Area of origin estimation from multiple arbitrarily oriented surfaces using marker-guided structure from motion.

Bloodstain pattern analysis plays a crucial role in forensic investigations. Projected patterns can offer valuable insights into the dynamics of crime scenes. In this paper, we propose and validate a novel approach that extends existing software, HemoVision, to analyze impact patterns that are distributed across multiple arbitrarily oriented surfaces. The proposed method integrates HemoVision's marker-based system with structure from motion (SfM) techniques to reconstruct the three-dimensional geometry of impact patterns using only two-dimensional photographs. Controlled experiments were used to validate the proposed approach, demonstrating robustness in reconstruction accuracy with median translation errors below 3 mm and median angular errors below 0.2°, irrespective of imaging device or image resolution. Comparing the estimated areas origin to their known ground truth, the proposed method achieved an average total error of 8.12 cm, with the primary source of error being the vertical dimension. Despite this, the overall error remains well within the ranges of error reported in prior work. This study demonstrates that HemoVision can be used to analyze complex impact patterns using only two-dimensional photographs, providing forensic experts with an efficient and accessible tool for investigating intricate crime scenes involving multi-surface impact patterns.

Virtual reconstruction of orbital defects using Gaussian process morphable models.

PURPOSE: The conventional method to reconstruct the bone level for orbital defects, which is based on mirroring and manual adaptation, is time-consuming and the accuracy highly depends on the expertise of the clinical engineer. The aim of this study is to propose and evaluate an automated reconstruction method utilizing a Gaussian process morphable model (GPMM). METHODS: Sixty-five Computed Tomography (CT) scans of healthy midfaces were used to create a GPMM that can model shape variations of the orbital region. Parameter optimization was performed by evaluating several quantitative metrics inspired on the shape modeling literature, e.g. generalization and specificity. The reconstruction error was estimated by reconstructing artificial defects created in orbits from fifteen CT scans that were not included in the GPMM. The developed algorithms utilize the existing framework of Gaussian process morphable models, as implemented in the Scalismo software. RESULTS: By evaluating the proposed quality metrics, adequate parameters are chosen for non-rigid registration and reconstruction. The resulting median reconstruction error using the GPMM was lower (0.35 ± 0.16 mm) compared to the mirroring method (0.52 ± 0.18 mm). In addition, the GPMM-based reconstruction is automated and can be applied to large bilateral defects with a median reconstruction error of 0.39 ± 0.11 mm. CONCLUSION: The GPMM-based reconstruction proves to be less time-consuming and more accurate than reconstruction by mirroring. Further validation through clinical studies on patients with orbital defects is warranted. Nevertheless, the results underscore the potential of GPMM-based reconstruction as a promising alternative for designing patient-specific implants.

Mapping genes for human face shape: exploration of univariate phenotyping strategies.

Human facial shape, while strongly heritable, involves both genetic and structural complexity, necessitating precise phenotyping for accurate assessment. Common phenotyping strategies include simplifying 3D facial features into univariate traits such as anthropometric measurements (e.g., inter-landmark distances), unsupervised dimensionality reductions (e.g., principal component analysis (PCA) and auto-encoder (AE) approaches), and assessing resemblance to particular facial gestalts (e.g., syndromic facial archetypes). This study provides a comparative assessment of these strategies in genome-wide association studies (GWASs) of 3D facial shape. Specifically, we investigated inter-landmark distances, PCA and AE-derived latent dimensions, and facial resemblance to random, extreme, and syndromic gestalts within a GWAS of 8,426 individuals of recent European ancestry. Inter-landmark distances exhibit the highest SNP-based heritability as estimated via LD score regression, followed by AE dimensions. Conversely, resemblance scores to extreme and syndromic facial gestalts display the lowest heritability, in line with expectations. Notably, the aggregation of multiple GWASs on facial resemblance to random gestalts reveals the highest number of independent genetic loci. This novel, easy-to-implement phenotyping approach holds significant promise for capturing genetically relevant morphological traits derived from complex biomedical imaging datasets, and its applications extend beyond faces. Nevertheless, these different phenotyping strategies capture different genetic influences on craniofacial shape. Thus, it remains valuable to explore these strategies individually and in combination to gain a more comprehensive understanding of the genetic factors underlying craniofacial shape and related traits. Author Summary: Advancements linking variation in the human genome to phenotypes have rapidly evolved in recent decades and have revealed that most human traits are influenced by genetic variants to at least some degree. While many traits, such as stature, are straightforward to acquire and investigate, the multivariate and multipartite nature of facial shape makes quantification more challenging. In this study, we compared the impact of different facial phenotyping approaches on gene mapping outcomes. Our findings suggest that the choice of facial phenotyping method has an impact on apparent trait heritability and the ability to detect genetic association signals. These results offer valuable insights into the importance of phenotyping in genetic investigations, especially when dealing with highly complex morphological traits.

A novel approach to craniofacial analysis using automated 3D landmarking of the skull.

Automatic dense 3D surface registration is a powerful technique for comprehensive 3D shape analysis that has found a successful application in human craniofacial morphology research, particularly within the mandibular and cranial vault regions. However, a notable gap exists when exploring the frontal aspect of the human skull, largely due to the intricate and unique nature of its cranial anatomy. To better examine this region, this study introduces a simplified single-surface craniofacial bone mask comprising of 6707 quasi-landmarks, which can aid in the classification and quantification of variation over human facial bone surfaces. Automatic craniofacial bone phenotyping was conducted on a dataset of 31 skull scans obtained through cone-beam computed tomography (CBCT) imaging. The MeshMonk framework facilitated the non-rigid alignment of the constructed craniofacial bone mask with each individual target mesh. To gauge the accuracy and reliability of this automated process, 20 anatomical facial landmarks were manually placed three times by three independent observers on the same set of images. Intra- and inter-observer error assessments were performed using root mean square (RMS) distances, revealing consistently low scores. Subsequently, the corresponding automatic landmarks were computed and juxtaposed with the manually placed landmarks. The average Euclidean distance between these two landmark sets was 1.5 mm, while centroid sizes exhibited noteworthy similarity. Intraclass coefficients (ICC) demonstrated a high level of concordance (> 0.988), with automatic landmarking showing significantly lower errors and variation. These results underscore the utility of this newly developed single-surface craniofacial bone mask, in conjunction with the MeshMonk framework, as a highly accurate and reliable method for automated phenotyping of the facial region of human skulls from CBCT and CT imagery. This craniofacial template bone mask expansion of the MeshMonk toolbox not only enhances our capacity to study craniofacial bone variation but also holds significant potential for shedding light on the genetic, developmental, and evolutionary underpinnings of the overall human craniofacial structure.

Whole genome sequencing identifies associations for nonsyndromic sagittal craniosynostosis with the intergenic region of BMP2 and noncoding RNA gene LINC01428.

Craniosynostosis (CS) is a major birth defect resulting from premature fusion of cranial sutures. Nonsyndromic CS occurs more frequently than syndromic CS, with sagittal nonsyndromic craniosynostosis (sNCS) presenting as the most common CS phenotype. Previous genome-wide association and targeted sequencing analyses of sNCS have identified multiple associated loci, with the strongest association on chromosome 20. Herein, we report the first whole-genome sequencing study of sNCS using 63 proband-parent trios. Sequencing data for these trios were analyzed using the transmission disequilibrium test (TDT) and rare variant TDT (rvTDT) to identify high-risk rare gene variants. Sequencing data were also examined for copy number variants (CNVs) and de novo variants. TDT analysis identified a highly significant locus at 20p12.3, localized to the intergenic region between BMP2 and the noncoding RNA gene LINC01428. Three variants (rs6054763, rs6054764, rs932517) were identified as potential causal variants due to their probability of being transcription factor binding sites, deleterious combined annotation dependent depletion scores, and high minor allele enrichment in probands. Morphometric analysis of cranial vault shape in an unaffected cohort validated the effect of these three single nucleotide variants (SNVs) on dolichocephaly. No genome-wide significant rare variants, de novo loci, or CNVs were identified. Future efforts to identify risk variants for sNCS should include sequencing of larger and more diverse population samples and increased omics analyses, such as RNA-seq and ATAC-seq.

A common cis-regulatory variant impacts normal-range and disease-associated human facial shape through regulation of PKDCC during chondrogenesis.

Genome-wide association studies (GWAS) identified thousands of genetic variants linked to phenotypic traits and disease risk. However, mechanistic understanding of how GWAS variants influence complex morphological traits and can, in certain cases, simultaneously confer normal-range phenotypic variation and disease predisposition, is still largely lacking. Here, we focus on rs6740960, a single nucleotide polymorphism (SNP) at the 2p21 locus, which in GWAS studies has been associated both with normal-range variation in jaw shape and with an increased risk of non-syndromic orofacial clefting. Using in vitro derived embryonic cell types relevant for human facial morphogenesis, we show that this SNP resides in an enhancer that regulates chondrocytic expression of PKDCC - a gene encoding a tyrosine kinase involved in chondrogenesis and skeletal development. In agreement, we demonstrate that the rs6740960 SNP is sufficient to confer chondrocyte-specific differences in PKDCC expression. By deploying dense landmark morphometric analysis of skull elements in mice, we show that changes in Pkdcc dosage are associated with quantitative changes in the maxilla, mandible, and palatine bone shape that are concordant with the facial phenotypes and disease predisposition seen in humans. We further demonstrate that the frequency of the rs6740960 variant strongly deviated among different human populations, and that the activity of its cognate enhancer diverged in hominids. Our study provides a mechanistic explanation of how a common SNP can mediate normal-range and disease-associated morphological variation, with implications for the evolution of human facial features.

Automated 3D Landmarking of the Skull: A Novel Approach for Craniofacial Analysis.

Automatic dense 3D surface registration is a powerful technique for comprehensive 3D shape analysis that has found a successful application in human craniofacial morphology research, particularly within the mandibular and cranial vault regions. However, a notable gap exists when exploring the frontal aspect of the human skull, largely due to the intricate and unique nature of its cranial anatomy. To better examine this region, this study introduces a simplified single-surface craniofacial bone mask comprising 9,999 quasi-landmarks, which can aid in the classification and quantification of variation over human facial bone surfaces. Automatic craniofacial bone phenotyping was conducted on a dataset of 31 skull scans obtained through cone-beam computed tomography (CBCT) imaging. The MeshMonk framework facilitated the non-rigid alignment of the constructed craniofacial bone mask with each individual target mesh. To gauge the accuracy and reliability of this automated process, 20 anatomical facial landmarks were manually placed three times by three independent observers on the same set of images. Intra- and inter-observer error assessments were performed using root mean square (RMS) distances, revealing consistently low scores. Subsequently, the corresponding automatic landmarks were computed and juxtaposed with the manually placed landmarks. The average Euclidean distance between these two landmark sets was 1.5mm, while centroid sizes exhibited noteworthy similarity. Intraclass coefficients (ICC) demonstrated a high level of concordance (>0.988), and automatic landmarking showing significantly lower errors and variation. These results underscore the utility of this newly developed single-surface craniofacial bone mask, in conjunction with the MeshMonk framework, as a highly accurate and reliable method for automated phenotyping of the facial region of human skulls from CBCT and CT imagery. This craniofacial template bone mask expansion of the MeshMonk toolbox not only enhances our capacity to study craniofacial bone variation but also holds significant potential for shedding light on the genetic, developmental, and evolutionary underpinnings of the overall human craniofacial structure.

DNA-guided transcription factor cooperativity shapes face and limb mesenchyme.

Transcription factors (TFs) can define distinct cellular identities despite nearly identical DNA-binding specificities. One mechanism for achieving regulatory specificity is DNA-guided TF cooperativity. Although in vitro studies suggest that it may be common, examples of such cooperativity remain scarce in cellular contexts. Here, we demonstrate how "Coordinator," a long DNA motif composed of common motifs bound by many basic helix-loop-helix (bHLH) and homeodomain (HD) TFs, uniquely defines the regulatory regions of embryonic face and limb mesenchyme. Coordinator guides cooperative and selective binding between the bHLH family mesenchymal regulator TWIST1 and a collective of HD factors associated with regional identities in the face and limb. TWIST1 is required for HD binding and open chromatin at Coordinator sites, whereas HD factors stabilize TWIST1 occupancy at Coordinator and titrate it away from HD-independent sites. This cooperativity results in the shared regulation of genes involved in cell-type and positional identities and ultimately shapes facial morphology and evolution.

An interactive atlas of three-dimensional syndromic facial morphology.

Craniofacial phenotyping is critical for both syndrome delineation and diagnosis because craniofacial abnormalities occur in 30% of characterized genetic syndromes. Clinical reports, textbooks, and available software tools typically provide two-dimensional, static images and illustrations of the characteristic phenotypes of genetic syndromes. In this work, we provide an interactive web application that provides three-dimensional, dynamic visualizations for the characteristic craniofacial effects of 95 syndromes. Users can visualize syndrome facial appearance estimates quantified from data and easily compare craniofacial phenotypes of different syndromes. Our application also provides a map of morphological similarity between a target syndrome and other syndromes. Finally, users can upload 3D facial scans of individuals and compare them to our syndrome atlas estimates. In summary, we provide an interactive reference for the craniofacial phenotypes of syndromes that allows for precise, individual-specific comparisons of dysmorphology.

OPG-based dental age estimation using a data-technical exploration of deep learning techniques.

Dental age estimation, a cornerstone in forensic age assessment, has been extensively tried and tested, yet manual methods are impeded by tedium and interobserver variability. Automated approaches using deep transfer learning encounter challenges like data scarcity, suboptimal training, and fine-tuning complexities, necessitating robust training methods. This study explores the impact of convolutional neural network hyperparameters, model complexity, training batch size, and sample quantity on age estimation. EfficientNet-B4, DenseNet-201, and MobileNet V3 models underwent cross-validation on a dataset of 3896 orthopantomograms (OPGs) with batch sizes escalating from 10 to 160 in a doubling progression, as well as random subsets of this training dataset. Results demonstrate the EfficientNet-B4 model, trained on the complete dataset with a batch size of 160, as the top performer with a mean absolute error of 0.562 years on the test set, notably surpassing the MAE of 1.01 at a batch size of 10. Increasing batch size consistently improved performance for EfficientNet-B4 and DenseNet-201, whereas MobileNet V3 performance peaked at batch size 40. Similar trends emerged in training with reduced sample sizes, though they were outperformed by the complete models. This underscores the critical role of hyperparameter optimization in adopting deep learning for age estimation from complete OPGs. The findings not only highlight the nuanced interplay of hyperparameters and performance but also underscore the potential for accurate age estimation models through optimization. This study contributes to advancing the application of deep learning in forensic age estimation, emphasizing the significance of tailored training methodologies for optimal outcomes.

netMUG: a novel network-guided multi-view clustering workflow for dissecting genetic and facial heterogeneity.

Introduction: Multi-view data offer advantages over single-view data for characterizing individuals, which is crucial in precision medicine toward personalized prevention, diagnosis, or treatment follow-up. Methods: Here, we develop a network-guided multi-view clustering framework named netMUG to identify actionable subgroups of individuals. This pipeline first adopts sparse multiple canonical correlation analysis to select multi-view features possibly informed by extraneous data, which are then used to construct individual-specific networks (ISNs). Finally, the individual subtypes are automatically derived by hierarchical clustering on these network representations. Results: We applied netMUG to a dataset containing genomic data and facial images to obtain BMI-informed multi-view strata and showed how it could be used for a refined obesity characterization. Benchmark analysis of netMUG on synthetic data with known strata of individuals indicated its superior performance compared with both baseline and benchmark methods for multi-view clustering. The clustering derived from netMUG achieved an adjusted Rand index of 1 with respect to the synthesized true labels. In addition, the real-data analysis revealed subgroups strongly linked to BMI and genetic and facial determinants of these subgroups. Discussion: netMUG provides a powerful strategy, exploiting individual-specific networks to identify meaningful and actionable strata. Moreover, the implementation is easy to generalize to accommodate heterogeneous data sources or highlight data structures.

Syndrome-informed phenotyping identifies a polygenic background for achondroplasia-like facial variation in the general population.

Human craniofacial shape is highly variable yet highly heritable with genetic variants interacting through multiple layers of development. Here, we hypothesize that Mendelian phenotypes represent the extremes of a phenotypic spectrum and, using achondroplasia as an example, we introduce a syndrome-informed phenotyping approach to identify genomic loci associated with achondroplasia-like facial variation in the normal population. We compared three-dimensional facial scans from 43 individuals with achondroplasia and 8246 controls to calculate achondroplasia-like facial scores. Multivariate GWAS of the control scores revealed a polygenic basis for normal facial variation along an achondroplasia-specific shape axis, identifying genes primarily involved in skeletal development. Jointly modeling these genes in two independent control samples showed craniofacial effects approximating the characteristic achondroplasia phenotype. These findings suggest that both complex and Mendelian genetic variation act on the same developmentally determined axes of facial variation, providing new insights into the genetic intersection of complex traits and Mendelian disorders.

Joint multi-ancestry and admixed GWAS reveals the complex genetics behind human cranial vault shape.

The cranial vault in humans is highly variable, clinically relevant, and heritable, yet its genetic architecture remains poorly understood. Here, we conduct a joint multi-ancestry and admixed multivariate genome-wide association study on 3D cranial vault shape extracted from magnetic resonance images of 6772 children from the ABCD study cohort yielding 30 genome-wide significant loci. Follow-up analyses indicate that these loci overlap with genomic risk loci for sagittal craniosynostosis, show elevated activity cranial neural crest cells, are enriched for processes related to skeletal development, and are shared with the face and brain. We present supporting evidence of regional localization for several of the identified genes based on expression patterns in the cranial vault bones of E15.5 mice. Overall, our study provides a comprehensive overview of the genetics underlying normal-range cranial vault shape and its relevance for understanding modern human craniofacial diversity and the etiology of congenital malformations.

Data-driven trait heritability-based extraction of human facial phenotypes.

A genome-wide association study (GWAS) of a complex, multi-dimensional morphological trait, such as the human face, typically relies on predefined and simplified phenotypic measurements, such as inter-landmark distances and angles. These measures are predominantly designed by human experts based on perceived biological or clinical knowledge. To avoid use handcrafted phenotypes (i.e., a priori expert-identified phenotypes), alternative automatically extracted phenotypic descriptors, such as features derived from dimension reduction techniques (e.g., principal component analysis), are employed. While the features generated by such computational algorithms capture the geometric variations of the biological shape, they are not necessarily genetically relevant. Therefore, genetically informed data-driven phenotyping is desirable. Here, we propose an approach where phenotyping is done through a data-driven optimization of trait heritability, defined as the degree of variation in a phenotypic trait in a population that is due to genetic variation. The resulting phenotyping process consists of two steps: 1) constructing a feature space that models shape variations using dimension reduction techniques, and 2) searching for directions in the feature space exhibiting high trait heritability using a genetic search algorithm (i.e., heuristic inspired by natural selection). We show that the phenotypes resulting from the proposed trait heritability-optimized training differ from those of principal components in the following aspects: 1) higher trait heritability, 2) higher SNP heritability, and 3) identification of the same number of independent genetic loci with a smaller number of effective traits. Our results demonstrate that data-driven trait heritability-based optimization enables the automatic extraction of genetically relevant phenotypes, as shown by their increased power in genome-wide association scans.

A statistical shape model for estimating missing soft tissues of the face in a black South African population.

PURPOSE: Facial disfigurement may affect the quality of life of many patients. Facial prostheses are often used as an adjuvant to surgical intervention and may sometimes be the only viable treatment option. Traditional methods for designing soft-tissue facial prostheses are time-consuming and subjective, while existing digital techniques are based on mirroring of contralateral features of the patient, or the use of existing feature templates/models that may not be readily available. We aim to support the objective and semi-automated design of facial prostheses with primary application to midline or bilateral defect restoration where no contralateral features are present. Specifically, we developed and validated a statistical shape model (SSM) for estimating the shape of missing facial soft tissue segments, from any intact parts of the face. MATERIALS AND METHODS: An SSM of 3D facial variations was built from meshes extracted from computed tomography and cone beam computed tomography images of a black South African sample (n = 235) without facial disfigurement. Various types of facial defects were simulated, and the missing parts were estimated automatically by a weighted fit of each mesh to the SSM. The estimated regions were compared to the original regions using color maps and root-mean-square (RMS) distances. RESULTS: Root mean square errors (RMSE) for defect estimations of one orbit, partial nose, cheek, and lip were all below 1.71 mm. Errors for the full nose, bi-orbital defects, as well as small and large composite defects were between 2.10 and 2.58 mm. Statistically significant associations of age and type of defect with RMSE were observed, but not with sex or imaging modality. CONCLUSION: This method can support the objective and semi-automated design of facial prostheses, specifically for defects in the midline, crossing the midline or bilateral defects, by facilitating time-consuming and skill-dependent aspects of prosthesis design.

Classifying high-dimensional phenotypes with ensemble learning.

Classification is a fundamental task in biology used to assign members to a class. While linear discriminant functions have long been effective, advances in phenotypic data collection are yielding increasingly high-dimensional datasets with more classes, unequal class covariances, and non-linear distributions. Numerous studies have deployed machine learning techniques to classify such distributions, but they are often restricted to a particular organism, a limited set of algorithms, and/or a specific classification task. In addition, the utility of ensemble learning or the strategic combination of models has not been fully explored.We performed a meta-analysis of 33 algorithms across 20 datasets containing over 20,000 high-dimensional shape phenotypes using an ensemble learning framework. Both binary (e.g., sex, environment) and multi-class (e.g., species, genotype, population) classification tasks were considered. The ensemble workflow contains functions for preprocessing, training individual learners and ensembles, and model evaluation. We evaluated algorithm performance within and among datasets. Furthermore, we quantified the extent to which various dataset and phenotypic properties impact performance.We found that discriminant analysis variants and neural networks were the most accurate base learners on average. However, their performance varied substantially between datasets. Ensemble models achieved the highest performance on average, both within and among datasets, increasing average accuracy by up to 3% over the top base learner. Higher class R2 values, mean class shape distances, and between- vs. within-class variances were positively associated with performance, whereas higher class covariance distances were negatively associated. Class balance and total sample size were not predictive.Learning-based classification is a complex task driven by many hyperparameters. We demonstrate that selecting and optimizing an algorithm based on the results of another study is a flawed strategy. Ensemble models instead offer a flexible approach that is data agnostic and exceptionally accurate. By assessing the impact of various dataset and phenotypic properties on classification performance, we also offer potential explanations for variation in performance. Researchers interested in maximizing performance stand to benefit from the simplicity and effectiveness of our approach made accessible via the R package pheble.

DNA-guided transcription factor cooperativity shapes face and limb mesenchyme.

Transcription factors (TFs) can define distinct cellular identities despite nearly identical DNA-binding specificities. One mechanism for achieving regulatory specificity is DNA-guided TF cooperativity. Although in vitro studies suggest it may be common, examples of such cooperativity remain scarce in cellular contexts. Here, we demonstrate how 'Coordinator', a long DNA motif comprised of common motifs bound by many basic helix-loop-helix (bHLH) and homeodomain (HD) TFs, uniquely defines regulatory regions of embryonic face and limb mesenchyme. Coordinator guides cooperative and selective binding between the bHLH family mesenchymal regulator TWIST1 and a collective of HD factors associated with regional identities in the face and limb. TWIST1 is required for HD binding and open chromatin at Coordinator sites, while HD factors stabilize TWIST1 occupancy at Coordinator and titrate it away from HD-independent sites. This cooperativity results in shared regulation of genes involved in cell-type and positional identities, and ultimately shapes facial morphology and evolution.

netMUG: a novel network-guided multi-view clustering workflow for dissecting genetic and facial heterogeneity.

Multi-view data offer advantages over single-view data for characterizing individuals, which is crucial in precision medicine toward personalized prevention, diagnosis, or treatment follow-up. Here, we develop a network-guided multi-view clustering framework named netMUG to identify actionable subgroups of individuals. This pipeline first adopts sparse multiple canonical correlation analysis to select multi-view features possibly informed by extraneous data, which are then used to construct individual-specific networks (ISNs). Finally, the individual subtypes are automatically derived by hierarchical clustering on these network representations. We applied netMUG to a dataset containing genomic data and facial images to obtain BMI-informed multi-view strata and showed how it could be used for a refined obesity characterization. Benchmark analysis of netMUG on synthetic data with known strata of individuals indicated its superior performance compared with both baseline and benchmark methods for multi-view clustering. In addition, the real-data analysis revealed subgroups strongly linked to BMI and genetic and facial determinants of these classes. NetMUG provides a powerful strategy, exploiting individual-specific networks to identify meaningful and actionable strata. Moreover, the implementation is easy to generalize to accommodate heterogeneous data sources or highlight data structures.

Precise modulation of transcription factor levels identifies features underlying dosage sensitivity.

Transcriptional regulation exhibits extensive robustness, but human genetics indicates sensitivity to transcription factor (TF) dosage. Reconciling such observations requires quantitative studies of TF dosage effects at trait-relevant ranges, largely lacking so far. TFs play central roles in both normal-range and disease-associated variation in craniofacial morphology; we therefore developed an approach to precisely modulate TF levels in human facial progenitor cells and applied it to SOX9, a TF associated with craniofacial variation and disease (Pierre Robin sequence (PRS)). Most SOX9-dependent regulatory elements (REs) are buffered against small decreases in SOX9 dosage, but REs directly and primarily regulated by SOX9 show heightened sensitivity to SOX9 dosage; these RE responses partially predict gene expression responses. Sensitive REs and genes preferentially affect functional chondrogenesis and PRS-like craniofacial shape variation. We propose that such REs and genes underlie the sensitivity of specific phenotypes to TF dosage, while buffering of other genes leads to robust, nonlinear dosage-to-phenotype relationships.

Initial Steps towards a Multilevel Functional Principal Components Analysis Model of Dynamical Shape Changes.

In this article, multilevel principal components analysis (mPCA) is used to treat dynamical changes in shape. Results of standard (single-level) PCA are also presented here as a comparison. Monte Carlo (MC) simulation is used to create univariate data (i.e., a single "outcome" variable) that contain two distinct classes of trajectory with time. MC simulation is also used to create multivariate data of sixteen 2D points that (broadly) represent an eye; these data also have two distinct classes of trajectory (an eye blinking and an eye widening in surprise). This is followed by an application of mPCA and single-level PCA to "real" data consisting of twelve 3D landmarks outlining the mouth that are tracked over all phases of a smile. By consideration of eigenvalues, results for the MC datasets find correctly that variation due to differences in groups between the two classes of trajectories are larger than variation within each group. In both cases, differences in standardized component scores between the two groups are observed as expected. Modes of variation are shown to model the univariate MC data correctly, and good model fits are found for both the "blinking" and "surprised" trajectories for the MC "eye" data. Results for the "smile" data show that the smile trajectory is modelled correctly; that is, the corners of the mouth are drawn backwards and wider during a smile. Furthermore, the first mode of variation at level 1 of the mPCA model shows only subtle and minor changes in mouth shape due to sex; whereas the first mode of variation at level 2 of the mPCA model governs whether the mouth is upturned or downturned. These results are all an excellent test of mPCA, showing that mPCA presents a viable method of modeling dynamical changes in shape.