find that founder-haplotype effects likely contribute to observed frequency differences via substantially lower mutation rates in Asian populations. By contrast, any premutation frequency differences present in founder populations would have disappeared in the several millennia since initial establishment of these groups. Differences in the reproductive fitness of female premutation carriers arising from fragile X primary ovarian insufficiency (FXPOI) and from differences in mean maternal age may also contribute to global variation in carrier frequencies.

Mathematical models can enhance our understanding of childhood infectious disease dynamics, but these models depend on appropriate parameter values that are often unknown and must be estimated from disease case data. In this paper, we develop a framework for efficient estimation of childhood infectious disease models with seasonal transmission parameters using continuous differential equations containing model and measurement noise. The problem is formulated using the simultaneous approach where all state variables are discretized, and the discretized differential equations are included as constraints, giving a large-scale algebraic nonlinear programming problem that is solved using a nonlinear primal-dual interior-point solver. The technique is demonstrated using measles case data from three different locations having different school holiday schedules, and our estimates of the seasonality of the transmission parameter show strong correlation to school term holidays. Our approach gives dramatic efficiency gains, showing a 40-400-fold reduction in solution time over other published methods. While our approach has an increased susceptibility to bias over techniques that integrate over the entire unknown state-space, a detailed simulation study shows no evidence of bias. Furthermore, the computational efficiency of our approach allows for investigation of a large model space compared with more computationally intensive approaches.

DNA methyltransferases establish methylation patterns in cells and transmit these patterns over cell generations, thereby influencing each cell's epigenetic states. Three primary DNA methyltransferases have been identified in mammals: DNMT1, DNMT3A and DNMT3B. Extensive in vitro studies have investigated key properties of these enzymes, namely their substrate specificity and processivity. Here we study these properties in vivo, by applying novel statistical analysis methods to double-stranded DNA methylation patterns collected using hairpin-bisulfite PCR. Our analysis fits a novel Hidden Markov Model (HMM) to the observed data, allowing for potential bisulfite conversion errors, and yields statistical estimates of parameters that quantify enzyme processivity and substrate specificity. We apply this model to methylation patterns established in vivo at three loci in humans: two densely methylated inactive X (Xi)-linked loci (FMR1 and G6PD), and an autosomal locus (LEP), where methylation densities are tissue-specific but moderate. We find strong evidence for a high level of processivity of DNMT1 at FMR1 and G6PD, with the mean association tract length being a few hundred base pairs. Regardless of tissue types, methylation patterns at LEP are dominated by DNMT1 maintenance events, similar to the two Xi-linked loci, but are insufficiently informative regarding processivity to draw any conclusions about processivity at that locus. At all three loci we find that DNMT1 shows a strong preference for adding methyl groups to hemi-methylated CpG sites over unmethylated sites. The data at all three loci also suggest low (possibly 0) association of the de novo methyltransferases, the DNMT3s, and are consequently uninformative about processivity or preference of these enzymes. We also extend our HMM to reanalyze published data on mouse DNMT1 activities in vitro. The results suggest shorter association tracts (and hence weaker processivity), and much longer non-association tracts than human DNMT1 in vivo.

Variability among individuals in the severity of fragile X syndrome (FXS) is influenced by epigenetic methylation mosaicism, which may also be common in other complex disorders. The epigenetic signal of dense promoter DNA methylation is usually associated with gene silencing, as was initially reported for FMR1 alleles in individuals with FXS. A paradox arose when significant levels of FMR1 mRNA were reported for some males with FXS who had been reported to have predominately methylated alleles. We have used hairpin-bisufite PCR, validated with molecular batch-stamps and barcodes, to collect and assess double-stranded DNA methylation patterns from these previously studied males. These patterns enable us to distinguish among three possible forms of methylation mosaicism, any one of which could explain FMR1 expression in these males. Our data indicate that cryptic inter-cell mosaicism in DNA methylation can account for the presence of FMR1 mRNA in some individuals with FXS.

We develop Bayesian inference methods for a recently-emerging type of epigenetic data to study the transmission fidelity of DNA methylation patterns over cell divisions. The data consist of parent-daughter double-stranded DNA methylation patterns with each pattern coming from a single cell and represented as an unordered pair of binary strings. The data are technically difficult and time-consuming to collect, putting a premium on an efficient inference method. Our aim is to estimate rates for the maintenance and de novo methylation events that gave rise to the observed patterns, while accounting for measurement error. We model data at multiple sites jointly, thus using whole-strand information, and considerably reduce confounding between parameters. We also adopt a hierarchical structure that allows for variation in rates across sites without an explosion in the effective number of parameters. Our context-specific priors capture the expected stationarity, or near-stationarity, of the stochastic process that generated the data analyzed here. This expected stationarity is shown to greatly increase the precision of the estimation. Applying our model to a data set collected at the human FMR1 locus, we find that measurement errors, generally ignored in similar studies, occur at a non-trivial rate (inappropriate bisulfite conversion error: 1.6% with 80% CI: 0.9-2.3%). Accounting for these errors has a substantial impact on estimates of key biological parameters. The estimated average failure of maintenance rate and daughter de novo rate decline from 0.04 to 0.024 and from 0.14 to 0.07, respectively, when errors are accounted for. Our results also provide evidence that de novo events may occur on both parent and daughter strands: the median parent and daughter de novo rates are 0.08 (80% CI: 0.04-0.13) and 0.07 (80% CI: 0.04-0.11), respectively.

Bisulfite treatment can be used to ascertain the methylation states of individual cytosines in DNA. Ideally, bisulfite treatment deaminates unmethylated cytosines to uracils, and leaves 5-methylcytosines unchanged. Two types of bisulfite-conversion error occur: inappropriate conversion of 5-methylcytosine to thymine, and failure to convert unmethylated cytosine to uracil. Conventional bisulfite treatment requires hours of exposure to low-molarity, low-temperature bisulfite ('LowMT') and, sometimes, thermal denaturation. An alternate, high-molarity, high-temperature ('HighMT') protocol has been reported to accelerate conversion and to reduce inappropriate conversion. We used molecular encoding to obtain validated, individual-molecule data on failed- and inappropriate-conversion frequencies for LowMT and HighMT treatments of both single-stranded and hairpin-linked oligonucleotides. After accounting for bisulfite-independent error, we found that: (i) inappropriate-conversion events accrue predominantly on molecules exposed to bisulfite after they have attained complete or near-complete conversion; (ii) the HighMT treatment is preferable because it yields greater homogeneity among sites and among molecules in conversion rates, and thus yields more reliable data; (iii) different durations of bisulfite treatment will yield data appropriate to address different experimental questions; and (iv) conversion errors can be used to assess the validity of methylation data collected without the benefit of molecular encoding.

Polymerase chain reaction (PCR) has become the mainstay of DNA sequence analysis. Yet there is always uncertainty concerning the source of the template DNA that gave rise to a particular PCR product. The risks of contamination, biased amplification, and product redundancy are especially high when limited amounts of template DNA are used. We have developed and applied molecular encoding principles to solve this source-uncertainty problem for DNA sequences generated by standard PCR. Batch-stamps specify the date and sample identity, and barcodes detect template redundancy. Our approach thus enables classification of each PCR-derived sequence as valid, contaminant, or redundant, and provides a measure of sequence diversity. We recommend that batch-stamps and barcodes be used when amplifying irreplaceable DNAs and cDNAs available for forensic, clinical, single cell, and ancient DNA analyses.

Cytosine methylation is an epigenetic mechanism in eukaryotes that is often associated with stable transcriptional silencing, such as in X-chromosome inactivation and genomic imprinting. Aberrant methylation patterns occur in several inherited human diseases and in many cancers. To understand how methylated and unmethylated states of cytosine residues are transmitted during DNA replication, we develop a population-epigenetic model of DNA methylation dynamics. The model is informed by our observation that de novo methylation can occur on the daughter strand while leaving the opposing cytosine unmethylated, as revealed by the patterns of methylation on the two complementary strands of individual DNA molecules. Under our model, we can infer site-specific rates of both maintenance and de novo methylation, values that determine the fidelity of methylation inheritance, from double-stranded methylation data. This approach can be used for populations of cells obtained from individuals without the need for cell culture. We use our method to infer cytosine methylation rates at several sites within the promoter of the human gene FMR1.

DNA methylation within the promoter region of human LINE1 (L1) transposable elements is important for maintaining transcriptional inactivation and for inhibiting L1 transposition. Determining methylation patterns on the complementary strands of repeated sequences is difficult using standard bisulfite methylation analysis. Evolutionary changes in each repeat and the variations between cells or alleles of the same repeat lead to a heterogeneous population of sequences. Potential sequence biases can arise during analyses that are different for the converted sense and antisense strands. These problems can be avoided with hairpin-bisulfite PCR, a double-stranded PCR method in which complementary strands of individual molecules are attached by a hairpin linker ligated to genomic DNA. Using human L1 elements to study methylation of repeated sequences, (i) we distinguish valid L1 sequences from redundant and contaminant sequences by applying the powerful new method of molecular barcodes, (ii) we resolve a controversy on the level of hemimethylation of L1 sequences in fetal fibroblasts in favor of relatively little hemimethylation, (iii) we report that human L1 sequences in different cell types also have primarily concordant CpG methylation patterns on complementary strands, and (iv) we provide evidence that non-CpG cytosines within the regions analyzed are rarely methylated.

PCR amplification of limited amounts of DNA template carries an increased risk of product redundancy and contamination. We use molecular barcoding to label each genomic DNA template with an individual sequence tag prior to PCR amplification. In addition, we include molecular 'batch-stamps' that effectively label each genomic template with a sample ID and analysis date. This highly sensitive method identifies redundant and contaminant sequences and serves as a reliable method for positive identification of desired sequences; we can therefore capture accurately the genomic template diversity in the sample analyzed. Although our application described here involves the use of hairpin-bisulfite PCR for amplification of double-stranded DNA, the method can readily be adapted to single-strand PCR. Useful applications will include analyses of limited template DNA for biomedical, ancient DNA and forensic purposes.

Epigenetic inheritance, the transmission of gene expression states from parent to daughter cells, often involves methylation of DNA. In eukaryotes, cytosine methylation is a frequent component of epigenetic mechanisms. Failure to transmit faithfully a methylated or an unmethylated state of cytosine can lead to altered phenotypes in plants and animals. A central unresolved question in epigenetics concerns the mechanisms by which a locus maintains, or changes, its state of cytosine methylation. We developed "hairpin-bisulfite PCR" to analyze these mechanisms. This method reveals the extent of methylation symmetry between the complementary strands of individual DNA molecules. Using hairpin-bisulfite PCR, we determined the fidelity of methylation transmission in the CpG island of the FMR1 gene in human lymphocytes. For the hypermethylated CpG island of this gene, characteristic of inactive-X alleles, we estimate a maintenance methylation efficiency of approximately 0.96 per site per cell division. For de novo methylation efficiency (E(d)), remarkably different estimates were obtained for the hypermethylated CpG island (E(d) = 0.17), compared with the hypomethylated island on the active-X chromosome (E(d) < 0.01). These results clarify the mechanisms by which the alternative hypomethylated and hypermethylated states of CpG islands are stably maintained through many cell divisions. We also analyzed a region of human L1 transposable elements. These L1 data provide accurate methylation patterns for the complementary strand of each repeat sequence analyzed. Hairpin-bisulfite PCR will be a powerful tool in studying other processes for which genetic or epigenetic information differs on the two complementary strands of DNA.

Chromosomal abnormalities associated with hypomethylation of classical satellite regions are characteristic for the ICF immunodeficiency syndrome. We, as well as others, have found that these effects derive from mutations in the DNMT3B DNA methyltransferase gene. Here we examine further the molecular phenotype of ICF cells and report several examples of extensive hypomethylation that are associated with advanced replication time, nuclease hypersensitivity and a variable escape from silencing for genes on the inactive X and Y chromosomes. Our analysis suggests that all genes on the inactive X chromosome may be extremely hypomethylated at their 5' CpG islands. Our studies of G6PD in one ICF female and SYBL1 in another ICF female provide the first examples of abnormal escape from X chromosome inactivation in untransformed human fibroblasts. XIST RNA localization is normal in these cells, arguing against an independent silencing role for this RNA in somatic cells. SYBL1 silencing is also disrupted on the Y chromosome in ICF male cells. Increased chromatin sensitivity to nuclease was found at all hypomethylated promoters examined, including those of silenced genes. The persistence of inactivation in these latter cases appears to depend critically on delayed replication of DNA because escape from silencing was only seen when replication was advanced to an active X-like pattern.

Background: One of the most dramatic events during the course of the mammalian cell cycle is mitosis, when chromosomes condense and segregate, the nuclear envelope breaks down, and the cell divides into two daughter cells. Although cells undergoing mitosis are cytologically distinguishable from nonmitotic cells, few molecular markers are available to specifically identify mitotic cells, especially cells within different stages of mitosis., Methods: We applied the flow cytometric method of Juan et al. (Cytometry 32:71-77, 1998) to obtain cells with various levels of the molecular markers cyclin B1 and phosphorylated histone H3; fluorescence microscopy was then used to identify sorted cells in different stages of mitosis., Results: We observed the substantial enrichment of submitotic cell populations., Conclusions: This method represents an effective approach to obtain an enriched population of submitotic cells without the use of drug treatments or prior synchronization., (Copyright 2000 Wiley-Liss, Inc.)

G2 was defined originally as the temporal gap between the termination of DNA replication and the beginning of mitosis. In human cells, the G2 period was estimated to be 3-4 h. However, the absence of replicative DNA synthesis during this period designated G2 has never been shown conclusively. In this report, we show that, at some autosomal and X linked loci, programmed DNA replication continues within 90 min of mitosis. Furthermore, the major accumulation of cyclin B1, a cell-cycle marker that is usually ascribed to G2, overlaps extensively with very late DNA replication. We conclude that the G2 period is much shorter than previously thought and may, in some cells, be nonexistent.

Fragile-X syndrome and myotonic dystrophy are caused by triplet repeat expansions embedded in CpG islands in the transcribed non-coding regions of the FMR1 and the DMPK genes, respectively. Although initial reports emphasized differences in the mechanisms by which the expanded triplet repeats caused these diseases, results published in the past year highlight remarkable parallels in the likely molecular etiologies. At both loci, expansion is associated with altered chromatin, aberrant methylation, and suppressed expression of the adjacent FMR1 and DMAHP genes, implicating epigenetic mediation of these genetic diseases.

The human fragile-X syndrome is associated with expansions of a (CGG)n triplet repeat within the FMR1 gene. Whilst normal FMR1 arrays consist of variable numbers of (CGG)7-13 blocks punctuated with single AGG triplets, unstable arrays contain longer blocks of uninterrupted (CGG)n. The degree of instability, and subsequent risk of expansion to the fragile-X mutation, is dependent upon the length of this uninterrupted repeat. Detailed analyses of normal FMR1 array structures suggest that longer uninterrupted blocks of repeat could arise either through a process of gradual slippage or a more dramatic loss of an intervening AGG triplet. Up to 15% of Japanese and Chinese individuals have FMR1 triplet arrays centred on 36 repeats in length, a modal group not found in Caucasians. As longer FMR1 arrays have been associated with high-risk fragile-X haplotypes in some populations, we investigated the nature of these larger arrays. Sequence analysis revealed that the unusual length is due to the presence of a novel (CGG)6 block within the array. Several haplotypically related arrays contain blocks of (CGG)16 or (CGG)15, consistent with the fusion of adjacent (CGG)9 and (CGG)6 blocks after loss of the intervening AGG triplet. This is compatible with inferences from the Caucasian population that AGG loss is a mechanism by which long blocks of identical repeats are generated.

Genomic methylation patterns of mammals can vary among individuals and are subject to dynamic changes during development. In order to gain a better understanding of this variation, we have analyzed patterns of cytosine methylation within a 200 bp region at the CpG island of the human FMR1 gene from leukocyte DNA. FMR1 is normally methylated during inactivation of the X chromosome in females and it is also methylated and inactivated upon expansion of CGG repeats in fragile-X syndrome. Patterns of methylation (epigenotypes) were determined by the sequencing of bisulfite-treated alleles from normal males and females and alleles from a family of five brothers who are methylation mosaics and are affected to various degrees by the fragile-X syndrome. Our data indicate that: (i) methylation of individual CpG cytosines is strikingly variable in hypermethylated epigenotypes obtained from a single individual, suggesting that maintenance of cytosine methylation is a dynamic process; (ii) methylation of non-CpG cytosines in the region studied may occur but is rare; (iii) mosaicism of methylation in the analyzed fragile-X males is remarkably similar to that found for the active X and inactive X alleles in normal females, suggesting that the methylation mosaicism of some fragile-X males reflects similar on and off states of FMR1 expression that exist in normal females; (iv) hypermethylation is slightly more pronounced on fragile-X alleles than on normal inactive X alleles of females; (v) the general dichotomy of hypo- and hypermethylated alleles persisted over the 5 year period that separated samplings of the fragile-X males; (vi) methylation variability was most pronounced at a consensus binding sequence for the alpha-PAL transcription factor, a sequence that may play a role in regulating expression of FMR1.

The timing of DNA replication in the Xq27 portion of the human X chromosome was studied in cells derived from normal and fragile X males to further characterize the replication delay on fragile X chromosomes. By examining a number of sequence-tagged sites (STSs) that span several megabases of Xq27, we found this portion of the normal active X chromosome to be composed of two large zones with different replication times in fibroblasts, lymphocytes, and lymphoblastoid cells. The centromere-proximal zone replicates very late in S, whereas the distal zone normally replicates somewhat earlier and contains FMR1, the gene responsible for fragile X syndrome when mutated. Our analysis of the region of delayed replication in fragile X cells indicates that it extends at least 400 kb 5' of FMR1 and appears to merge with the normal zone of very late replication in proximal Xq27. The distal border of delayed replication varies among different fragile X males, thereby defining three replicon-sized domains that can be affected in fragile X syndrome. The distal boundary of the largest region of delayed replication is located between 350 and 600 kb 3' of FMR1. This example of variable spreading of late replication into multiple replicons in fragile X provides a model for the spread of inactivation associated with position-effect variegation or X chromosome inactivation.

Multivariate flow cytometry using specific cyclin proteins and DNA content can identify cell populations at different points within the cell cycle. Quantification of cyclin B1 and DNA content reveals that cells with high levels of cyclin B1 predominantly have a 4C DNA content and are therefore in G2 or mitosis. We have examined whether separation of cells by levels of cyclin B1 could be used to discriminate cells at discrete times within these phases. Post-replicative cells progressively enter into fractions with higher levels of cyclin B1, indicating that this protein can be used as a marker of time in G2. Furthermore, cells in particular phases of mitosis can be greatly enriched by separation based on cyclin B1 levels. This method can thus be used to isolate cells at specific times within G2 and mitosis, periods of the cell cycle that have been difficult to study by cell fractionation.

The human fragile-X syndrome, a major cause of inherited mental retardation, is associated with expansion of the trinucleotide repeat GGC:GCC. Repetitive sequences in DNA are subject to slippage during catalysis by DNA polymerases. We characterized the extent of slippage of synthetic GGC:GCC repeats by various DNA polymerases: Taq DNA polymerase, Klenow fragment of DNA polymerase I, DNA Sequence, DNA polymerase-alpha and polymerase-beta, as well as HIV reverse transcriptase. All of these enzymes were found to expand GGC:GCC repeats, with the most extensive expansion exhibited by Taq DNA polymerase. Starting with a template and primer, each 15 nucleotides (nt) in length, the product of one round of synthesis by Taq polymerase is as long as 250 nt. Sequence analysis of cloned DNA fragments expanded by Taq polymerase indicates that expansion involves multiple triplet additions and that it is asymmetric. The asymmetric distribution of terminal nucleotides in the expanded product is consistent with active expansion of the GCC strand and passive additions onto the GGC strand. The preferential elongation and expansion of the GCC strand was confirmed in studies utilizing longer repeats within a single-stranded M-13 template.

The fragile X syndrome is commonly associated with mutant alleles of the FMR1 gene that are hypermethylated and have large expansions of CGG repeats. We present data here on the replication timing of FMR1 that confirm predictions of delayed replication of alleles from affected males. The normal FMR1 allele replicates late in S phase, while alleles from affected males replicate later, the major peak of replication occurring in the flow cytometry fraction usually referred to as G2/M. The delayed timing of replication is not the direct result of a single replication fork stalling at the expanded CGG repeat, because delayed replication was observed for regions on both sides of the repeat. The domain of altered replication timing includes sites at least 150 kb 5' and 34 kb 3' of the repeat, indicating that genes in addition to FMR1 may be affected.

The fragile-X syndrome of mental retardation is associated with an expansion in the number of CGG repeats present in the FMR1 gene. The repeat region is within sequences characteristic of a CpG island. Methylation of CpG dinucleotides that are 5' to the CGG repeat has been shown to occur on the inactive X chromosome of normal females and on the X chromosome of affected fragile-X males, and is correlated with silencing of the FMR1 gene. The methylation status of CpG sites 3' to the repeat and within the repeat itself has not previously been reported. We have used two methylation-sensitive restriction enzymes, AciI and Fnu4HI, to further characterize the methylation pattern of the FMR1 CpG island in normal individuals and in those carrying fragile-X mutations. Our results indicate that: (i) CpG dinucleotides on the 3' side of the CGG repeat are part of the CpG island that is methylated during inactivation of a normal X chromosome in females; (ii) the CGG repeats are also part of the CpG island and are extensively methylated as a result of normal X-chromosome inactivation; (iii) similar to normal males, unaffected fragile-X males with small CGG expansions are unmethylated in the CpG island; for affected males, the patterns of methylation are similar to those of a normal, inactive X chromosome; (iv) in contrast to the partial methylation observed for certain sites in lymphocyte DNA, complete methylation was observed in DNA from cell lines containing either a normal inactive X chromosome or a fragile-X chromosome from an affected male.(ABSTRACT TRUNCATED AT 250 WORDS)

Epigenetic modification of DNA is now recognized as a potentially important factor in the inheritance and expression of some mutations; its ability to complicate human genetic analysis is concurrently becoming apparent. One unusual form of epigenetic modification, dominant position-effect variegation (PEV), has been used as a model for Huntington disease. In dominant PEV, a fully dominant mutant phenotype results from stable epigenetic inactivation of an allele adjacent to the structural alteration (cis-inactivation) combined with a complementary inactivation of the homologous normal allele (trans-inactivation). We now propose that trans-inactivation of the normal allele may occasionally persist through meiosis. Such "epigene conversion" occurring at the Huntington disease locus in a few percent of meioses would largely account for the published anomalies in that region's genetic map. This concept could also explain anomalous linkage map data for other disease-causing alleles in humans.

Fragile-X syndrome is a major cause of mental retardation in humans. The X-inactivation imprinting model accounts for the unusual pattern of inheritance and expression of this syndrome. According to this model, the fragile-X mutation creates a local block to the attempted reactivation of the mutant X chromosome prior to oogenesis. This local block results in an "imprinted" fragile-X chromosome that is deleterious in males and in females for whom this chromosome is predominantly the active X chromosome. The imprinted state of the fragile-X mutation is inferred to be stable when transmitted by an imprinted female because the penetrance of the syndrome in sons of affected females is estimated to be 1.0. To provide a more precise estimate of the stability of the proposed fragile-X imprint, we have analyzed published pedigrees that include restriction fragment length polymorphism and cytogenetic data from sibships with mothers who are interpreted as having an imprinted fragile-X allele. We conclude that the fragile-X imprint was stable in 46 out of 48 female meioses. This analysis leads to a preliminary estimate of about 96% for the stability of the imprint through female meiosis. Two imprinted females had progeny who appeared to be carriers of a nonimprinted fragile-X allele. If this interpretation is correct, then reversion from the imprinted to the nonimprinted state, or "erasure," can occasionally occur when the mutant fragile-X allele is transmitted by an imprinted female. We discuss the genetic and epigenetic significance of possible female erasure. We request DNA and cytogenetic information from unpublished pedigrees to quantify further the stability, during female meiosis, of the proposed imprinted state of the mutant fragile-X allele.

The steroid hormone 20-hydroxyecdysone (20HE) and the Broad-Complex locus (BRC) are involved in regulating developmental changes in gene expression around the time of metamorphosis in Drosophila. We have investigated the regulatory interactions between 20HE, BRC, and a set of genes expressed in the fat body of third-instar Drosophila larvae. RNA levels for two hormone-inducible genes, Larval Serum Protein-2 and P1, accumulate to normal levels in BRC-mutant larvae. In contrast, RNA levels for the P6 gene were affected by mutations at BRC. On the basis of the results of experiments in which hormone concentrations were varied in BRC-mutant or wild-type larvae, we conclude that 20HE can both increase and decrease P6 RNA levels in the absence of BRC product(s). BRC appears to be a trans-acting modulator of the response of P6 to the hormone. We propose that BRC attenuates the repressive effect of the hormone, expanding the range of hormone concentrations that induce the gene, thus allowing P6 RNA to reach high levels during the third larval instar. The results are discussed in relation to other genes that are regulated by the same two trans-acting factors. A model is presented that refines the model of Ashburner et al. (1974, Cold Spring Harbor Symp. Quant. Biol. 38: 655-662) for the hormonal regulation of gene activity.

Although most males with the fragile-X [fra(X)] syndrome do not reproduce, there are 2 published pedigrees that include affected males who have daughters and who thus appear to have transmitted the fragile-X chromosome to their progeny. In addition, one published fra(X) pedigree includes an apparently normal male who expresses cytogenetically the fra(X) site at high frequency and who has 3 daughters. In the 6 daughters of these 3 males, there is little or no cytogenetic expression of the fra(X). I interpret these pedigrees within the context of my X-inactivation imprinting model of the fra(X) syndrome (Genetics 117:587-599): the cytogenetic manifestation of the imprinted state of the mutant fra(X) chromosome [high percentage of cytogenetic expression] is no longer present in daughters of imprinted males. I propose that the imprinted state is erased when an imprinted fragile-X chromosome is passed through a male. Such erasure in the gender opposite to the gender that established the imprint is in accord with other examples of chromosome imprinting in mammals. Additional data from unpublished fra(X) pedigrees are requested.

The X-inactivation imprinting model of the fragile-X syndrome (1), the inference from this model and from pedigree data that human oogonia are derived from two progenitor cells present after the initial event that leads to chromosome imprinting (13), and the general model of fragile sites (8), provide a theoretical framework that is consistent with data on the fragile-X syndrome. This framework has led to novel predictions, some of which have been tested. Results of most tests have been consistent with predictions (10, 13, 17, 18, 27, 28). More direct tests are necessary to explore the underlying mechanisms of chromosome change, here termed imprinting, of the molecular basis of the change, and of the mutation itself.

I propose that Huntington's disease (HD) is caused by dominant position-effect variegation, a phenomenon for which new information is available in Drosophila melanogaster. The essential features of this proposal are that (1) the HD mutation is the result of a chromosome alteration that inactivates transcription of a nearby structural gene or genes (cis-inactivation); the combination of this proposed chromosome alteration and the structural gene(s) is termed the HD allele; (2) there is pairing in some somatic cells between the HD and HD+ alleles on homologous chromosomes; (3) as a result of this somatic pairing, the HD mutation also inactivates transcription of the HD+ structural gene on the normal homologue (trans-inactivation), resulting in complete dominance of the mutation; (4) polymorphism for an X-linked recessive modifier of position-effect variegation means that the age of onset of symptoms of HD will depend on which parent the HD mutation was inherited from. The fully dominant nature of HD and the parental-source effect on the age of onset are thus both understandable within the genetic and epigenetic paradigm of position-effect variegation.

Laird has proposed that the human fragile-X syndrome is caused by abnormal chromosome imprinting. The analysis presented here supports and extends this proposal. Using published pedigrees that include DNA polymorphism (RFLP) data, we establish that the states of the fragile-X mutation termed "imprinted" and "nonimprinted" usually can be distinguished by the level of cytogenetic expression of the fragile-X chromosome. This information is then used to assess the state of the fragile-X allele in carrier progeny of individual women who inherited a nonimprinted fragile-X chromosome. From this assessment, an estimate is made of the frequency, in individual women, of primary oocytes with an imprinted fragile-X chromosome. The results of this analysis provide additional support for the specific model in which chromosome imprinting occurs in a female in, on average, half of her primary oocytes. This is the expected frequency if X-chromosome inactivation is the initial step in the imprinting of the mutant fragile-X allele. Moreover, this analysis suggests a biological explanation for peculiarities of fragile-X inheritance described by others as "clustering" and the "Sherman paradox." We interpret these peculiarities as consequences of a very small number of oogonial progenitor cells. Two progenitor cells for oogonia is the best integer estimate of the number of such cells at the time of the initial event that leads to chromosome imprinting.

We have examined the population genetic consequences of the model of Laird (Genetics 117:587-599, 1987) in which the fragile-X syndrome is caused by "imprinting" of a mutant chromosome. The imprinting event in this model results from a block to reactivation of an inactive X chromosome prior to oogenesis. If it is assumed that males carrying the imprinted chromosome never reproduce, the frequencies of females and males carrying the imprinted chromosome are expected to be equal. When a mutation-selection balance is established, there are expected to be somewhat more than twice as many females carrying the nonimprinted fragile X as carry the imprinted fragile-X chromosome, the excess depending on the fertility of fragile-X females. Nonpenetrant (transmitting) males, i.e., those with the nonimprinted fragile-X chromosome, are expected to be present at about the same frequency as are males with the syndrome. More than one-third of the nonimprinted chromosomes in the population are expected to be newly arisen in each generation. We have considered possible alternatives to the model of a mutation-selection balance. Nonimprinted carrier females would need to have 100% fertility excess to avoid postulating a high mutation rate to account for the very high prevalence of the syndrome.

In the nurse cells of Drosophila, nuclear DNA is replicated many times without nuclear division. Nurse cells differ from salivary gland cells, another type of endoreplicated Drosophila cell, in that banded polytene chromosomes are not seen in large nurse cells. Cytophotometry of Feulgen stained nurse cell nuclei that have also been labeled with 3H-thymidine shows that the DNA contents between S-phases are not doublings of the diploid value. In situ hybridization of cloned probes for 28S + 18S ribosomal RNA, 5S RNA, and histone genes, and for satellite, copia, and telomere sequences shows that satellite and histone sequences replicate only partially during nurse cell growth, while 5S sequences fully replicate. However, during the last nurse cell endoreplication cycle, all sequences including the previously under-replicated satellite sequences replicate fully. In situ hybridization experiments also demonstrate that the loci for the multiple copies of histone and 5S RNA genes are clustered into a small number of sites. In contrast, 28S + 18S rRNA genes are dispersed. We discuss the implications of the observed distribution of sequences within nurse cell nuclei for interphase nuclear organization. In the ovarian follicle cells, which undergo only two or three endoreplication cycles, satellite, histone and ribosomal DNA sequences are also found by in situ hybridization to be underrepresented; satellite sequences may not replicate beyond their level in 2C cells. Hence the pathways of endoreplication in three cell types, salivary gland, nurse, and follicle cells, share basic features of DNA replication, and differ primarily in the extent of association of the duplicated chromatids.

Electron microscopic examination of chromatin from embryonic nuclei of Oncopeltus fasciatus and Drosophila melanogaster reveals arrays of chromatin associated fibers. The lengths and spacings of these fibers were analyzed to provide a basis for defining and interpreting regions of transcriptionally active chromatin. The results of the analysis are consistent with the interpretation of some fibers as nascent RNA with associated protein (RNP). The chromatin segments underlying these fiber arrays were classified as ribosomal or non-ribosomal transcription units according to definitions and criteria described by Foe et al. (1976). Nascent fibers on active ribosomal transcription units were analyzed and compared for Drosophila melanogaster, Triturus viridescens, and Oncopeltus fasciatus. A common feature of the fiber patterns on ribosomal TUs is that origin-distal fibers exhibit greater length variability and a lower slope relative to proximal fibers. The region of increased variability in fiber lengths is correlated with the expected location of 28S ribosomal RNA sequences in the distal half of each ribosomal transcription unit. Because 28S ribosomal RNA appears to contain more extensive regions of base sequence complementarity, we suggest that the length of ribosomal RNP fibers is influenced under our spreading conditions by the secondary structure of the nascent RNA. In order to calculate the RNA content of RNP fibers, chromatin morphology was used to estimate lengths of transcribed DNA. The packing ratio of DNA in chromatin, which we express as the length of B-structure DNA divided by length of chromatin, is 1.1-1.2 and 1.6 for the DNA in active ribosomal and non-ribosomal chromatins, respectively. These DNA packing ratios are used to determine the extent to which nascent RNP fibers are shorter than the transcribed DNA (expressed as DNA/RNP length ratio). For non-ribosomal transcription units and for proximal fibers of ribosomal transcription units. DNA/RNP length ratios are relatively constant within each array. However, considerable variability in this ratio (4-23) is observed for different arrays of fibers. Possible sources of this variability are considered by comparing ratios derived from the presumably identical ribosomal transcription units. Further analysis of the morphology of nascent fibers may elucidate the contributions of proteins and successive RNA sequences to RNP structure.

We summarize our proposal that "intercalary heterochromatin" of Drosophila is a useful model for human fragile sites. Comparison with Drosophila site 11A suggests that the normal allele of fragile site Xq27 is a meiotic pairing site.

In dividing cells, each sequence replicates exactly once in each S-phase, but in cells with polytene chromosomes, some sequences may replicate more than once or fail to replicate during S-phase. Because of this differential replication, the control of replication in polytene cells must have some unusual features. Dennhöfer (1982a) has recently concluded that the total DNA content of the polytene cells of Drosophila salivary glands exactly doubles in each S-phase. This observation, along with previous studies demonstrating satellite underreplication in salivary gland cells, led us to consider the hypothesis that there is a "doubling of DNA" mechanism for the control of DNA replication in polytene cells. With this mechanism, a doubling of DNA content, rather than the replication of each sequence, would signal the end of a cycle of DNA replication. To test this hypothesis, we have reinvestigated the replication of several sequences (satellite, ribosomal, histone and telomere) in salivary gland cells using quantitative in situ hybridization. We find that underreplication of some sequences does occur. In addition we have repeated Dennhöfer's cytophotometric and labeling studies. In contrast to Dennhöfer, we find that the total DNA contents of nonreplicating nuclei do reflect this partial replication, in accord with Rudkin's (1969) result. We conclude that DNA replication in polytene cells is controlled by modifications of the mechanism operating in dividing cells, where control is sequence autonomous, and not by a "doubling of DNA" mechanism. In situ hybridization to unbroken salivary gland nuclei reveals the distribution of specific sequences. As expected, satellite, histone and 5S sequences are usually in a single cluster.(ABSTRACT TRUNCATED AT 250 WORDS)

The observation of thick chromatin fibers in interbands of Dipteran polytene chromosomes suggests that there should be 5 to 10 times more mass and DNA in interbands than is commonly thought to be present. To resolve this paradox, the chromatin content of interbands was estimated, using whole-mounted polytene chromosomes from Drosophila melanogster. Densitometry of high voltage electron microscopic negatives provides an estimate of less than 4:1 for the average ratio of cross-sectional dry mass (or mass per unit chromosome length) of bands relative to interbands. This ratio, combined with an estimate of the length of chromosome composed of interbands, indicates that at least 26% of chromosome mass is contributed by interband chromatin. Since DNA comprises a similar proportion of chromatin mass in bands and interbands (Laird et al., 1980b), these data imply that DNA sequences in interbands represent at least 26% of the euchromatic genome of D. melanogaster. This result calls for reinterpretation of some of the genetic and molecular data from Diptera. The discrepancy between this higher estimate of interband mass and DNA, and previous estimates of 3-5%, is discussed. One possibility is that previous measurements were made on prominent interbands, which are proposed here to be in regions that are delayed in DNA replication. Such interbands would be reduced in polyteny and DNA content compared with the average interband region. The concept of local variations in polyteny is also used here to explain major differences in the cross-sectional mass of bands. This leads to a revised model of polytene chromosomes in which at least three levels of polyteny, rather than one or two levels, can be present within one euchromatic region.

The size range of poly(A)-containing RNA from Drosophila melanogaster embryos has been estimated by hybridization with 3H-labeled poly(U) and subsequent fractionation on sucrose gradients. The median size of nuclear poly(A)-containing RNA is about 30 S (6000 nucleotides), and the median size of cytoplasmic poly(A)-containing RNA is about 17 S (1800 nucleotides). The relationship of these sizes to messenger RNA needed to code for protein and to the length of DNA contained in a chromomere is discussed.

I discuss two aspects of my proposal that fra(X) chromosomes exist in two states, imprinted and non-imprinted: why do males not imprint the fra(X); does the "Sherman paradox" rule out my proposal?

P-element transformants of a single rRNA gene (rDNA) were used to investigate the relationship between the organization of the nucleolus organizer (NO) and rDNA function in Drosophila melanogaster. In situ hybridization to rRNA in polytene nuclei of salivary glands demonstrated that an rRNA gene can be transcribed at a high rate when inserted into chromosomal sites other than the NO. Structures that resemble morphologically the endogenous nucleoli ('mininucleoli') were associated with four different euchromatic sites of rDNA insertion. Molecular analyses revealed that these mininucleoli contained both rRNA and an antigen specific to nucleoli. Phenotypes resulting from rDNA deficiencies were rescued partially by the presence of the transformed rDNA, indicating that the transcripts and mininucleoli associated with the rDNA insertion sites were functional. Thus, two conserved features of rDNA organization in eukaryotes, namely tandem repetition and heterochromatic localization, are not required for rRNA gene function. We conclude that 'nucleolar organizing activity' is an intrinsic property of the rDNA or its RNA products.