Computational and Modeling Strategies for Cell Motility - Computational Modeling of Biological Systems - page 277

D 2 I

Tr. r v /

s;d r v CN Tr. r v / I ;

3

1

X

ij rN j C N i h j i D C i p ;

j D 0

h
1 1 p ;

DC N i rN i C P d

X

1

r d D i p rN i C 1 p h C ƒ; (50)

i D 0

where . ij / is nonnegative definite, ƒ; 1 are nonnegative. The reactive terms are
proposed as follows:

X

1

X
j D 0 N j p

1

2 p

rN j Cr N j p

j 1

2 . ph

s;r

D r N j I C C

hp /

i D 0

2 I ;

CN 1 p hI 1 pp 2 I 3 k p k

j r

i D i r

v p N i Tr. r v / p ;

P r

D 1 r v p N 1 Tr. r v / p ;

r r

2 Tr. r

D 1 pp Wr v C 2 Tr. r v / C 3 k p k v /; (51)

where 1;2;3 are the coefficients for the active terms. By applying the Onsager
reciprocal principle and verifying the long and short time asymptotic behavior,
the constitutive equation can be extended to account for viscoelastic behavior and
chirality.

D D A

1 1

X X

j D 0 N j p

2 p

rN j Cr N j p

j

s;r

Dt s;d

C r N j I

i D 0

1
2 . ph

2 I

C C hp / CN 1 p hI 1 pp 2 I 3 k p k

X

1

2 p

r N j ;

… 1
2 . p

… 2

C hp C pp h / C r N j p C pp

j D 0

j r i D i r v p N i Tr. r v / p … 2 r v p p ;

D
Dt

D D
Dt

h
1 1 r

p r v p N 1 Tr. r v / p … 1 r v p p ;

r r

2 Tr. r

D 1 pp Wr v C 2 Tr. r v / C 3 k p k v /; (52)