PDF Central dogma of molecular biology - MIT OpenCourseWare

10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. K. Dane Wittrup

Lecture 15: Gene Expression and Trafficking Dynamics

This lecture covers: Approach to steady state and receptor trafficking

Central dogma of molecular biology:

DNA ? mRNA ? protein

transcription

translation

Material balance on one specific mRNA

Accumulation = synthesis ? degradation

CmRNA

moles mRNA cell volume

Kr

mol mRNA

(time) (cell volume)

,

transcription

(function

of

gene

dosage,

inducers,

etc.)

Vi

cell volume vessel volume

( ) d CmRNA Vi

dt

= Kr Vi - Cr mRNA Vi

r first order rate constant for mRNA degredation

Vi a function of time (cells grow, divide)

? can't pull out of the derivative

Do the chain rule:

CmRNA

d Vi dt

+ Vi

dCmRNA dt

=

Kr

Vi - rCmRNA

Vi

dCmRNA dt

=

Kr

- rCmRNA

- CmRNA

1 Vi

d Vi dt

simplify: 1 d Vi = Vi dt

(specific growth rate in exponential growth)

dCmRNA dt

=

Kr

- rCmRNA

- CmRNA

dilution by growth term (b/c concentration is on a per-cell volume basis)

Cite as: K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare (), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].

dCmRNA dt

=

Kr

- ( r

+ )CmRNA

at steady-state:

CmRNA, SS

=

Kr ( r + )

transient case, analytical solution (just integrate)

CmRNA

=

Kr ( r + )

1

-

e-

(

+

r

)t

independent of the transcription rate constant Kr

S.S.

CmRNA

1

t

r +

Figure 1. Concentration of CmRNA versus time. At long times steady state is approached.

Similar rate expression for the protein: (again, per-cell volume basis, analogous constants)

dC p dt

= K Cp mRNA - ( p

+ )Cp

function of time, solved for above

( ) dCp

dt

=

Kp

(

Kr r+

)

1- e-(r +)t

- ( p + )Cp

steady-state: d = 0 , t dt

C p, SS

=

( r

Kr K p + )( p

+ )

10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. K. Dane Wittrup

Lecture 15 Page 2 of 4

Cite as: K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare (), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].

C p, SS = K p CmRNA, SS p +

Note: K p , p vary from protein to protein and condition

to condition

Integrate dCp : dt

Cp

=

C p, SS

1 +

( r

+ )e-( p +)t p

- ( p -r

+

)e-(r + )t

Usually, p r

in E. coli ln 2 7 minutes on average. r

for most proteins, ln 2 hours to days. p

also, r

Apply assumptions to get:

( ) Cp

= KpKr r ( p + )

1- e-( p +)t

Delays in synthesis

mRNA ? 1 kb gene Protein ? 400 a.a.

E. coli 10-20

20

time (seconds) Yeast 30-50 20

Mammals 30-50 60-400

10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. K. Dane Wittrup

Lecture 15 Page 3 of 4

Cite as: K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare (), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].

Cp

t

1

Delay is generally small compared to

p +

Figure 2. Concentration of protein versus time.

However, the delay can dramatically destabilize feedback loops.

Cellular compartmentalization

Cp, 1 Cp,2 where Cp, 1 Cp for compartment 1, and Cp, 2 Cp for compartment 2 rate = K C transport p,1

+

kon

koff

prod. rec.

cytoo.ut.

endocytosis cell Figure 3. Diagram of protein-ligand binding on the cell surface.

10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. K. Dane Wittrup

Lecture 15 Page 4 of 4

Cite as: K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare (), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].

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