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Table 2 Theoretical and measured values of the perimeter scaling factor ξ for small neighbourhood sizes, needed for calculating the effective J value in the CPM

From: The biophysical nature of cells: potential cell behaviours revealed by analytical and computational studies of cell surface mechanics

 

2D

3D

neigh.

neigh.

ξ , estimated

ξ , numer.

% error

neigh.

ξ , estimated

ξ , numer.

% error

number

radius

using Eq. 29

determined

 

radius

using Eq. 33

determined

 

1

1

0.67

1

50.00

1

0.79

1

27.32

2

\(\sqrt {2}\)

1.89

3

59.10

\(\sqrt {2}\)

3.14

5

59.15

3

2

5.33

5

-6.25

\(\sqrt {3}\)

7.07

9

27.32

4

\(\sqrt {5}\)

7.45

11

47.58

2

12.57

11

-12.46

5

\(2\sqrt {2}\)

15.08

15

-0.56

\(\sqrt {5}\)

19.64

23

17.14

6

3

18.00

18

0

\(\sqrt {6}\)

28.27

39

37.93

7

\(\sqrt {10}\)

21.08

26

23.33

\(2\sqrt {2}\)

50.27

47

-6.50

8

\(\sqrt {13}\)

31.25

36

15.21

3

63.62

70

10.03

12

\(2\sqrt {5}\)

59.63

68

14.04

\(\sqrt {13}\)

132.73

134

0.96

20

\(2\sqrt {10}\)

168.66

173

2.58

\(\sqrt {22}\)

380.13

410

7.86

100

\(3\sqrt {29}\)

2811.06

2850

1.39

\(\sqrt {118}\)

1.09·104

11127

1.75

1000

\(\sqrt {3365}\)

130133

130181

0.037

\(3\sqrt {133}\)

1.13·106

1127539

0.20