On the Finite Dimensionality of Closed Subspaces in Lp(M,dμ)∩Lq(M,dν)

Finding effective finite-dimensional criteria for closed subspaces in Lp, endowed with some additional functional constraints, is a well-known and interesting problem. In this work, we are interested in some sufficient constraints on closed functional subspaces, Sp⊂Lp, whose finite dimensionality is not fixed a priori and can not be checked directly. This is often the case in diverse applications, when a closed subspace Sp⊂Lp is constructed by means of some additional conditions and constraints on Lp with no direct exemplification of the functional structure of its elements. We consider a closed topological subspace, Sp(q), of the functional Banach space, Lp(M,dμ), and, moreover, one assumes that additionally, Sp(q)⊂Lq(M,dν) is subject to a probability measure ν on M. Then, we show that closed subspaces of Lp(M,dμ)∩Lq(M,dν) for q>max{1,p},p>0 are finite dimensional. The finite dimensionality result concerning the case when q>p>0 is open and needs more sophisticated techniques, mainly based on analysis of the complementary subspaces to Lp(M,dμ)∩Lq(M,dν).

The Distinct Properties of the Consecutive Disordered Regions Inside or Outside Protein Domains and Their Functional Significance

The consecutive disordered regions (CDRs) are the basis for the formation of intrinsically disordered proteins, which contribute to various biological functions and increasing organism complexity. Previous studies have revealed that CDRs may be present inside or outside protein domains, but a comprehensive analysis of the property differences between these two types of CDRs and the proteins containing them is lacking. In this study, we investigated this issue from three viewpoints. Firstly, we found that in-domain CDRs are more hydrophilic and stable but have less stickiness and fewer post-translational modification sites compared with out-domain CDRs. Secondly, at the protein level, we found that proteins with only in-domain CDRs originated late, evolved rapidly, and had weak functional constraints, compared with the other two types of CDR-containing proteins. Proteins with only in-domain CDRs tend to be expressed spatiotemporal specifically, but they tend to have higher abundance and are more stable. Thirdly, we screened the CDR-containing protein domains that have a strong correlation with organism complexity. The CDR-containing domains tend to be evolutionarily young, or they changed from a domain without CDR to a CDR-containing domain during evolution. These results provide valuable new insights about the evolution and function of CDRs and protein domains.

How Molecules Became Signs

To explore how molecules became signs I will ask: “What sort of process is necessary and sufficient to treat a molecule as a sign?” This requires focusing on the interpreting system and its interpretive competence. To avoid assuming any properties that need to be explained I develop what I consider to be a simplest possible molecular model system which only assumes known physics and chemistry but nevertheless exemplifies the interpretive properties of interest. Three progressively more complex variants of this model of interpretive competence are developed that roughly parallel an icon-index-symbol hierarchic scaffolding logic. The implication of this analysis is a reversal of the current dogma of molecular and evolutionary biology which treats molecules like DNA and RNA as the original sources of biological information. Instead I argue that the structural characteristics of these molecules have provided semiotic affordances that the interpretive dynamics of viruses and cells have taken advantage of. These molecules are not the source of biological information but are instead semiotic artifacts onto which dynamical functional constraints have been progressively offloaded during the course of evolution.

The cichlid oral and pharyngeal jaws are evolutionarily and genetically coupled

Evolutionary constraints may significantly bias phenotypic change, while “breaking” from such constraints can lead to expanded ecological opportunity. Ray-finned fishes have broken functional constraints by developing two jaws (oral-pharyngeal), decoupling prey capture (oral jaw) from processing (pharyngeal jaw). It is hypothesized that the oral and pharyngeal jaws represent independent evolutionary modules and this facilitated diversification in feeding architectures. Here we test this hypothesis in African cichlids. Contrary to our expectation, we find integration between jaws at multiple evolutionary levels. Next, we document integration at the genetic level, and identify a candidate gene, smad7, within a pleiotropic locus for oral and pharyngeal jaw shape that exhibits correlated expression between the two tissues. Collectively, our data show that African cichlid evolutionary success has occurred within the context of a coupled jaw system, an attribute that may be driving adaptive evolution in this iconic group by facilitating rapid shifts between foraging habitats, providing an advantage in a stochastic environment such as the East African Rift-Valley.

Functional constraints on insect immune system components govern their evolutionary trajectories

The role of constraints in shaping evolutionary outcomes is often investigated in the contexts of developmental biology and population genetics, in terms of the capacity to generate new variants as well as how selection either limits or promotes consequent phenotypic change. Comparative genomics also recognises the role of constraints, in terms of shaping the evolution of gene and genome architectures, sequence evolutionary rates, and gene gains and losses, as well as on molecular phenotypes. Characterising patterns of genomic change where putative functions and interactions of system components are relatively well-described offers opportunities to explore whether genes with similar or analogous roles exhibit similar evolutionary trajectories, possibly governed by common constraints. Using insect innate immunity as our study system, we hypothesise that quantitative characterisation of gene evolutionary histories can define distinct dynamics associated with different functional roles. We develop metrics that quantify gene evolutionary histories, employ these to characterise evolutionary features of immune gene repertoires, and explore relationships between gene family evolutionary profiles and their roles in immunity to understand how different constraints may relate to distinct dynamics. We identified three main axes of evolutionary trajectories characterised by gene duplication and synteny, maintenance/stability and sequence conservation, and loss and sequence divergence, highlighting similar and contrasting patterns across these axes amongst subsets of immune genes. Our results indicate that where and how genes participate in immune responses limit the range of possible evolutionary scenarios they exhibit. Comparative genomics approaches therefore offer opportunities to characterise how functional constraints on different components of biological systems govern their evolutionary trajectories.

In vivo and in vitro human gene essentiality estimations capture contrasting functional constraints

Gene essentiality estimation is a popular empirical approach to link genotypes to phenotypes. In humans, essentiality is estimated based on loss-of-function (LoF) mutation intolerance, either from population exome sequencing (in vivo) data or CRISPR-based in vitro perturbation experiments. Both approaches identify genes presumed to have detrimental consequences on the organism upon mutation. Are these genes constrained by having key cellular/organismal roles? Do in vivo and in vitro estimations equally recover these constraints? Insights into these questions have important implications in generalizing observations from cell models and interpreting disease risk genes. To empirically address these questions, we integrate genome-scale datasets and compare structural, functional and evolutionary features of essential genes versus genes with extremely high mutational tolerance. We found that essentiality estimates do recover functional constraints. However, the organismal or cellular context of estimation leads to functionally contrasting properties underlying the constraint. Our results suggest that depletion of LoF mutations in human populations effectively captures organismal-level functional constraints not experimentally accessible through CRISPR-based screens. Finally, we identify a set of genes (OrgEssential), which are mutationally intolerant in vivo but highly tolerant in vitro. These genes drive observed functional constraint differences and have an unexpected preference for nervous system expression.

Research of a mathematical model for designing a barge-towing complex for the Republic of the Union of Myanmar

В статье описана математическая модель проектирования барже-буксирного комплекса с учётом особенности эксплуатации в условиях Республики Союз Мьянма. В статье исследуются особенности ББК как объекта оптимизации, описана математическая модель ББК, отображается его как сложную техническую систему. В рамках модели приведены математические зависимости и алгоритмы для определения элементов теоретического чертежа, мощности главных двигателей, для решения некоторых вопросов общего расположения с учетом расстояния главных водонепроницаемых переборок корпуса, для расчета нагрузки и устойчивости. Метод комплексной оценки эффективности применения барже-буксирного комплекса на стадии технико-экономического обоснования проекта в условиях развивающихся стран, в частности в условиях Республики Союз Мьянмы. В результате работы были полностью определены параметры основных типов барже-буксировочных комплексов для перспективной системы внутреннего водного транспорта Республики Союза Мьянма. На базе методов случайного поиска создан алгоритм оптимизации элементов ББК, решающий задачу математического программирования с процедурным характером функции критерия и функциональных ограничений. Математическая модель и алгоритм оптимизации реализованы в виде программы для обеспечения компьютерного эксперимента. Программа, реализующая математическую модель проектирования ББК, состоит из отдельных программных модулей, что облегчает ее совершенствование в анализе результатов решения задачи. Создан программный комплекс с использованием языка программирования Паскаль в среде Delphi для обеспечения автоматизирования проектирования. Указанные программы могут быть использованы в исследовательском проектировании на начальных стадиях проектирования. The article describes a mathematical models for designing a barge-towing complex, taking into account the peculiarities of operation in the conditions of the Republic of the Union of Myanmar. The article examines the features of the BBK as an object of optimization, describes the mathematical model of the BBK, displays it as a complex technical system. Within the framework of the model, mathematical dependencies and algorithms are given for determining the elements of the theoretical drawing, the power of the main engines, for solving some issues of the general location, taking into account the distance of the main watertight bulkheads of the hull, for calculating the load and stability. The method of comprehensive assessment of the effectiveness of the use of the barge-tow complex at the stage of the feasibility study of the project in the conditions of developing countries, in particular in the conditions of the Republic of the Union of Myanmar. As a result of the work, the parameters of the main types of barge-towing complexes for the prospective inland water transport system of the Republic of the Union of Myanmar were fully determined. On the basis of random search methods, an algorithm for optimizing the BBK elements is created, which solves the problem of mathematical programming with the procedural nature of the criterion function and functional constraints. The mathematical model and the optimization algorithm are implemented as a program to provide a computer experiment. The program that implements the mathematical model of the design of the BBK consists of separate program modules, which facilitates its improvement in the analysis of the results of solving the problem. A software package was created using the Pascal programming language in the Delphi environment to provide design automation. These programs can be used in research design at the initial stages of design.

Mapping Potential Antigenic Drift Sites (PADS) on SARS-CoV-2 Spike in Continuous Epitope-Paratope Space

SARS-CoV-2 mutations with antigenic effects pose a risk to immunity developed through vaccination and natural infection. While vaccine updates for current variants of concern (VOCs) are underway, it is likewise important to prepare for further antigenic mutations as the virus navigates the heterogeneous global landscape of host immunity. Toward this end, a wealth of data and tools exist that can augment existing genetic surveillance of VOC evolution. In this study, we integrate published datasets describing genetic, structural, and functional constraints on mutation along with computational analyses of antibody-spike co-crystal structures to identify a set of potential antigenic drift sites (PADS) within the receptor binding domain (RBD) and N-terminal domain (NTD) of SARS-CoV-2 spike protein. Further, we project the PADS set into a continuous epitope-paratope space to facilitate interpretation of the degree to which newly observed mutations might be antigenically synergistic with existing VOC mutations, and this representation suggests that functionally convergent and synergistic antigenic mutations are accruing across VOC NTDs. The PADS set and synergy visualization serve as a reference as new mutations are detected on VOCs, enable proactive investigation of potentially synergistic mutations, and offer guidance to antibody and vaccine design efforts.

The Diversity of Eyes and Vision

Every aspect of vision, from the opsin proteins to the eyes and the ways that they serve animal behavior, is incredibly diverse. It is only with an evolutionary perspective that this diversity can be understood and fully appreciated. In this review, I describe and explain the diversity at each level and try to convey an understanding of how the origin of the first opsin some 800 million years ago could initiate the avalanche that produced the astonishing diversity of eyes and vision that we see today. Despite the diversity, many types of photoreceptors, eyes, and visual roles have evolved multiple times independently in different animals, revealing a pattern of eye evolution strictly guided by functional constraints and driven by the evolution of gradually more demanding behaviors. I conclude the review by introducing a novel distinction between active and passive vision that points to uncharted territories in vision research. Expected final online publication date for the Annual Review of Vision Science, Volume 7 is September 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.