Modelling active cell processes in multicellular sheets

Timothy Newman
Professor of Biophysics
SULSA Research Chair of Systems Biology
College of Life Sciences
Presented in the Embryo Physics Course, January 11, 2012


Early stages of metazoan embryogenesis require large-scale topological and morphological transitions, involving hundreds or thousands of cells. A central aim of developmental biology is to understand and quantify the underlying mechanisms driving and regulating these transitions. A particular challenge is to understand the relative roles of genetic regulation and emergence, which, crudely speaking, reflect the biological and physical aspects of the process. In this talk I will describe our efforts to construct an agent-based computer algorithm, the Subcellular Element Model (ScEM), which allows simulation of large three-dimensional multicellular systems, and the implementation of physical and biological mechanisms. In particular, the ScEM naturally accommodates cell shape deformations and biomechanics, upon which can be layered cell biological processes such as cell growth and division. I will focus on recent advances in our group in which the ScEM has been used to model active cell processes. I will show how such processes, at the micron scale, lead to emergent fluid-like properties of embryonic epithelia, with effective tissue viscosities in agreement with experimental data. I will also describe the application of this model to primitive streak formation in the chick embryo, and show how our model was used to test a recent hypothesis that chemotaxis is the underlying driver.




Timothy Newman received his BA in Physics from the University of Oxford in 1988, and his PhD in Theoretical Physics from the University of Manchester in 1991. His doctoral and post-doctoral training focused on the quantitative understanding of non-equilibrium processes in physical systems. In 2000, while at the University of Virginia, Prof Newman began studying biological systems, focusing initially on population dynamics. He joined the physics faculty of Arizona State University in 2002, and around that time his interests shifted more to multicellular, cellular, and intracellular dynamics. In 2008 Prof Newman became Director of the Arizona State University Center for Biological Physics. He accepted the position of Professor of Biophysics and SULSA Research Chair in Systems Biology at the University of Dundee in January 2011, and, on moving to the UK, became the new Editor-in-Chief of the UK biophysics journal, Physical Biology. The main emphasis of his work is understanding and quantifying the effect of fluctuations due to the discreteness of components in complex biological systems. His research utilises both large-scale computer simulations and analysis of stochastic processes. He is currently working on three main problems: multicellular dynamics in embryo development, rare event statistics of metastasis formation, and spatio-temporal fluctuations in intracellular interactions.


9 responses to “Modelling active cell processes in multicellular sheets”

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  1. Dick Gordon says:

    Thanks for a great talk! It’s neat that you confirmed the viscosity I found empirically in:

    Gordon, R., N.S. Goel, M.S. Steinberg & L.L. Wiseman (1972). A rheological mechanism sufficient to explain the kinetics of cell sorting. J. Theor. Biol. 37(1), 43-73.

    Gordon, R., N.S. Goel, M.S. Steinberg & L.L. Wiseman (1975). A rheological mechanism sufficient to explain the kinetics of cell sorting. In: Mathematical Models for Cell Rearrangement. Eds.: G.D. Mostow. New Haven, Yale University Press: 196-230.

    In trying to explain it, I used absolute rate theory for viscosity:

    Glasstone, S., K.J. Laidler & H. Eyring (1941). The Theory of Rate Processes: The Kinetics of Chemical Reactions, Viscosity, Diffusion and Electrochemical Phenomena. New York, McGraw-Hill Book Co.

    Now, except for the titles of some of the references in:

    Manning, M.L., R.A. Foty, M.S. Steinberg & E.-M. Schoetz (2010). Coaction of intercellular adhesion and cortical tension specifies tissue surface tension. Proceedings of the National Academy of Sciences of the United States of America 107(28), 12517-12522.

    viscosity is not considered. Can we have a theory that explains both the differential adhesion hypothesis for embryonic cell sorting and the viscosity of the tissues? The answer may lie in the adhesion component discussed in Manning et al.: “A recent study by Foty and Steinberg (18) experimentally verified a linear relationship between adhesion molecule expression levels and tissue surface tension.“ This paper is:

    Foty, R.A. & M.S. Steinberg (2005). The differential adhesion hypothesis: a direct evaluation. Developmental Biology 278(1), 255-263.

    Consider two cell types with surface densities d1 and d2 of adhesion molecules. To model their viscous interaction when they slide over one another, we would have to take into account a number of possibilities. These molecules could be clumped or randomly distributed. They could be held rigidly in place by the cell cortex below, or float freely in the cell membrane. They could bind to one another passively (van der Waals or ionic forces) or via active chemical reactions in holding cells together.

    It seems to me that a way to unravel these possibilities is empirically, by direct measurement of the viscosities of individual tissues and pairs of tissues. Once we have these numbers, we could delve further into the composition of the interfaces between cells, using freeze fracture electron microscopy and AFM, and perhaps using labelled surface antibodies to the putative adhesion molecules, to get their spatial distributions.

    Let me make a simple prediction. Malcolm Steinberg published a model in which differential adhesion was proportional to sqrt(d1d2), from Eq E1 in Gordon et al. (1975). I need to get a copy of the original:

    Steinberg, M.S. (1964). The problem of adhesive selectivity in cellular interactions. In: Cellular Membranes in Development. Eds.: M. Locke. New York, Academic Press: 321-366.

    Let us assume that each adhesion molecule on cell 1 makes and breaks connections with adhesion molecules on cell 2 whenever there is one nearby. Then the activation energy that needs to be overcome is proportional to min(d1,d2). This goes into the exponential in Eq 2 for the viscosity in Gordon et al. (1975).

    The prediction then is that the viscosity of a single tissue (#1) is monotonic (exponentially) with -d1, and that the viscosity between two unlike tissues is monotonic (exponentially) with -min(d1,d2). If d1=d2, this gives a consistent result.

    The importance of such modelling is that it attempts to bridge the gap between the molecular and embryo scales. Thus the theory and the experiments may be well worth pursuing.

  2. From Steve Levin/Ezekiel Zepp.
    I much enjoyed your excellent lecture. To me, there are astounding parallels between your work on the micro and mine on the macro. For background, I am an orthopedic surgeon (ret.), with a very limited background in physics, and I can hardly be considered a biologist, either, but that doesn’t keep me from venturing into the quicksands of systems biology. I did have the advantage of seeing how the system works, live and up close. I have been working on tensegrity mechanics, primarily as applied to humans, (far to the right on your length scales, slide 8), for at least as long as Ingber has been working on cellular tensegrity, (see my website, ).

    The concept that biologic forms “behave’, not just react, is expressed in the musculoskeletal system as Wolff’s Law (1892), that states that bone stiffens or weakens in relation with the forces applied. Evidently, this is what also happens at the cytoskeleton, just at a different timescale, (independence of scale). This happens in bone, (weeks), muscle, (days), and fascia, (), (Gumberteu, 2007). The illustrations you give show closest packing that lead to structures that are triangulated and resemble Fuller’s geodesics and tensegrities. The ScEM growth you show in slide 13, looks remarkably like the rice virus, accepted as a tensegrity structure. Tensegrities behave nonlinearly and are consistent with the viscoelastic behavior that you describe. Your cell stretch and grow, (slide 19), is exactly what Gerald de Jong,, show as on his dynamic tensegrity modeling. He presented them at the Embryo course and Dick might have them archived. Unfortunately, he has taken them down from the internet, but you can write to him and I am sure he will send them to you, he is always generous in sharing his models. What you demonstrate fits Ingber’s tensegrity model of the cell as well as the biotensegrity model of the organism that I describe. A point of discussion: Could it be that the rheology may not be of liquids, but of ‘soft matter’, colloids, emulsions and foams, and the mechanics is consistent with the mechanics of foams, (Plateau), with the added proviso of ‘behavior’? It is not liquid flow, but mechanical restructuring that occurs in soft matter, (like shaving cream), ‘flow’.

    If you get a chance to read some of the articles on my website, you will see that the same mechanics you see ScEM can be applied to the whole organism, independent of size. This would change the paradigm of musculoskeletal mechanics from the present Newtonian lever/post-and-lintel mechanics, with all its shear, torque and moments, to tensegrity-truss mechanics, devoid of moments, shear, torque. It is a much more energy efficient system, and entirely consistent with your ScEM modeling. If biologic systems operate independent of scale, then studying the macro might be a bit easier than studying the micro, and may give valuable insights as to the mechanisms at every level.

    If I were about fifty years younger, I would gladly take up your post-doc offer ☺.

  3. I have a question to the slide 7 where you discuss active behavior of a cell. Let me suggest the next series:

    1) A ballcock in the toilet
    2) An automatic door
    3) A self-driving car
    4) A living cell

    Which objects above have active behavior and which do not?

  4. Timothy Newman says:

    In reply to Evgenii’s comment:

    Naturally, the answer to this question depends on one’s definition of active behaviour. In my presentation, I was thinking of active behaviour being exhibited by an entity which is performing two functions: integrating information from its environment, and converting stored energy into e.g. mechanical energy in order to respond in a non-trivial way to environmental perturbations. The ballcock is a good example of a feedback unit, but it only has one response. The automatic door is similar. The self-driving car is much closer to what I have in mind, in that it has feedback, along with more sophisticated ways to integrate information and create non-trivial outputs, ditto with the cell.

  5. Timothy Newman says:

    In reply to Steve’s comment:
    Thank you for pointing out the parallels with the tensegrity concept. I actually met Don Ingber at a workshop a few years ago and we have some enthusiastic conversations about using the ScEM to interrogate tensegrity at the cellular scale. We didn’t follow up on the idea, unfortunately, but it is a valuable line of thought. I will take a look at your website – thanks!

  6. There is a nice small video that shows what you mean quite nicely

    The video is from the course Introduction to AI that I have recently attended ( Yet, not only the ballcock and the automatic door fit this scheme but also a rock (I have forgotten to mention it) see for example

    I would agree with you that presumably there are some quantitative differences (but not qualitative).

  7. vincent fleury says:


    sorry I was unable to attend your lecture, which seemed interesting

    I have two questions, after reading the plates :
    1-you write v=grad(phi), does this mean that you assume no interaction whatsoever between cells? Stated otherwise, suppose by gedanken experiment that you switch off the sensing of the chemotactant by all cells except one, would the cell sensing the chemotactant move acroos the others withou moving the others at all? Please forgive this question if I misunderstood what the field phi is

    2-the pattern of movement is not quite realistic, in the true blastula there is a radial movement especially in the posterior area, with a hyperbolic point. Does your model account for it without introducing other sources of cehmotactants? (maybe a growth?)

    Best regards
    V. Fleury

  8. Timothy Newman says:

    Dear Vincent,

    Thank you for your questions.

    The v=grad phi on one of the slides is just meant to motivate the idea that, mathematically, chemotaxis is similar to electrostatics. In the simulations we use a switch-like chemotactic response – if the gradient is larger than a certain amount (calibrated from simple biophysical arguments) then the cell senses it and will attempt to polarise its actin polymerisation in the direction of the gradient. So, the direction of grad phi is what is important, not the magnitude. The biomechanics of cell-cell interactions, including mutual exclusion, are the foundation of the ScEM. The details are provided in the published papers.

    We were not trying to capture other details of the cell movement in the epiblast, such as cells moving in a posterior direction in the posterior region (which I have seen from Kees Weijer’s data). A more detailed analysis would certainly require a careful treatment of the a.p./a.o. boundary, for example.

    Regards, Tim

  9. vf says:

    ok, so in fact the equation is not v=grad(phi) but rather F=grad(phi), that sounds better. I will have a look at the paper.

    I have a High definition movie of these movements at the address

    it is probably similar to Weijer’s, but it seems to me the boundaries are better resolved

    that might interest you (it exists with time interval of 1minute and about 1000×1000 pixesl
    Best regards