Resolution of large and small differences in gene expression using models for the Bayesian analysis of gene expression levels and spotted DNA microarrays

BACKGROUND: The detection of small yet statistically significant differences in gene expression in spotted DNA microarray studies is an ongoing challenge. Meeting this challenge requires careful examination of the performance of a range of statistical models, as well as empirical examination of the effect of replication on the power to resolve these differences. RESULTS: New models are derived and software is developed for the analysis of microarray ratio data. These models incorporate multiplicative small error terms, and error standard deviations that are proportional to expression level. The fastest and most powerful method incorporates additive small error terms and error standard deviations proportional to expression level. Data from four studies are profiled for the degree to which they reveal statistically significant differences in gene expression. The gene expression level at which there is an empirical 50% probability of a significant call is presented as a summary statistic for the power to detect small differences in gene expression. CONCLUSIONS: Understanding the resolution of difference in gene expression that is detectable as significant is a vital component of experimental design and evaluation. These small differences in gene expression level are readily detected with a Bayesian analysis of gene expression level that has additive error terms and constrains samples to have a common error coefficient of variation. The power to detect small differences in a study may then be determined by logistic regression

Multifactorial experimental design and the transitivity of ratios with spotted DNA microarrays

BACKGROUND: Multifactorial experimental designs using DNA microarrays are becoming increasingly common, but the extent of the transitivity of cDNA microarray expression measurements across multiple samples has yet to be explored. RESULTS: A strong correlation between direct and transitive inference for significantly differentially expressed genes is demonstrated, using subsets of a dye-swap loop design. CONCLUSIONS: In experimental design, opportunities for transitive inference should be exploited, while always ensuring that comparisons of greatest interest comprise direct hybridizations

Spin Dependence of D0-brane Interactions

The long-range, spin-dependent forces between D0-branes are related to long-range fundamental string interactions using duality. These interactions can then be computed by taking the long distance non-relativistic expansion of string four-point amplitudes. The results are in accord with the general constraints of Matrix Theory.Comment: 6 pages, latex, no figures, talk presented at STRINGS97, substantial revisions in results and conclusion

The Price of Pleasure: Children Hurt Too

In her two recent articles on pregnancy support, “Preglimony” in the Stanford Law Review and “The Price of Pleasure” in the Northwestern Law Review, Professor Shari Motro argues that American laws should no longer treat “lovers as strangers.” To minimize “the fundamental gender imbalance,” she urges that the relationship between an unwed heterosexual couple whose sex prompts pregnancy “demands it own legal category.” She calls for a new paradigm that generally holds men financially responsible to women for the burdens of pregnancy, employing both contract and tort principles. Professor Motro invites conversation on her self-described utopian notions. Most curious for us is Professor Motro’s failure to discuss children. Any conversation about the price of sex when children are born must include the children as well as their mothers. They are inextricably linked, as are the paternity opportunity interests of genetic fathers. In accepting Professor Motro’s invitation to converse, we urge new dialogues about expanded duties and rights of prospective fathers, including new prebirth monetary support obligations; enhanced opportunities for prebirth paternity acknowledgments; and, greater protections of “unitary” families into which children are born. Our conversations should also include couples with children where sex did not prompt birth

Legal Paternity (and Other Parenthood) After Lehr and Michael H.

Actual genetic ties do not always establish, or even help to establish, legal paternity of children born of consensual sex, that is, male parental rights and/or duties as of the time of birth. Paternity status, typically governed by state law, is often dependent upon the marital status of the mothers, or the nonsex acts of men preconception, prebirth, or shortly after birth. For example, husbands of mothers are often deemed parents at birth because genetic ties are presumed. Thus, for nonmarital children born to certain married women, legal paternity is not founded on actual genetic ties. Similarly, actual male genetic ties may not lead to paternity when children are born of sex to unmarried women. Again preconception, prebirth or at birth conduct may be important. The 1983 United States Supreme Court decision in Lehr v. Robertson recognizes that American states can require natural fathers, at least in the adoption setting, to do more than prove genetic ties in order to acquire paternity. When such fathers do enough, they acquire “substantial” federal constitutional childrearing interests so that any proposed adoption requires their consent. When such fathers do not do enough, Lehr allows states to deny them legal parentage. Lehr does forbid states from omitting too many natural fathers from governmental schemes for eliminating parental interests. And Lehr does not forbid a state, at least within adoption, from designating legal paternity for a nonmarital child in a man with no genetic ties. Many American states, in fact, say that genetic ties alone are an insufficient basis for legal paternity. And, within adoption, and often elsewhere, states recognize childrearing interests in nonmarital children for certain nongenetic fathers. The U.S. Supreme Court has said little since Lehr about male parentage under law for nonmarital children born of sex. It has, however, spoken on legal paternity for children of married mothers whose husbands are not the genetic fathers, a different breed of nonmarital children. In Michael H. v. Gerald D. in 1989, the court recognized that an American state could create an irrebuttable presumption of genetic ties in a husband for a child born during marriage where the marriage remains intact after birth and the married couple chooses to raise the child. After reviewing Lehr and Michael H., we find the Lehr guidelines have not been properly followed in and outside of adoption, including safe haven and custody/visitation settings. We also review American paternity laws in child support, torts and inheritance settings where male childrearing is not always at issue. Along the way we explore the possible expansion of Lehr’s childrearing opportunity interests in children born of sex to those uninvolved in sex. We conclude that Lehr rights should be expanded to natural fathers outside adoption and to certain nongenetic parents, including both women and men

Procreative Sex and Same Sex Parents

New state-sanctioned family units headed by couples in committed relationships are on the rise. They include marriages encompassing same sex couples, civil unions, and domestic partnerships. These new family units can originate in state statutes or in judicial decisions. The pace of change is so fast that new units occasionally replace units only recently recognized, as when same sex marriages replace civil unions or domestic partnerships. U.S. Supreme Court precedents permit broad governmental discretion in sanctioning new families and in recognizing parentage therein. Yet such discretion is limited by constitutionally-recognized parental rights and interests when children are born of sex. At times states can and do deny parental status under law at birth to biological fathers. Differences in parentage laws will likely continue for some time. When same sex marriages, civil unions, or domestic partnerships are expanded or created, the new family units typically are deemed equal to, or the same as, longstanding opposite sex marriages. However, when there are children born of sex, equality and sameness are impossible. Same sex couples simply cannot produce children through intrafamily intercourse as can opposite sex couples. Yet, extrafamily intercourse by those in same sex, as well as opposite sex, families can produce children. Given the policies of equality and sameness, should all children conceived through adultery similarly be deemed born into sanctioned family units? That is, should there always operate a presumption of parentage as now typically operates for a husband in an opposite sex marriage? If so, are new written laws needed since the existing parentage presumptions for husbands usually require the possibility of genetic ties – an impossibility in same sex settings? Further, are there limits on any equality between same and opposite sex couples? Finally, are additional laws beyond parentage presumptions at birth needed for children born of sex to same sex couples? This article posits that explicit statutory presumptions are needed for children born to state-sanctioned same sex female couples although there cannot be genetic ties in both mates. Further, it proposes that current voluntary parentage acknowledgment processes, now operating for men who prompt children born of sex to married and unmarried women, be expanded to allow certain same sex male mates to become legal parents at birth, or sooner, to children born of sex into their family units

For Those Not John Edwards: More and Better Paternity Acknowledgments at Birth

When former U.S. Senator and Presidential candidate John Edwards (finally) declared his paternity of Quinn, born of sex to Rielle Hunter, many assumed he could then begin to raise as well as financially support the child he once publicly shunned. Many assumed legal paternity could arise through a court order, if not Rielle’s wishes. Had he been on the Maury Povich television show, the positive genetic tests would have prompted the host to declare John the father. Yet notwithstanding these declarations, there would be no childrearing by John if Rielle determined he should have no contact with Quinn, even if Rielle sought child support from John and even if Quinn’s best interests favored contact between her and John. For genetic fathers like John whose bedmates are not like Rielle, there are often no opportunities to present Christmas gifts. As John and Rielle were never married and as Rielle was not married to another, Quinn was a nonmarital child with no federal constitutional legal father at birth. At birth, John may have had a federal constitutional opportunity interest in establishing parentage, seized by stepping up to parental responsibilities. Yet, as John only declared paternity two years after birth, after denying fatherhood and prompting another man to declare his genetic ties with Quinn, he may have been too late to seize the federal opportunity interest in order to fully parent Quinn without Rielle’s cooperation. Only with Rielle’s consent could John now complete a voluntary paternity acknowledgment, a prerequisite to placing John on Quinn’s birth certificate. And with Rielle’s opposition, any paternity lawsuit by John to establish regular contacts with Quinn would most likely fail even though any paternity lawsuit to establish John’s financial support of Quinn would most likely succeed. Popular misconceptions about legal paternity for nonmarital children born of sex largely arise due to confusion and ignorance about voluntary paternity acknowledgments. Our exploration of the federal and state acknowledgment laws reveals that a John Edwards is often no new father with legal childrearing rights so that without a Rielle Hunter’s help, his relationship with a Quinn would be limited to checks in the mail. Voluntary acknowledgment laws are especially important today because about 1.7 million nonmarital children are born of sex each year in the United States, with about one third, like Quinn, having no legal father at birth. In 1940, there were only about 90,000 nonmarital children. Like Quinn, some of today’s fatherless children have late arriving declarations about genetic ties, and perhaps paternal child care. Far more nonmarital children remain fatherless, though possibly the subject of later suits seeking child support. Many nonmarital children will be born fatherless under law even though U.S. governments proclaim that these children should have both a mother and father under law at birth. Voluntary paternity acknowledgment laws can better prompt dual parentage. After reviewing contemporary acknowledgment forms, we suggest laws to prompt more, and more reliable, paternity acknowledgments, and thus more legal fathers at birth for nonmarital children

Bayesian Analysis of Gene Expression Levels: Statistical Quantification of Relative mRNA Level across Multiple Strains or Treatments

Background: Methods of microarray analysis that suit experimentalists using the technology are vital. Many methodologies discard the quantitative results inherent in cDNA microarray comparisons or cannot be flexibly applied to multifactorial experimental design. Here we present a flexible, quantitative Bayesian framework. This framework can be used to analyze normalized microarray data acquired by any replicated experimental design in which any number of treatments, genotypes, or developmental states are studied using a continuous chain of comparisons. Results: We apply this method to Saccharomyces cerevisiae microarray datasets on the transcriptional response to ethanol shock, to SNF2 and SWI1 deletion in rich and minimal media, and to wild-type and zap1 expression in media with high, medium, and low levels of zinc. The method is highly robust to missing data, and yields estimates of the magnitude of expression differences and experimental error variances on a per-gene basis. It reveals genes of interest that are differentially expressed at below the twofold level, genes with high 'fold-change' that are not statistically significantly different, and genes differentially regulated in quantitatively unanticipated ways. Conclusions: Anyone with replicated normalized cDNA microarray ratio datasets can use the freely available MacOS and Windows software, which yields increased biological insight by taking advantage of replication to discern important changes in expression level both above and below a twofold threshold. Not only does the method have utility at the moment, but also, within the Bayesian framework, there will be considerable opportunity for future development.Organismic and Evolutionary Biolog