Genetic models to estimate additive and non-additive effects of marker-associated QTL using multiple regression techniques

Summary The development of molecular markers has recently raised expectations for their application in selection programs. However, some questions related to quantitative trait loci (QTL) identification are still unanswered. The objectives of this paper are (1) to develop statistical genetic models for detecting and locating on the genome multi-QTL with additive, dominance and epistatic effects using multiple linear regression analysis in the backcross and F_n generations from the cross of two inbred lines; and (2) to discuss the bias caused by linked and unlinked QTL on the genetic estimates. Non-linear models were developed for different backcross and F_n generations when both epistasis and no epistasis were assumed. Generation analysis of marked progenies is suggested as a way of increasing the number of observations for the estimates without additional cost for molecular scoring. Some groups of progenies can be created in different generations from the same scored individuals. The non-linear models were transformed into approximate multivariate linear models to which combined stepwise and standard regression analysis could be applied. Expressions for the biases of the marker classes from linked QTL were obtained when no epistasis was assumed. When epistasis was assumed, these expressions increased in complexity, and the biases were caused by both linked and unlinked QTL.     

双交组合种子性状的遗传模型及蒙特卡罗模拟分析

将Cockerham广义遗传模型的建模原理应用于双交方式的交配设计,针对二倍体种子和三倍体胚乳数量性状的遗传特点,提出了2个适用于分析种子品质性状的加性-显性-细胞质-母体模型,介绍了相应的统计分析方法,并进行了蒙特卡罗模拟分析。     

Comparison of RAPD and RFLP markers for mapping F2 generations in maize (Zea mays L.)

The F₂ generations from two maize crosses were used to compare the ability of RAPD and RFLP marker systems to create a genetic linkage map. Both RFLPs and RAPDs were shown to provide Mendelian-type markers. Most of the RFLPs (80%) could be placed with a good level of certainty (LOD>4) on the genetic linkage map. However, because of their dominant nature, only between 37% and 59% of the RAPDs could be placed with such a LOD score. The use of combined data from RFLPs and RAPDs increases the level of information provided by RAPDs and allows the creation of a combined RFLP/RAPD genetic linkage map. Thus, the RAPD technique was found to be a powerful method to provide improved probes coverage on a previously created RFLP map and to locate markers linked to chromosomal regions of interest.     

Pyramiding QTL for multiple lateral branching in cucumber using inbred backcross lines

Multiple lateral branching (MLB) is a quantitatively inherited trait associated with yield in cucumber (Cucumis sativus L.; 2n = 2x = 14). Although quantitative trait loci (QTL) have been identified for MLB and QTL-marker associations have been verified by marker-assisted selection, the individual effects of these QTL have not been characterized. To test the effects of pyramiding QTL for MLB, molecular genotyping was utilized to create two sets (standard- and little-leaf types) of inbred backcross (IBC) lines possessing various numbers of QTL that promote branching. These IBC lines were evaluated for lateral branch number in two Wisconsin environments at three plant densities. Highly significant differences in the number of primary lateral branches were detected between spacings, leaf types, and lines, but not between locations. Lateral branch number decreased at higher plant densities in all genotypes, while genotype by environment and QTL by environment interactions were marginally non-significant. As the number of QTL increased among IBC lines, the number of branches did not generally change in the little-leaf lines, but decreased in the standard-leaf lines, demonstrating an epistatic effect related to genetic background during lateral branch development. The genomic location with the greatest effect on MLB was confirmed as the QTL that was previously mapped near the little-leaf locus (ll), while the addition of one specific QTL consistently decreased the number of lateral branches in standard-leaf lines. Although pyramiding QTL for MLB did not uniformly increase the number of lateral branches, pyramiding QTL in IBC lines allowed further characterization of individual QTL involved in MLB. Our results, coupled with those of previous studies indicate that lateral branch development in cucumber is determined by growing environment (i.e., plant spacing), genetic background, and QTL composition.     

Grandparental effects in marine sticklebacks: transgenerational plasticity across multiple generations

Nongenetic inheritance mechanisms such as transgenerational plasticity (TGP) can buffer populations against rapid environmental change such as ocean warming. Yet, little is known about how long these effects persist and whether they are cumulative over generations. Here, we tested for adaptive TGP in response to simulated ocean warming across parental and grandparental generations of marine sticklebacks. Grandparents were acclimated for two months during reproductive conditioning, whereas parents experienced developmental acclimation, allowing us to compare the fitness consequences of short‐term vs. prolonged exposure to elevated temperature across multiple generations. We found that reproductive output of F1 adults was primarily determined by maternal developmental temperature, but carry‐over effects from grandparental acclimation environments resulted in cumulative negative effects of elevated temperature on hatching success. In very early stages of growth, F2 offspring reached larger sizes in their respective paternal and grandparental environment down the paternal line, suggesting that other factors than just the paternal genome may be transferred between generations. In later growth stages, maternal and maternal granddam environments strongly influenced offspring body size, but in opposing directions, indicating that the mechanism(s) underlying the transfer of environmental information may have differed between acute and developmental acclimation experienced by the two generations. Taken together, our results suggest that the fitness consequences of parental and grandparental TGP are highly context dependent, but will play an important role in mediating some of the impacts of rapid climate change in this system.     

The correlation of substitution effects across populations and generations in the presence of nonadditive functional gene action

Allele substitution effects at quantitative trait loci (QTL) are part of the basis of quantitative genetics theory and applications such as association analysis and genomic prediction. In the presence of nonadditive functional gene action, substitution effects are not constant across populations. We develop an original approach to model the difference in substitution effects across populations as a first order Taylor series expansion from a “focal” population. This expansion involves the difference in allele frequencies and second-order statistical effects (additive by additive and dominance). The change in allele frequencies is a function of relationships (or genetic distances) across populations. As a result, it is possible to estimate the correlation of substitution effects across two populations using three elements: magnitudes of additive, dominance, and additive by additive variances; relationships (Nei’s minimum distances or Fst indexes); and assumed heterozygosities. Similarly, the theory applies as well to distinct generations in a population, in which case the distance across generations is a function of increase of inbreeding. Simulation results confirmed our derivations. Slight biases were observed, depending on the nonadditive mechanism and the reference allele. Our derivations are useful to understand and forecast the possibility of prediction across populations and the similarity of GWAS effects.     

Monte Carlo simulation of damascene electroplating: effects of additives

The influence of additives on the filling process of via holes in damascene electroplating is investigated with use of a kinetic Monte Carlo method. The basic system is the solid-by-solid model for crystal growth which includes the vacancy formation during the growth of thin film. Three kinds of additives are included in the model to control the local surface growth rate. Inhibitors and levelers have the effect of preventing the deposition, while accelerators increase the local growth rate. Levelers are modeled to stick to the tips of the surface. We performed a series of simulations by changing the parameters which characterize the additives to see their influence on the filling mechanism. It is shown that void-free filling is possible by the combination of the effects of the additives.     

Optimising muscle parameters in musculoskeletal models using Monte Carlo simulation

The use of musculoskeletal simulation software has become a useful tool for modelling joint and muscle forces during human activity, including in reduced gravity because direct experimentation is difficult. Knowledge of muscle and joint loads can better inform the design of exercise protocols and exercise countermeasure equipment. In this study, the LifeModeler? (San Clemente, CA, USA) biomechanics simulation software was used to model a squat exercise. The initial model using default parameters yielded physiologically reasonable hip-joint forces but no activation was predicted in some large muscles such as rectus femoris, which have been shown to be active in 1-g performance of the activity. Parametric testing was conducted using Monte Carlo methods and combinatorial reduction to find a muscle parameter set that more closely matched physiologically observed activation patterns during the squat exercise. The rectus femoris was predicted to peak at 60.1% activation in the same test case compared to 19.2% activation using default parameters. These results indicate the critical role that muscle parameters play in joint force estimation and the need for exploration of the solution space to achieve physiologically realistic muscle activation.     

Evaluating spatial constraints in cellular assembly processes using a Monte Carlo approach

Biomolecular behavior commonly involves complex sets of interacting components that are challenging to understand through solution-based chemical theories. Molecular assembly is especially intriguing in the cellular environment because of its links to cell structure in processes such as chemotaxis. We use a coarse-grained Monte Carlo simulation to elucidate the importance of spatial constraints in molecular assembly. We have performed a study of actin filament polymerization through this space-aware probabilistic lattice-based model. Quantitative results are compared with nonspatial models and show convergence over a wide parameter space, but marked divergence over realistic levels corresponding to macromolecular crowding inside cells and localized actin concentrations found at the leading edge during cell motility. These conclusions have direct implications for cell shape and structure, as well as tumor cell migration.     

Uncertainty analysis of penicillin V production using Monte Carlo simulation

Uncertainty and variability affect economic and environmental performance in the production of biotechnology and pharmaceutical products. However, commercial process simulation software typically provides analysis that assumes deterministic rather than stochastic process parameters and thus is not capable of dealing with the complexities created by variance that arise in the decision-making process. Using the production of penicillin V as a case study, this article shows how uncertainty can be quantified and evaluated. The first step is construction of a process model, as well as analysis of its cost structure and environmental impact. The second step is identification of uncertain variables and determination of their probability distributions based on available process and literature data. Finally, Monte Carlo simulations are run to see how these uncertainties propagate through the model and affect key economic and environmental outcomes. Thus, the overall variation of these objective functions are quantified, the technical, supply chain, and market parameters that contribute most to the existing variance are identified and the differences between economic and ecological evaluation are analyzed. In our case study analysis, we show that final penicillin and biomass concentrations in the fermenter have the highest contribution to variance for both unit production cost and environmental impact. The penicillin selling price dominates return on investment variance as well as the variance for other revenue-dependent parameters.     

A Monte Carlo Study to Evaluate the Performance of Selected Tests of Homogeneity in Sparse Contingency Tables

We address the problem of tests of homogeneity in two-way contingency tables in case-control studies when the case category is subdivided into k subcategories. In this situation, we have two cells with large frequencies and 2 X k cells with frequencies that become small as k increases. We propose two ad hoc statistics in which a statistic for the sparse cells is combined with a statistic for the cells with large frequencies. We will study these tests along with the Pearson test (using a chi-square approximation) in a Monte Carlo simulation study. Two sets of null hypothesis models and two sets of alternative hypothesis models are considered. The best test for the models considered is the usual Pearson test (using an approximate chi-square distribution) although the ad hoc models are more powerful under one alternative model considered.     

Tertiary structure prediction of the KIX domain of CBP using Monte Carlo simulations driven by restraints derived from multiple sequence alignments

Using a recently developed protein folding algorithm, a prediction of the tertiary structure of the KIX domain of the CREB binding protein is described. The method incorporates predicted secondary and tertiary restraints derived from multiple sequence alignments in a reduced protein model whose conformational space is explored by Monte Carlo dynamics. Secondary structure restraints are provided by the PHD secondary structure prediction algorithm that was modified for the presence of predicted U-turns, i.e., regions where the chain reverses global direction. Tertiary restraints are obtained via a two-step process: First, seed side-chain contacts are identified from a correlated mutation analysis, and then, a threading-based algorithm expands the number of these seed contacts. Blind predictions indicate that the KIX domain is a putative three-helix bundle, although the chirality of the bundle could not be uniquely determined. The expected root-mean-square deviation for the correct chirality of the KIX domain is between 5.0 and 6.2 Å. This is to be compared with the estimate of 12.9 Å that would be expected by a random prediction, using the model of F. Cohen and M. Sternberg (J. Mol. Biol. 138:321–333, 1980). Proteins 30:287–294, 1998. © 1998 Wiley-Liss, Inc.     

A review on Monte Carlo simulation methods as they apply to mutation and selection as formulated in Wright-Fisher models of evolutionary genetics

A case has made for the use of Monte Carlo simulation methods when the incorporation of mutation and natural selection into Wright-Fisher gametic sampling models renders then intractable from the standpoint of classical mathematical analysis. The paper has been organized around five themes. Among these themes was that of scientific openness and a clear documentation of the mathematics underlying the software so that the results of any Monte Carlo simulation experiment may be duplicated by any interested investigator in a programming language of his choice. A second theme was the disclosure of the random number generator used in the experiments to provide critical insights as to whether the generated uniform random variables met the criterion of independence satisfactorily. A third theme was that of a review of recent literature in genetics on attempts to find signatures of evolutionary processes such as natural selection, among the millions of segments of DNA in the human genome, that may help guide the search for new drugs to treat diseases. A fourth theme involved formalization of Wright-Fisher processes in a simple form that expedited the writing of software to run Monte Carlo simulation experiments. Also included in this theme was the reporting of several illustrative Monte Carlo simulation experiments for the cases of two and three alleles at some autosomal locus, in which attempts were to made to apply the theory of Wright-Fisher models to gain some understanding as to how evolutionary signatures may have developed in the human genome and those of other diploid species. A fifth theme was centered on recommendations that more demographic factors, such as non-constant population size, be included in future attempts to develop computer models dealing with signatures of evolutionary process in genomes of various species. A brief review of literature on the incorporation of demographic factors into genetic evolutionary models was also included to expedite and stimulate further development on this theme.     

Mapping QTL controlling yield and yield components in a spring barley (Hordeum vulgare L.) cross using marker regression

An RFLP map constructed from 99 doubled haploid lines of a cross between two spring barley varieties (Blenheim × Kym) was used to localize quantitative trait loci (QTL) controlling grain yield and yield components by marker regression and single-marker analysis. Trials were conducted over three years. Genotype-by-year interaction was detected for plant grain weight and ear grain weight so they were analysed separately for each year. None was detected for thousand-grain weight and ear grain number so data were pooled over years. A total of eleven QTL were detected for plant grain weight over two years and fourteen for ear grain weight over three years. Seven QTL were detected for plot yield. The locus with the largest effect was on chromosome 2(2H)L and accounted for 19% of the variation in the progeny. Eight QTL were detected for thousand-grain weight and five for ear grain number. Many of the QTL detected were in comparable positions in each year. Yield and yield components were only partly correlated. Comparisons based on common RFLP markers showed that some QTL were found in positions similar to those identified in other studies. For a number of QTL the identification of linked markers provided suitable opportunities for marker-assisted selection and improvement of barley and reference markers with which to analyse the homoeologous chromosome regions of wheat and other cereals.     

Prediction of protein conformation in water and on surfaces by Monte Carlo simulations using united-atom method

The united-atom method has been used to model an avian pancreatic polypeptide (APP) in water and the adsorption process of an albumin subdomain (AS) onto graphite surface to observe the capability of this lumped modelling approach to generate structures observed in protein data bank (PDB) and from atomistic modelling. The subdomain structure of a protein is simplified by the united-atom approximation where the side chains and peptide groups are represented by lumped spheres. The total potential energy of the adsorption process involves the interaction between these lumped spheres by means of virtual bond chain interaction and the interaction of the spheres with the graphite surface by means of Lennard-Jones potential. The protein/polypeptide structure has been perturbed by Monte Carlo with energy minimisation to obtain the global minimum. Results on the APP in water showed a near-to-experimental PDB conformation revealing the two α-helix structures of this small protein molecule with the root mean square deviation among carbon backbone atoms of 5.9 Å. Protein adsorption on biosurfaces has been made by modelling AS, which has 60 amino acids. The surface is graphite, which is characterised by its hydrophobicity. Graphite was chosen because of its widely used applications in certain implants that interact with blood. Our simulation results showed final conformation close to that obtained by atomistic modelling. It also proved that the whole pattern of intramolecular hydrogen bonds was distorted. The model also demonstrated the random conformation of the original α-helix secondary structures of AS consistent with experimental and atomistic results. While atomistic simulation works well for simulating individual small proteins, the united-atom model is more efficient when simulating macromolecular and multiple protein adsorption where time and limiting computer capacity are key factors.     

Studies on evolutionary and selective properties of hypercycles using a Monte Carlo method

Summary The most relevant properties of hypercycles were previously studied mainly from a theoretical point of view. We have developed a Monte Carlo method simulating hypercyclic organization to obtain information about the dynamics of this prebiotic organization. Nucleation, growth, and selective properties have been tested and the results obtained are in good agreement with those of the theoretical predictions. The influence of hypercyclic organization of the error threshold has also been studied. As a consequence of the emergence of a hypercycle, the value of this threshold decreases. The amount of this decrease depends on the population size. Moreover, for some interval of quality factor values, either the hypercycle organization or an error catastrophe can be produced, depending on the initial conditions. The influence of these phenomena on both the dynamic behavior and evolutionary advantages of the hypercycle, as well as their decisive roles on genome size, are discussed.Presented at the FEBS Symposium on Genome Organization and Evolution, held in Crete, Greece, September 1–5, 1986     

QTL mapping of naturally-occurring variation in flowering time of Arabidopsis thaliana

A segregating F₂ population of Arabidopsis thaliana derived from a cross between the late-flowering ecotype Hannover/Münden (HM) and the early-flowering ecotype Wassilewskija (WS) was analyzed for flowering time and other morphological traits. Two unlinked quantitative trait loci (QTLs) affecting days to first flower (DFF-a and DFF-b) mapped to chromosome 5. QTLs which affect node number (NN), leaf length at flowering (LLF), and leaf length at 35 days (LL35) also mapped to chromosome 5; LLF-a, LL35-a, NN-a map to the same region of chromosome 5 as DFF-a; LLF-b and LL35-bmap to the same region of chromosome 5 as DFF-b. Another QTL affecting leaf length at flowering (LLF-c) maps to chromosome 3. The proximity of DFF-a, LLF-a, LL35-a and NN-a, as well as the similarity in gene action among these QTLs (additivity), suggest that they may be pleiotropic consequences of a single gene at this locus. Similarly, LL35-b and LLF-b map near each other and both display recessive gene action, again suggesting the possibility of pleiotropy. DFF-b, which also maps near LL35-b and LLF-b, displays largely additive gene action (although recessive gene action could not be ruled out). This suggests that DFF-b may represent a different gene from LL35-b and/or LLF-b. DFF-a maps near two previously identified mutants: co (which also affects flowering time and displays gene action consistent with additivity) and flc. Similar map locations and gene actions of QTLs affecting the correlated traits DFF, LLF, LL35 and NN suggest that these genomic regions harbor naturally occurring allelic variants involved in the general transition of the plant from vegetative to reproductive growth.     

Monte Carlo dose verification of VMAT treatment plans using Elekta Agility 160-leaf MLC

In this study, we verified volumetric modulated arc therapy (VMAT) plans in an Elekta Synergy system with an integrated Agility 160-leaf multileaf collimator (MLC) by comparing them with Monte Carlo (MC)-calculated dose distributions using the AAPM TG-119 structure sets. The head configuration of the linear accelerator with the integrated MLC was simulated with the EGSnrc/BEAMnrc code. Firstly, the dosimetric properties of the MLC were evaluated with the MC technique and film measurements. Next, VMAT plans were created with the Pinnacle³ treatment planning system (TPS) for four regions in the AAPM TG-119 structures. They were then verified by comparing them with MC-calculated dose distributions using dose volume histograms (DVHs) and three-dimensional (3D) gamma analysis. The MC simulations for the Agility MLC dosimetric properties were in acceptable agreement with measurements. TPS-VMAT plans using TG-119 structure sets agreed with MC dose distributions within 2% in the comparison of D₉₅ in planning target volumes (PTVs) evaluated from DVHs. In contrast, higher dose regions such as D₂₀, D₁₀, and D₅ in PTVs for TPS tended to be smaller than MC values. This tendency was particularly noticeable for mock head and neck with complicated structures. In 3D gamma analysis, the passing rates with 3%/3mm criteria in PTVs were ≥99%, except for mock head and neck (89.5%). All passing rates for organs at risk (OARs) were in acceptable agreement of >96%. It is useful to verify dose distributions of PTVs and OARs in TPS-VMAT plans by using MC dose calculations and 3D gamma analysis.     

Monte Carlo estimates of natural variation in HIV infection

We describe a Monte Carlo simulation of the within-host dynamics of human immunodeficiency virus 1 (HIV-1). The simulation proceeds at the level of individual T-cells and virions in a small volume of plasma, thus capturing the inherent stochasticity in viral replication, mutation and T-cell infection. When cell lifetimes are distributed exponentially in the Monte Carlo approach, our simulation results are in perfect agreement with the predictions of the corresponding systems of differential equations from the literature. The Monte Carlo model, however, uniquely allows us to estimate the natural variability in important parameters such as the T-cell count, viral load, and the basic reproductive ratio, in both the presence and absence of drug therapy. The simulation also yields the probability that an infection will not become established after exposure to a viral inoculum of a given size. Finally, we extend the Monte Carlo approach to include distributions of cell lifetimes that are less-dispersed than exponential.     

Fine mapping of porcine chromosome 6 QTL and LEPR effects on body composition in multiple generations of an Iberian by Landrace intercross

The leptin receptor gene (LEPR) is a candidate for traits related to growth and body composition, and is located on SSC6 in a region where fatness and meat composition quantitative trait loci (QTL) have previously been detected in several F2 experimental designs. The aims of this work were: (i) to fine map these QTL on a larger sample of animals and generations (F3 and backcross) of an Iberian x Landrace intercross and (ii) to examine the effects of LEPR alleles on body composition traits. Eleven single nucleotide polymorphisms (SNPs) were detected by sequencing LEPR coding regions in Iberian and Landrace pig samples. Three missense polymorphisms were genotyped by pyrosequencing in 33 F0, 70 F1, 418 F2, 86 F3 and 128 individuals coming from the backcross of four F2 males with 24 Landrace females. Thirteen microsatellites and one SNP were also genotyped. Traits analysed were: backfat thickness at different locations (BF(T)), intramuscular fat percentage (IMF(P)), eye muscle area (EM(A)), loin depth (LO(D)), weight of shoulder (SH(W)), weight of ribs (RIB(W)) and weight of belly bacon (BB(W)). Different statistical models were applied in order to evaluate the number and effects of QTL on chromosome 6 and the possible causality of the LEPR gene variants with respect to the QTL. The results support the presence of two QTL on SSC6. One, at position 60-100 cM, affects BF(T) and RIB(W). The other and more significant maps in a narrow region (130-132 cM) and affects BF(T), IMF(P), EM(A), LO(D), SH(W), RIB(W) and BB(W). Results also support the association between LEPR alleles and BF(T) traits. The possible functional implications of the analysed polymorphisms are considered.