Albert Sorribas Rui Alves Ester Vilaprinyó Grup de Bioestadística i Biomatemàtica

1. Identifying selective pressures that shape the adaptive responses of yeast to stress: design and operating principles in metabolism Albert Sorribas Rui Alves Ester Vilaprinyó Grup de Bioestadística i Biomatemàtica Departament de Ciències Mèdiques Bàsiques Institut de Recerca Biomèdica de Lleida (IRBLLEIDA) Universitat de Lleida web.udl.es/Biomath/Group

2. Summary • Introduction: Design and operating principles in metabolism • Strategies for identifying design and operating principles • The role of mathematical models • Examples • Results: Adaptive responses of yeast to stress • Phisiological contraints that shape the response to heat shock • Common selective pressures in different stress conditions Abril 2008 CRG

3. Introduction • Identifying design and operating principles in metabolism • Design principles: recurring qualitative organizational rules of biological systems with the same function • Operating principles: set of quantitative changes, limited by the qualitative design of the system (design principles), that create an effective adaptive response in a biological system • Examples: • Regulatory gene circuits • Functional constraints in metabolic pathways • Evolution of enzyme molecules • Response to stress conditions Abril 2008 CRG

4. Issues at stake while identifying design and operational principles in metabolism • Biological systems are a result of evolution • Natural selection results in designs that optimize (in some sense…) survival and reproductive success. • Different biological functional effectiveness criteria are important • Metabolic efficiency (maximize fluxes, etc.) • Energetic limitations (minimize energy expenditure) • Cost of gene expression changes (gene expression profiles) • Temporal responsiveness (time scales) • Parameter sensitivity (robustness) • Metabolite concentrations (limited capacity) • Salvador A, Savageau MA. Proc Natl Acad Sci U S A. 2006, 14;103(7):2226-31. • Wall ME et al. J Mol Biol. 2003, 332(4):861-76. • Hlavacek WS, Savageau MA. J Mol Biol. 1995, 248(4):739-55. • Kollmann et al. (2005) Nature 438(7067):504-7. • Vilaprinyo E, Alves R, Sorribas A. (2006) BMC Bioinformatics. 7:184.

5. (-) (b) Xn+1 X1 X2 Xn-1 Xn (-) (-) Xn+1 X1 X2 Xn-1 Xn (c) (-) A basic example: Why is feedback inhibition a prevalent regulatory design? (-) (a) Xn+1 X1 X2 Xn-1 Xn Savageau MA. Optimal design of feedback control by inhibition. J Mol Evol. (1974) 4(2):139-56.

6. Design and operating principles in feedback regulation • Design: Feedback by end-product is the preferred design • Robustness, stability, dynamic response • Operation: Once the feedback is in place, which are the optimal changes as to adapt to some new condition? • Interplay between different designs • System-level response Abril 2008 CRG

7. Strategy for identifying design principles in metabolism • Evaluate design alternatives: Analyze class of systems • Mathematical controlled comparisons • Define criteria for functional effectiveness • Best design that realizes the different criteria for functional effectiveness • Statistical analysis of design performance • Simulate alternative scenarios • Appropriate mathematical models are required • Systematic representation • Semi-quantitative models (lack of precise parameters, incorporate model assumptions..) • Ensure comparability between alternative designs Abril 2008 CRG

8. Investigating design principles in metabolismMathematical controlled comparisons • Define the basic systemic structure and its design alternatives (biological knowledge) • Write an S-system (aggregated node equations in power-law) representation (or equivalent (log)linear/lin-log) for each design • Find the analytical steady-state solution and fix parameter constraints between alternative designs (external and internal equivalences) • Compare equivalent systemic properties of alternative designs (based oncriteria for functional effectiveness) • If the advantage of a given design depends on parameter values, a systematic parameter screening is required. • Use the SC formalism for extending the steady-state conclusions and explore dynamic responses Abril 2008 CRG

9. (-) (a) X5 X1 X2 X3 X4 (-) (b) X5 X1 X2 X3 X4 (-) Example Internal equivalence: Same parameters for all those processes that do not change Fix external equivalence: Same flux, same responsiveness to changes in the source metabolite. Compare system performance: What is left after those equivalences?

10. Some well established results • So far, the issue of design principles has been mainly analyzed by using the power-law formalism and S-system models • Regulatory gene circuits (demand theory) • Savageau MA. Design of molecular control mechanisms and the demand for gene expression. Proc Natl Acad Sci U S A. (1977) 74(12):5647-51. • Savageau MA. Demand theory of gene regulation. I. Quantitative development of the theory. Genetics. (1998) 149(4):1665-76. • Wall ME, Hlavacek WS, Savageau MA. Design principles for regulator gene expression in a repressible gene circuit. J Mol Biol. (2003) 332(4):861-76. • Wall ME, Hlavacek WS, Savageau MA. Design of gene circuits: lessons from bacteria. Nat Rev Genet. 2004 Jan;5(1):34-42. • Signal transduction • Alves R, Savageau MA. Comparative analysis of prototype two-component systems with either bifunctional or monofunctional sensors: differences in molecular structure and physiological function. Mol Microbiol. (2003 ) 48(1):25-51. • Igoshin O, Alves R, Savageau MA. (2007) Hysteretic and graded responses in bacterial two-component signal transduction. Mol Microbiol. 2008 (in press) • Igoshin OA, Brody MS, Price CW, Savageau MA. Distinctive topologies of partner-switching signaling networks correlate with their physiological roles. J Mol Biol. 2007 Jun 22;369(5):1333-52 • Igoshin OA, Price CW, Savageau MA. Signalling network with a bistable hysteretic switch controls developmental activation of the sigma transcription factor in Bacillus subtilis.Mol Microbiol. 2006 Jul;61(1):165-84. Abril 2008 CRG

11. Operating principlesAdaptive responses at a cellular level • Search for common changes that allows adaptive response to new conditions • Gene expression patterns • Changes in enzyme activity • Activation of specific pathways • Identify the physiological constraints that shape those changes • Understand the evolution outcome • Operating principles are constrained by physiological requirements • Specific for a prevalent situation (for instance, heat shock) • Common to different situations (for instance economy in protein synthesis) Abril 2008 CRG

12. Identification of constraints that shape the gene expression response of yeast to stress

13. Motivations and Goals • Environmental stresses (heat shock, osmotic...) trigger gene expression changes in yeast • ADAPTATION:There is a redistribution of fluxes and metabolite concentrations (physiology). • This can be achieved by different strategies. Only one of them have been selected. • Voit & Radivoyevitch (2000) Bioinformatics. 16(11):1023-37. • Seek the constraints that shape the gene expression profile (GEP) of yeast to stress conditions Abril 2008 CRG

14. Methodology • Collect information on the physiological (macroscopic) response of yeast to heat shock • Identify appropriate response in terms of fluxes, metabolite levels, etc. • Which are the involved pathways? • Define performance criteria: physiological requirements Fluxes, metabolites, cost of over-expression, etc. • Build-up a mathematical model of the main pathways involved • Consider kinetic properties, regulatory effects, etc. • We shall use the power-law formalism so that it provides an appropriate framework for modeling and analysis • Perform an exhaustive set of simulations to explore the effect of different levels of enzymes on the resulting fluxes and metabolite levels. • Identify those patterns that are compatible with an appropriate physiological response • Compare the selected patterns with actual gene expression data Voit & Radivoyevitch (2000) Bioinformatics. 16(11):1023-37. Vilaprinyo, Alves, Sorribas (2006) BMC Bioinformatics 7(1):184

15. Main characteristics of heat shock response in yeast • Adaptive response of yeast to heat shock • Physiological requirements • Increase of trehalose synthesis • Stabilization of proteins, general protection of cellular structures • Need for appropriate NADPH levels • Reducing power is mainly needed for an appropriate response • Need for ATP • Stress conditions increase energy demand • Main pathways involved: Glycolysis, Glycerol, Trehalose, Pentoses. • Many genes are overexpressed: chaperones, heat shock proteins,…, and glycolytic enzymes, glucose transporters, etc. Abril 2008 CRG

16. Glycogen Trehalose Metabolic network REDUCING POWER New synthesis of sphingolipids in order to change the membrane fluidity C3 NADPH STRUCTURAL INTEGRITY -Avoids aggregation of denatured proteins -Membrane -Acts in synergism with chaperones C2 HIGH ENERGY DEMAND C1 Curto, Sorribas, Cascante (1995) Math. Biosci. 130, 25-50 Voit, Radivovevitch (2000) Bioinformatics 16: 1023-1037

17. ×5 ×2 ×3 ×3 7 × 3 × 5 × ×7 ×3 ×5 Glycogen Trehalose ×3 ×3 ×2 ×3 ×5 Methodology NADPH 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: 4.637.360 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]

18. Implementation of stress responses Evaluate HS performance Metabolic network Mathematical model Gene expression changes Power Law form Biochemical System Theory (Savageau, 1969) Generalised Mass Action Each GEP has associated a new steady state→ functional changes → HS index of performance Reproduce basal conditions (25ºC) Abril 2008 CRG

19. Define Heat Shock performance • Eisen et al. PNAS. 1998 Dec 8;95(25):14863-8. DB1http://genome-www.stanford.edu/clustering • Causton et al. Mol Biol Cell. 2001 Feb;12(2):323-37 DB2http://web.wi.mit.edu/young/environment • Gasch et al. Mol Biol Cell. 2000 Dec;11(12):4241-57 DB3http://WW-genome.stanford.edu/yeast_stress SIMULATIONS 4.637.360 hypothetical gene expression profiles (GEPs)

20. C1- Synthesis of ATP C2- Synthesis of trehalose C3- Synthesis of NADPH Criteria of performance “Well-known” and studied by experimentalist Abril 2008 CRG

21. % of total GEPs Fold change in gene expression C1-C3 Production of trehalose, ATP, and NADPH • If we only consider the criteria concerning an increase of fluxes selects a wide set of possible GEPs (27.8 %, 1.290.454) • The enzymes involved directly in the synthesis should be over-expressed. No clear conclusion can be reached. • In many cases, flux increase involve large metabolite accumulation, which is an undesirable situation in terms of appropriate response ■% of the change-folds before any selection ■% of the change-folds after selecting by C1-C3 HXT: Hexose transporters GLK: Glucokinase PFK: Phosphofructokinase TDH: Glyceraldhyde 3P dehydrogenase PYK: Pyruvate kinase TPS: Trehalose phosphate syntase G6PDH: Glucose-6-P dehydrogenase

22. C4- Accumulation of intermediates: High fluxes with high metabolite concentrations are considered a sub-optimal adaptation Reactivity Cell solubility Metabolic waste C5- Cost of changing gene expression:GEPs that allow adaptation with minimal changes in gene expression are favoured Adaptation should be economic Minimize protein burden 50 % cost Criteria of performance “Well-known” and studied by experimentalist • C1- Synthesis of ATP • C2- Synthesis of trehalose • C3- Synthesis of NADPH Well-studied within a system biology perspective No experimental measures are available, so we have chosen as a threshold the value that includes de 50% of all the cases

23. Evaluation of physiological requerimentsAccumulation of intermediates (C4) • High fluxes with unnecessary high metabolite concentrations are considered a sub-optimal adaptation • G6P is required for trehalose synthesis • F16P is required for glycerol synthesis • We allow for increase in some metabolites but select those cases that fulfill C1-C3 with the lowest metabolite increment Abril 2008 CRG

24. Evaluation of physiological requerimentsAdaptation should be economic (C5) • GEPs that allow adaptation with minimal changes in gene expression should be favoured, among other things because they minimize protein burden to the cell and avoid an exaggerated cost in changing the gene expression. 50% Cost • Compute the Cost for each pattern • Select those cases that have a Cost below the median

25. C1- Synthesis of ATP C2- Synthesis of trehalose C3- Synthesis of NADPH C4- Accumulation of intermediates C5- Cost of changing gene expression C6- Glycerol production C7- TPS and PFK over-expression C8- F16P levels should be maintained Criteria of performance “Well-known” and studied by experimentalist Well-studied within a system biology perspective Abril 2008 CRG

26. Glycerol production helps in producing NADPH from NADH New synthesis of glycerolipids required Genes are over-expressed C6- Glycerol production 50% Selecting GEPs with the highest glycerol production is synonymous of selecting GEPs with low PYK over-expression Glicerol rate Abril 2008 CRG

27. TPS is directly related with vtrehalose PFK is inversely related with vtrehalose If PFK is over-expressed, then TPS should also be over-expressed, which compromises the cost Sensitivity analysis shows that the system is highly sensible to change PFK F16P is required for glycerol synthesis F16P feed-forward effect to the lower part of the glycolysis PYK velocity is increased in vitro by as much as 20 by F16P and hexose phosphates in their physiological concentration ranges This enzyme modulation facilitates the flow of material and avoids accumulation of intermediates Glycogen Trehalose C7- TPS and PFK 50%  C8- F16P levels should be maintained Abril 2008 CRG

28. Results based on all previous criteria Abril 2008 CRG

29. % of total GEPs Fold change in gene expression Selected profiles ■% of the change-folds before any selection ■% of the change-folds after selecting by ALL criteria HXT: Hexose transporters GLK: Glucokinase PFK: Phosphofructokinase TDH: Glyceraldhyde 3P dehydrogenase PYK: Piruvate kinase TPS: Trehalose phosphate syntase G6PDH: Glucose-6-P dehydrogenase Fulfill all criteria of HS performance: • SIMULATION: 0.06% of GEPs (4238 ) • All experimental databases Abril 2008 CRG

30. Interpretation • To generate an appropriate HS response some enzymes have a restricted range of allowable variation. • High sensitivity towards these enzymes can explain this result • Enzymes (genes) that show no changes may be very important to understand adaptive responses • Fine tuning of fluxes and metabolite levels should be achieved through coordinated changes in several enzyme levels. • The experimental GEPs are situated within the predicted ranges • Our analysis helps identifying the more appropriate GEPs. Also, we can explain why most of the hypothetical GEPs are inappropriate for HS response. • The considered criteria can be seen as constrains for heat shock performance Abril 2008 CRG

31. Dynamic gene expression after heat shock • Obtain precise measurements of gene expression changes • Heat shock from 25ºC to 37ºC • 12 data points to characterize the time profile • 8 replicates (2+3+3) for each data point Abril 2008 CRG

32. Preliminary results and questions • Gene expression profiles • Maximum increases (decreases) are observed after 10-20 min • Short time effects must have an important role (activity changes due to temperature) • This analysis requires dynamic models and a combination of genomic, proteomic, and metabolomic data (not yet available). • Mapping into each pathway • Within the same pathway, up- and down-regulation may occur • Which is the meaning of the unchanged genes? Abril 2008 CRG

33. Protein biosynthesis Heat shock proteins Abril 2008 CRG

34. A coordinated rearrangement of fluxes and metabolites is required for an adaptive response. Evolution of specific gene expression profiles allow to fulfill these requirements.

35. trehalose phosphatases Trehalose is very important in heat shock response. Trehalose phosphatases genes increase their expression after heat shock (although it takes about 10 min. to reach a maximum in expression) Short term effects on activity may play an important role in increasing trehalose Abril 2008 CRG

36. ORF that are almost undetectable a t=0 and that reach high values after heat shock Abril 2008 CRG

37. PNC1 (YGL037C ): Nicotinamidase that converts nicotinamide to nicotinic acid as part of the NAD(+) salvage pathway, required for life span extension by calorie restriction; PNC1 expression responds to all known stimuli that extend replicative life span Which is the connection of these changes with survival after heat shock? Abril 2008 CRG

38. Dynamic changes Questions, problems, and more • Dynamic changes at the gene level should be correlated to enzyme levels • Delays in changing enzyme levels must be considered • Post-transcriptional changes can be very important • Which are the relevant changes short after heat shock? • Changes in enzyme activity due to temperature and other factors (independent from gene expression changes) • Metabolite profiles would be required to reconstruct the adaptive response at the level of enzyme changes • Models are required to interpret and understand the dynamic changes Abril 2008 CRG

39. Conclusions • Adaptive response to stress conditions requires a fine tuning of metabolic processes • Compensatory changes in enzyme activity leads to an appropriate response • Gene expression changes remain to be fully understood • Mathematical models play a central role in solving this puzzle Abril 2008 CRG

40. Relevance of models based in approximated representations for Systems Biology applications • Approximated representations are required for practical reasons. • Systematic representation. Models can be produced automatically from schemes. • Qualitative information can be incorporated into these models. • Models can be easily updated and shared. • The power-law formalism has a whole set of tools and strategies that facilitates the investigation of design and operational principles. • (log)linear and lin-log approximations, at best, can produced results similar to those obtained using a power-law formalism. • The SC formalism can be used to complement the results of the power-law formalism, particularly in the dynamic range. Abril 2008 CRG

41. Research projects in our groupweb.udl.es/Biomath/Group • Mathematical models for Systems Biology • Sorribas A, Hernandez-Bermejo B, Vilaprinyo E, Alves R Cooperativity and saturation in biochemical networks: a saturable formalism using Taylor series approximations. Biotechnol Bioeng. (2007) 97(5):1259-77. • Alves R, Antunes F, Salvador A. Tools for kinetic modeling of biochemical networks. Nat Biotechnol. (2006) Jun;24(6):667-72. • Pathway identification through integration of information and automatic model generation and screening • Alves R, Sorribas A. In silico pathway reconstruction: Iron-sulfur cluster biogenesis in Saccharomyces cerevisiae. BMC Syst Biol. (2007) 1:10. • Alves R, Herrero E, Sorribas A. Predictive reconstruction of the mitochondrial iron-sulfur cluster assembly metabolism. II. Role of glutaredoxin Grx5. Proteins. (2004) 57(3):481-92. • Alves R, Herrero E, Sorribas A. Predictive reconstruction of the mitochondrial iron-sulfur cluster assembly metabolism: I. The role of the protein pair ferredoxin-ferredoxin reductase (Yah1-Arh1). Proteins. (2004) 56(2):354-66. • Design principles in the yeast stress response • Vilaprinyo E, Alves R, Sorribas A. Use of physiological constraints to identify quantitative design principles for gene expression in yeast adaptation to heat shock. BMC Bioinformatics. (2006) 7:184. Abril 2008 CRG

42. Acknowledgements • Benito Hernández-Bermejo URJ Madrid, Spain • Armindo Salvador, U.Coimbra, Portugal • Eberhard O. Voit, Georgia Tech, Atlanta, USA • Michael A. Savageau, UCDavis, USA • José Enrique Perez Ortín, U.Valencia, Spain • Enric Herrero, Gemma Bellí, U.Lleida, Spain • Alex Sánchez, Maria del Carmen Ruiz de Villa, U.Barcelona, Spain • MEC BFU2005-00234/BMC • Ramon y Cajal Fellowship Abril 2008 CRG