Oct. 25-26, 2023, online

INI-RIMS joint seminar is planned online in collaboration with Issac Newton Institute (INI), Cambridge, UK, and Research Institute for Mathematical Science (RIMS), Kyoto University, Japan. This joint seminar is a part of INI programme “Mathematics of movement: an interdisciplinary approach to mutual challenges in animal ecology and cell biology“, and also a part of RIMS workshop “Role of boundaries in biofluid problems” (in Japanese).


Oct. 25th (Wed) 9:00-10:00 GMT = 17:00-18:00 JST

Prof. Luca Giuggioli (University of Bristol, UK)

The multi-target problem on Cartesian, hexagonal and triangular lattices in homogeneous and heterogeneous environments

Lecture movie is available here.

In many complex systems the emergence of spatio-temporal patterns depends on the interaction between pairs of individuals, agents or subunits comprising the whole system. Theoretical predictions of such patterns rely upon quantifying when and where interaction events might occur. Even in simple scenarios when the dynamics are Markovian, it has been challenging to obtain estimates of encounter statistics between individuals due to the lack of a mathematical formalism to represent the occurrence of multiple random processes at the same time, the so-called splitting probability. With the help of a resolution of a hundred year old  problem on lattice random walks, I will present such formalism and develop a general theory that allows to quantify the spatio-temporal dynamics of interactions when a token of information is transferred upon co-location or proximity. Spatial discretisation is key to develop such a theory bypassing the need to solve unwieldy boundary value problems, giving predictions that are either fully analytical or obtained through the simple inversion of a generating function. The formalism is also applied to hexagonal and triangular lattices for which an analytical exact description of the occupation probability has recently been derived. In heterogeneous environments, a modification of the original formalism has been developed to quantify the interactions of a lattice random walk with the so-called inert heterogeneities. Such heterogeneities may represent locations with long-range connections to distant sites, areas with different diffusivity, or when permeable or impenetrable barriers are present. In this latter context, in the space-time continuous limit, a new fundamental equation that go beyond the diffusion and the Smoluchowski equation in the presence of permeable barriers has been found. Time permitting, I will show some applications of the formalism: from transdermal drug delivery and animal thigmotaxis, i.e. the tendency of an animal to remain close to the boundaries of a confining domain, to the search of a promoter region on DNA by transcription factors, a prototypical two-particle coalescent process. 


Giuggioli, Exact spatiotemporal dynamics of confined lattice random walks in arbitrary dimensions: a century after Smoluchowski and Pólya, Physycal Review X 10:021045 (2020)

Sarvaharman & Giuggioli (2020) Closed-form solutions to the dynamics of confined biased lattice random walks in arbitrary dimensions, Physical Review E 102(6):062124 (2020)

Kenkre & Giuggioli, Theory of the spread of epidemics and movement ecology of animals: an interdisciplinary approach with methodologies from physics and mathematics, Cambridge University Press (2021)

Das & Giuggioli, Discrete space-time resetting model: application to first-passage and transmission statisticsJournal of Physics A: Mathematical and Theoretical55(42):424004 (2022) 

Kay and Giuggioli, Diffusion through permeable interfaces: Fundamental equations and their application to first-passage and local time statisticsPhysical Review Research 4(3):L032039 (2022)

Giuggioli and Sarvaharman, Spatio-temporal dynamics of random transmission events: from information sharing to epidemic spreadJournal of Physics A: Mathematical and Theoretical 55(37):375005 (2022)

Das & Giuggioli, Dynamics of lattice random walk within regions composed of different media and interfacesJournal of Statistical Mechanics: Theory and Experiment, 013201 (2023)

Sarvaharman and Giuggioli, Particle-environment interactions in arbitrary dimensions: a unifying analytic framework to model diffusion with inert spatial heterogeneities, under revision, arXiv preprint arXiv:2209.09014.

Marris, Sarvaharman and Giuggioli, Exact Spatio-Temporal Dynamics of Lattice Random Walks in Hexagonal and Honeycomb Domains, under revision.

Oct 26th (Thu)  9:00-10:00 GMT = 17:00-18:00 JST

Prof. Kogiku Shiba (University of Tsukuba, Japan)

Regulatory mechanism for sperm chemotaxis and flagellar motility

Lecture movie is available here.

Eukaryotic flagella and cilia are extremely important organelles in cell motility and signal reception, such as sperm motility and control of water flow in the body, and their structure and function are highly conserved throughout evolution. I aim to elucidate the molecular and cellular biology of the regulation of sperm flagellar motility by using the original experimental and analytical systems for the functional analysis of fine and fast-moving flagella and cilia. I use the ascidian, Ciona sperm as experimental animal. Ciona spermatozoa have long been used for the analysis of sperm and flagellar motility due to their advantages in terms of ease of sample handling, simplicity of morphology, internal structure and motility [1]. Egg-derived sperm attractants have also been identified, and the dramatic changes in swimming direction and flagellar waveform during sperm chemotaxis can be recorded under a microscope [2]. Sperm chemotactic behavior is characterized by a change of direction when sperm swim away the attractant source. This feature is widely conserved among organisms. The sperm flagellar wave generates propulsion by the alternating propagation of two bends from the base to tip. If the curvature of two bends is equal, the sperm swim straight ahead. On the other hand, if the curvature of one bend is larger than another bend, the sperm perform a circular motion. Analysis of the changes in the flagellar waveforms of Ciona sperm during chemotaxis revealed that the difference between the two bends curvature increases significantly when the sperm swim away from the attractant source, leading to a turn movement that changes direction, and then the curvatre of the two bends becomes equal and the sperm swim straight towards the attractant source. The series of changes in the waveforms are repeated and finally the sperm reaches the attractant source. Realtime calcium imaging using fluorescent calcium indicator also showed that a transient increase in the concentration of calcium ions in the flagellum triggers the waveform change [3]. Calcium ions are important second messengers in the signaling pathway of attractant reception and directly regulate the molecular motor dynein that drives flagellar movement.

Our goal is understanding how sperm sense the attractant concentration gradient, drive calcium signaling, and regulate the flagellar motor. In this talk, I will introduce our biological experiments and studies to reveal the function of the calcium-binding protein calaxin, which directly interact dynein activity, and the role of ion channels in chemoattractant sensing signaling in flagellar waveform regulation [4-5]. I would also like to discuss our recent challenge to understand the skillful behavioral strategies of swimming single cells through “Ethological dynamics in diorama environments” [6].


[1] Brokaw, J Cell Biol. 114(6):1201-15 (1991)

[2] Yoshida et al., Proc Natl Acad Sci U S A. 99(23):14831-6 (2002)

[3] Shiba et al., Proc Natl Acad Sci U S A. 105(49):19312-7 (2008)

[4] Shiba et al., Int J Mol Sci. 23(3):1648 (2022)

[5] Shiba et al., Front Cell Dev Biol. 11:1136404 (2023)

[6] https://diorama-ethology.jp/eng/

Makoto Iima (Hiroshima U)
Kosuke Suzuki (Shinshu U)
Hiroshi Yamashita (Hiroshima U)
Yusuke Fujita (Hiroshima U)

Biofluid Workshop へ戻る