(I-355) Computational model to predict the pressure effects of ultrasonic waves on cytoskeletal reorganization in plant cells

An active area of mechanobiology research is investigation of cellular remodeling due to the application of external mechanical forces.  Relationships between external mechanical force and cytoskeletal reorganization have been established in many different cellular systems (1, 2, 3), and recent studies expand our understanding of cell signaling pathways impacted by perturbation of force-transduction elements, such as actin filaments and microtubules (4). Additionally, high intensity ultrasound has been extensively investigated for cellular disruptive and ablative applications, yet lower intensity US is less well understood (5), and there is no consensus on US parameters for cellular applications (6).

In the absence of external forces, plant cytoskeletal structures develop improperly and responses to environmental stressors are altered (7), a phenomenon comparable to muscle atrophy experienced by astronauts in micro-gravity. Plants require externally applied forces including Earth’s gravity and random mechanical fluctuations due to wind. Accurate characterization and control of the pressure/force landscape will provide a tunable system in which a variety of different plant bioreactors can be designed to compensate for the micro-gravity experienced in space. 

We have developed a computational model to explore the effect of the pressure produced by ultrasonic waves on cytoskeletal reorganization in plant cells.  Our model builds on previous investigation of sound on cell growth (5,6) and uses the root-mean-square (RMS) pressure produced by standing waves established in cell culture plates due to the US source oriented above the plate, and acoustically reflective material below the plate.

Modeling of RMS pressure produced by the MHz standing wave patterns was carried out using finite element analysis.  Simulations were carried out using Python.  The model assumes a point sound source located above the geometric center of the array. The model assumes standard 4x3 12-well plate with 35 mm well diameters and 20 mm well depths (Figs 1 and 2).

In our model, the RMS pressure depends on the number and dimensions of the well established in the wells of the plate.  The solutions to the wave equation in this geometry are Bessel functions of the first kind, which can be directly related to the RMS pressure by the acoustic impedance and the reflection coefficient to the amplitude of the standing wave within each individual well.

            Our next steps are to experimentally characterize the RMS pressure in the 12-well plate, and other common cell culture configurations, under the assumptions of our model.  We will use a thin film pressure sensor to carry out direct measurements within each well for direct comparison with the pattern predicted by the model.  The sensor is a flat, circular force transducer whose electrical resistance is inversely proportional to pressure.

Our model predicts that there should be a strong dependence on the maximum magnitude of the RMS pressure on frequency, array dimension, and acoustic impedance.  We can exert a considerable amount of theoretical control over the pressure by varying the frequency, and increasing or decreasing the number of wells in the overall array.  We observe in our model that overall RMS pressures are proportional to the total number of wells in the array, as expected, due to the constructive interference that results from the sound waves scattering off the embedded wells.  We assume that the sound intensity of the source is constant everywhere.

We present a three-dimensional rendering of the pressure landscape across the 12-well plate, and an accompanying two-dimensional contour graph (Figures 3a and 3b).  The RMS pressure pattern is consistent with what would be expected by solving the wave equation in a cylinder. 

Once the model is adjusted to account for any experimental deviations that may arise, we will proceed with culturing our first cellular system and imaging of the cytoskeletal development in our low intensity ultrasound chamber. As indicated above, our model can be applied to cell culture plates and chambered slides with a variety of layouts. Further work will include using data from the validated model to inform the design and fabrication of cell bioreactors for a variety of growth applications including facilitating plant growth in fluctuating or micro-gravity conditions.

1. Walker, M., Rizzuto, P., Godin, M., Lautenschläger, F., & Franze, K. (2020). Structural and mechanical remodeling of the cytoskeleton maintains tensional homeostasis in 3D microtissues under acute dynamic stretch. Scientific Reports, 10, 7696. https://doi.org/10.1038/s41598-020-64725-7.

2. Lim, S. M., Trzeciakowski, J. P., Sreenivasappa, H., Dangott, L. J., & Trache, A. (2012). RhoA-induced cytoskeletal tension controls adaptive cellular remodeling to mechanical signaling. Integrative Biology (Cambridge), 4(6), 615-627. doi: 10.1039/c2ib20008b. PMID: 22546924.

3. Szarama, K. B., Gavara, N., Petralia, R. S., Kelley, M. W., & Chadwick, R. S. (2012). Cytoskeletal changes in actin and microtubules underlie the developing surface mechanical properties of sensory and supporting cells in the mouse cochlea. Development, 139(12), 2187-2197. doi: 10.1242/dev.073734.

4. Secomski W, Bilmin K, Kujawska T, Nowicki A, Grieb P, Lewin PA. In vitro ultrasound experiments: Standing wave and multiple reflections influence on the outcome. Ultrasonics. 2017;77:203-213. ISSN 0041-624X. https://doi.org/10.1016/j.ultras.2017.02.008.

5. Mizrahi, N., Zhou, E. H., Lenormand, G., Krishnan, R., Weihs, D., Butler, J. P., Weitz, D. A., Fredberg, J. J., & Kimmel, E. (2012). Low intensity ultrasound perturbs cytoskeleton dynamics. Soft Matter, 8(8), 2438-2443. doi: 10.1039/C2SM07246G.

6. Gupta D, Savva J, Li X, Chandler JH, Shelton RM, Scheven BA, Mulvana H, Valdastri P, Lucas M, Walmsley AD. Traditional Multiwell Plates and Petri Dishes Limit the Evaluation of the Effects of Ultrasound on Cells In Vitro. Ultrasound Med Biol. 2022 Sep;48(9):1745-1761. doi: 10.1016/j.ultrasmedbio.2022.05.001. Epub 2022 Jun 24. PMID: 35760602.

7 Hamant, O., Haswell, E.S. Life behind the wall: sensing mechanical cues in plants. BMC Biol 15, 59 (2017). https://doi.org/10.1186/s12915-017-0403-5