DOI: 10.1002/cphc.200800572 A Single-Molecule Perspective on the Role of Solvent Hydrogen Bonds in Protein Folding and Chemical Reactions Lorna Dougan,* [a] Ainavarapu Sri Rama Koti, [b] Georgi Genchev, [c] Hui Lu, [c] and Julio M. Fernandez* [a] 1. Introduction The structure and dynamics of proteins and enzymatic activity is intrinsically linked to the strength and positions of hydrogen bonds in the system. [1] A hydrogen bond results from an at- tractive force between an electronegative atom and a hydro- gen atom. [2] The hydrogen is attached to a strongly electroneg- ative heteroatom, such as oxygen or nitrogen, termed the hy- drogen-bond donor. This electronegative atom decentralizes the electron cloud around the hydrogen nucleus, leaving the hydrogen atom with a positive partial charge. Since the hydro- gen atom is smaller than other atoms, the resulting partial charge represents a large charge density. A hydrogen bond re- sults when this strong positive charge density attracts a lone pair of electrons on another heteroatom, which becomes the hydrogen-bond acceptor. Although stronger than most other intermolecular forces, the hydrogen bond is much weaker than both the ionic and the covalent bonds. [2] Within macromole- cules such as proteins and nucleic acids, it can exist between two parts of the same molecule, and provides an important constraint on the molecule’s overall shape. [3] The hydrogen bond was first introduced in 1912 by Moore and Winmill [4] and its importance in protein structure was first made apparent in the 1950s by Pauling [5–7] and in the earl y treatise of Pimental & McClellan. [8] More recently, detailed structural patterns of hy- drogen bonding have been analyzed using techniques such as X-ray diffraction to identify recurrent properties in proteins. [9] Along with its importance in protein structure, the relative strength of hydrogen bonding interactions is thought to deter- mine protein folding dynamics. [1,10] The breaking and reforma- tion of hydrogen bonds within the protein and with the sol- vent environment is therefore a key determinant of protein dy- namics. [11] In solution, hydrogen bonds are not rigid, but rather fluxional on a timescale of ~50 ps. [12] This fluxional behaviour is due to the low activation energy of hydrogen bond rupture ~1–1.5 kcalmol À1 . Indeed, in the absence of water considerably higher activation energies have been calculated and it has been proposed that diminished fluxional motions would not support many life processes, since physio logical temperatures could not lead to rupture and realignment of hydrogen bonds. [12] One model system for exploring the structure and dynamics of hydrogen bonds is that of water (H 2 O) and heavy water, deuterium oxide (D 2 O). [13] The oxygen atom of a water mole- cule has two lone pairs, each of which can form a hydrogen bond with hydrogen atoms on two other water molecules. This arrangement allows water molecules to form hydrogen bonds with four other molecules. [14] On the macroscopic level, both experimental [15] and theoretical studies [16] studies have demonstrated that in water, deuterium bonds are stronger than hydrogen bonds by ~0.1 to 0.2 kcalmol À1 . The increased strength of A Single Population Mean using the Student t Distribution A Single Population Mean using the Student t Distribution By: OpenStaxCollege In practice, we rarely know the population standard deviation In the past, when the sample size was large, this did not present a problem to statisticians They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results However, statisticians ran into problems when the sample size was small A small sample size caused inaccuracies in the confidence interval William S Goset (1876–1937) of the Guinness brewery in Dublin, Ireland ran into this problem His experiments with hops and barley produced very few samples Just replacing σ with s did not produce accurate results when he tried to calculate a confidence interval He realized that he could not use a normal distribution for the calculation; he found that the actual distribution depends on the sample size This problem led him to "discover" what is called the Student's t-distribution The name comes from the fact that Gosset wrote under the pen name "Student." Up until the mid-1970s, some statisticians used the normal distribution approximation for large sample sizes and only used the Student's t-distribution only for sample sizes of at most 30 With graphing calculators and computers, the practice now is to use the Student's t-distribution whenever s is used as an estimate for σ If you draw a simple random sample of size n from a population that has an approximately a normal distribution with mean μ and unknown population standard deviation σ and calculate the t-score t = ¯ x–μ ( √sn ) , then the t-scores follow a Student's t- distribution with n – degrees of freedom The t-score has the same interpretation as ¯ the z-score It measures how far x is from its mean μ For each sample size n, there is a different Student's t-distribution 1/21 A Single Population Mean using the Student t Distribution The degrees of freedom, n – 1, come from the calculation of the sample standard ¯ deviation s In [link], we used n deviations (x – xvalues) to calculate s Because the sum of the deviations is zero, we can find the last deviation once we know the other n – deviations The other n – deviations can change or vary freely We call the number n – the degrees of freedom (df) Properties of the Student's t-Distribution • The graph for the Student's t-distribution is similar to the standard normal curve • The mean for the Student's t-distribution is zero and the distribution is symmetric about zero • The Student's t-distribution has more probability in its tails than the standard normal distribution because the spread of the t-distribution is greater than the spread of the standard normal So the graph of the Student's t-distribution will be thicker in the tails and shorter in the center than the graph of the standard normal distribution • The exact shape of the Student's t-distribution depends on the degrees of freedom As the degrees of freedom increases, the graph of Student's tdistribution becomes more like the graph of the standard normal distribution • The underlying population of individual observations is assumed to be normally distributed with unknown population mean μ and unknown population standard deviation σ The size of the underlying population is generally not relevant unless it is very small If it is bell shaped (normal) then the assumption is met and doesn't need discussion Random sampling is assumed, but that is a completely separate assumption from normality Calculators and computers can easily calculate any Student's t-probabilities The TI-83,83+, and 84+ have a tcdf function to find the probability for given values of t The grammar for the tcdf command is tcdf(lower bound, upper bound, degrees of freedom) However for confidence intervals, we need to use inverse probability to find the value of t when we know the probability For the TI-84+ you can use the invT command on the DISTRibution menu The invT command works similarly to the invnorm The invT command requires two inputs: invT(area to the left, degrees of freedom) The output is the t-score that corresponds to the area we specified The TI-83 and 83+ not have the invT command (The TI-89 has an inverse T command.) A probability table for the Student's t-distribution can also be used The table gives t-scores that correspond to the confidence level (column) and degrees of freedom (row) (The TI-86 does not have an invT program or command, so if you are using 2/21 A Single Population Mean using the Student t Distribution that calculator, you need to use a probability table for the Student's t-Distribution.) When using a t-table, note that some tables are formatted to show the confidence level in the column headings, while the column headings in some tables may show only corresponding area in one or both tails A Student's t table (See [link]) gives t-scores given the degrees of freedom and the righttailed ...[...]... or research hypothesis The usual notation is: pronounced H ‘nought’ H0: — the ‘null’ hypothesis HA: — the ‘alternative’ or ‘research’ hypothesis The null hypothesis (H0) will always state that the parameter equals the value specified in the 13 alternative hypothesis (HA) Concepts of Hypothesis Testing… Consider Example 12.1 (mean computer assembly time) again Rather than estimate the mean assembly... manager knows that the accounts are approximately normally distributed with a standard deviation of $65 Can the manager conclude from this that the new system will be cost-effective? 22 Example 1… IDENTIFY The system will be cost effective if the mean account balance for all customers is greater than $170 We express this belief as our research hypothesis, that is: HA: µ > 170 (this is what we want... 28 Example 1… COMPUTE All that’s left to do is calculate compare it to 170 and we can calculate this based on any level of significance (α) we want… 29 Example 1… COMPUTE At a 5% significance level (i.e α =0.05), we get Solving we compute = 175.34 Since our sample mean (178) is greater than the critical value we calculated (175.34), we reject the null hypothesis in favour of H1, i.e that: µ > 170 and... decisions that can be made: Conclude that there is enough evidence to support the alternative hypothesis (also stated as: rejecting the null hypothesis in favour of the alternative) Conclude that there is not enough evidence to support the alternative hypothesis (also stated as: not rejecting the null hypothesis in favour of the alternative) NOTE: we do not say that we accept the null hypothesis 17... manually), and The p-value approach (which is generally used with a computer and statistical software) We will explore both in turn… 25 The Rejection Region Method The rejection region is a range of values such that, if the test statistic falls into that range, the null hypothesis is rejected in favour of the alternative hypothesis Define the value of x that is just large enough to reject the null hypothesis. .. Concepts of Hypothesis Testing… Once the null and alternative hypotheses are stated, the next step is to randomly sample the population and calculate a test statistic (in this example, the sample mean) If the test statistic’s value is inconsistent with the null hypothesis we reject the null hypothesis and infer that the alternative hypothesis is true 18 Concepts of Hypothesis Testing… For example, if... H0 in favour of HA… 32 Example 1: The Big Picture Again 05 H0: µ = 170 0 Z HA: µ > 170 Z.05=1.645 z = 2.46 Reject H0 in favour of 33 Example 1: In summary… • Step 1: Null and alternative hypotheses: H0: µ = 170 HA: µ > 170 • Step 2: Test statistic: x−µ Z= σ n Z has a standard normal distribution as X This Provisional PDF corresponds to the article as it appeared upon acceptance. Fully formatted PDF and full text (HTML) versions will be made available soon. The management of advanced oral cancer in a Jehovah's Witness using the Ultracision Harmonic Scalpel World Journal of Surgical Oncology 2011, 9:115 doi:10.1186/1477-7819-9-115 Peter J Kullar (peterkullar@hotmail.com) Kristian Sorenson (kristian.sorenson@nuth.nhs.uk) Ruwan Weerakkody (wruwan@cantab.net) James Adams (james.adams1@nuth.nhs.uk) ISSN 1477-7819 Article type Case report Submission date 31 January 2011 Acceptance date 3 October 2011 Publication date 3 October 2011 Article URL http://www.wjso.com/content/9/1/115 This peer-reviewed article was published immediately upon acceptance. It can be downloaded, printed and distributed freely for any purposes (see copyright notice below). Articles in WJSO are listed in PubMed and archived at PubMed Central. For information about publishing your research in WJSO or any BioMed Central journal, go to http://www.wjso.com/authors/instructions/ For information about other BioMed Central publications go to http://www.biomedcentral.com/ World Journal of Surgical Oncology © 2011 Kullar et al. ; licensee BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Case report: The management of advanced oral cancer in a Jehovah’s Witness using the Ultracision Harmonic Scalpel Peter J Kullar 1* , Kristian Sorenson 2 , Ruwan Weerakkody 1 and James Adams 1 1 Department of Maxillofacial Surgery Royal Victoria Hospital Newcastle-Upon-Tyne United Kingdom 2 Department of Plastic Surgery Royal Victoria Hospital Newcastle-Upon-Tyne United Kingdom *Corresponding Author Peter Kullar E-mail : peterkullar@hotmail.com Keywords Harmonic scalpel, Head and neck cancer, Jehovah’s Witness Abstract We present the first case of a head and neck oncological procedure accomplished in a Jehovah’s Witness using the Ultracision Harmonic Scalpel (Ethicon, Cincinnati, OH). Jehovah’s Witnesses present a serious challenge to the head and neck cancer surgeon due to their refusal to accept transfusion of any blood products. However, our experience reinforces the view that surgical management of head and neck cancer is possible in these patients. We show the Harmonic Scalpel, an ultrasonic tissue dissector, to be a useful surgical tool in obviating the need for blood transfusion. Preoperative optimisation, intra-operative surgical and anaesthetic techniques are also fully discussed. Background Jehovah’s Witnesses (JW) are a substantial Christian denomination, numbering up to 7 million with a presence in almost all countries worldwide. They are governed by a group of elders exercising authority on all doctrinal matters based on their own translation of the bible. Of particular relevance to medical practice is their refusal, since 1945, to accept blood transfusions even in cases of medical emergency[1] This has been the centre of a number of high profile medical ethics cases[2]. The Harmonic Scalpel (HS), an ultrasonic dissector coagulator (Figure 1; Ethicon, Cincinnati, OH), is a new surgical tool which simultaneous cuts and coagulates tissues. Here we report a case of a large oral cancer and neck dissection with free flap reconstruction performed in a JW with the HS obviating the need for blood products. Case presentation A 48 year old female Caucasian JW presented with non-healing ulcerated lower right second and third molar extraction sockets in 2005. Her past medical history was unremarkable. She Genet. Sel. Evol. 34 (2002) 1–21 1 © INRA, EDP Sciences, 2002 DOI: 10.1051/gse:2001001 Original article Bayesian QTL mapping using skewed Student-t distributions Peter VON R OHR a, b , Ina H OESCHELE a, ∗ a Departments of Dairy Science and Statistics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0315, USA b Institute of Animal Sciences, Animal Breeding, Swiss Federal Institute of Technology (ETH), Zurich, Switzerland (Received 23 April 2001; accepted 17 September 2001) Abstract – In most QTL mapping studies, phenotypes are assumed to follow normal distribu- tions. Deviations from this assumption may lead to detection of false positive QTL. To improve the robustness of Bayesian QTL mapping methods, the normal distribution for residuals is replaced with a skewed Student-t distribution. The latter distribution is able to account for both heavy tails and skewness, and both components are each controlled by a single parameter. The Bayesian QTL mapping method using a skewed Student-t distribution is evaluated with simulated data sets under five different scenarios of residual error distributions and QTL effects. Bayesian QTL mapping / skewed Student-t distribution / Metropolis-Hastings sampling 1. INTRODUCTION Most of the methods currently used in statisticalmapping of quantitative trait loci (QTL) share the common assumption of normally distributed phenotypic observations. According to Coppieters et al. [2], these approaches are not suitable for analysis of phenotypes, which are known to violate the normality assumption. Deviations from normality are likely to affect the accuracy of QTL detection with conventional methods. A nonparametric QTL interval mapping approach had been developed for experimental crosses (Kruglyak and Lander [8]) which was extended by Coppieters et al. [2] for half-sib pedigrees in outbred populations. Elsen and co- workers ([3,7,10]) presented alternative models for QTL detection in livestock populations. In a collection of papers these authors used heteroskedastic models ∗ Correspondence and reprints E-mail: inah@vt.edu 2 P. von Rohr, I. Hoeschele to address the problem of non-normally distributed phenotypic observations. None of these methods can be applied to general and more complex pedigrees. According to Fernandez and Steel [4], the existing toolbox for handling skewed and heavy-tailed data seems rather limited. These authors reviewed some of the existing approaches and concluded that they are all rather complic- ated to implement and lack flexibility and ease of interpretation. Fernandez and Steel [4] have made an important contribution to the devel- opment of more flexible error distributions. They showed that by the method of inverse scaling of the probability density function on the left and on theright side of the mode, any continuous symmetric unimodal distribution can be skewed. This method requires a single scalar parameter, which completely determines the amount of skewness introduced into the distribution. This parameter must be estimated from the data. The procedure does not affect unimodality or tail behavior of the distribution. Simultaneously capturing heavy tails and skewness can be achieved by applying this method to a symmetric heavy-tailed distribution such as the Student-t distribution. We believe that the approach developed by Fernandez and Steel [4] is one of the most promising methods to accommodate non-normal, continuous phenotypic observations with maximum flexibility. Fernandez and Steel [4] also demonstrated that this method is relatively easy to implement in a Bayesian framework. They designed a Gibbs sampler using data augmentation to obtain posterior inferences for a regression model with skewed Student-t distributed residuals. The objective of this study was to incorporate the approach developed by Fernandez and Steel [4] into a Bayesian QTL mapping method, and to implement it with a Metropolis Hastings algorithm, instead of a Gibbs sampler with Genetics Selection Evolution Ginja et al. Genetics Selection Evolution 2010, 42:18 http://www.gsejournal.org/content/42/1/18 Open Access RESEARCH © 2010 Ginja et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Research Molecular genetic analysis of a cattle population to reconstitute the extinct Algarvia breed Catarina Ginja 1 , Maria CT Penedo 1 , Maria F Sobral 2 , José Matos 3 , Carla Borges 3 , Dina Neves 4 , Teresa Rangel- Figueiredo 5 and Alfredo Cravador* 6 Abstract Background: Decisions to initiate conservation programmes need to account for extant variability, diversity loss and cultural and economic aspects. Molecular markers were used to investigate if putative Algarvia animals could be identified for use as progenitors in a breeding programme to recover this nearly extinct breed. Methods: 46 individuals phenotypically representative of Algarvia cattle were genotyped for 27 microsatellite loci and compared with 11 Portuguese autochthonous and three imported breeds. Genetic distances and factorial correspondence analyses (FCA) were performed to investigate the relationship among Algarvia and related breeds. Assignment tests were done to identify representative individuals of the breed. Y chromosome and mtDNA analyses were used to further characterize Algarvia animals. Gene- and allelic-based conservation analyses were used to determine breed contributions to overall genetic diversity. Results: Genetic distance and FCA results confirmed the close relationship between Algarvia and southern Portuguese breeds. Assignment tests without breed information classified 17 Algarvia animals in this cluster with a high probability (q > 0.95). With breed information, 30 cows and three bulls were identified (q > 0.95) that could be used to reconstitute the Algarvia breed. Molecular and morphological results were concordant. These animals showed intermediate levels of genetic diversity (MNA = 6.0 ± 1.6, R t = 5.7 ± 1.4, H o = 0.63 ± 0.19 and H e = 0.69 ± 0.10) relative to other Portuguese breeds. Evidence of inbreeding was also detected (F is = 0.083, P < 0.001). The four Algarvia bulls had Y-haplotypes H6Y2 and H11Y2, common in Portuguese cattle. The mtDNA composition showed prevalence of T3 matrilines and presence of the African-derived T1a haplogroup. This analysis confirmed the genetic proximity of Algarvia and Garvonesa breeds (F st = 0.028, P > 0.05). Algarvia cattle provide an intermediate contribution (CB = 6.18, CW = -0.06 and D1 = 0.50) to the overall gene diversity of Portuguese cattle. Algarvia and seven other autochthonous breeds made no contribution to the overall allelic diversity. Conclusions: Molecular analyses complemented previous morphological findings to identify 33 animals that can be considered remnants of the Algarvia breed. Results of genetic diversity and conservation analyses provide objective information to establish a management program to reconstitute the Algarvia breed. Background Breeding practices designed to alleviate production con- straints are prejudicial to the survival of traditional domestic animal breeds, and tend to lead to impoverish- ment of the gene pool [1]. The Food and Agriculture Organization of the United Nations has encouraged a series of conservation measures designed to help prevent irreversible loss of diversity of domesticated animal spe- cies [2]. A heightened awareness of the cultural, historical and social heritage represented by traditional breeds has led to increased interest in their preservation [3]. Despite its small geographic area, Portugal hosts a wide variety of domestic breeds [4], with as many as 13 autochthonous cattle breeds recognized [4,5]. Analysis of genetic diver- ... spread of the t- distribution is greater than the spread of the standard normal So the graph of the Student' s t- distribution will be thicker in the tails and shorter in the center than the graph... Student' s t- distribution is zero and the distribution is symmetric about zero • The Student' s t- distribution has more probability in its tails than the standard normal distribution because the. .. Mean using the Student t Distribution A random sample of statistics students were asked to estimate the total number of hours they spend watching television in an average week The responses are