Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.mce.biophys.msu.ru/archive/doc15825/doc.pdf Дата изменения: Tue Oct 30 16:24:28 2007 Дата индексирования: Mon Oct 1 20:51:07 2012 Кодировка:

.. () , - - . , , . ­ «-». - . THE DYNAMICS OF AGE DISTRIBUTION OF CELLULAR POPULATIONS Minkevich I.G. (Pushchino) A distributed model of continuous microbial culture has been studied that describes the effect of substrate concentration on the population age structure during transients. Oscillatory behavior of these processes has been shown which is not inherent to the corresponding lumped model. Yet the distributed model retains some important features of the lumped model, viz., the time scaling of transients and the existence of saddle point on the plane "cellssubstrate". A phenomenon of culture synchronization at constant form of age distribution has been found. - , [1]. 211


2. ,

, , «» - (). - , . , . - ( , , ). - , , . , «-». . [2] dx (1) = ar (s )x - x dt



ds = b[- ar (s )x + 1 - s dt

]

(2)

: x , , a

s - , r (s ) - b . K ds = S - dt S0 . K S S 0 , << 1 . , , ,
212


.. -- -10, 2002, .211-213

. r (s ) , 0 : s (3) r (s ) = const в 1+ s + s2

. 1. (1)-(2). S1 S2 - , S3 - , L - .

(1)-(2) (. . 1): 1) - , ; 2) . s - , L. , , (2) : ds (4) 0 ar (s )x 1 dt .
213


2. ,

, , , , . ( ), , [3]: n n + = -[W (s, ) + 1] n(t , ) (4) t
n(0, t ) = 2 W (s, )n( , t )d
0

(5) (6) (7) (8) (9) (10)

n( ,0) = G ( ) -



ds = - (s ) n( , t )d + 1 - s dt 0



s(0 ) = W (s, ) = A( - T (s

))

(s ) =

s 1 + s + s

2

: t - , - , n( , t ) - t t, s() - , W (s, ) - , ( - T (s )) - ( = 0 < T (s ) , = 1 T (s ) ). T (s()) - , t A = const . (s ) - . : a) (1) --- (4); b) (5), ; c) 214


.. -- -10, 2002, .211-215

(6), . : ; «-». W (s, ) . :
N () = n( , t )d t
0

-





,

( , t ) = n( , t ) N (t ) - , : ( , t )d 1 . (0, t ) 0

. P( ) = Ae - A( -T )( - T ) . . 2 P( ) (A=50, AT=10) (A=5, AT=1) ( T = 0,2 ). T + 1 A , 1 A . = AT . , = T + 1 A .
T (s ) = T0 +

1 1 T1 + T2 s , T1 = 1 + T0 , T2 = 1 + T0 s

(11)

215


2. ,

. 2. (. ).

. 3. (S) (A)

[3]:

st ( ) = 2 exp[- - A( - T (s ))( - T (s

))]

(12)

, = T (s ) . st ( ) W ( ) ( ). (12) . ( , t ) , (12), , - , [4]. , ( ,0) . (12) (. . 3). : = 0,001 , T0 = 0,2 , = 1, 5 10, = 0 0,005. ( ,0) = G ( ) N (0) , (12) ( ), : ( ,0) = 10 0 < < 0,1 , ( ,0) = 0 > 0,1 ( ). ( ,0) . 3. , . ,
216


.. -- -10, 2002, .211-217

, 0 T. , [3], . («» ) . . 4 N (0) = 0,1 , s(0) = 1000 ; (. ). : = 0. ( - ), , (0, t ) . T (s ) T0 = const . s T (s ) s . , A ( ). , «» - , 1 ( - ). ( = 1 ) s . s , T (s ) . - . , - st ( ) , (. (12)), . , . = 1 ,
217


2. ,

t 1 3,5 ( (0, t ) = const , T () = const , . 4), t , . (0, t ) T ( . 4).

. 4. , . : = 1 . : = 10 .

. 5. .

- - , , . 218


.. -- -10, 2002, .211-219

, T (s ) . (. 5).

. 6. «» ( ,0) . - ( = 1 ), - ( = 10 ). , - . s(0) = 1000, N (0) .

, s (. 1). . {N , s} . , N () s() t t , , , {N , s} . «» N s (s ) {N , s} , , s , N N s (s ) {N (), s ()} tt
219


2. ,

. . 6. 7 {N , s} , , . , . 7, «» - s (0 ) = 1000.

. 7. , «». , ( N 0 ), ( N = 0 ). - . - ( = 1 ), - ( = 10 ). , , . . s (0 ) = 1000, N (0) .

N (0) , . 220


.. -- -10, 2002, .211-221

, . , ( , ), . . 7 , ( N 0 ) (). (7) , . : (s )N 1 . , . 7, . 8. , (- s() N () ), t t , . , s() N () . t t

. 8. ( = 10 ) . - , . - . - ( ).

, , , .
221


2. ,

. 1. .. . 1978, : . 331. 2. Minkevich I.G., Utkina L.I. Biotechnol. Bioeng. 1979. 21(3): p. 357-391. 3. Minkevich, I.G., Abramychev A.Y. Bull. Math. Biol. 1994. 56(5): p. 837-862. 4. Zeuthen, E., ed. Synchrony in Cell Division and Growth. 1964, Interscience Publ. NY.

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