Matemáticos finalmente descobriram um elusivo azulejo 'einstein'.

quinta-feira, março 30, 2023

An aperiodic monotile

David Smith, Joseph Samuel Myers, Craig S. Kaplan, Chaim Goodman-Strauss

Image/Imagem: Science News

A longstanding open problem asks for an aperiodic monotile, also known as an "einstein": a shape that admits tilings of the plane, but never periodic tilings. We answer this problem for topological disk tiles by exhibiting a continuum of combinatorially equivalent aperiodic polygons. We first show that a representative example, the "hat" polykite, can form clusters called "metatiles", for which substitution rules can be defined. Because the metatiles admit tilings of the plane, so too does the hat. We then prove that generic members of our continuum of polygons are aperiodic, through a new kind of geometric incommensurability argument. Separately, we give a combinatorial, computer-assisted proof that the hat must form hierarchical -- and hence aperiodic -- tilings.



"einstein": is a 13-sided shape called ‘the hat’ forms a pattern that never repeats/é uma configuração de 13 lados chamada 'o chapéu' formando um padrão que nunca se repete.

Nanomotores biológicos rotativos: mero acaso, fortuita necessidade ou design inteligente?

sábado, março 25, 2023

Front. Microbiol., 21 September 2022

Sec. Microbial Physiology and Metabolism

Volume 13 - 2022 |

Editorial: Biological rotary nanomotors

Michael D. Manson1*, Beiyan Nan1, Pushkar P. Lele2, Jun Liu3 and Thomas M. Duncan4

1Department of Biology, Texas A&M University, College Station, TX, United States

2Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, TX, United States

3Microbial Sciences Institute, Department of Microbial Pathogenesis, Yale University, New Haven, CT, United States

4Department of Biochemistry & Molecular Biology, Upstate Medical University, Syracuse, NY, United States

Editorial on the Research Topic

Biological rotary nanomotors

This Research Topic of 20 review articles covers the incredible variety of molecular rotary nanomachines that have evolved over billions of years. The details of their molecular mechanisms are well-known for the Bacterial Flagellar Motor (BFM) and FoF1 ATP synthase/ATPase. They are inferred by analogy to the BFM for others: the 5:2 motors of gliding bacteria and the 5:2 motors of the Ton and Tol systems that govern events at the outer membrane of gram-negative bacteria. All of these systems couple a transmembrane ion motive force to useful work. Two additional articles consider the unique propulsion generator of the Archaea, the archaellum, which appears to be driven entirely by ATP hydrolysis and has an evolutionary history completely independent of those for the 5:2 motors and FoF1.

This Research Topic originated with Mike Manson, who was inspired by the recently published structures of 5:2 rotary motors and the desire to create a fitting tribute to Howard Berg, who introduced rotary motors into biology. The effort was augmented by recruitment of Tom Duncan, Pushkar Lele, Jun Liu, and Beiyan Nan, who possess the expertise to select the authors best able to tell the story of rotary nanomotors and to edit their contributions.

The Research Topic has six sections. The first two chapters serve as an introduction to the history, structure, and energetics of rotary motors driven by an ion motive force. The second of these provides a detailed consideration of the structure of 5:2 rotary motors and how their function and energetics compare with the Fo motor of ATP synthases, which has a gearing ratio ranging from 8:1 to 15:1 in different species. The next seven articles provide detailed reviews about different aspects and incarnations of BFMs. The following two articles discuss the function of ion-powered motors in gliding bacteria, which do not depend on flagella. Next, two reviews cover the Exb/Ton and Tol/Pal systems, both of which are driven by 5:2-type motors. As a segue into the FoF1 motors that drive ATP synthesis, the next two articles cover the archaellum, a helical propeller like the bacterial flagellum, but one driven by ATP hydrolysis rather than an ion motive force and possessing a completely different evolutionary trajectory. The last five articles review different aspects of what is known about the FoF1 ATP synthase, a crucial and ubiquitous energy-transducing enzyme that couples two rotary motor devices.

The editors thank all 49 authors who generously agreed to put their collective knowledge about rotary nanomotors into words. They represent the leading research groups worldwide studying rotary molecular machines. The positive responses to our invitations were doubtless aided by the recognition that this was a tribute to the visionary insight of Howard Berg, whose paper with Robert Anderson in 1973 first declared that “Bacteria Swim by Rotating Helical Filaments.”

We hoped that Howard would write an introduction to this Research Topic. Unfortunately, he passed away on December 30, 2021, just as it became clear that our vision was going to become reality. That sad event adds both poignancy and timeliness to this Research Topic. We also want to thank the four editors who supplemented the efforts of the five designated guest editors mentioned above and the 33 reviewers who, together with the guest editors, ensured that everything presented in the reviews was as clear, complete, and accurate as possible.

We hope this Research Topic serves as a fitting tribute to Howard Berg, the unconventional intellect whose insight ushered in an entire field of molecular biophysics: the study of rotary molecular motors. Savor what is presented here and anticipate the new revelations which doubtless await in the coming years.


Controlando a sinalização periódica de longo alcance para conduzir uma transição morfogenética: mero acaso, fortuita necessidade ou design inteligente?

quinta-feira, março 23, 2023

Controlling periodic long-range signalling to drive a morphogenetic transition

Hugh Z Ford, Angelika Manhart, Jonathan R Chubb 

Laboratory for Molecular Cell Biology and Department of Cell and Developmental Biology, University College London, United Kingdom; Department of Mathematics, University College London, United Kingdom; Faculty of Mathematics, University of Vienna, Austria

Mar 1, 2023 

Image/Imagem: Spiral tip circulation and spiral wave progression.


Cells use signal relay to transmit information across tissue scales. However, the production of information carried by signal relay remains poorly characterised. To determine how the coding features of signal relay are generated, we used the classic system for long-range signalling: the periodic cAMP waves that drive Dictyostelium collective migration. Combining imaging and optogenetic perturbation of cell signalling states, we find that migration is triggered by an increase in wave frequency generated at the signalling centre. Wave frequency is regulated by cAMP wave circulation, which organises the long-range signal. To determine the mechanisms modulating wave circulation, we combined mathematical modelling, the general theory of excitable media, and mechanical perturbations to test competing models. Models in which cell density and spatial patterning modulate the wave frequency cannot explain the temporal evolution of signalling waves. Instead, our evidence leads to a model where wave circulation increases the ability for cells to relay the signal, causing further increase in the circulation rate. This positive feedback between cell state and signalling pattern regulates the long-range signal coding that drives morphogenesis.

Editor's evaluation

This fundamental work substantially advances our understanding of how multicellular structures transmit information over long ranges. Compelling approaches combining experiments and theory unravel the mechanism by which amoeba form migrating cellular waves by chemotaxis. The work will be of broad interest to cell and developmental biologists.


Darwin, nós tivemos um problema: as ilusões da Síntese Moderna!

terça-feira, março 21, 2023

The Illusions of the Modern Synthesis

Denis Noble 

Biosemiotics volume 14, pages5–24 (2021)

Image/Imagem: The Guardian


The Modern Synthesis has dominated biology for 80 years. It was formulated in 1942, a decade before the major achievements of molecular biology, including the Double Helix and the Central Dogma. When first formulated in the 1950s these discoveries and concepts seemed initially to completely justify the central genetic assumptions of the Modern Synthesis. The Double Helix provided the basis for highly accurate DNA replication, while the Central Dogma was viewed as supporting the Weismann Barrier, so excluding the inheritance of acquired characteristics. This article examines the language of the Modern Synthesis and reveals that it is based on four important misinterpretations of what molecular biology had shown, so forming the basis of the four Illusions: 1. Natural Selection; 2. The Weismann Barrier; 3. The Rejection of Darwin’s Gemmules; 4. The Central Dogma. A multi-level organisation view of biology avoids these illusions through the principle of biological relativity. Molecular biology does not therefore confirm the assumptions of the Modern Synthesis.

FREE PDF GRATIS: Biosemiotics

O que há de errado com a causalidade evolutiva?

segunda-feira, março 20, 2023

What’s Wrong with Evolutionary Causation?

Jan Baedke 

Acta Biotheoretica volume 69, pages79–89 (2021)

Image/Imagem: MIT Press


This review essay reflects on recent discussions in evolutionary biology and philosophy of science on the central causes of evolution and the structure of causal explanations in evolutionary theory. In this debate, it has been argued that our view of evolutionary causation should be rethought by including more seriously developmental causes and causes of the individual acting organism. I use Tobias Uller’s and Kevin Laland’s volume Evolutionary Causation as well as recent reviews of it as a starting point to reflect on the causal role of agency, individuality, and the environment in evolution. In addition, I critically discuss classical philosophical frameworks of theory change (i.e. Popper’s, Kuhn’s and Lakatos’) used in this debate to understand changing views of evolutionary causation.

FREE PDF GRATIS: Acta Biotheoretic

A síntese evolutiva estendida acarreta poder explicativo ampliado?

Does the extended evolutionary synthesis entail extended explanatory power?

35, Article number: 20 (2020)


Biologists and philosophers of science have recently called for an extension of evolutionary theory. This so-called ‘extended evolutionary synthesis’ (EES) seeks to integrate developmental processes, extra-genetic forms of inheritance, and niche construction into evolutionary theory in a central way. While there is often agreement in evolutionary biology over the existence of these phenomena, their explanatory relevance is questioned. Advocates of EES posit that their perspective offers better explanations than those provided by ‘standard evolutionary theory’ (SET). Still, why this would be the case is unclear. Usually, such claims assume that EES’s superior explanatory status arises from the pluralist structure of EES, its different problem agenda, and a growing body of evidence for the evolutionary relevance of developmental phenomena (including developmental bias, inclusive inheritance, and niche construction). However, what is usually neglected in this debate is a discussion of what the explanatory standards of EES actually are, and how they differ from prevailing standards in SET. In other words, what is considered to be a good explanation in EES versus SET? To answer this question, we present a theoretical framework that evaluates the explanatory power of different evolutionary explanations of the same phenomena. This account is able to identify criteria for why and when evolutionary explanations of EES are better than those of SET. Such evaluations will enable evolutionary biology to find potential grounds for theoretical integration.

FREE PDF GRATIS: Biology & Philosophy