Official web site of Takeuchi Lab, Univ. Tokyo

In the cell, long DNA molecules carry the genetic information and must be stored yet remain accessible to interact with various biomolecules which control for read out and processing. DNA-binding proteins often mediate these processes by bringing two distant DNA sites together, thereby inducing (transient) topological domains. In order to understand the dynamics and molecular architecture of protein-induced topological domains in DNA, quantitative and time-resolved approaches are required. Here we present a methodology to determine the size and dynamics of topological domains using the analysis of fluctuations: a protein-binding event causes a drop in the variance in the end-end distance of a stretched over-wound DNA molecule. Using a combination of high-speed magnetic tweezers experiments, Monte Carlo simulations, and analytical theory, we map out the dependence of DNA extension fluctuations as a function of supercoiling density and external force. We demonstrate how transient (partial) dissociation of DNA bridging proteins results in dynamic sampling of different topological states. Our work highlights how considering DNA extension fluctuations, in addition to the mean extension, provides additional information and enables the investigation of protein-DNA interactions that are otherwise not detectable.

References

1. E. Skoruppa, E. Carlon, "Equilibrium Fluctuations of DNA Plectonemes" Phys. Rev. E 106, 024412 (2022)
https://arxiv.org/pdf/2205.07735.pdf
2. W. Vanderlinden, E. Skoruppa, P. Kolbeck, E. Carlon, J. Lipfert, "DNA fluctuations reveal the size and dynamics of topological domains" biorXiv:2021.12.21.473646
https://www.biorxiv.org/content/10.1101/2021.12.21.473646v1

The colocalization of density modulations and particle polarization is a characteristic emergent feature of motile active matter in activity gradients. I employ the active-Brownian-particle model to derive precise analytical expressions for the density and polarization profiles of a single Janus-type swimmer in the vicinity of an abrupt activity step. The analysis allows for an optional (but not necessary) orientation-dependent propulsion speed, as often employed in force-free particle steering. The results agree well with measurement data for a thermophoretic microswimmer, which can serve as a template for more complex applications, e.g., to motility-induced phase separation or studies of physical boundaries. The essential physics behind these formal results is robustly captured and elucidated by a schematic two-species “run-and-tumble” model.

Replisomes are multi-protein complexes that replicate genomes with remarkable speed and accuracy. In bacteria, two replisomes initiate replication at a well-defined origin site on the circular genome, progress in opposite directions, and complete replication upon encountering each other in a terminal region. Precise features of replisome dynamics, such as whether their speed is approximately constant or varies along the genome, are important to determine the location of their encounter point and the distribution of replication errors on the genome. But this detailed information is hard to obtain. We developed a mathematical model to infer the replisome dynamics from the DNA abundance in a growing bacterial population. I will discuss our findings in detail in this seminar.

Topological order and phases represent an exciting frontier of modern research [1]. Starting with Gauss and Kelvin, knots in fields, like the magnetic field, were postulated to behave like particles. However, experimentally they were found only as transient features and could not self-assemble into three-dimensional crystals. I will describe energetically stable solitonic knots that emerge in the physical fields of chiral liquid crystals and magnets [2,3]. While spatially localized and freely diffusing in all directions, they behave like colloidal particles and atoms, self-assembling into crystalline lattices with open and closed structures, as well as forming low-symmetry mesophases and gas- or liquid-like states [2]. A combination of energy-minimizing numerical modeling and nonlinear optical imaging uncovers the internal structure and topology of individual solitonic knots and the various hierarchical crystalline and other organizations that they form. Being classified as the elements of the third homotopy group of two-spheres, these solitonic knots are robust and topologically distinct from the host medium, though they can be morphed and reconfigured by weak stimuli like electric or magnetic fields. I will show how low-voltage electric fields can switch between the heliknoton [2,3] and hopfion [4] embodiments of such knot solitons while preserving their topology. Finally, I will discuss how this emergent paradigm of knotted solitonic matter could allow for imparting new designable material properties and for realizing phases of matter that so far could not be found in naturally occurring materials [5-7].

1. I. I. Smalyukh. Rep. Prog. Phys. 83, 106601 (2020).
2. J.-S. B. Tai and I. I. Smalyukh. Science 365, 1449 (2019).
3. R. Voinescu, J.-S. B. Tai and I. I. Smalyukh. Phys Rev Lett 125, 057201 (2020)
4. P. J. Ackerman and I. I. Smalyukh. Nature Materials 16, 426 (2017)
5. H. Mundoor, S. Park, B. Senyuk, H. Wensink and I. I. Smalyukh. Science 360, 768 (2018).
6. Y. Yuan, Q. Liu, B. Senyuk and I.I. Smalyukh. Nature 570, 214 (2019).
7. H. Mundoor, J.-S. Wu, H. Wensink and I.I. Smalyukh. Nature 590, 268 (2021).

ゴムや高分子ゲルは、鎖状高分子の（永続的な）三次元網目構造からなるやわらかい物質である。この内、大量の溶媒を含むものを高分子ゲル、含まないものをゴムという。熱力学や統計力学の学部講義や教科書において、ゴムの弾性は熱力学第二法則に由来する「エントロピー的な力」の代表例として登場する [1,2]。現実のゴムの弾性において「エントロピー的な力」が支配的であることは、体積一定の条件下における、ずり弾性率(G)の絶対温度(T) 依存性の測定から確かめられる。なぜなら、熱力学の一般論から、エントロピー変化由来の弾性（エントロピー弾性）が、TG'(T)となるからである[1,3,4]。天然ゴムや合成ゴムにおいては、それらの弾性がほとんどエントロピー変化由来であることが実験的に確かめられている [3,4]。一方、高分子ゲルにおいては、実験的検証なしに、その弾性がエントロピー変化由来であると仮定して、ゴム弾性論が慣習的に使用されてきた [5]。

本研究は、高分子ゲルにおいて、この仮定が誤りであることを発見した [6]。高分子ゲルは、エントロピー弾性に加えて、内部エネルギー変化由来の「負のエネルギー弾性」を持ち、その合計で弾性が決まる。我々は、50種類以上の相異なる網目構造を持つゲルを作り分けたが、その全てに無視できないほど大きな負のエネルギー弾性が存在した。さらに、負のエネルギー弾性には、現象論的な支配法則があることも明らかになった。ゲルの含む溶媒を減らす（ゴムに近づける）と、負のエネルギー弾性はゼロに近づくため、ゴム弾性の実験結果とも整合的である。逆に言えば、溶媒由来の「負のエネルギー弾性」が、ゴム弾性とゲル弾性の本質的な違いである。セミナーでは、時間が許せば、ゲルの浸透圧における普遍法則 [7] についても軽く触れる。二つの研究 [6,7] を合わせると、高分子ゲルの「完全な熱力学関数」は比較的シンプルな構造を持つことがわかる。

[1] 前野昌弘『よくわかる熱力学』(東京図書, 2020) 10.5節
[2] 田崎晴明『統計力学1』(培風館, 2008) 5.6.4節
[3] 久保亮五『ゴム弾性論』(河出書房1947、裳華房1996)
[4] P.J.フローリ『高分子化学(上・下)』(丸善1955)
[5] 例えば、M. Zhong, et al., Science (2016)
　　https://doi.org/10.1126/science.aag0184
[6] Yoshikawa, Sakumichi, Chung, Sakai, PRX (2021)
　　https://doi.org/10.1103/PhysRevX.11.011045
[7] Yasuda, Sakumichi, Chung, Sakai, PRL (2020)
　　https://doi.org/10.1103/PhysRevLett.125.267801

Migration is a ubiquitous kind of eukaryotic cell behavior. Some cells migrate around on a substrate according to intracellular signals that localize at their front or back, even without extracellular cues. In light of this, we theoretically investigated single eukaryotic cell migration with such intrinsic polarity [1,2] and recently applied the theory to the multicellular case where cells communicate with each other [3,4,5].
In this talk, I will address what forms of multicellular dynamic patterns, or dynamic self-organization, can be formed through intercellular contact communication of migrating cells. I plan to explain the concept and the results of our numerical simulations based on an individual cell-based model in which migrating cells perform contact following and inhibition/attraction of locomotion [3,5]. In particular, I would like to present the results showing that (i) tuning those strengths causes varieties of dynamic self-organization, and (ii) this includes a novel form of collective migration, snake-like dynamic assembly [5]. I will compare some of our results with experimental observations of a social cellular slime mold, Dictyosteloum discoideum, and its mutant, showing the traveling density wave formation [4]. I may also talk about how such dynamic self-organization can contribute to the accuracy of taxis behaviour in population [3,5].
[1] T. Hiraiwa et al., “Relevance of intracellular polarity to accuracy of eukaryotic chemotaxis” Physical Biology 11, 056002 (2014).
[2] T. Hiraiwa, A. Baba and T. Shibata, “Theoretical model for cell migration with gradient sensing and shape deformation” Euro. Phys. J. E 36, 32 (2013).
[3] T. Hiraiwa, “Two types of exclusion interactions for self-propelled objects and collective motion induced by their combination” Phys. Rev. E 99, 012614 (2019).
[4] M. Hayakawa, T. Hiraiwa, Y. Wada, H. Kuwayama and T. Shibata, “Polar pattern formation induced by contact following locomotion in a multicellular system” eLife 9: e53609 (2020).
[5] T. Hiraiwa, “Dynamic self-organization of idealized migrating cells by contact communication”, Phys. Rev. Lett. 125, 268104 (2020).

外部エネルギーを用いて自己駆動する粒子系はアクティブマターと呼ばれ、フロッキング転移、モティリティ誘起相分離、ミクロ相分離といった非平衡特有の相転移現象が生じることが知られている [1]。このような相転移の性質は、古典モデルのシミュレーションや人工粒子系の観察などにより、近年理解が進んできた。一方、量子系に目を向けると、冷却原子系に代表される人工量子系の制御技術の発展に伴い、エネルギー流入や散逸を伴う開放量子系の研究が盛んに進められている。特に、非エルミートハミルトニアンによる有効記述を用いて、特有の臨界現象やトポロジカル相などが議論されてきた [2]。

このような背景のもと我々は、量子多体系におけるアクティブマターモデルを初めて提案し、古典系での自己駆動力が量子系では非エルミート性として表現されることを明らかにした [3]。このモデルでは、自己駆動力に起因した量子相転移が生じ、フロッキング状態やモティリティ誘起相分離状態の量子対応物が現れることがわかった。さらに、量子相転移が古典確率過程モデルにおける動的相転移に対応することを見出し、この対応を相図の解釈に利用した。また、このモデルは散逸を導入した光格子中の冷却原子気体によって実現できると考えられ、その実装方法も提案した。

セミナーでは、アクティブマターで生じる相転移について概説したあと、古典アクティブマターモデルに基づいて量子モデルを構築する方法を説明し、量子モデルの数値シミュレーション結果について議論する。

[1] G. Gompper et al., J. Phys. Condens. Matter 32, 193001 (2020).
[2] Y. Ashida, Z. Gong, and M. Ueda, arXiv:2006.01837.
[3] K. Adachi, K. Takasan, and K. Kawaguchi, arXiv:2008.00996.

量子多体系でパラメータをクエンチさせて非平衡ダイナミクスを調べると、そこに動的スケーリングが現れる場合があり、その普遍性クラスが活発に研究されている。特にここ数年、冷却原子系の実験でスピン相関関数や運動量分布の動的スケーリングが実験的に観測されている[1,2,3]。このような背景のもと、我々は古典系で知られている揺らぐ界面の動的スケーリング、つまりFamily-Vicsek(FV)スケーリングに注目して、孤立量子多体系における界面荒さのFVスケーリングを理論的に研究した。具体的には1次元Bose-Hubbardモデルを用いて、古典系の揺らぐ流体力学とKardar-Parisi-Zhang方程式のアナロジーから界面高さ演算子を導入して、その界面荒さの時間発展をFVスケーリングの視点から調べた。本セミナーでは論文[4]の結果に基づいてその詳細を議論する。

[1] M. Prüfer et al., Nature 563, 217 (2018).
[2] S. Erne et al., Nature 563, 225 (2018).
[3] J. A. P. Glidden et al., arXiv:2006.01118.
[4] K. Fujimoto, R. Hamazaki, and Y. Kawaguchi, Phys. Rev. Lett. 124, 210604 (2020).

It is well known that external perturbations evolve a frictional granular pack jammed in an initial metastable configuration to an eventual stable one. Beneficial in achieving efficient packing, athermal perturbations can also cause catastrophic failure. Understanding pack response to perturbations naturally carries both fundamental and applied significance. In a related context, the power law pressure increase against packing fraction is considered one signature of the frictionless jamming transition. In contrast, independent studies reveal frictional jamming exhibits an initial exponential pressure rise before deviating towards the putative power law. The range of packing fraction values over which pressure rises exponentially is marked by a marginally stable solid (fragile state) sensitive to perturbations. In this talk, I report experiments on frictional granular pack pressure response to controlled perturbations in this fragile state. In particular, I will deduce an empirical result from the experimental data which establishes a close correspondence between this classical (frictional jamming) problem and a well known quantum effect for electron transport in amorphous semiconductors.

Ray systems, or set of radial streaks that encircle an impact crater, became known shortly after the advent of the telescope, perhaps in 1647, when Johannes Hevelius published what might have been the first map of the Moon to show them. Although they were recognized as settled ejecta, that is, deposits of debris thrown out when a meteorite impacts the surface of a planetary body, their origin proved to be the sort of question for which competing theories abound to date. Motivated by observations of ray systems in planetary cratering, we study an analog system: granular cratering. In classical experiments of granular cratering, a ball dropped on an evened-out bed of grains ends up within a crater surrounded by a uniform blanket of ejecta. We show that the uniform blanket of ejecta changes to a ray system where the surface of the granular bed includes undulations, a factor that has not been addressed to date. By carrying out numerous experiments and computational simulations thereof, we ascertain that the number of rays in a ray system ∝ D/λ, where D is the diameter of the ball and λ is the wavelength of the undulations. Further, we show that the ejecta in a ray system originates in a narrow annulus of diameter D with the center at the site of impact. Our findings may help shed light on the enigmatic ray systems on the Moon and other planetary bodies.
This research was carried out in collaboration with Tapan Sabuwala, Christian Butcher, and Gustavo Gioia.