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Design Principles in Systems Molecular Biology

Prof:Rui Alvesralves@cmb.udl.es

973702406Dept Ciencies Mediques Basiques,

1st Floor, Room 1.08Website of the Course:http://web.udl.es/usuaris/pg193845/Courses/Bioinformatics_2007/

Course: http://10.100.14.36/Student_Server/

Outline

What are design principles

How to study design principles

Examples

What are design principles?

Recurrent qualitative or quantitative rules that are observed in similar types of systems as a solution to a given functional problem

Exist at different levelsNuclear Targeting Sequences

Operon

Gene 1 Gene 2 Gene 3

Outline

Design Principles in Network Topology Overall Feedback Signal Transduction Gene Circuits

Regulation by overall feedback

X0 X1

_

+

X2 X3

X4

X0 X1

+

X2 X3

X4

___

Overall feedback

Cascade feedback

Why overall feedback

Why is overall feedback so prevalent? Hypothesis:

Random thing

Alternative hypothesis: There are functional advantages to this type of

overall feedback that led to its selection and account for its maintenance

How to test the alternative hypothesis?1 – Identify functional criteria that have physiological relevance

X0 X1

_

X2 X3

+

X4

Appropriate Flux

Flux Responsive to Demand

Low concentrations

Low gains with respect to supply

Low sensitivities to parameter fluctuations

How to test the alternative hypothesis?1 – Identify functional criteria that have physiological relevance

X0 X1

_

X2 X3

+

X4

Time

[X3]

Change in X4

Fast transient response

Stable steady state

Fluctuation in X3

Functionality criteria for effectiveness

Low concentrations Appropriate fluxes Sharp flux regulation by demand Low log gains to supply Low sensitivities to parameter changes Fast transient responses Large margins of stability

How to test the alternative hypothesis?1 – Identify functional criteria that have physiological relevance

2 – Create Mathematical models for the alternativesS-system has analytical steady state solutionAnalytical solutions → General features of the model that

are independent of parameter values

A model with overall feedback

10 13 111 1 0 3 1 1/ g g hdX dt X X X

11 222 1 1 2 2/ h hdX dt X X

X0 X1

_

+

X2 X3

X4

22 33 343 2 2 3 3 4/ h h hdX dt X X X

Constant

Protein using X3

A model without overall feedback

'10 111 1 0 1 1/ ' g hdX dt X X

11 222 1 1 2 2/ h hdX dt X X

X0 X1

+

X2 X3

X4

22 33 343 2 2 3 3 4/ h h hdX dt X X X

How to test the alternative hypothesis?1 – Identify functional criteria that have physiological relevance

2 – Create Mathematical models for the alternatives S-system has analytical steady state solutionAnalytical solutions → General features of the model that

are independent of parameter values

3 – Compare the behavior of the two models with respect to the functional criteria determined in 1

Comparison must be made appropriately

Mathematicaly Controlled Comparison10 13 11

1 1 0 3 1 1/ g g hdX dt X X X

11 222 1 1 2 2/ h hdX dt X X

22 33 343 2 2 3 3 4/ h h hdX dt X X X

111 0 1 1

'101'/ g hdX dt X X

11 222 1 1 2 2/ h hdX dt X X

22 33 343 2 2 3 3 4/ h h hdX dt X X X

Internal Constraints:

All processes that are equal must have the same parameter values

External Constraints:

Parameters that are different are degrees of freedom that the system can use to squeeze out differences (e.g. mutation in catalytic power)

Implementing external constraintsExternal Constraint 1:

Both systems can achieve the same steady state concentrations AND fluxes

Fixes 10’

Both systems can achieve the same Log gains to substrate

Fixes g10’

How to test the alternative hypothesis?1 – Identify functional criteria that have physiological relevance

2 – Create Mathematical models for the alternatives S-system has analytical steady state solutionAnalytical solutions → General features of the model that

are independent of parameter values

3 – Compare the behavior of the two models with respect to the functional criteria determined in 1

Use a Mathematically controlled comparison

Functionality criteria for effectiveness

Low Concentrations → Both Systems = Appropriate Fluxes → Both Systems = Sharp flux regulation by demand → Overall Better Low log gains to supply → Both Systems = Low sensitivities to parameter changes → Overall

Better Fast transient responses → Overall Better Large margins of stability → Overall worst

Complications to the comparisons

More complicated models Results may depend on parameter values

Smaller models How much better or worst?

A solution to both problems

Use Statistical mathematically controlled comparisons

Sample parameters exhaustively and use statistical methods to analyze the results

Functionality criteria for effectiveness

Sharp flux regulation by demand → Overall Better

~5-10% Low sensitivities to parameter changes → Overall

~5-10% Better Fast transient responses → Overall Better

~5-10% Large margins of stability → Overall worst

=<1%Alves & Savageau 2000,a,b; 2001 Bioinformatics; 2000, 2001 Biophysical Journal

Outline

Design Principles in Network Topology Overall Feedback Signal Transduction Gene Circuits

Alternative sensor design in Two Component Systems

S

S*

R*

R

Q1 Q2

Monofunctional Sensor Bifunctional Sensor

S

S*

R*

R

Q1 Q2

Studying physiological differences of alternative designs

31 34 32 33 363 3 1 4 3 2 3 6

...

...

g g h h hX X X X X X '34 32 33 363 3 4 3 2 3 6

...

'

...

g h h hX X X X X

A

Q

A

Q

A

Q

A

Q

Physiological Predictions

Bifunctional design lowers Q2 signal amplification prefered when cross-talk is undesirable

Monofunctional design elevates Q2 signal amplification prefered when cross-talk is desirable.

Predicting Monofunctionality from structure

Alves & Savageau 2003 Mol. Microbiol.

~1000 sequences from genomic data of dozens of bacteria

Bifunctional Sensor

Monofunctional Sensor

Differences in ATP lid

100s predicted structures by modeling

25 monofunctional sensors

A new design principle

04/20/23 27

Existence of a dead end complex and of a flux channel for the dephosphorylation of the RR that is independent of the sensor allow for TCS that have bistable responses.

A new design principle

04/20/23 28

Outline

Design Principles in Network Topology Overall Feedback Signal Transduction Gene Circuits

Dual Modes of gene control

Demand theory of gene control

Wall et al, 2004, Nature Genetics Reviews

• High demand for gene expression→ Positive Regulation

• Low demand for gene expression → Negative mode of regulation

Acknowledgments

Mike Savageau Albert Sorribas Armindo Salvador

PGDBM JNICT FCT Spanish Government Portuguese Government NIH (Mike Savageau) DOD (ONR) (Mike Savageau)