MS07 - CDEV-03

From data to mechanisms: advancement in modeling in cell and developmental biology (Part 2)

Thursday, July 17 at 3:50pm

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Note: this minisymposia has multiple sessions. The other session is: and Part-1.

Keisha Cook, Anna Nelson (Clemson University), Alessandra Bonfanti (Politecnico di Milano) Giulia Celora (University of Oxford) Kelsey Gasior (University of Notre Dame) Qixuan Wang (University of California, Riverside)

Description:

In many cell and developmental processes, both modeling and data analytic approaches are necessary in order to generate useful modeling predictions to guide the design of further experiments for both validating and improving biological insight. There is an increased understanding that the application of machine learning methods can also be used to enhance common data-driven modeling techniques, including parameter and equation inference, classification, and sensitivity analysis. The speakers in this session will discuss how differential equation models, stochastic models, and methods from machine learning can be combined to address questions related to cell growth, intracellular transport, cell differentiation, cell migration, and tissue development. The speakers will highlight current research progress and challenges associated with combining modeling and inference approaches in cell and developmental biology.

Merlin Pelz

University of Minnesota

"Effect of compartmentalization: synchronization and symmetry-breaking of diffusively coupled cells in 2-D and 3-D"

The Kuramoto model has been used in the last decades to gain insight into the behaviour of coupled discrete oscillators, as it is simple enough to be analyzed and exhibits a breadth of possible behaviours, such as synchronization, oscillation quenching, and chaos. However, the question arises how one can derive precise coupling terms between spatially localized oscillators, e.g., cells, that interact through a time-dependent diffusion field. We focus on a compartmental-reaction diffusion system with nonlinear intracellular kinetics of two species inside each small and well-separated cell with reactive boundary conditions. For the case of one bulk-diffusing species in ℝ² and ℝ³, we derive new memory-dependent integro-ODE systems that characterize how intracellular oscillations in the collection of cells are coupled through the PDE bulk-diffusion field. By using a fast numerical approach relying on the ``sum-of-exponentials'' method to derive a time-marching scheme for this nonlocal system, diffusion induced synchrony (in-phase, anti-phase, mixed-mode etc.) is examined for various spatial arrangements of cells. This theoretical modelling framework, relevant when spatially localized nonlinear oscillators are coupled through a PDE diffusion field, is distinct from the traditional Kuramoto paradigm for studying oscillator synchronization on networks or graphs. It opens up new avenues for characterizing synchronization phenomena associated with various discrete oscillatory systems in the sciences, such as quorum-sensing behaviour. Allowing for two bulk-diffusing species, our systems show that cell group symmetry-breaking can be achieved due to an exceeding cell membrane permeability ratio of the two species while their diffusivities in the bulk are on the same order. This behaviour cannot be obtained with standard two-species reaction-diffusion systems that were mentioned first in Turing's pioneering work on morphogenesis. Our systems expose a simple way through which cell specialization may emerge robustly. (This is joint work with Michael J. Ward.)

Sharon Lubkin

North Carolina State University

"Geometry, pattern, and mechanics of notochords"

Chordocytes, in early zebrafish and other teleost notochords, have been shown to pack in a small number of stereotyped patterns. Mutations or treatments which disrupt the typical patterning are associated with developmental defects, including scoliosis. The dominant WT “staircase” pattern is the only regular pattern displaying transverse eccentricity. Morphometry and pattern analysis have established a length ratio governing which patterns will be observed. Physical models of cell packing in the notochord have established relationships between this geometric ratio, a mechanical tension ratio, the transverse aspect ratio, pattern, pressure, and taper. Since a major function of the early notochord is to act as both a column and a beam, we aim to understand the overall resistance to compression and bending in terms of these mesoscale cell/tissue properties. To frame the relationships between these properties, we have developed a model of the notochord as an elastic closed-cell foam, packed in either the “staircase” or “bamboo” pattern. A pressure study reveals a surprising lack of shape change as internal notochord pressure is varied, and determines the tension ratio between different surfaces in the notochord in terms of the relative stiffnesses and internal pressure. A bending study reveals that deformations of the model notochords are well described by classical beam theory, and determines the flexural rigidity of the model notochords in terms of relative stiffnesses and pressure. We find that the staircase pattern is more than twice as stiff as the bamboo pattern. Moreover, the staircase pattern is more than twice as stiff in lateral bending as in dorsoventral bending. This biomechanical difference may provide a specific developmental advantage to regulating the cell packing pattern in early-stage notochords. Partially funded by Simons Foundation grant 524764.

Anna Nelson

University of New Mexico

"Modeling mechanisms of microtubule growth and nucleation in living neurons"

The stability and polarity of the microtubule cytoskeleton is required for long-range, sustained transport within neuronal cells. In particular, the healthy microtubule cytoskeleton is comprised of tubulin protein and is stable with a particular orientation. However, when injured, these microtubules are dynamic, rearrange their orientation, and the appearance of microtubules is up-regulated. It is unknown what mechanisms are involved in this balance between dynamic rearrangement and sustained function. Using a stochastic mathematical model that incorporates experimental data, we seek to understand how nucleation can impact microtubule growth dynamics in dendrites of fruit fly neurons. In the stochastic model, we assume two mechanisms limit microtubule growth: limited tubulin availability and the dependence of shrinking events on microtubule length. To better understand our stochastic model, we develop a partial differential equation (PDE) model that describes microtubule growth and nucleation dynamics, and we compare analytical results to results from the complex stochastic model. Insights from these models can then be used to understand what mechanisms are used organize into polarized structures in neurons, and how microtubule dynamics, like nucleation, may impact cargo localization post-injury.

Julio Belmonte

North Carolina State University

"Brillouin Microscopy and Physical Modelling Reveal the Role of Dynamic Changes in Cell Material Properties During Gastrulation"

During animal development, the acquisition of three-dimensional morphology is a direct consequence of the dynamic interaction between cellular forces and cell/tissue compliance. While the generation and transmission of cellular forces has been widely explored, less is known about cell material properties, which are often assumed to be uniform and constant during morphogenesis. Using line-scan Brillouin microscopy we found that cells in the Drosophila embryo undergo rapid and spatially varying changes in their material properties along their apical-basal axis during gastrulation. We identify microtubules as potential effectors of cell mechanics in this system, which show progressive enrichment and alignment along the apical-basal axis of central mesodermal cells during furrow formation. We corroborate our experimental findings with a novel agent-based physical model of gastrulation using the Cellular Potts model. Our model highlights for the first time the importance of cell's longitudinal (apical-basal) stiffness in translating actin-driven apical constriction into cell shape changes; shows that only variation in cells' sub-apical compartment stiffness contributes to furrow formation; and predicts that, while stiffer mesoderm correlates with deeper furrows, better outcomes are achieved if cells are initially softer and stiffen over time, as seen in our Brillouin measurements. Our work provides the first spatio-temporal description of the rapidly evolving material properties of cell populations during morphogenesis, highlights the potential of Brillouin microscopy in studying the dynamic changes in cell material properties, and suggests a new role for microtubules during gastrulation.

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Annual Meeting for the Society for Mathematical Biology, 2025.