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In many scientific investigations, the interest lies in the study of effects of two or more factors simultaneously. Factorial designs are most commonly used for this type of investigation. This chapter considers the important class of factorial designs for factors at two levels. It also considers the estimation and testing of factorial effects for location and dispersion models for replicated and unreplicated experiments. The chapter discusses optimal blocking schemes for full factorial designs. It describes how the factorial effects can be computed using regression analysis. The chapter also discusses three fundamental principles: effect hierarchy principle, effect sparsity principle, and effect heredity principle. These principles are often used to justify the development of factorial design theory and data analysis strategies. The chapter also describes a graphical method that uses the normal probability plot for assessing the normality assumption.

We present a non-equilibrium thermodynamics approach to the multilevel theory of learning for the study of molecular evolution. This approach allows us to study the explicit time dependence of molecular evolutionary processes and their impact on entropy production. Interpreting the mathematical expressions, we can show that two main contributions affect entropy production of molecular evolution processes which can be identified as mutation and gene transfer effects. Accordingly, our results show that the optimal adaptation of organisms to external conditions in the context of evolutionary processes is driven by principles of minimum entropy production. Such results can also be interpreted as the basis of some previous postulates of the theory of learning. Although our macroscopic approach requires certain simplifications, it allows us to interpret molecular evolutionary processes using thermodynamic descriptions with reference to well-known biological processes.

Foramen magnum stenosis is a serious, and potentially life-threatening complication of achondroplasia. The foramen magnum is smaller in infants with achondroplasia, compared with the general population, and both restricted growth in the first 2 years and premature closure of skull plate synchondroses can contribute to narrowing. Narrowing of the foramen magnum can lead to compression of the brainstem and spinal cord, and result in sleep apnoea and sudden death. There is a lack of clarity in the literature on the timing of regular monitoring for foramen magnum stenosis, which assessments should be carried out and when regular screening should be ceased. The European Achondroplasia Forum (EAF) is a group of clinicians and patient advocates, representative of the achondroplasia community. Members of the EAF Steering Committee were invited to submit suggestions for guiding principles for the detection and management of foramen magnum stenosis, which were collated and discussed at an open workshop. Each principle was scrutinised for content and wording, and anonymous voting held to pass the principle and vote on the level of agreement. A total of six guiding principles were developed which incorporate routine clinical monitoring of infants and young children, timing of routine MRI screening, referral of suspected foramen magnum stenosis to a neurosurgeon, the combination of assessments to inform the decision to decompress the foramen magnum, joint decision making to proceed with decompression, and management of older children in whom previously undetected foramen magnum stenosis is identified. All principles achieved the ≥ 75% majority needed to pass (range 89–100%), with high levels of agreement (range 7.6–8.9). By developing guiding principles for the detection and management of foramen magnum stenosis, the EAF aim to enable infants and young children to receive optimal monitoring for this potentially life-threatening complication.

Regular use of aspirin reduces incidence and mortality of various cancers, including colorectal cancer. Anticancer effect of aspirin represents one of the ‘Provocative Questions’ in cancer research. Experimental and clinical studies support a carcinogenic role for PTGS2 (cyclooxygenase-2), which is an important enzymatic mediator of inflammation, and a target of aspirin. Recent ‘molecular pathological epidemiology’ (MPE) research has shown that aspirin use is associated with better prognosis and clinical outcome in PIK3CA -mutated colorectal carcinoma, suggesting somatic PIK3CA mutation as a molecular biomarker that predicts response to aspirin therapy. The PI3K (phosphatidylinositol-4,5-bisphosphonate 3-kinase) enzyme has a pivotal role in the PI3K-AKT signaling pathway. Activating PIK3CA oncogene mutations are observed in various malignancies including breast cancer, ovarian cancer, brain tumor, hepatocellular carcinoma, lung cancer and colon cancer. The prevalence of PIK3CA mutations increases continuously from rectal to cecal cancers, supporting the ‘colorectal continuum’ paradigm, and an important interplay of gut microbiota and host immune/inflammatory reaction. MPE represents an interdisciplinary integrative science, conceptually defined as ‘epidemiology of molecular heterogeneity of disease’. As exposome and interactome vary from person to person and influence disease process, each disease process is unique (the unique disease principle). Therefore, MPE concept and paradigm can extend to non-neoplastic diseases including diabetes mellitus, cardiovascular diseases, metabolic diseases, and so on. MPE research opportunities are currently limited by paucity of tumor molecular data in the existing large-scale population-based studies. However, genomic, epigenomic and molecular pathology testings (for example, analyses for microsatellite instability, MLH1 promoter CpG island methylation, and KRAS and BRAF mutations in colorectal tumors) are becoming routine clinical practices. In order for integrative molecular and population science to be routine practice, we must first reform education curricula by integrating both population and molecular biological sciences. As consequences, next-generation hybrid molecular biological and population scientists can advance science, moving closer to personalized precision medicine and health care.

Abstract We use first principles of population genetics to model the evolution of proteins under persistent positive selection (PPS). PPS may occur when organisms are subjected to persistent environmental change, during adaptive radiations, or in host–pathogen interactions. Our mutation–selection model indicates protein evolution under PPS is an irreversible Markov process, and thus proteins under PPS show a strongly asymmetrical distribution of selection coefficients among amino acid substitutions. Our model shows the criteria ω>1 (where ω is the ratio of nonsynonymous over synonymous codon substitution rates) to detect positive selection is conservative and indeed arbitrary, because in real proteins many mutations are highly deleterious and are removed by selection even at positively selected sites. We use a penalized-likelihood implementation of the PPS model to successfully detect PPS in plant RuBisCO and influenza HA proteins. By directly estimating selection coefficients at protein sites, our inference procedure bypasses the need for using ω as a surrogate measure of selection and improves our ability to detect molecular adaptation in proteins.

The problem of interaction selection in high-dimensional data analysis has recently received much attention. This note aims to address and clarify several fundamental issues in interaction selection for linear regression models, especially when the input dimension p is much larger than the sample size n. We first discuss how to give a formal definition of \"importance\" for main and interaction effects. Then we focus on two-stage methods, which are computationally attractive for high-dimensional data analysis but thus far have been regarded as heuristic. We revisit the counterexample of Turlach and provide new insight to justify two-stage methods from the theoretical perspective. In the end, we suggest new strategies for interaction selection under the marginality principle and provide some simulation results.

Due to the craniofacial anatomy of people with achondroplasia, sleep-disordered breathing (SDB) occurs more frequently than in the average stature population. SDB, which comprises obstructive sleep apnoea (OSA), more rarely central sleep apnoea (CSA), and nocturnal alveolar hypoventilation (NH), may present at any age in patients with achondroplasia. Untreated SDB is associated with neurocognitive dysfunction, cardiovascular, and metabolic complications in children and adults. There continues to be debate on the optimal assessment and management of SDB in achondroplasia. To help address this, the European Achondroplasia Forum (EAF), a network of clinicians and patient advocates representative of the achondroplasia clinical community, organised a virtual workshop in October 2023 to scrutinise, vote and agree upon five guiding principles for managing SDB in achondroplasia. This workshop was attended by 40 healthcare professionals, including clinical geneticists, general practitioners and consultants, orthodontic and orthopaedic surgeons, paediatricians, paediatric endocrinologists and pulmonologists, sleep researchers and specialists, and two patient advocacy group representatives. The five guiding principles focus on lifelong assessment and proactive management, incorporating individualised sleep studies, screening, and a stepwise approach to therapeutic management. The EAF was in favour of all guiding principles, with all achieving 100% consensus with high levels of agreement (range 8.9–9.7/10). In developing guiding principles for the management of SDB in achondroplasia, the EAF aims to facilitate optimal screening and management of SDB in infants, young children, and adults with achondroplasia.

Background Achondroplasia is the most common form of skeletal dysplasia, with serious comorbidities and complications that may occur from early infancy to adulthood, requiring lifelong management from a multidisciplinary team expert in the condition The European Achondroplasia Forum guiding principles of management highlight the importance of accurate diagnosis and timely referral to a centre specialised in the management of achondroplasia to fully support individuals with achondroplasia and their families, and to appropriately plan management. The European Achondroplasia Forum undertook an exploratory audit of its Steering Committee to ascertain the current situation in Europe and to understand the potential barriers to timely diagnosis and referral. Results Diagnosis of achondroplasia was primarily confirmed prenatally (66.6%), at Day 0 (12.8%) or within one month after birth (12.8%). For suspected and confirmed cases of achondroplasia, a greater proportion were identified earlier in the prenatal period (87.1%) with fewer diagnoses at Day 0 (5.1%) or within the first month of life (2.6%). Referral to a specialist centre took place after birth (86.6%), predominantly within the first month, although there was a wide variety in the timepoint of referral between countries and in the time lapsed between suspicion or confirmed diagnosis of achondroplasia and referral to a specialist centre. Conclusions The European Achondroplasia Forum guiding principles of management recommend diagnosis of achondroplasia as early as possible. If concerns are raised at routine ultrasound, second line investigation should be implemented so that the diagnosis can be reached as soon as possible for ongoing management. Clinical and radiological examination supported by molecular testing is the most effective way to confirm diagnosis of achondroplasia after birth. Referral to a centre specialised in achondroplasia care should be made as soon as possible on suspicion or confirmation of diagnosis. In countries or regions where there are no official skeletal dysplasia reference or specialist centres, priority should be given to their creation or recognition, together with incentives to improve the structure of the existing multidisciplinary team managing achondroplasia. The length of delay between diagnosis of achondroplasia and referral to a specialist centre warrants further research.

Background Many genome-wide association studies have detected genomic regions associated with traits, yet understanding the functional causes of association often remains elusive. Utilizing systems approaches and focusing on intermediate molecular phenotypes might facilitate biologic understanding. Results The availability of exome sequencing of two populations of African-Americans and European-Americans from the Atherosclerosis Risk in Communities study allowed us to investigate the effects of annotated loss-of-function (LoF) mutations on 122 serum metabolites. To assess the findings, we built metabolomic causal networks for each population separately and utilized structural equation modeling. We then validated our findings with a set of independent samples. By use of methods based on concepts of Mendelian randomization of genetic variants, we showed that some of the affected metabolites are risk predictors in the causal pathway of disease. For example, LoF mutations in the gene KIAA1755 were identified to elevate the levels of eicosapentaenoate ( p -value = 5E-14), an essential fatty acid clinically identified to increase essential hypertension. We showed that this gene is in the pathway to triglycerides, where both triglycerides and essential hypertension are risk factors of metabolomic disorder and heart attack. We also identified that the gene CLDN17, harboring loss-of-function mutations, had pleiotropic actions on metabolites from amino acid and lipid pathways. Conclusion Using systems biology approaches for the analysis of metabolomics and genetic data, we integrated several biological processes, which lead to findings that may functionally connect genetic variants with complex diseases.

Understanding how plants respond to salinity stress is essential for developing tolerant genotypes, to keep human food secure since it is threaten by climate changes and increasing population worldwide. Barley ( Hordeum vulgare ) is a crop that possesses various salinity tolerance mechanisms that remain to be explored. In this study, data from an RNA-Seq experiment in barley was analyzed to identify changes in genome activities as well as differentially expressed genes (DEGs) in response to salinity stress. A gene network was predicted among identified DEGs and was subjected to network topology analysis, which resulted in the prediction of a hub gene, namely low expression of osmotically responsive gene 2 ( LOS2 ). LOS2 and its two hierarchical downstream genes, salt-tolerant zinc finger ( ZAT10 ) and ascorbate peroxidase 1 ( APX1 ), were used in a genome-wide association (GWA) survey to confirm their importance. A field experiment was conducted to recognize susceptible and tolerant genotypes among 10 different barley genotypes based on the principle component analysis (PCA) of stress-related indices. In a separate salinity experiment, two of the genotypes were assessed to assign their physiological and biochemical responses as well as to identify expression profiles of LOS2 , ZAT10 , and APX1 . From the results, the activity of the barley genome was significantly altered toward response to stress. In total, 5692 DEGs were identified and the gene network derived from these genes contained 131 nodes and 257 edges. The identified genotypes clearly showed the difference in water status, osmolyte accumulation, cell membrane damages, and ion homeostasis as well as in expression profiles for studied genes during salinity stress. Our results suggest that LOS2 along with the ZAT10 and APX1 genes may serve as an important part of barley salinity stress tolerance pathways. To our knowledge, this is the first report on the role(s) of LOS2 in barley salinity stress tolerance in a gene network system.