Abstract: Cell movement plays an important role in many biological process, and experimental work shows that physical forces are critical in modulating the biochemistry that controls cell movement. Forces are exerted on the cell through the interaction of a cell with the surface over which it moves through cell-surface attachments. These attachments also allow the cell to sense its surrounding environment and modulate its behavior in response to properties of the environment. For example, experimental results show that cells plated on stiff surfaces spread more than those plated on soft surfaces. The aim of this project is to enhance a previously developed mathematical model and simulation tool with additional components that model more details of the biochemistry of cell movement so that we can understand how the interaction of mechanics and biochemistry affects cell spreading. This work is one step in understanding how a cell’s environment affects movement and other behavior.
BACKGROUND, CONTEXT, AND GOALS: The movement of biological cells playsa vital role in many biological processes, such as embryonic development, wound healing, and the spread of cancer [1]. As the understanding of many biological processes often begins at a biochemical level, research in cell movement to date has primarily focused on relating cell movement with the biochemical interaction of cell components. However, recent experiments have uncovered that physical forces exerted on a moving cell by its surrounding environment can affect intracellular biochemistry [2, 3]. As a result of these experimental results, the need to begin elucidating how forces affect intracellular biochemistry has emerged, and mathematical modeling can play a role in explaining this phenomenon.
The main way through which a cell interacts with its environment is through the formation of attachment sites, called focal adhesions. Focal adhesions are chemical bonds between receptors on the cell membrane and chemicals on the surface over which a cell crawls or spreads (in experiments) or the extracellular matrix through which a cell moves (in a human or animal body). The attachments at focal adhesions affect cell movement in two ways. First, they initiate a biochemical reaction cascade that ultimately leads to local changes in the polymerization rates of actin, a critical component of a cell’s cytoskeleton (a structural component inside the cell akin to our skeleton but on a much smaller level) [4]. Not only does actin give a cell its shape, but by localizing areas where actin polymerization occurs, the cell can move in a particular direction. Second, it is through focal adhesion attachments that the cell can sense the mechanical properties of its environment and through focal adhesion attachments that the environment applies physical forces to the cell [5].
Over the last several years my research has focused on modeling themechanical aspects of cell-surface interactions, and I have written two papers on this subject [6,7]. The preliminary modeling approach, which is based on modifications to equations commonly used to describe deformable objects and accounts for the mechanical interactions that take place between a moving cell and a deformable surface to which it is attached, was set up in Stolarska et al. [6]. More recently, my collaborator and Iextended this preliminary approach by incorporating a model of growth and shrinkage of focal adhesions. We used this model to gain a better understanding of what role the location of focal adhesions plays during cell spreading. (When plated on deformable surfaces, initially round cells spread, and the degree of the spreading depends on the stiffness of the surface.) Using our mathematical model we showed that a spreading cell whose focal adhesions are found at the periphery of the cell-surface contact area responds much more sensitively to changes in surface stiffness than do cells with focal adhesions found in the interior of the cell-surface contact region. A paper that describes this model and the results on the placement of focal adhesions was recently accepted for publication [7].
One important set of experimental results that is directly related to the proposed research project shows that when cells are plated and allowed to spread on surfaces with different stiffnesses, cell spread areas are larger over stiff surfaces than spread areas over soft surfaces [8, 9]. Through some of the modeling work that I have outlined above [7], we show that if biochemical reactions are ignored and only the balance of mechanical forces is considered, spread areas over stiff surfaces are smaller than over soft surfaces.
This discrepancy indicates that in experiments cell spread areas on stiff surfaces are larger because there is an interaction between actin polymerization, the biochemical process which drives cell spreading, and the mechanical interaction between the cell and the surface, which occurs at the site of the focal adhesion. My aim in the proposed project is to incorporate more details describing the biochemistry with my previously developed mathematical model outlined above. By running simulations based on the new model, I hope to determine what mechanical-biochemical interactions are necessary to obtain experimentally observed increases in cell spread area with surface stiffness.
PLAN OF WORK: The preliminary work that will be done to reach the goals of thisproject is to do a broad literature search of experimental research and new mathematical models of cell spreading and cell-surface interaction. From ongoing literature searches, I have found the cell spreading over surfaces is modulated by, at minimum, (1) the location and strength of the chemical bonds that occur at the focal adhesion [10] (2) the influence of the cell-substrate attachment bonds on local actin polymerization [11], and (3) the contraction of bundled actin in the cell interior (these actin bundles give the cell its strength and prevent it from collapsing when physical forces are applied via surface interactions). Some mathematical background for modeling these components exists (e.g. [12] and [13]), and a former UST undergraduate research student developed a simple mathematical model that can be used as a basis for modeling the biochemistry at the focal adhesion. However, the solution methods that solve the governing equations of each of these component models must first be programmed so that they can interact with the code I have written to solve the equations that model the mechanical aspects of cell-surface interactions.
Once the new components are combined with the computer code I have previously developed, the combined code must be tested to determine if our modeling assumptions are correct. In this case, we look to compare the results that arise from the simulations to experimental data. Most importantly, we will look for a quantitative comparison of how cell spread areas depend on surface stiffness [8,9]. Generally, tuning mathematical models so that they compare to experimental data is an iterative process, so it is likely that the mathematical model will have to be adjusted so that it correctly captures observable behavior.
The course release time will be spent combining the computer code that solves the governing equations of the new components with my existing code. I have found that large portions of uninterrupted time are critical for programming and testing code. Once I am confident that the simulations correctly correspond to experimental data, I will spend course release time running final simulations whose results can be used in a manuscript and interpreting the results of these simulations. Time permitting, during the course release I will begin work on a manuscript and at the very least have good momentum to complete the manuscript over the subsequent summer.
PROJECT’S VALUE: In the scientific community, the results of this project will beparticularly valuable to biologists. A model and a simulation tool that incorporates aspects of both mechanical and biochemical interactions between a cell and the surface to which it attaches provides a tool by which experimental hypotheses can be made and can thereby guide the design of experiments. Furthermore, an understanding of how a cell’s environment affects cellular response is critical because it is often easier to modify the environment rather than manipulating a cell itself.
In addition, one of my career research goals is to develop a “computational cell”, i.e. a computational tool based on mathematical models that can be used to model all aspects of cell movement over surfaces. In this computational environment one could modify a biochemical pathway by changing a term in one of the governing equations or change the interaction between a biochemical component and the response of the cell by changing the function that defines the way the two interact. In making these changes to the mathematics, one could predict how these changes affect cell movement (e.g. is the spreading rate, the chemical concentration of a signaling molecule, or the local actin polymerization rate altered?). I recognize that this is a lofty goal that will be difficult to reach in my career. However, this project is one small but significant step in this direction.
EVALUATION AND DISSEMINATION OF PROJECT: By the end of Summer 2018 Iwould like to submit a manuscript describing this project to the journals RoyalSociety Interface or Biophysical Journal. Both of these journals are highlyinterdisciplinary attracting readers from the fields of mathematics, physics, biology, and engineering, which is important because I feel the greatest impact can be made if applied mathematics can be used to inform the area of application.
To further disseminate this work, I plan to submit an abstract for a talk at the 2019 Biophysical Society Annual Meeting. I have presented posters at this meeting for the last six years, and while posters are peer-reviewed, talks at this conference are significantly more competitive but reach a much larger audience. I believe that this project is significant enough that aiming to give a talk is warranted.
APPENDIX 1: Timetable
February 2017-May 2017:
Begin broad literature search on experiments and mathematical models relating to cell spreading and cell-surface interaction.
June 2017-August 2017:
Complete literature search and develop mathematical models describing biochemistry at focal adhesions, actin polymerization rates, actin bundle contraction, and any other mechanisms that are important to cell spreading that are discovered during the literature search.
Begin writing computer code that will solve the governing equations of each newly developed individual component needed in the full biochemistry-mechanics model of cell spreading.
September 2017- January 2018:
Continued programming and testing of newly developed individual model components. By the end of J-term 2018 the goal is to have models and code that can individually simulate the biochemistry at the focal adhesion, actin-dependent spreading rates, and actin bundle contractions.
February 2018-May 2018 (Course release):
Incorporation of each portion of code that solves the governing equations of the biochemistry into previously developed computer code that simulates the mechanical aspects of cell-surface interaction. Testing of this combined code.
Run and analyze simulations to generate data that can be incorporated into a manuscript.
Possibly, begin manuscript that describes model and results.
June 2018 – August 2018:
Finish and submit manuscript for publication based on the work accomplished during the course release period.
October 2018
•Submit abstract to give a talk at the 2019 Biophysical Society Annual Meeting.