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Design Principles in Systems Molecular Biology Prof:Rui Alves Dept Ciencies Mediques Basiques, 1st Floor, Room 1.08 Website of the Course: Course:

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 levels Nuclear Targeting Sequences Operon Gene 1 Gene 2Gene 3

Outline Design Principles in Network Topology  Overall Feedback  Signal Transduction  Gene Circuits

Regulation by overall feedback X0X0 X1X1 _ + X2X2 X3X3 X4X4 X0X0 X1X1 + X2X2 X3X3 X4X4 ___ 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 X0X0 X1X1 _ X2X2 X3X3 + X4X4 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 X0X0 X1X1 _ X2X2 X3X3 + X4X4 Time [X 3 ] Change in X 4 Fast transient response Stable steady state Fluctuation in X 3

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 alternatives S-system has analytical steady state solution Analytical solutions → General features of the model that are independent of parameter values

A model with overall feedback X0X0 X1X1 _ + X2X2 X3X3 X4X4 Constant Protein using X 3

A model without overall feedback X0X0 X1X1 + X2X2 X3X3 X4X4

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 solution Analytical 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 Comparison 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 constraints External 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 g 10 ’

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 solution Analytical 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 10/28/ AMAM Q ABAB Q ABAMABAM Q 1

Bi/Mono Signal Amplification ratios are different for primary (Q1) or secondary (Q2) signals 10/28/ Primary Signal Secondary Signal Ratio of signal amplification

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.

Graded vs. Switch-like behavior Bacterial signal transduction systems can have graded responses. They can also have switch-like responses [Igoshin et al Mol Microbiol. 61:165]. 10/28/ Signal Response Are there specific topological elements in a TCS Module that allow switch-like behavior?

X3 X1 X2 X4 X5 X6 Alternative topology for TCS modules 10/28/ X7 [Dead end complex] Independent Phosphatase 7 alternative topologies MonofunctionalBifunctional No dead end complex With dead end complex No independent phosphatase Independent phosphatase Independent phosphatase & dead end complex

Signal RR-P Switch-like behavior is possible 10/28/201529

X3 X1 X2 X4 X5 X6 TCS modules that allow bistability 10/28/ X7 [Dead end complex] Independent Phosphatase Topologies allowing for switching behavior Bifunctional Module Independent phosphatase & dead end complex Monofunctional Module With dead end complex

Summary  In TCS we found that:  Bifunctionality vs. Monofunctionality may be selected based on the requirements for cross talk.  Wiring of the circuit (dead end complex and flux channel for the dephosphorylation of the RR, independent of the sensor) constraint dynamic behavior (switch vs. graded).  This does not ensure that switch like behavior will be found but:  Points to systems where it is more likely to be found.  May helps in designing artificial TCS with switch-like (or other) behavior. 10/28/201531

Outline Design Principles in Network Topology  Overall Feedback  Signal Transduction  Gene circuits & Gene expression

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

Quantitative design principles The wiring of the network (topological design principles) constrains the possible range of dynamic responses for the network. This response in principle has evolved to ensure survival under specific conditions (fine tuning). Given the functional requirements for a specific cellular response it should be possible to explain the quantitative aspects of the response Analysis of gene expression changes in heat shock response to test this hypothesis 10/28/201535

Changes in gene expression in S. cerevisiae during response to heat shock Well characterized. Physiology well understood → easy to frame the changes in the physiology of the response. Experimental data to validate the response are available. 10/28/ Oposiciones CSIC, Diciembre 2008

How to test this? 10/28/ – Identify functional criteria that have physiological relevance. 2 – Create mathematical model describing main aspects of the metabolic adaptation during the response. 3 – Decide range of allowable variation for gene expression & do large scale scanning of gene expression. 4 – Map gene expression onto model. 5 – Calculate how different GEP perform according to the functionality criteria.

Performance criteria 10/28/2015 C1- ATP synthesis. C2- Threalose synthesis. C3- NADPH synthesis. C4- Low accumulation of intermediates. C5- Burden of change. C6- Glycerol production. C7- Specific relationship in changes of activity between certain enzymes that are important to create an appropriate metabolic response. C8- Maintenance of F16P levels to keep a high glycolytic flux. 38

Modeling metabolic changes during heat shock 10/28/ Glycogen Trehalose NADPH HXT: Hexose transporters GLK: Glucokinase PFK: Phosphofructokinase TDH: Glyceraldhyde 3P dehydrogenase PYK: Pyruvate kinase TPS: Trehalose phosphate syntase G6PDH: Glucose-6-P dehydrogenase Curto et al Math. Biosci. 130: 25 Voit, Radivoyevitch 2000 Bioinformatics 16: 1023

Glycogen Trehalose Allowable ranges of gene expression 10/28/ SIMULATIONS To explain why expression of particular genes is changed, we scanned the gene expression space and translated that procedure into different gene expression profiles (GEP). Consider a set of possible values for each enzyme. Explore all possible combinations. Total: hypothetical GEPs. GLK, TPS → [ 1, 2.5, 4,..., 14.5, 16, 17.5, 19] HXT → [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] G6PDH → [1, 2, 3, 4, 5, 6, 7, 8] PFK, TDH, PYK → [ 0.25, 0.33, 0.5, 1, 2, 3, 4] HXTGLKPFKTDHPYKTPSG6PDH hip hip hip hip NADPH

Solo determinados perfiles de expresión genética generan respuestas adecuadas HXT: Transportadores de Hexoses GLK: Glucoquinasa PFK: Fosfofructoquinasa TDH: Glyceraldeido 3P desidrogenasa PYK: Piruvato quinase TPS: Trehalosa-fosfato sintetasa G6PDH: Glucosa-6-P desydrogenasa ■ % change-folds pre selección ■ % change-folds pos selección por criterios funcionales Fold change en expresión % Perfiles totales Cumplen todos los criterios: ■ 0.06% (2800/ ) ■ 18 experimentos Vilaprinyo et al BMC Bioinformatics. 7: 184 Vilaprinyo et al Philipines Info. Tech. J. 1: 36; 37 10/28/ Oposiciones CSIC, Diciembre 2008 Vilaprinyo et al. 2008, Sometido; Sorribas et al. 2009, en preparación

Specificity of HS criteria 10/28/ Principal component analysis C1C2C3C4C5C6C7C8 Alcalino   H202H202   Diamida  ... HS Group of criteria is specific, individual criteria are promiscuous.

Summary Identification of a set of constraints that are specific for heat shock response. Identification of the quantitative design of the heat shock GEP. 10/28/201543