A stochastic model for stress response in CHO mammalian

cells

Ovidiu LipanPhysics Department

University of Richmond, Virginia

SAMSI

Discrete Models in Systems Biology

December 3-5, 2008

From: Moore-Ede, Sulzman and Fuller (eds.) The Clock That Times Us

Supra-chiasmatic nucleus (SCN):

The master pacemaker in mammals

Experimental design

• Mice were entrained to a 12:12 light-dark cycle for 2 weeks

• Animals were then placed in constant dim white light (<1 Lux) for 42 hr

• Tissues were collected at 4-hr intervals over two circadian cycles (12time-points)

• RNA of one mouse per time point was analyzed on oligonucleotide arrays (Affymetrix U74Av2)

Single profiles of genes showing circadian regulation in both liver and heart

A m a jor qu est ion in b io logy is h ow cel ls cop e

w it h rap id ch an ges in th eir env ironm en t , su ch

as ex p osu re to elevat ed t em p era tu res, h eav y m eta ls,

b ac t er ia l an d v ira l in fect ion s.

I t h as b ecom e c lea r th a t a ll o rgan ism s sh a re a

com m on m olecu la r resp on se th at in c lu d es a d ram at ic

ch an ge in th e p a t t ern of gen e ex p ression an d th e

eleva t ed sy n th esis o f a fam ily o f h eat sh o ck

or st ress- in d u ced p rotein s.

H eat sh o ck p ro tein s en su re su rv iva l u n d er

st r essfu l con d it ion s th a t , i f left u n ch ecked ,

w ou ld lead u lt im a tely to cel l d ea th .R . I . M o r i m o t o , C e l l s i n S t r es s :T r a n s c r i p t i o n a l A c t i v a t i o n o f H ea t S h o c k

G en es . ( 1 9 9 3 ) S c i en c e , 2 5 9 , 1 4 0 9

STRESS

R . I . M o r i m o t o , C e l l s i n S t r es s :T r a n s c r i p t i o n a l A c t i v a t i o n o f H ea t S h o c kG en es . ( 1 9 9 3 ) S c i en c e , 2 5 9 , 1 4 0 9

I n t h e u n st r essed cel l ,

H S F 1 is m a in t a in ed in a

m on om er ic , n on -D N A b in d in g

fo rm . U p on h ea t sh o ck , H S F 1

assem b les in t o a t r im er ,

b in d s t o sp ec i¯ c sequ en ce

elem en t s in h ea t sh o ck

p rom oter . T ran sc r ip t ion a l

a c t iva t ion o f h eat sh o ck gen e

lead es t o in c reased lev els o f

h sp 70 . F in a l ly, H S F d isso c ia t es

fr om th e D N A an d is

ev en tu a l ly con v er t ed t o

n on -b in d in g m on om ers

h t t p : / / w w w .m i c r o s c o p y u . c o m /

Chinese-hamster ovary cells (CHO)

G en era l ap p roach to stu d y a b io logica l sy st em

P l a s m i d c o n s t r u c t i o n : A 5 .3 - k i l o b a se D N A c o n t a i n i n g p r o m o t e r a n d 5 ' -u n t r a n s l a t ed r eg i o n o f t h e m o u s e h s p 7 0 .1 g en e w a s s u b c l o n ed f r o m a l a m b d ap h a g e c l o n e c a r r y i n g a n h s p 7 0 . 1 g en e i d en t i ¯ ed b y g en o m i c l i b r a r y s c r een i n g( S t r a t a g en e ) u s i n g a h u m a n h s p 7 0 .1 c D N A a s a p r o b e . A c D N A c o d i n g f o r t h eG F P w i t h a p o l y A s i g n a l f r o m S V 4 0 l a r g e T a n t i g en g en e w a s en g i n ee r ed t o f u s et o t h e s t a r t c o d o n ( A T G ) o f t h e h s p 7 0 . 1 g en e . T h e c h i m er a g en e w a s i n s e r t edi n t o a p S P 7 2 v ec t o r c o n t a i n i n g a h y g r o m y c i n r es i s t a n c e g en e i n o r d e r t o s e l ec tf o r s t a b l e t r a n s f ec t a n t s .

P r e p a r a t i o n o f t r a n s f e c t a n t s : C H O - K 1 c e l l s ( A T C C , M a n a ssa s , V A )w er e g r o w n i n M E M - a l p h a ( C e l l g r o ) c o n t a i n i n g p en i c i l l i n , s t r ep t o m y c i n a n d a m -p h o t er i c i n ( C e l l g r o ) a n d c o m p l em en t ed w i t h 1 0 % F B S ( G em i n i B i o - P r o d u c t s ) .C e l l s w er e t r a n s f ec t ed b y l i p o f ec t i o n u s i n g L i p o f ec t a m i n e ( I n v i t r o g en ) a s p r ev i -o u s l y d es c r i b ed . A f t e r 1 0 d a y s o f s e l ec t i o n i n h y g r o m y c i n ( 5 0 0 ¹ g / m L ) , s i n g l ec e l l c l o n es w er e d er i v ed b y l i m i t i n g d i l u t i o n . T h e s c r een i n g w a s p er f o r m ed b yep i ° u o r es c en c e ( N i k o n T E 2 0 0 0 E ) a n d c l o n es w i t h a l o w b a s a l ° u o r es c en c e i n -t en s i t y w er e se l ec t ed a n d a m p l i ¯ ed f o r a d d i t i o n a l t es t i n g b y ° o w c y t o m et r y .

The HSP70-GFP construct

www.panomics.com/images/36_3_CELLS_2_V1.jpg

An example of GFP in CHO cells

http://home.ncifcrf.gov/ccr/flowcore/instru_LSR.JPG

Flow cytometry

BD Biosciences LSR II.

T h e d o u b l e e x p o n e n t i a l r e s p o n s e t o h e a t s h o c k s

The stochastic modelfor the heat shock

State

Moments

State

Master equation

A finite set of transitions

Transition probability rates

Generating function

Falling factorial polynomials

Factorial moments

Stirling numbers of the second kind

Boundary condition

State

Subgroup

Factorial cumulants, Young tableaux and Faa di Bruno formula

Concatenation

Time evolution equation for factorial cumulants

State

Signal generators

Transition probability

rates

Solution to the linear stochastic genetic network

, ,

Optimal discovery of a stochastic genetic network

Collaboration with:Robin L. Raffard, Claire J. Tomlin –Aeronautics and

Astronautics, Stanford Univ.Wing H. Wong- Statistics Department, Stanford

Univ.

Notation: X1(t)=k1(t), X2(t)=k2(t), X12(t)=k3(t),…

H is a m x m matrix whose entries are nonlinear functions of

k(t). Here q is a d-dimensional vector, and A and B are m-

dimensional column vectors

Suppose we measure k(t) at n time points: kk

obs ,with k=1…n

Need the gradient of the cost function J.

The gradient depends both on the variation of the parameters of interest , and on the functions k(t)

The goal is to eliminate the

dependence on dk(t).

Adjoint method

The equation for p(t)

Conclusions

1) The Master Equation can be used to incorporate experimental

data into a mathematical model.

2) It is not difficult to write Master Equation. However, it requires a

theoretical development to solve it.

3) Parameters can be estimated using an optimization algorithm

with ordinary differential equations as constraints.

Collaborators:

Wing H. Wong, Stanford University

Kai-Florian Storch, Univ. of Montreal

Charles J. Weitz Harvard University

Sever Achimescu, Mathematical Institute of Romanian Academy

Stephen C. Peiper, Thomas Jefferson Medical College

Jean-Marc Navenot, Thomas Jefferson Medical College

Zixuan Wang, Thomas Jefferson Medical College

Lei Huang, Medical College of Georgia

Robin L. Raffard, Claire J. Tomlin, Stanford University

I would like to thank the organizers of SAMSI workshop

for the invitation.

Expression patterns and phase-histograms

of liver and heart selected sets