Functional mapping of growth and development

Computational dissection of genetic variation modulating the response of multiple photosynthetic phenotypes to the light environment

BACKGROUND

The expression of biological traits is modulated by genetics as well as the environment, and the level of influence exerted by the latter may vary across characteristics. Photosynthetic traits in plants are complex quantitative traits that are regulated by both endogenous genetic factors and external environmental factors such as light intensity and CO2 concentration. The specific processes impacted occur dynamically and continuously as the growth of plants changes. Although studies have been conducted to explore the genetic regulatory mechanisms of individual photosynthetic traits or to evaluate the effects of certain environmental variables on photosynthetic traits, the systematic impact of environmental variables on the dynamic process of integrated plant growth and development has not been fully elucidated.

RESULTS

In this paper, we proposed a research framework to investigate the genetic mechanism of high-dimensional complex photosynthetic traits in response to the light environment at the genome level. We established a set of high-dimensional equations incorporating environmental regulators to integrate functional mapping and dynamic screening of gene‒environment complex systems to elucidate the process and pattern of intrinsic genetic regulatory mechanisms of three types of photosynthetic phenotypes of Populus simonii that varied with light intensity. Furthermore, a network structure was established to elucidate the crosstalk among significant QTLs that regulate photosynthetic phenotypic systems. Additionally, the detection of key QTLs governing the response of multiple phenotypes to the light environment, coupled with the intrinsic differences in genotype expression, provides valuable insights into the regulatory mechanisms that drive the transition of photosynthetic activity and photoprotection in the face of varying light intensity gradients.

CONCLUSIONS

This paper offers a comprehensive approach to unraveling the genetic architecture of multidimensional variations in photosynthetic phenotypes, considering the combined impact of integrated environmental factors from multiple perspectives.

Phenomics based prediction of plant biomass and leaf area in wheat using machine learning approaches

Introduction

Phenomics has emerged as important tool to bridge the genotype-phenotype gap. To dissect complex traits such as highly dynamic plant growth, and quantification of its component traits over a different growth phase of plant will immensely help dissect genetic basis of biomass production. Based on RGB images, models have been developed to predict biomass recently. However, it is very challenging to find a model performing stable across experiments. In this study, we recorded RGB and NIR images of wheat germplasm and Recombinant Inbred Lines (RILs) of Raj3765xHD2329, and examined the use of multimodal images from RGB, NIR sensors and machine learning models to predict biomass and leaf area non-invasively.

Results

The image-based traits (i-Traits) containing geometric features, RGB based indices, RGB colour classes and NIR features were categorized into architectural traits and physiological traits. Total 77 i-Traits were selected for prediction of biomass and leaf area consisting of 35 architectural and 42 physiological traits. We have shown that different biomass related traits such as fresh weight, dry weight and shoot area can be predicted accurately from RGB and NIR images using 16 machine learning models. We applied the models on two consecutive years of experiments and found that measurement accuracies were similar suggesting the generalized nature of models. Results showed that all biomass-related traits could be estimated with about 90% accuracy but the performance of model BLASSO was relatively stable and high in all the traits and experiments. The R² of BLASSO for fresh weight prediction was 0.96 (both year experiments), for dry weight prediction was 0.90 (Experiment 1) and 0.93 (Experiment 2) and for shoot area prediction 0.96 (Experiment 1) and 0.93 (Experiment 2). Also, the RMSRE of BLASSO for fresh weight prediction was 0.53 (Experiment 1) and 0.24 (Experiment 2), for dry weight prediction was 0.85 (Experiment 1) and 0.25 (Experiment 2) and for shoot area prediction 0.59 (Experiment 1) and 0.53 (Experiment 2).

Discussion

Based on the quantification power analysis of i-Traits, the determinants of biomass accumulation were found which contains both architectural and physiological traits. The best predictor i-Trait for fresh weight and dry weight prediction was Area_SV and for shoot area prediction was projected shoot area. These results will be helpful for identification and genetic basis dissection of major determinants of biomass accumulation and also non-invasive high throughput estimation of plant growth during different phenological stages can identify hitherto uncovered genes for biomass production and its deployment in crop improvement for breaking the yield plateau.

Multiple dynamic models reveal the genetic architecture for growth in height of Catalpa bungei in the field

Growth in height (GH) is a critical determinant for tree survival and development in forests and can be depicted using logistic growth curves. Our understanding of the genetic mechanism underlying dynamic GH, however, is limited, particularly under field conditions. We applied two mapping models (Funmap and FVTmap) to find quantitative trait loci responsible for dynamic GH and two epistatic models (2HiGWAS and 1HiGWAS) to detect epistasis in Catalpa bungei grown in the field. We identified 13 co-located quantitative trait loci influencing the growth curve by Funmap and three heterochronic parameters (the timing of the inflection point, maximum acceleration and maximum deceleration) by FVTmap. The combined use of FVTmap and Funmap reduced the number of candidate genes by >70%. We detected 76 significant epistatic interactions, amongst which a key gene, COMT14, co-located by three models (but not 1HiGWAS) interacted with three other genes, implying that a novel network of protein interaction centered on COMT14 may control the dynamic GH of C. bungei. These findings provide new insights into the genetic mechanisms underlying the dynamic growth in tree height in natural environments and emphasize the necessity of incorporating multiple dynamic models for screening more reliable candidate genes.

Functional Mapping of Phenotypic Plasticity of Staphylococcus aureus Under Vancomycin Pressure

Phenotypic plasticity is the exhibition of various phenotypic traits produced by a single genotype in response to environmental changes, enabling organisms to adapt to environmental changes by maintaining growth and reproduction. Despite its significance in evolutionary studies, we still know little about the genetic control of phenotypic plasticity. In this study, we designed and conducted a genome-wide association study (GWAS) to reveal genetic architecture of how Staphylococcus aureus strains respond to increasing concentrations of vancomycin (0, 2, 4, and 6 μg/mL) in a time course. We implemented functional mapping, a dynamic model for genetic mapping using longitudinal data, to map specific loci that mediate the growth trajectories of abundance of vancomycin-exposed S. aureus strains. 78 significant single nucleotide polymorphisms were identified following analysis of the whole growth and development process, and seven genes might play a pivotal role in governing phenotypic plasticity to the pressure of vancomycin. These seven genes, SAOUHSC_00020 (walR), SAOUHSC_00176, SAOUHSC_00544 (sdrC), SAOUHSC_02998, SAOUHSC_00025, SAOUHSC_00169, and SAOUHSC_02023, were found to help S. aureus regulate antibiotic pressure. Our dynamic gene mapping technique provides a tool for dissecting the phenotypic plasticity mechanisms of S. aureus under vancomycin pressure, emphasizing the feasibility and potential of functional mapping in the study of bacterial phenotypic plasticity.

Functional mapping of tillering QTLs using the Wang-Lan-Ding model and a SSSL population

Understanding dynamic changes in the genetic architecture of quantitative traits is crucial in developmental genetics. Functional mapping is an appropriate method that passes a mathematical equation to describe a biological developmental process with the genetic mapping framework. Appropriate genetic model and applicable mapping population are indispensable condition for functional mapping of important agronomic traits in plants. Based on the Wang-Lan-Ding model, we ever applied a DH population to carry out functional mapping QTLs underlying growth trajectory on tiller number. However, inconsistent genetic background among the DH lines might disturb the mapping results. With the advent of innovative research materials, single segment substitution lines, allows us to do more precise genetic analyses. Thus functional mapping was again conducted on tiller number using the Wang-Lan-Ding model and a single segment substitution line population with the genetic background of Huajingxian 74 so as to explore QTL dynamic mechanism to regulate developmental traits. We detected that all five single segment substitution lines harbored tillering QTLs with additives and/or dominances to influence the four functional parameters, the optimum tillering time (t₀), the maximum tiller number (K), the tillering increased rate (r) and the tillering decreased rate (c), which were estimated from the Wang-Lan-Ding model and with some biological meaning. They mainly brought the inflexion point (t₀) delay, the peak increase (K) and the degradation (c) acceleration, while the growth (r) slow down. Moreover, epistatic interactions among these QTLs were confirmed to be prevalent. A total of 39 significant epistatic effects were detected to associate with the four parameters, occupying 34.8% of 112 pairs of epistatic interactions investigated. Contrary to the QTL effects, these epistatic effects largely decreased t₀, K and c, while increased r. Our results indicated that the five QTL effects and their epistatic effects significantly changed the shape and trajectory of tiller number via influence of the four functional parameters. Rational use of these QTLs is expected to improve tillering number of rice by molecular design breeding.

Quantitative trait loci for growth-related traits in Japanese quail (Coturnix japonica) using restriction-site associated DNA sequencing

This study aimed to identify quantitative trait loci (QTLs) for growth-related traits by constructing a genetic linkage map based on single nucleotide polymorphism (SNP) markers in Japanese quail. A QTL mapping population of 277 F₂ birds was obtained from an intercross between a male of a large-sized strain and three females of a normal-sized strain. Body weight (BW) was measured weekly from hatching to 16 weeks of age. Non-linear regression growth models of Weibull, Logistic, Gompertz, Richards, and Brody were analyzed, and growth curve parameters of Richards was selected as the best model to describe the quail growth curve of the F₂ birds. Restriction-site associated DNA sequencing developed 125 SNP markers that were informative between their parental strains. The SNP markers were distributed on 16 linkage groups that spanned 795.9 centiMorgan (cM) with an average marker interval of 7.3 cM. QTL analysis of phenotypic traits revealed four main-effect QTLs. Detected QTLs were located on chromosomes 1 and 3 and were associated with BW from 4 to 16 weeks of age and asymptotic weight of Richards model at genome-wide significant at 1% or 5% level. No QTL was detected for BW from 0 to 3 weeks of age. This is the first report identified QTLs for asymptotic weight of the Richards parameter in Japanese quail. These results highlight that the combination of QTL studies and the RAD-seq method will aid future breeding programs identify genes underlying the QTL and the application of marker-assisted selection in the poultry industry, particularly the Japanese quail.

Functional physiological phenotyping with functional mapping: A general framework to bridge the phenotype-genotype gap in plant physiology

The recent years have witnessed the emergence of high-throughput phenotyping techniques. In particular, these techniques can characterize a comprehensive landscape of physiological traits of plants responding to dynamic changes in the environment. These innovations, along with the next-generation genomic technologies, have brought plant science into the big-data era. However, a general framework that links multifaceted physiological traits to DNA variants is still lacking. Here, we developed a general framework that integrates functional physiological phenotyping (FPP) with functional mapping (FM). This integration, implemented with high-dimensional statistical reasoning, can aid in our understanding of how genotype is translated toward phenotype. As a demonstration of method, we implemented the transpiration and soil-plant-atmosphere measurements of a tomato introgression line population into the FPP-FM framework, facilitating the identification of quantitative trait loci (QTLs) that mediate the spatiotemporal change of transpiration rate and the test of how these QTLs control, through their interaction networks, phenotypic plasticity under drought stress.

The genetic control of leaf allometry in the common bean, Phaseolus vulgaris

BACKGROUND

To maximize photosynthetic efficiency, plants have evolved a capacity by which leaf area scales allometrically with leaf mass through interactions with the environment. However, our understanding of genetic control of this allometric relationship remains limited.

RESULTS

We integrated allometric scaling laws expressed at static and ontogenetic levels into genetic mapping to identify the quantitative trait loci (QTLs) that mediate how leaf area scales with leaf mass and how such leaf allometry, under the control of these QTLs, varies as a response to environment change. A major QTL detected by the static model constantly affects the allometric growth of leaf area vs. leaf mass for the common bean (Phaseolus vulgaris) in two different environments. The ontogenetic model identified this QTL plus a few other QTLs that determine developmental trajectories of leaf allometry, whose expression is contingent heavily upon the environment.

CONCLUSIONS

Our results gain new insight into the genetic mechanisms of how plants program their leaf morphogenesis to adapt to environmental perturbations.

Model-based QTL detection is sensitive to slight modifications in model formulation

Classical crop models have been developed to predict crop yield and quality, and they are based on physiological and environmental inputs. After molecular discoveries, models should integrate genetic variation to allow predictions that are more genotype-dependent. An interesting approach, Quantitative Trait Locus (QTL)-based ecophysiological modeling, has shown promising results for the design of ideotypes that are adapted to biotic and abiotic stresses, but there are still limitations to attaining a fully integrated model. The aim of this case study is to clarify the impact of choosing different model equations (closely related and with different numbers of parameters) and optimization methods on the detection of QTLs controlling the parameters of crop growth. Different growth equations were parameterized based on a genetic population by following different approaches. The correlations between parameters were analyzed, and two different strategies were adopted to address the correlation issue. QTL analysis was performed on the optimized values of the parameters of the growth equations and on the observed dry mass (DM) data to validate the QTLs detected. Overall, models and strategies resulted in different QTLs being detected. Similar LOD profiles but with peaks of different heights were observed, some of which were significant, resulting in different numbers of QTLs. In some cases, peaks had slightly different positions or were absent. Even closely related growth models led to the detection of different QTLs. The goodness of fit and complexity of the growth models were found to be insufficient to select the best model. Calculating parameters independently of observed data may not be a good strategy, whereas setting parameters independent of the genotype is recommended. Given the large-scale global optimization problem and the strong correlations between parameters, the two algorithms tested showed poor performance. Currently, the lack of effective algorithms is the main obstacle to answering the question posed. The authors therefore suggest testing different model formulations and comparing the QTLs detected before choosing the best formulation to use in an ecophysiological modeling approach based on QTLs.

A dissection model for mapping complex traits

Many quantitative traits are composites of other traits that contribute differentially to genetic variation. Quantitative trait locus (QTL) mapping of these composite traits can benefit by incorporating the mechanistic process of how their formation is mediated by the underlying components. We propose a dissection model by which to map these interconnected components traits under a joint likelihood setting. The model can test how a composite trait is determined by pleiotropic QTLs for its component traits or jointly by different sets of QTLs each responsible for a different component. The model can visualize the pattern of time-varying genetic effects for individual components and their impacts on composite traits. The dissection model was used to map two composite traits, stemwood volume growth decomposed into its stem height, stem diameter and stem form components for Euramerican poplar adult trees, and total lateral root length constituted by its average lateral root length and lateral root number components for Euphrates poplar seedlings. We found the pattern of how QTLs for different components contribute to phenotypic variation in composite traits. The detailed understanding of the genetic machineries of composite traits will not only help in the design of molecular breeding in plants and animals, but also shed light on the evolutionary processes of quantitative traits under natural selection.

MVQTLCIM: composite interval mapping of multivariate traits in a hybrid F1 population of outbred species

Background

With the plummeting cost of the next-generation sequencing technologies, high-density genetic linkage maps could be constructed in a forest hybrid F₁ population. However, based on such genetic maps, quantitative trait loci (QTL) mapping cannot be directly conducted with traditional statistical methods or tools because the linkage phase and segregation pattern of molecular markers are not always fixed as in inbred lines.

Results

We implemented the traditional composite interval mapping (CIM) method to multivariate trait data in forest trees and developed the corresponding software, mvqtlcim. Our method not only incorporated the various segregations and linkage phases of molecular markers, but also applied Takeuchi’s information criterion (TIC) to discriminate the QTL segregation type among several possible alternatives. QTL mapping was performed in a hybrid F₁ population of Populus deltoides and P. simonii, and 12 QTLs were detected for tree height over 6 time points. The software package allowed many options for parameters as well as parallel computing for permutation tests. The features of the software were demonstrated with the real data analysis and a large number of Monte Carlo simulations.

Conclusions

We provided a powerful tool for QTL mapping of multiple or longitudinal traits in an outbred F₁ population, in which the traditional software for QTL mapping cannot be used. This tool will facilitate studying of QTL mapping and thus will accelerate molecular breeding programs especially in forest trees. The tool package is freely available from https://github.com/tongchf /mvqtlcim.

Electronic supplementary material

The online version of this article (10.1186/s12859-017-1908-1) contains supplementary material, which is available to authorized users.

The genetic architecture of shoot-root covariation during seedling emergence of a desert tree, Populus euphratica

The coordination of shoots and roots is critical for plants to adapt to changing environments by fine-tuning energy production in leaves and the availability of water and nutrients from roots. To understand the genetic architecture of how these two organs covary during developmental ontogeny, we conducted a mapping experiment using Euphrates poplar (Populus euphratica), a so-called hero tree able to grow in the desert. We geminated intraspecific F₁ seeds of Euphrates Poplar individually in a tube to obtain a total of 370 seedlings, whose shoot and taproot lengths were measured repeatedly during the early stage of growth. By fitting a growth equation, we estimated asymptotic growth, relative growth rate, the timing of inflection point and duration of linear growth for both shoot and taproot growth. Treating these heterochronic parameters as phenotypes, a univariate mapping model detected 19 heterochronic quantitative trait loci (hQTLs), of which 15 mediate the forms of shoot growth and four mediate taproot growth. A bivariate mapping model identified 11 pleiotropic hQTLs that determine the covariation of shoot and taproot growth. Most QTLs detected reside within the region of candidate genes with various functions, thus confirming their roles in the biochemical processes underlying plant growth.

Computational identification of genes modulating stem height-diameter allometry

The developmental variation in stem height with respect to stem diameter is related to a broad range of ecological and evolutionary phenomena in trees, but the underlying genetic basis of this variation remains elusive. We implement a dynamic statistical model, functional mapping, to formulate a general procedure for the computational identification of quantitative trait loci (QTLs) that control stem height-diameter allometry during development. Functional mapping integrates the biological principles underlying trait formation and development into the association analysis of DNA genotype and endpoint phenotype, thus providing an incentive for understanding the mechanistic interplay between genes and development. Built on the basic tenet of functional mapping, we explore two core ecological scenarios of how stem height and stem diameter covary in response to environmental stimuli: (i) trees pioneer sunlit space by allocating more growth to stem height than diameter and (ii) trees maintain their competitive advantage through an inverse pattern. The model is equipped to characterize 'pioneering' QTLs (piQTLs) and 'maintaining' QTLs (miQTLs) which modulate these two ecological scenarios, respectively. In a practical application to a mapping population of full-sib hybrids derived from two Populus species, the model has well proven its versatility by identifying several piQTLs that promote height growth at a cost of diameter growth and several miQTLs that benefit radial growth at a cost of height growth. Judicious application of functional mapping may lead to improved strategies for studying the genetic control of the formation mechanisms underlying trade-offs among quantities of assimilates allocated to different growth parts.

A computational framework for mapping the timing of vegetative phase change

Phase change plays a prominent role in determining the form of growth and development. Although considerable attention has been focused on identifying the regulatory control mechanisms of phase change, a detailed understanding of the genetic architecture of this phenomenon is still lacking. We address this issue by deriving a computational model. The model is founded on the framework of functional mapping aimed at characterizing the interplay between quantitative trait loci (QTLs) and development through biologically meaningful mathematical equations. A multiphasic growth equation was implemented into functional mapping, which, via a series of hypothesis tests, allows the quantification of how QTLs regulate the timing and pattern of vegetative phase transition between independently regulated, temporally coordinated processes. The model was applied to analyze stem radial growth data of an interspecific hybrid family derived from two Populus species during the first 24 yr of ontogeny. Several key QTLs related to phase change have been characterized, most of which were observed to be in the adjacent regions of candidate genes. The identification of phase transition QTLs, whose expression is regulated by endogenous and environmental signals, may enhance our understanding of the evolution of development in changing environments.

Integrating Evolutionary Game Theory into Mechanistic Genotype-Phenotype Mapping

Natural selection has shaped the evolution of organisms toward optimizing their structural and functional design. However, how this universal principle can enhance genotype-phenotype mapping of quantitative traits has remained unexplored. Here we show that the integration of this principle and functional mapping through evolutionary game theory gains new insight into the genetic architecture of complex traits. By viewing phenotype formation as an evolutionary system, we formulate mathematical equations to model the ecological mechanisms that drive the interaction and coordination of its constituent components toward population dynamics and stability. Functional mapping provides a procedure for estimating the genetic parameters that specify the dynamic relationship of competition and cooperation and predicting how genes mediate the evolution of this relationship during trait formation.

Plastic expression of heterochrony quantitative trait loci (hQTLs) for leaf growth in the common bean (Phaseolus vulgaris)

Heterochrony, that is, evolutionary changes in the relative timing of developmental events and processes, has emerged as a key concept that links evolution and development. Genes associated with heterochrony encode molecular components of developmental timing mechanisms. However, our understanding of how heterochrony genes alter the expression of heterochrony in response to environmental changes remains very limited. We applied functional mapping to find quantitative trait loci (QTLs) responsible for growth trajectories of leaf area and leaf mass in the common bean (Phaseolus vulgaris) grown in two contrasting environments. We identified three major QTLs pleiotropically expressed under the two environments. Further characterization of the temporal pattern of these QTLs indicates that they are heterochrony QTLs (hQTLs) in terms of their role in influencing four heterochronic parameters: the timing of the inflection point, the timing of maximum acceleration and deceleration, and the duration of linear growth. The pattern of gene action by the hQTLs on each parameter was unique, being environmentally dependent and varying between two allometrically related leaf growth traits. These results provide new insights into the complexity of genetic mechanisms that control trait formation in plants and provide novel findings that will be of use in studying the evolutionary trends.

Mapping complex traits as a dynamic system

Despite increasing emphasis on the genetic study of quantitative traits, we are still far from being able to chart a clear picture of their genetic architecture, given an inherent complexity involved in trait formation. A competing theory for studying such complex traits has emerged by viewing their phenotypic formation as a "system" in which a high-dimensional group of interconnected components act and interact across different levels of biological organization from molecules through cells to whole organisms. This system is initiated by a machinery of DNA sequences that regulate a cascade of biochemical pathways to synthesize endophenotypes and further assemble these endophenotypes toward the end-point phenotype in virtue of various developmental changes. This review focuses on a conceptual framework for genetic mapping of complex traits by which to delineate the underlying components, interactions and mechanisms that govern the system according to biological principles and understand how these components function synergistically under the control of quantitative trait loci (QTLs) to comprise a unified whole. This framework is built by a system of differential equations that quantifies how alterations of different components lead to the global change of trait development and function, and provides a quantitative and testable platform for assessing the multiscale interplay between QTLs and development. The method will enable geneticists to shed light on the genetic complexity of any biological system and predict, alter or engineer its physiological and pathological states.

An allometric model for mapping seed development in plants

Despite a tremendous effort to map quantitative trait loci (QTLs) responsible for agriculturally and biologically important traits in plants, our understanding of how a QTL governs the developmental process of plant seeds remains elusive. In this article, we address this issue by describing a model for functional mapping of seed development through the incorporation of the relationship between vegetative and reproductive growth. The time difference of reproductive from vegetative growth is described by Reeve and Huxley’s allometric equation. Thus, the implementation of this equation into the framework of functional mapping allows dynamic QTLs for seed development to be identified more precisely. By estimating and testing mathematical parameters that define Reeve and Huxley’s allometric equations of seed growth, the dynamic pattern of the genetic effects of the QTLs identified can be analyzed. We used the model to analyze a soybean data, leading to the detection of QTLs that control the growth of seed dry weight. Three dynamic QTLs, located in two different linkage groups, were detected to affect growth curves of seed dry weight. The QTLs detected may be used to improve seed yield with marker-assisted selection by altering the pattern of seed development in a hope to achieve a maximum size of seeds at a harvest time.

2HiGWAS: a unifying high-dimensional platform to infer the global genetic architecture of trait development

Whole-genome search of genes is an essential approach to dissecting complex traits, but a marginal one-single-nucleotide polymorphism (SNP)/one-phenotype regression analysis widely used in current genome-wide association studies fails to estimate the net and cumulative effects of SNPs and reveal the developmental pattern of interplay between genes and traits. Here we describe a computational framework, which we refer to as two-side high-dimensional genome-wide association studies (2HiGWAS), to associate an ultrahigh dimension of SNPs with a high dimension of developmental trajectories measured across time and space. The model is implemented with a dual dimension-reduction procedure for both predictors and responses to select a sparse but full set of significant loci from an extremely large pool of SNPs and estimate their net time-varying effects on trait development. The model can not only help geneticists to precisely identify an entire set of genes underlying complex traits but also allow them to elucidate a global picture of how genes control developmental and dynamic processes of trait formation. We investigated the statistical properties of the model via extensive simulation studies. With the increasing availability of GWAS in various organisms, 2HiGWAS will have important implications for genetic studies of developmental compelx traits.

Genetic linkage map construction and QTL identification of juvenile growth traits in Torreya grandis

Torreya grandis Fort. ex Lindl, a conifer species widely distributed in Southeastern China, is of high economic value by producing edible, nutrient seeds. However, knowledge about the genome structure and organization of this species is poorly understood, thereby limiting the effective use of its gene resources. Here, we report on a first genetic linkage map for Torreya grandis using 96 progeny randomly chosen from a half-sib family of a commercially cultivated variety of this species, Torreya grandis Fort. ex Lindl cv. Merrillii. The map contains 262 molecular markers, i.e., 75 random amplified polymorphic DNAs (RAPD), 119 inter-simple sequence repeats (ISSR) and 62 amplified fragments length polymorphisms (AFLP), and spans a total of 7,139.9 cM, separated by 10 linkage groups. The linkage map was used to map quantitative trait loci (QTLs) associated with juvenile growth traits by functional mapping. We identified four basal diameter-related QTLs on linkage groups 1, 5 and 9; four height-related QTLs on linkage groups 1, 2, 5 and 8. It was observed that the genetic effects of QTLs on growth traits vary with age, suggesting the dynamic behavior of growth QTLs. Part of the QTLs was found to display a pleiotropic effect on basal diameter growth and height growth.

A model framework for identifying genes that guide the evolution of heterochrony

Heterochrony, the phylogenic change in the time of developmental events or rate of development, has been thought to play an important role in producing phenotypic novelty during evolution. Increasing evidence suggests that specific genes are implicated in heterochrony, guiding the process of developmental divergence, but no quantitative models have been instrumented to map such heterochrony genes. Here, we present a computational framework for genetic mapping by which to characterize and locate quantitative trait loci (QTLs) that govern heterochrony described by four parameters, the timing of the inflection point, the timing of maximum acceleration of growth, the timing of maximum deceleration of growth, and the length of linear growth. The framework was developed from functional mapping, a dynamic model derived to map QTLs for the overall process and pattern of development. By integrating an optimality algorithm, the framework allows the so-called heterochrony QTLs (hQTLs) to be tested and quantified. Specific pipelines are given for testing how hQTLs control the onset and offset of developmental events, the rate of development, and duration of a particular developmental stage. Computer simulation was performed to examine the statistical properties of the model and demonstrate its utility to characterize the effect of hQTLs on population diversification due to heterochrony. By analyzing a genetic mapping data in rice, the framework identified an hQTL that controls the timing of maximum growth rate and duration of linear growth stage in plant height growth. The framework provides a tool to study how genetic variation translates into phenotypic innovation, leading a lineage to evolve, through heterochrony.

Towards a comprehensive picture of the genetic landscape of complex traits

The formation of phenotypic traits, such as biomass production, tumor volume and viral abundance, undergoes a complex process in which interactions between genes and developmental stimuli take place at each level of biological organization from cells to organisms. Traditional studies emphasize the impact of genes by directly linking DNA-based markers with static phenotypic values. Functional mapping, derived to detect genes that control developmental processes using growth equations, has proven powerful for addressing questions about the roles of genes in development. By treating phenotypic formation as a cohesive system using differential equations, a different approach-systems mapping-dissects the system into interconnected elements and then map genes that determine a web of interactions among these elements, facilitating our understanding of the genetic machineries for phenotypic development. Here, we argue that genetic mapping can play a more important role in studying the genotype-phenotype relationship by filling the gaps in the biochemical and regulatory process from DNA to end-point phenotype. We describe a new framework, named network mapping, to study the genetic architecture of complex traits by integrating the regulatory networks that cause a high-order phenotype. Network mapping makes use of a system of differential equations to quantify the rule by which transcriptional, proteomic and metabolomic components interact with each other to organize into a functional whole. The synthesis of functional mapping, systems mapping and network mapping provides a novel avenue to decipher a comprehensive picture of the genetic landscape of complex phenotypes that underlie economically and biomedically important traits.

Systems mapping: how to map genes for biomass allocation toward an ideotype

The recent availability of high-throughput genetic and genomic data allows the genetic architecture of complex traits to be systematically mapped. The application of these genetic results to design and breed new crop types can be made possible through systems mapping. Systems mapping is a computational model that dissects a complex phenotype into its underlying components, coordinates different components in terms of biological laws through mathematical equations and maps specific genes that mediate each component and its connection with other components. Here, we present a new direction of systems mapping by integrating this tool with carbon economy. With an optimal spatial distribution of carbon fluxes between sources and sinks, plants tend to maximize whole-plant growth and competitive ability under limited availability of resources. We argue that such an economical strategy for plant growth and development, once integrated with systems mapping, will not only provide mechanistic insights into plant biology, but also help to spark a renaissance of interest in ideotype breeding in crops and trees.

Systems mapping of HIV-1 infection

Mathematical models of viral dynamics in vivo provide incredible insights into the mechanisms for the nonlinear interaction between virus and host cell populations, the dynamics of viral drug resistance, and the way to eliminate virus infection from individual patients by drug treatment. The integration of these mathematical models with high-throughput genetic and genomic data within a statistical framework will raise a hope for effective treatment of infections with HIV virus through developing potent antiviral drugs based on individual patients’ genetic makeup. In this opinion article, we will show a conceptual model for mapping and dictating a comprehensive picture of genetic control mechanisms for viral dynamics through incorporating a group of differential equations that quantify the emergent properties of a system.

Dynamic semiparametric Bayesian models for genetic mapping of complex trait with irregular longitudinal data

Many phenomena of fundamental importance to biology and biomedicine arise as a dynamic curve, such as organ growth and HIV dynamics. The genetic mapping of these traits is challenged by longitudinal variables measured at irregular and possibly subject-specific time points, in which case nonnegative definiteness of the estimated covariance matrix needs to be guaranteed. We present a semiparametric approach for genetic mapping within the mixture-model setting by jointly modeling mean and covariance structures for irregular longitudinal data. Penalized spline is used to model the mean functions of individual quantitative trait locus (QTL) genotypes as latent variables, whereas an extended generalized linear model is used to approximate the covariance matrix. The parameters for modeling the mean-covariances are estimated by MCMC, using the Gibbs sampler and the Metropolis-Hastings algorithm. We derive the full conditional distributions for the mean and covariance parameters and compute Bayes factors to test the hypothesis about the existence of significant QTLs. We used the model to screen the existence of specific QTLs for age-specific change of body mass index with a sparse longitudinal data set. The new model provides powerful means for broadening the application of genetic mapping to reveal the genetic control of dynamic traits.

Dynamic modeling of genes controlling cancer stem cell proliferation

The growing evidence that cancer originates from stem cells (SC) holds a great promise to eliminate this disease by designing specific drug therapies for removing cancer SC. Translation of this knowledge into predictive tests for the clinic is hampered due to the lack of methods to discriminate cancer SC from non-cancer SC. Here, we address this issue by describing a conceptual strategy for identifying the genetic origins of cancer SC. The strategy incorporates a high-dimensional group of differential equations that characterizes the proliferation, differentiation, and reprogramming of cancer SC in a dynamic cellular and molecular system. The deployment of robust mathematical models will help uncover and explain many still unknown aspects of cell behavior, tissue function, and network organization related to the formation and division of cancer SC. The statistical method developed allows biologically meaningful hypotheses about the genetic control mechanisms of carcinogenesis and metastasis to be tested in a quantitative manner.

A mathematical framework for functional mapping of complex phenotypes using delay differential equations

All biological phenomena occurring at different levels of organization from cells to organisms can be modeled as a dynamic system, in which the underlying components interact dynamically to comprehend its biological function. Such a systems modeling approach facilitates the use of biochemically and biophysically detailed mathematical models to describe and quantify "living cells," leading to an in-depth and precise understanding of the behavior, development and function of a biological system. Here, we illustrate how this approach can be used to map genes or quantitative trait loci (QTLs) that control a complex trait using the example of the circadian rhythm system which has been at the forefront of analytical mathematical modeling for many years. We integrate a system of biologically meaningful delay differential equations (DDEs) into functional mapping, a statistical model designed to map dynamic QTLs involved in biological processes. The DDEs model the ability of circadian rhythm to generate autonomously sustained oscillations with a period close to 24h, in terms of time-varying mRNA and protein abundances. By incorporating the Runge-Kutta fourth order algorithm within the likelihood-based context of functional mapping, we estimated the genetic parameters that define the periodic pattern of QTL effects on time-varying mRNA and protein abundances and their dynamic association as well as the linkage disequilibrium of the QTL and a marker. We prove theorems about how to choose appropriate parameters to guarantee periodic oscillations. We further used simulation studies to investigate how a QTL influences the period and the amplitude of circadian oscillations through changing model parameters. The model provides a quantitative framework for assessing the interplay between genetic effects of QTLs and rhythmic responses.

Whole genome QTL mapping for growth, meat quality and breast meat yield traits in turkey

Background

The turkey (Meleagris gallopavo) is an important agricultural species and is the second largest contributor to the world's poultry meat production. Demand of turkey meat is increasing very rapidly. Genetic markers linked to genes affecting quantitative traits can increase the selection response of animal breeding programs. The use of these molecular markers for the identification of quantitative trait loci, and subsequently fine-mapping of quantitative trait loci regions, allows for pinpointing of genes that underlie such economically important traits.

Results

The quantitative trait loci analyses of the growth curve, body weight, breast yield and the meat quality traits showed putative quantitative trait loci on 21 of the 27 turkey chromosomes covered by the linkage map. Forty-five quantitative trait loci were detected across all traits and these were found in 29 different regions on 21 chromosomes. Out of the 45 quantitative trait loci, twelve showed significant (p < 0.01) evidence of linkage while the remaining 33 showed suggestive evidence (p < 0.05) of linkage with different growth, growth curve, meat quality and breast yield traits.

Conclusion

A large number of quantitative trait loci were detected across the turkey genome, which affected growth, breast yield and meat quality traits. Pleiotropic effects or close linkages between quantitative trait loci were suggested for several of the chromosomal regions. The comparative analysis regarding the location of quantitative trait loci on different turkey, and on the syntenic chicken chromosomes, along with their phenotypic associations, revealed signs of functional conservation between these species.

Systems mapping: how to improve the genetic mapping of complex traits through design principles of biological systems

BACKGROUND

Every phenotypic trait can be viewed as a "system" in which a group of interconnected components function synergistically to yield a unified whole. Once a system's components and their interactions have been delineated according to biological principles, we can manipulate and engineer functionally relevant components to produce a desirable system phenotype.

RESULTS

We describe a conceptual framework for mapping quantitative trait loci (QTLs) that control complex traits by treating trait formation as a dynamic system. This framework, called systems mapping, incorporates a system of differential equations that quantifies how alterations of different components lead to the global change of trait development and function through genes, and provides a quantitative and testable platform for assessing the interplay between gene action and development. We applied systems mapping to analyze biomass growth data in a mapping population of soybeans and identified specific loci that are responsible for the dynamics of biomass partitioning to leaves, stem, and roots.

CONCLUSIONS

We show that systems mapping implemented by design principles of biological systems is quite versatile for deciphering the genetic machineries for size-shape, structural-functional, sink-source and pleiotropic relationships underlying plant physiology and development. Systems mapping should enable geneticists to shed light on the genetic complexity of any biological system in plants and other organisms and predict its physiological and pathological states.

3FunMap: full-sib family functional mapping of dynamic traits

MOTIVATION

Functional mapping that embeds the developmental mechanisms of complex traits shows great power to study the dynamic pattern of genetic effects triggered by individual quantitative trait loci (QTLs). A full-sib family, produced by crossing two heterozygous parents, is characteristic of uncertainties about cross-type at a locus and linkage phase between different loci. Integrating functional mapping into a full-sib family requires a model selection procedure capable of addressing these uncertainties. 3FunMap, written in VC++ 6.0, provides a flexible and extensible platform to perform full-sib functional mapping of dynamic traits. Functions in the package encompass linkage phase determination, marker map construction and the pattern identification of QTL segregation, dynamic tests of QTL effects, permutation tests and numerical simulation. We demonstrate the features of 3FunMap through real data analysis and computer simulation.

AVAILABILITY

http://statgen.psu.edu/software.