ICTS

The mitotic spindle is a microtubule-based bipolar assembly that physically separates the chromosomes into two equal groups during cell division. The complexity of the mitotic spindle is constantly motivating the development of a variety of experimental approaches that are complementary to and work together with the classical genetics and biochemistry methods. Because the spindle is basically a mechanical micro-machine, the understanding of its functioning requires techniques based on mechanical perturbations, such as laser ablation, microneedle pulling, and optical or magnetic tweezers. We will discuss the mechanobiology of the spindle, putting into context the types of tools and techniques to experimentally dissect the spindle and the benefits of combining them with theoretical approaches. We will focus on the metaphase spindle and the forces acting on chromosomes, kinetochore fiber ends, and along the kinetochore fiber length. In addition to these linear forces, we will consider rotational forces that act within the spindle and make it a chiral structure. The tools and concepts that will be discussed are not only relevant for the mechanobiology of a well-functioning spindle, but will also help to understand the origins of errors in chromosome segregation.

Membrane-bound cellular organelles perform many essential functions, among which the sorting and biochemical maturation of cellular components. Organelles along the secretory and endocytic pathways are strongly out-of-equilibrium structures, which display large stochastic fluctuations of composition and shape resulting from inter-organelle exchange and enzymatic reactions. Understanding how the different molecular mechanisms controlling these processes are orchestrated to yield robust fluxes of matter and to direct particular components to particular locations within the cell is an outstanding problem of great interest for cell biologist, but also for physicists. 
In this talk, I will discuss a conceptual model of organelle biogenesis and maintenance that include vesicular exchange (budding, transport, and fusion) and biochemical maturation, i.e. the change of identity of an organelle over time (early to late endosomes, cis to trans Golgi cisternae…). I will show how the non-equilibrium steady-state of an organelle or a network of organelles may be varied in a controlled manner by modifying a limited number of coarse-grained parameters (essentially, the budding, fusion and maturation rates) and discuss the relevance of these results for the structure of the endosomal network and Golgi apparatus.

Actin filaments and myosin motors in concert, represent the molecular agencies of biological force in living cells. These mechanochemical elements are associated with biochemical reaction cycles operating out-of-equilibrium by energy inputs, resulting in the generation of nonequilibrium active forces. The patterning of these active forces depends on the many ways in which actin filaments and myosin motors assemble together. The profile of these active forces influence shape, rheology, transport and molecular patterning in cells and tissues. I will discuss theoretical approaches to understand the physical properties of actomyosin in cells and tissues.

The physics of morphogenesis
Kinneret Keren and Erez Braun

Biological systems provide a prime example for naturally occurring complex, far from equilibrium, processes that exemplify the emergence of order from the underlying microscopic disorder. The approach to this complexity reflects the tension between a reductionist, reverse engineering stance and the more abstract, systemic one attempting to uncover the organization principles underlying living matter. Our previous work challenges the ability to reverse engineer biological systems (see [1]). In particular, it demonstrates the difficulty in identifying the relevant degrees of freedom underlying biological phenomena. One of the main reasons for this challenge is the inherent difficulty in separating any given level of organization from the coupled dynamics at all the other levels, including the environment within which the system is embedded. We will discuss these coupled dynamics in the context of morphogenesis—the emergence of form and function in a developing animal, which is one of the most remarkable examples of pattern formation in nature. The current picture of morphogenesis relies on biochemical patterning. However, as we are going to discuss, morphogenesis involves the integrated symbiotic interplay of three type of processes: biochemical, mechanical and electrical, which span all scales from the molecular to the entire organism [2].

In the first part, we will discuss the role of mechanics and the integration of mechanical processes with the biochemical processes, utilizing Hydra regeneration as a model. In the second part, we will generalize the discussion, focusing on the ways living systems close the loop to stabilize the emergence of a viable body plan in development. We then utilize Hydra again, and study its regeneration under external electric fields. These examples paint morphogenesis as a physical dynamic pattern-forming process and call for a new theoretical framework for this phenomenon.

Specifically, our plan for these two parts is as follows:

Part 1 – Kinneret Keren
Morphogenesis in regenerating Hydra: actin dynamics and the influence of mechanical constraints

In this part we focus on the mechanical aspects of morphogenesis using Hydra, which provides a flexible platform to explore how mechanical forces and feedback contribute to the formation and stabilization of the body plan during morphogenesis. We will discuss our results showing that structural inheritance of the supra-cellular actin fiber organization directs the alignment of the new body axis in regenerating Hydra [3]. We will further describe our efforts to develop a framework relating the dynamics of the nematic organization of these supra-cellular actin fibers to the morphogenesis process [4]. In particular, we show that topological defects in the nematic order act as effective organizing centers in Hydra morphogenesis. Finally, we will present our recent studies on the establishment of body axis polarity in regenerating Hydra, showing that body axis determination is a dynamic process that involves mechanical feedback together with signaling processes.

Part 2 – Erez Braun
Reversal morphogenesis in Hydra regeneration under external electric fields

The robustness of the morphogenetic process is typically attributed to the presence of a well-defined hierarchy of forward-driven processes, such as threshold-crossing cellular processes and the development of symmetry-breaking fields. Is it possible to modulate the course of morphogenesis in a whole animal on demand and alter its developmental trajectory in a controlled manner? We demonstrate that an external electric field can be tuned to drive morphogenesis in Hydra regeneration, backward and forward, around a critical point in a controlled manner [5]. Interestingly, a backward-forward cycle of morphogenesis leads to a newly emerged body plan in the re-developed folded tissue, which is not necessarily similar to the one before the reversal process. Thus, a controlled drive of morphogenesis allows in principle, multiple re-initiation of novel developmental trajectories for the same tissue. We will discuss the main experimental observations and their implications. Controlled reversal trajectories open a new vista on morphogenesis and suggest a novel approach to study the physics of this fascinating process as a dynamic phase transition.

References:

1. E. Braun, The unforeseen challenge: from genotype-to-phenotype in cell populations, Rep. Prog. Phys. 78, 036602 (2015).
2. E. Braun & K. Keren, Hydra Regeneration: Closing the Loop with Mechanical Processes in Morphogenesis, BioEssays 1700204 (2018).
3. Anton Livshits, Lital Shani-Zerbib, Yonit Maroudas-Sacks, Erez Braun & Kinneret Keren, Structural inheritance of the actin cytoskeletal organization determines the body axis in regenerating Hydra, Cell Reports 18(6), 1410-1421 (2017).
4. Yonit Maroudas-Sacks, Liora Garion, Lital Shani-Zerbib, Anton Livshits, Erez Braun & Kinneret Keren, Topological defects in the nematic order of actin fibers as organization centers of Hydra morphogenesis, Nature Physics (2020).
5. E, Braun & H. Ori, Electric-Induced Reversal of Morphogenesis in Hydra. Biophysical Journal 117, 1514–1523 (2019).

Active matter models have been used to describe a number of biophysical phenomena. I will describe how such models can be used to study the large-scale properties of chromosomes contained within the nuclei of human cells between cell divisions. Polymer models for chromosomes that incorporate inhomogeneous activity reproduce many general, yet little understood, features of large-scale nuclear architecture. These include: (i) the spatial separation of gene-rich, low-density euchromatin, predominantly found towards the centre of the nucleus, vis a vis. gene-poor, denser heterochromatin, typically enriched in proximity to the nuclear periphery, (ii) the differential positioning of individual gene-rich and gene-poor chromosomes, (iii)  the formation of chromosome territories, as well as (iv), the weak size-dependence of the positions of individual chromosome centres-of-mass relative to the nuclear centre that is seen in some cell types. Such structuring is induced purely by the combination of activity and confinement and is absent in thermal equilibrium. I'll explore the consequences of such active matter models for chromosomes, discussing how our model can be generalized to study variations in chromosome positioning across different cell types. This work  represents a preliminary attempt towards a quantitative, first-principles description of the large-scale architecture of the cell nucleus. I'll point to the ideas that cross physics and biology in this model, stressing general physical principles of importance and the need to choose what level of biological detail must be included.

Motile cilia and flagella are slender appendages of eukaryotic cells that perform regular bending waves. This ciliary beat is a result of the collective dynamics of molecular dynein motors distributed along the length of the axoneme, the evolutionary conserved scaffold of cilia and flagella. The beating of cilia propels microswimmers such as unicellular alga and sperm cells suspended in fluid media.  On larger scales, collections of cilia present on epithelial surfaces of multicellular organisms can spontaneously synchronize and thus coordinate their individual oscillatory motions to achieve efficient fluid transport and motility, e.g., mucus clearance in mammalian airways, or directed motion of cells propelled by cilia during phototaxis.

In this pair of talks, we will address a number of key features of cilia dynamics, spanning experiment and theory.

We will characterize the cilia beat as a noisy biological oscillator [1,2]. The instantaneous frequency of this oscillator can deviate from the intrinsic cilia beat frequency in response to a change in hydrodynamic load [3]. In fact, measuring this cilia load response allows to estimate the amount of internal dissipation inside beating cilia. These experiments are complemented by a measurement of the viscous and elastic stresses acting on an isolated cilium beating in a quiescent fluid, providing a direct methodology to characterize the nature and extent of internal dissipation in cilia [4].

The load response of cilia is an indispensable prerequisite in theories of cilia synchronization by mutual hydrodynamic interactions. We will spotlight a physical mechanism of cilia synchronization in the bi-ciliate green alga Chlamydomonas based on mechanical self-stabilization by a rocking motion [1]. We will then address metachronal coordination in cilia carpets, i.e., synchronization in the form of traveling waves, similar to a Mexican wave in a soccer stadium [5]. Our multi-scale simulations based on experimentally measured beat patterns predict multiple stable wave solutions, yet most random initial conditions converge to a single dominant wave mode, corresponding to the dexioplectic wave observed in experiments. Like ciliary beating, collective swimming of cells propelled by cilia also shows emergent features. We will show that the phototaxis efficiency of algal cells increases significantly above a critical cell concentration due to a density-dependent slowing down of the swimming speed of the cells [6].

[1] V. F. Geyer, F. Jülicher, J. Howard, B. M. Friedrich, Cell-body rocking is a dominant mechanism for flagellar synchronization in a swimming alga, PNAS, 110, 18058–18063 (2013).
[2] Ma et al. Active Phase and Amplitude Fluctuations of Flagellar Beating, Phys. Rev. Lett. 113, 048101 (2014).
[3] G. S. Klindt, C. Ruloff, C. Wagner, and B. M. Friedrich, The load response of the flagellar beat, Phys. Rev. Lett. 117, 258101 (2016).
[4] D. Mondal, R. Adhikari, P. Sharma, Internal friction controls active ciliary oscillations near the instability threshold, Science Advances, 6, eabb0503 (2020).
[5] A. Solovev, B. M. Friedrich, Global metachronal synchronization and active noise in cilia carpets, https://arxiv.org/abs/2012.11741
[6] S. K. Choudhary, A. Baskaran and P. Sharma, Reentrant efficiency of phototaxis in Chlamydomonas reinhardtii cells, Biophysical Journal Biophysical Journal 117, 1508–1513 (2019).

Motile cilia and flagella are slender appendages of eukaryotic cells that perform regular bending waves. This ciliary beat is a result of the collective dynamics of molecular dynein motors distributed along the length of the axoneme, the evolutionary conserved scaffold of cilia and flagella. The beating of cilia propels microswimmers such as unicellular alga and sperm cells suspended in fluid media.  On larger scales, collections of cilia present on epithelial surfaces of multicellular organisms can spontaneously synchronize and thus coordinate their individual oscillatory motions to achieve efficient fluid transport and motility, e.g., mucus clearance in mammalian airways, or directed motion of cells propelled by cilia during phototaxis.

In this pair of talks, we will address a number of key features of cilia dynamics, spanning experiment and theory.

We will characterize the cilia beat as a noisy biological oscillator [1,2]. The instantaneous frequency of this oscillator can deviate from the intrinsic cilia beat frequency in response to a change in hydrodynamic load [3]. In fact, measuring this cilia load response allows to estimate the amount of internal dissipation inside beating cilia. These experiments are complemented by a measurement of the viscous and elastic stresses acting on an isolated cilium beating in a quiescent fluid, providing a direct methodology to characterize the nature and extent of internal dissipation in cilia [4].

The load response of cilia is an indispensable prerequisite in theories of cilia synchronization by mutual hydrodynamic interactions. We will spotlight a physical mechanism of cilia synchronization in the bi-ciliate green alga Chlamydomonas based on mechanical self-stabilization by a rocking motion [1]. We will then address metachronal coordination in cilia carpets, i.e., synchronization in the form of traveling waves, similar to a Mexican wave in a soccer stadium [5]. Our multi-scale simulations based on experimentally measured beat patterns predict multiple stable wave solutions, yet most random initial conditions converge to a single dominant wave mode, corresponding to the dexioplectic wave observed in experiments. Like ciliary beating, collective swimming of cells propelled by cilia also shows emergent features. We will show that the phototaxis efficiency of algal cells increases significantly above a critical cell concentration due to a density-dependent slowing down of the swimming speed of the cells [6].

[1] V. F. Geyer, F. Jülicher, J. Howard, B. M. Friedrich, Cell-body rocking is a dominant mechanism for flagellar synchronization in a swimming alga, PNAS, 110, 18058–18063 (2013).
[2] Ma et al. Active Phase and Amplitude Fluctuations of Flagellar Beating, Phys. Rev. Lett. 113, 048101 (2014).
[3] G. S. Klindt, C. Ruloff, C. Wagner, and B. M. Friedrich, The load response of the flagellar beat, Phys. Rev. Lett. 117, 258101 (2016).
[4] D. Mondal, R. Adhikari, P. Sharma, Internal friction controls active ciliary oscillations near the instability threshold, Science Advances, 6, eabb0503 (2020).
[5] A. Solovev, B. M. Friedrich, Global metachronal synchronization and active noise in cilia carpets, https://arxiv.org/abs/2012.11741
[6] S. K. Choudhary, A. Baskaran and P. Sharma, Reentrant efficiency of phototaxis in Chlamydomonas reinhardtii cells, Biophysical Journal Biophysical Journal 117, 1508–1513 (2019).

In these two lectures we will discuss our joint attempts to understand cell behavior in the context of the tissue scale in the developing zebrafish retina. First, we will give insights into the experimental system and how questions of cell and developmental biology can be approached here in a quantitative way that allow for modeling at the cell and tissue scale. We will concentrate on stages of optic cup development and the biology of pseudostratified epithelia and nuclear migration phenomena. In the second talk, we will outline and dissect theoretical approaches to analyzing and modeling these cell behaviors, especially with regard to their complex spatio- temporal environments. By paying special attention to how these complexities may be partitioned to geometric or topological sources we show how such models can inform future experimental studies, thus closing the experiment-theory-experiment loop at the heart of the scientific method.