Abstract
The motivation for this project was to analyse how the biological process of cell mitosis and subsequent cell rounding, has an effect with the patterning of cells on an epithelium. Complete details of the cell rounding process are still unknown. Although both the biological factors and mechanical mechanisms have been researched by many people as a route to modelling this behaviour.
I have discussed the numerous factors involved and the models that have been developed.

0.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
0.2
Project outline . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
0.3
Movies and images of the Drosophila notum epithelium . . . . .
4
0.3.1
Brief description of the movies and images being used . .
4
0.3.2
Analysis of the movies and images . . . . . . . . . . . . .
5
0.4
Possible reasons for the patterning of cells in an epithelium . . .
5
0.4.1
Morphogen gradients . . . . . . . . . . . . . . . . . . . . .
6
0.5
Why is gaining understanding about cell mitosis and the packing of cells important? . . . . . . . . . . . . . . . . . . . . . . . . . .
6
0.6
Cell patterning effects caused by cell division . . . . . . . . . . .
7
0.6.1
Cell elasticity . . . . . . . . . . . . . . . . . . . . . . . . .
7
0.6.2
Cell contractility . . . . . . . . . . . . . . . . . . . . . . .
8
0.6.3
Cell adhesion . . . . . . . . . . . . . . . . . . . . . . . . .
10
0.7
Explanation of the code for the topology of cells in an epithelium provided by Aida Mehonic . . . . . . . . . . . . . . . . . . . . . .
11
0.8
Evaluation of data obtained from the code . . . . . . . . . . . . .
13
0.8.1
Varying the preferred area of a dividing cell in the code .
13
0.9
Conclusion and further work . . . . . . . . . . . . . . . . . . . .
14
0.10 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . .
16
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
0.11 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
2

In this project I will be discussing the phenomena that is cell mitosis with a focus on cell rounding. Cell mitosis consists of four main processes: prophase; metaphase; anaphase; and cell division. During prophase the chromosomes are duplicated, so two copies of each chromosome will exist. The process now moves onto metaphase and anaphase whereby, one copy of each chromosome moves to one side of the cell. This happens to both chromosomes, resulting in one pair of chromosomes being positioned each side of the cell. The final stage is cell division, which separates the cell into two identical cells, each consisting of a pair of chromosomes. The name given to a new cell is a daughter cell.[7] Cell rounding occurs prior to the anaphase, causing the cell to transform from a flat cell into one that is spherical in shape.[8] Cell rounding is an interesting biological and mechanical concept, there are questions asking how this shape change occurs and by what factors it is controlled. There are contributions from proteins such as actin, myosin and moesin[4].
The mechanisms behind cell rounding and in general cell mitosis are still not fully understood and questions remain concerning these events such as: what initiates cell division and when will it occur? A related interest is how cells are distributed along an epithelium and how cell mitosis effects this topological arrangement[2]. When a cell divides, it will have an effect on its neighbouring cells, resulting in an effect on the next set of neighbouring cells. Alternatively, could the pattern of these cells in an epithelium have an effect on when and how a cell will divide? In nature, patterns consisting of a hexagonal array appear frequently; some examples can be seen in the structure of honeycomb, soap froths and the Giant’s Causeway in Northern Ireland[1]. Recent work has been carried out to look at the pattern and composition of cells and to determine if this particular arrangement occurs for a functional reason[13].
This project is a collaboration with Sophie Atkinson. We were provided with images of epithelium on the Drosophila notum and Sophie Atkinson’s task was to analyse them for the occurrence of cell rounding and subsequent cell mitosis.
A program was produced in Matlab that Aida Mehonic supplied, which enabled me to model the topology of cells in an epithelium. Our task was to compare the data found from the movies with data obtained from the code in matlab.
This could give an insight into how biologically relevant the code in matlab was and what improvements could be introduced. This current area of research
3

is of great importance; if the mechanisms behind patterning formation in the epithelium can be understood, we can gain a valuable insight into when and why this patterning can go wrong.
The images and movies were provided by Buzz Baum’s lab and most of the experiments were carried out by Eliana Marinari. There was a wide choice of images for this project from which we have chosen to study the images of the
Drosophila notum epithelium with GFP, used to indicate the membranes of the cells.
The first movie that I viewed was the Ecad GFP, these images are used as the wild type for the Drosophila notum. The GFP is used as a membrane marker, allowing analysis of the images for cell division and cell shape changes to be carried out efficiently.
The movie of the Ecad GFP illustrates the cells in the epithelium rearranging and dividing with time. It is observed that when a cell is approaching the point of division the cell initially rounds up and then divides. Various numbers of cells seem to divide at each point in time and the position of the dividing cells appear to be random. At present, this random pattern of cell mitosis is unexplained. Another phenomenon is the orientation of the axis at the point which the cell divides into two, this also seems to be random.
EcadGFP pnr-GAL4 UAS-p110-myc - this type is a p110 mutant, where p110 has been over expressed to enhance growth and GAL4 is the driver. These images are useful to look at the way cell mitosis is affected when growth is enhanced. They also illustrate that the number of cells dividing at each point in time do in fact increase. Another interesting observation is that of the cells becoming much smaller over time, due to their high number of divisions when compared to the wild type as described earlier.
Cell mitosis is apparent throughout all the movies, therefore creating new daughter cells. I have noticed that as the cells round up, they appear to increase in
4

area, but I have learnt that in fact they do not. The cell volume remains constant and actually moves upward, towards the surface of the epithelium. Therefore, in this project the distortion of the cells is being measured. Another point worth noting is that as the cells divide the cell areas actually decrease with time.
The Ecad GFP wildtype movie was analysed by Sophie Atkinson with ‘ImageJ’ and ‘Packing Analyser’ software. Both facilitate the measurement of areas and perimeters of cells. The task was to obtain data consisting of the preferred area of a cell during three stages of cell division - prior to the cell rounding up, at the point of rounding and when the cell divides into two daughter cells. This data is important because it can be used as a comparison to the output obtained from the program in Matlab which looks at the topology of cells in an epithelium.
Hexagonal patterns arise in a range of areas within nature[1].
An example quoted from the paper ‘ Physical modeling of cell geometric order in an epithelial tissue ’ was “hexagonal packing in the vertebrate lens minimizes light scattering from plasma membranes and increases transparency”[9]. This example alone is evidence of the functional importance of cell packing.
There are biologically functioning reasons for the patterning of cells as exampled by bristle cells (p1 precursors) in a Drosophila wing epithelium which are used as sensors to aid flight navigation. During the early stages of development, these bristle cells are randomly distributed along the epithelium with an irregular neighbour count of each cell. However, after a period of time their arrangement is regulated by changing neighbours and cell division just prior to the formation of hair or bristles[2]. There must be an explanation as to why this happens.
There are a number of hypotheses as to why an irregular pattern of cells evolve into a hexagonal formation. Research has shown that forces exist from both actin and myosin which together can effect cell shape and its movement[5], moesin also makes a contribution to cell rounding, and consequently has an effect on the cell patterning[4,5].
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Another influence on cell packing and tissue development arises from the theory of morphogen gradients. They assist in patterns of gene expression, which subsequently have an effect on growth regulation and involved processes such as cell division. Morphogen gradients serve this process by providing position details to cells in an epithelium[14]. An example of one morphogen found in the wing epithelium of a drosophila, is known as Decapentaplgic (Dpp). In the paper on ‘Quantification of growth asymmetries in developing epithelia’ , reference[14] they quoted that “Findings provide strong evidence that Dpp is involved in the control of both size and shape of the wing disk by controlling the area growth and anisotropies.”[14]. Therefore there are a large number of factors effecting cells, cell division and subsequently, cell patterning in an epithelium. However, the key question for modelling an epithelium pattern is what are the key factors.
Patterns are important and a greater understanding of cell patterning in an epithelium is required, so that it can be recognised why it can sometimes go wrong. This is especially important when looking at how to prevent cell patterning errors and why they occur.
If knowledge can be improved on this subject, it can lead onto a better understanding of cochlea hearing loss. There are hair cells arranged in rows within the cochlea, which detect movement and then convert this movement into an electric current[15]. Packing in the inner ear has a functional importance as can be seen from the quote ref[9] “regular packing of sensory hair cells in the inner ear allows the precise alignment of stereocilia bundles and maximises sensitivity displacement”. Hearing loss often occurs due to the inner and outer hair cells becoming damaged[15]. And the possible benefits of gaining a greater understanding of the ‘regular packing of these sensory hair cells’[9] are the regeneration of hair cells within the inner ear[17].
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An interesting area of study considers how cell division effects cell patterning.
Once a cell divides, its original neighbours must be shared between the two new daughter cells that have been created. An important question to ask is how is this decided and what rules do they follow. Gibson et al. [2] discusses the point that “these topological rules are not based on the physical properties of the cells. However, we expect the redistribution of neighbours after cell division to depend on physical cellular properties”. I will be focussing on the physical cellular properties that have been considered in the paper [2], these are area elasticity, contractility caused by the ring of actin-myosin and adhesion[2]. In this paper, a 2D model has been produced to describe the cell packing in an epithelium. They examine how the vertices are displaced by forces which are present and how the epithelium stabilises as these forces vanish. An energy function is created based on the relationship between force and energy as shown in Equation 1[2].
F i
δE
= −
δR j
(1)
The energy function is then minimised at each of the vertices, which is equivalent to a zero force, and therefore representative of a stable cell patterning in the epithelium. Equation 2 illustrates this energy function and the three physical cellular properties that have been considered[2].
E ( R i
) =
X
α
K
α
( A
α
2
− A
(0)
α
)
2
+
X
<i,j>
Λ ij l ij
+
X
Γ
α
2
L
2
α
α
(2)
The energy function in Equation 2, is made up of three important terms: area elasticity; contractility caused by the ring of actin-myosin; and adhesion.
Cell elasticity is denoted by the term below:
P
α
K
α
2
( A
α
− A
(0)
α
) 2
Cell elasticity takes into account various factors of a cell denoted α , the elasticity coefficient K
α
, the actual area of a cell A
α cell A
(0)
α and the preferred area of a which corresponds to the target area of the cell required to minimise
7

the energy function[2]. The elasticity coefficient K
α originates from Hooke’s
Law theory. Hooke’s Law is used to describe the relationship between the force applied to a spring and its extension. They are proportional to each other and can be set equal to one another with the addition of a spring constant k[3]. This spring constant k measures the stiffness of a spring, establishing how easily it can be stretched or compressed. The elasticity coefficient K
α for a cell in this case has been used to describe the ease at which a cell membrane will expand or contract. The value of k is dependent upon the material of the spring. This implies that the value of K
α
, may differ with different cells or different types of cell.
Cell contractility is denoted by the term below:
P
α
Γ
α
2
L 2
α
This section of the equation considers the cell perimeter L
α and its contractility coefficient Γ
α
. The cell contractility coefficient is related to the ring of
Actin and Myosin that lines the perimeter of a cell[2].
Actin and myosin ring
Rings of both actin and myosin within the cell membrane exist along the cell perimeter[2]. Both actin in the form of actin filaments and myosin contribute to muscle contraction. On a cellular level they have an input into the cell contractility and therefore can cause a rearrangement in the packing of cells[2].
Myosin is a motor protein, making use of the chemical energy provided from a source ATP and transfers this energy into mechanical work[16]. Recent studies have seen another influence upon cortical tension from the ERM protein moesin, which is phosphorylated by Slik[4,5]. It is believed that the phosphorylation of moesin promotes the formation of cross links between the actin filaments inside the cell and the cell membrane, thus contributing to the process of cell rounding[5] as illustrated in Figure 1. This has been confirmed by the results from a
RNAi knockdown of either moesin or Slik, where it has been observed that the cell does not round correctly[5].
Coupled with the defects in cell rounding, reduced levels of moesin also indicated faults in the structure of the mitotic spindle, which consequently lead to errors in division of the chromosomes[4]. If this division is incorrectly performed, it can lead to cancer[4].
8

Figure 1: Phosphorylation of Moesin with Slik - Diagram on the left represents the inactive moesin(pale blue), prior to its phosphorylation with Slik. After phosphorylation the cell rounds and the diagram on the right shows this result.
It can be seen that the carboxyl end attaches to the actin filaments(red) and the amino end attached to the membrane protein(grey). The mitotic spindle(dark blue) is positioned in the centre of the cell with the microtubules(green) taking a more stable position, compared with before. The ? represents the unknown process between the microtubules to the actin filaments.[5]
Spindle and microtubules
In the process of cell division, it is a requirement that the chromosomes are duplicated and ultimately separated into two identical daughter sets. This separation process is controlled by the mitotic spindle, which is formed from microtubules within the cytoskeleton[10]. When the chromosomes are duplicated ‘symmetric attachments are made to each chromosome’[10]. Once the attachments have been checked, the chromosomes are separated into two identical daughter sets by the mitotic spindle and moved to each side of the pole[10]. The orientation of the mitotic spindle has been studied from both an experimental and theoretical perspective[11]. Its position is very important, and if oriented incorrectly, can result in an uneven cell division. This could suggest that the chromosomes have not been divided equally between the two daughter cells[11]. Also, on a much larger scale, if a cell divides unevenly in an epithelium, this could have an effect on the topological patterning of the cells. Theoretically, the environment around a cell such as those of adhesive forces created from neighbouring cells, could have an effect on the orientation of the spindle. These adhesive forces from neighbouring cells could form ‘cortical cues’ along the boundary between the two cells in contact. These ‘cortical cues’ may activate ‘cortical force generators’, which are attached to the microtubules and subsequently cause orientation of the spindle[11], illustrated in Figure 2.
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Figure 2: Cortical forces involved in orienting the mitotic spindle - This illustrates a spherical cell during mitosis. There exists retraction fibres(green) at points of adhesion. The assumption of their model is that cortical force generators(blue) are initiated by the density of these retraction fibres, which subsequently cause a force to act on the mitotic spindle(red) and metaphase plate(cyan). The metaphase plate will be oriented until a stable position is reached.[11]
Experimental evidence has found that the mitotic spindle can be orientated from looking at heLa human cells in vivo, and placing these mitotic cells onto various fibronectin micropatterns[11].
The results showed that a number of mitotic spindle orientations were observed, indicating that the pattern environment around the cell had an effect.
However, there are several limitations with this evidence, firstly it would be useful if this result was extended to other types of cells and secondly focusing on cells in vivo, may result in cells behaving differently in an epithelium. For example the retraction fibres that are illustrated in Figure 2 would be replaced with the adhesion to neighbouring cells[11]. Another unknown parameter is the distribution of these cortical cues, so at present an accurate prediction as to how the mitotic spindle will position itself cannot be made.
This is denoted by the term below:
P
<i,j>
Λ ij l ij
In this section of the equation, two properties of the cell junction are taken
10

into consideration between the two vertices i and j, these are cell adhesion Λ ij and cell length l ij
. Cell adhesion can have a number of contributing factors affecting its value, one example mentioned is the "actin-myosin belt" quoted from
[2].
It can be seen that there are a number of influences which the energy function of cell packing is based upon and this can make the task of studying the dynamics of cell packing extremely complex. This leads on to the discussion of a code that was produced which models the topology of cells in an epithelium.
Aida Mehonic produced and is currently working on the code looking at the topology of cells. Her code is based upon the theory relating to the energy function in Equation 2 and based upon the paper [2].
Figure 3 shows the structural set up of a cell.
Figure 3: The structure of a cell in an epithelium - Top diagram shows the structure of actin, cadherin and myosin within the cell. Lower diagram illustrates the structural set up of cells in an epithelium. Each cell has an individual identity α , vertices i and j and the junction length l ij
.[2]
This structure exists for all cells in the epithelium and continuous boundary conditions have been set, so the edges of the epithelium have no effect[17].
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The system contains Boltzmannian noise and at every time step a randomly chosen cell vertex is moved a distance d , which is set as 1% of the length of the side of the cell, l x in Figure 3, through an angle θ [17]. The new energy function at time t’ is calculated and the change in energy(∆ E ) is found by equation
3[12,17].
∆ E = E
0
− E (3)
The probability of the vertex remaining in this new position, a distance d from its original position is based upon the change in energy. The model is based on the idea that the topology of the epithelium aims to minimise the energy function in order for the cell structure to be at equilibrium. The probabilities of the new position becoming a permanent move is based on equation 4[12,17], with slight modifications carried out by Aida Mehonic. In this paper titled ‘ Mitosis and growth in biological tissue ’[12], a program was produced which modelled tissue structure in two dimensions. The program allowed the process of mitosis to take place, which resulted from the ratio of the cell ( area ) / ( perimeter ) reaching a particular value. This is different to the code that I have been provided with in this project.
P =
(
1 exp
− ∆ E if δE < 0 if δE ≥ 0
(4)
Therefore, if there is a decrease in the energy from time t to t’, the change will be permanent with probability 1. And if the energy increases between time t and t’, the change will be permanent with probability exp
− ∆ E , to allow for errors caused by noise[12,17].
The code also allows for a T1 process, which is known as a neighbour exchange.
If the value of l x falls below a certain value, the neighbour exchange takes place.
For the event to occur, the energy must be minimised, or in other words ∆ E must be less than 0. The probability of a neighbour exchange is based upon
Equation 4[12,17].
Cell division, is also taken into account. However this process does not occur automatically and is set up by the user. The dividing cell is an arbitrary selection and a dividing line is positioned through the centre of the cell at a randomly chosen angle. Following this cell division, the aim of the system is to reach equilibrium once again; as cell division causes the system to move away from a position of equilibrium[17].
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T2 processes also known as cell death results from a cell in the code becoming a point in the epithelium[17].
The cell division process was the main consideration in the code and its effect on the pattern formation of cells in an epithelium. One question was whether the code imitated an accurate process of cell division, that would actually be seen in an epithelium. At present, the code sets a preferred area for all cells at equilibrium in an epithelium. However, for cell division to occur the dividing cell must have a greater preferred area. This evidence is backed up by the results found by Sophie Atkinson[18], which showed that prior to division, the cell will round up to a factor less than double its initial area. This lead to focussing on the preferred area for a dividing cell in the code. In the first instance, it had to be implemented into the code and appropriately set so the preferred area could be varied. Once this was achieved I could analyse the results using packing analyser.
Initially, I began with using a preferred area of the dividing cell equal to the preferred area of all the cells in an epithelium. The code has been simulated with different multiples of the preferred area for a dividing cell. The tables in both figure 4 and 5, display the results for the areas of the cell prior to division, at the point of division and just after division have been recorded. The only differences are the number of time steps between the event of division.
Figure 4: Table shows results obtained from varying the preferred area of the dividing cell in the program provided by Aida Mehonic in matlab. The data illustrates how the areas changed before division, at the point of division and a short time afterwards with 1,000 time steps between each event[17].
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Figure 5: Table shows results obtained from varying the preferred area of the dividing cell in the program provided by Aida Mehonic in matlab. The data illustrates how the areas changed before division, at the point of division and a short time afterwards with 5,000 time steps between each event[17].
The results indicate that the cell area is much greater at the point of division compared with the short period of time after division. Concluding that at some point after the cell rounds in the code and subsequently divides; the area of the two daughter cells will decrease and allow the system to equilibrate. In the movies, this change in the value of distortion was also observed. The results also imply that there is no correlation between modifying the preferred area of a dividing cell and the area it reaches at division. However, this maybe due to the number of time steps that the code ran through. If the data obtained from
1,000 time steps is compared to that of 5,000; it is seen that at the point of division, the cell in the simulation of 5,000 steps obtains a greater area value. It would probably be recommended that the code is simulated for a higher number of time steps. The code is still under construction and currently, it does not have this facility.
I appreciate that cell topology and cell division is complex and there are many factors both physical and biological which effect these processes. Even though this code simplifies the process of equilibrium, there are a number of limitations and much further work can be achieved. The code has many positive points with respect to its function and results. Continuous boundary conditions are applied which means that boundaries do not restrict cellular movement within the epithelium[17]. Also, the energy function which the program is based upon depends on three important factors: line tension; cell contractility; and cell adhesion[2]. The random processes by which a vertex is repositioned and a cell is chosen to divide, could be realistic, it might actually be a completely random process. Progress has been made in this area and can be seen from results taken relating to the daughter cell areas between the point of division and a short time after. The decrease in area between these two time points on the epithelium
14

and this is coherent with what was seen in the images and movies provided.
However, there is scope for further work in this area and the possibility of improving the biological accuracy of the code.
There are a number of improvements that I think could be made to this code, which may help in increasing its biological accuracy. One improvement is setting the program to automatically carry out a cell division and allowing for more than one division to occur at a time. From the images a number of cell divisions seem to occur in bursts. This could be due to cells in an epithelium being effected by more than just their direct neighbours, and once a cell division occurs in one area of the epithelium, it could have a domino effect on cells dividing in other areas of the epithelium. Also, when considering the adhesion between cells, it has been considered uniform along a boundary, however this may not be true and also different cells may have different values of adhesion. This has also been commented upon in reference [2], whereby it was suggested that the direction of growth could be effected by line tension not being uniform along a cell boundary. There is also the question of cell death, at present the code does not take ‘programmed cell death’ [13] into account. Another point of interest could be whether the axis along which division arises has an effect on the other cells in the epithelium, this could be found with image analysis. Another region of image analysis, could be looking at whether the preferred area of a dividing cell is dependent upon time or the number of divisions that has already taken place.
Currently the code is based on a stochastic process, a vertex is randomly chosen and randomly repositioned and this modification is fixed if the final energy function is less than the initial energy function. However, what if this selection process of repositioning a vertex was based upon the size of the cell, the length of the vertices surrounding the cell or the quantities of actin or myosin present[12]. The list of factors are endless but this modification of the cell shape could be based on its stability[2,12] and a number of vertices may move at once or cause the movement of a neighbouring vertex.
15

I would like to thank Buzz Baum and Tom Duke for supervising this project, their guidance and assisting with modifying the code provided by Aida Mehonic.
Additionally, I would like to thank Aida Mehonic for the valuable use of her code for topology of cells on an epithelium and Eliana Marinari for providing images and movies of the Drosophila notum.
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1
2
3
4
5
Phosphorylation of Moesin with Slik . . . . . . . . . . . . . . . .
9
Cortical forces involved in orienting the mitotic spindle . . . . . .
10
The structure of a cell in an epithelium . . . . . . . . . . . . . .
11
Table shows results obtained from varying the preferred area of the dividing cell in the program provided by Aida Mehonic in matlab. The data illustrates how the areas changed before division, at the point of division and a short time afterwards with
1,000 time steps between each event[17]. . . . . . . . . . . . . . .
13
Table shows results obtained from varying the preferred area of the dividing cell in the program provided by Aida Mehonic in matlab. The data illustrates how the areas changed before division, at the point of division and a short time afterwards with
5,000 time steps between each event[17]. . . . . . . . . . . . . . .
14
17

[1] Radhika Nagpal, Ankit Patel and Matthew C. Gibson (2008). Epithelial
Topology. BioEssays 30:260-266, 2008 Wiley Periodicals, Inc.
[2] Reza Farhadifar, Jens-Christian R¨ per, Benoit Aigouy, Suzanne Eaton and
Frank J¨ licher (18 December 2007). Influence of Cell Mechanics, Cell-Cell
Interactions and Proliferation on Epithelial Packing. Current Biology 17,
2095-2104.
[3] P.Smith and R.C.Smith. Mechanics. Second Edition
[4] Patricia Kunda, Andrew E. Pelling, Tao Liu, and Buzz Baum (22 January 2008). Moesin Controls Cortical Rigidity, Cell Rounding, and Spindle
Morphogenesis during Mitosis. Current Biology 18, 91-101.
[5] Jody Rosenblatt (2008), Mitosis: Moesin and the Importance of Being
Round. Current Biology, Vol 18, Issue 7.
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[7] Lodish, Berk, Zipursky, Matsudaira, Baltimore, Darnell. Molecular cell biology, Fourth Edition.
[8] Amy Shaub Maddox and Keith Burridge (20 January 2003). RhoA is required for cortical retraction and rigidity during mitotic cell rounding. The
Journal of Cell Biology, Volume 160, Number 2, 255-265.
[9] Sascha Hilgenfeldt, Sinem Erisken and Richard W. Carthew (22 January
2008). Physical modeling of cell geometric order in an epithelial tissue.
PNAS, Vol. 105, No. 3, 907-911.
[10] Rob Phillips, Jane Kondev, Julie Theriot, Illustrated by Nigel Orme. Physical biology of the cell, Page 100.
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[11] Manuel Th´ e nez-Dalmaroni, Victor Racine, Michel Bornens
& Frank J¨ licher (24 May 2007). Experimental and theoretical study of mitotic spindle orientation. Nature 447, 493-496.
[12] J.C.M Mombach, Rita M. C. de Almeida and J. R. Iglesias (July 1993).
Mitosis and growth in biological tissues. Physical Review E, Vol 48, No. 1.
[13] A. Hoˇ evar and P. Ziherl (July 2009). Degenerate polygonal tilings in simple animal tissues. Physical Review E, vol. 80, Issue 1, id. 011904.
[14] T. Bittig, O. Wartlick, M. Gonz´ lez-Gait´ n, and F. J¨ licher (2009). Quantification of growth asymmetries in developing epithelia, Eur. Phys. J. E
30, 93-99.
[15] Brian C. J. Moore. Cochlear Hearing Loss: Physiological, Psychological and Technical Issues. Pages 33, 266.
[16] Alberts, Bray, Hopkin, Johnson, Lewis, Raff, Roberts, Walter. Essential
Cell Biology Third Edition, Page 597.
[17] Aida Mehonic. Transfer Report: Modelling Tissue Dynamics.
[18] Sophie Atkinson. Image analysis carried out by Sophie Atkinson. Images supplied by Eliana Marinari.
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