Albert Sorribas Rui Alves Ester Vilaprinyó Grup de Bioestadística i Biomatemàtica

Identifying selective pressures that shape the adaptive responses of yeast to stress: design and operating principles in metabolism

Albert SorribasRui Alves Ester Vilaprinyó

Grup de Bioestadística i BiomatemàticaDepartament de Ciències Mèdiques BàsiquesInstitut de Recerca Biomèdica de Lleida (IRBLLEIDA)Universitat de Lleida

web.udl.es/Biomath/Group

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

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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

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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.

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A basic example: Why is feedback inhibition a prevalent regulatory design?

Xn+1 X1 X2 Xn-1 Xn

(-)

(a)

Xn+1 X1 X2 Xn-1 Xn

(-)

(-)

(b)

(c) Xn+1 X1 X2 Xn-1 Xn

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Savageau MA. Optimal design of feedback control by inhibition.J Mol Evol. (1974) 4(2):139-56.

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

►6Abril 2008 CRG

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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

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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 on criteria 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

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Example

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(-)

(a)

X5 X1 X2 X3 X4

(-)

(-)

(b)

ahagg XXXX 111514115411

bb hhbgg XXXXX 121115142115411

Internal equivalence: Same parameters for all those processesthat do not changeFix external equivalence: Same flux, same responsivenessto changes in the source metabolite.Compare system performance: What is left after those equivalences?

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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.

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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)

►11Abril 2008 CRG

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

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

►13Abril 2008 CRG

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

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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.

►15Abril 2008 CRG

Metabolic network

Glycogen Trehalose

NADPH

HIGH ENERGY DEMANDC1

STRUCTURAL INTEGRITY-Avoids aggregation of denatured proteins-Membrane -Acts in synergism with chaperonesC2

REDUCING POWERNew synthesis of sphingolipids in order to change the membrane fluidityC3

Curto, Sorribas, Cascante (1995) Math. Biosci. 130, 25-50Voit, Radivovevitch (2000) Bioinformatics 16: 1023-1037

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Glycogen Trehalose

Methodology

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HXT GLK PFK TDH PYK TPS G6PDH

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hip1 5 1 1 1 5 5 5hip2 3 3 3 3 3 3 3


hip1 5 1 1 1 5 5 5hip2 3 3 3 3 3 3 3

hip3 2 1 1 1 2 7 7

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×7

×2

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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]

HXT

GLK PFK TDH PYKTPS G6PDH

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hip3 2 1 1 1 2 7 7......

...

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NADPH

Implementation of stress responses

Metabolic network

Mathematical model

Power Law form Biochemical System Theory

(Savageau, 1969)

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25 27 32 35 38 62 611 72 71521

83 84 85 812

32 35 38 43 45 49 414

43 45 49

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X X X X

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Each GEP has associated a new steady state→ functional changes → HS index of performance

Reproduce basal conditions (25ºC)

Generalised Mass Action

Gene expression changes

Evaluate HS performance

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Eisen et al. PNAS. 1998 Dec 8;95(25):14863-8. DB1 http://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

Conceptual model

Mathematical model

Reproduce basal conditions 25ºC

Calculate new steady states (37º)

SIMULATION OF GEPs

Select which fulfill the criteria of performance

CASE 1CASE 2………

etc

MICROARRAY (3DB)

Conceptual model

Mathematical model

Reproduce basal conditions 25ºC

Calculate new steady states (37º)

SIMULATION OF GEPs

Select which fulfill the criteria of performance

CASE 1CASE 2………

etc

MICROARRAY (3DB)

Define Heat Shock performance

SIMULATIONS

4.637.360 hypothetical gene expression profiles (GEPs)

http://genome-www.stanford.edu/clustering

http://web.wi.mit.edu/young/environment

http://ww-genome.stanford.edu/yeast_stress

Criteria of performance

C1- Synthesis of ATP C2- Synthesis of trehalose C3- Synthesis of NADPH

“Well-known” and studied by experimentalist

►20Abril 2008 CRG

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

Fold change in gene expression

% o

f to

tal G

EP

s

HXT: Hexose transporters

GLK: Glucokinase

PFK: Phosphofructokinase

TDH: Glyceraldhyde 3P dehydrogenase

PYK: Pyruvate kinase

TPS: Trehalose phosphate syntase

G6PDH: Glucose-6-P dehydrogenase

21


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


Well-studied within a system biology perspective


abs ln mRNA change foldCost cost

50 %

No experimental measures are available, so we have chosen as a threshold the value that includes de 50% of all the cases

Evaluation of physiological requeriments Accumulation 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

Values for Criteria Percentage of GEPs selected using each

criteria

Absolute values Ratio to basal values Individual Accumulated

C1 VATPa > 180.6 3 45.13e

C2 VTREa > 0.03 25 60.95e

C3 VNADPHa > 3.54 2 85.86e 27.83

C4 GLCb < 0.04 1.2 86.40f

G6Pb < 20.22 20 76.04f

F16Pb < 22.86 2.5 51.91f

PEPb < 0.01 1.2 65.44f

ATPb < 6.77 6 89.32f 2.40

C5 Costc < 12.06 12.06 50 0.59

C6 VGlycerola > 0.39 0.22 50 0.25

C7 d < 28.10 0.391 50 0.16

C8 F16Pb > 8.64 0.95 61.93 0.06

►23Abril 2008 CRG

Evaluation of physiological requeriments Adaptation 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.

Values for Criteria Percentage of GEPs selected using each

criteria

Absolute values Ratio to basal values Individual Accumulated

C1 VATPa > 180.6 3 45.13e

C2 VTREa > 0.03 25 60.95e

C3 VNADPHa > 3.54 2 85.86e 27.83

C4 GLCb < 0.04 1.2 86.40f

G6Pb < 20.22 20 76.04f

F16Pb < 22.86 2.5 51.91f

PEPb < 0.01 1.2 65.44f

ATPb < 6.77 6 89.32f 2.40

C5 Costc < 12.06 12.06 50 0.59

C6 VGlycerola > 0.39 0.22 50 0.25

C7 d < 28.10 0.391 50 0.16

C8 F16Pb > 8.64 0.95 61.93 0.06

fold changelnabsCost

Compute the Cost for each pattern

Select those cases that have a Cost below the median

Cost

50%

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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


Well-studied within a system biology perspective

►25Abril 2008 CRG

C6- Glycerol production

Glycerol production helps in producing NADPH from NADH

New synthesis of glycerolipids required

Genes are over-expressed

Glicerol rate

50%Selecting GEPs with the highest glycerol production is synonymous of selecting GEPs with low PYK over-expression

►26Abril 2008 CRG

C7- TPS and PFK

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

/ t r e h a lo s eT P S P F K v

50%

C8- F16P levels should be maintained

Glycogen Trehalose

►27Abril 2008 CRG

Results based on all previous criteria

Values for Criteria Percentage of GEPs selected

using each criteria

Absolute values Ratio to basal

values Individual Accumulated

C1 VATPa > 180.6 3 45.13e

C2 VTREa > 0.03 25 60.95e

C3 VNADPHa > 3.54 2 85.86e 27.83

C4 GLCb < 0.04 1.2 86.40f G6Pb < 20.22 20 76.04f F16Pb < 22.86 2.5 51.91f PEPb < 0.01 1.2 65.44f ATPb < 6.77 6 89.32f 2.40

C5 Costc < 12.06 12.06 50 0.59 C6 VGlycerol

a > 0.39 0.22 50 0.25 C7 d < 28.10 0.391 50 0.16 C8 F16Pb > 8.64 0.95 61.93 0.06

►28Abril 2008 CRG

Selected profiles

HXT: Hexose transporters

GLK: Glucokinase

PFK: Phosphofructokinase

TDH: Glyceraldhyde 3P dehydrogenase

PYK: Piruvate kinase

TPS: Trehalose phosphate syntase

G6PDH: Glucose-6-P dehydrogenase

■ % of the change-folds before any selection ■ % of the change-folds after selecting by ALL criteria

Fold change in gene expression

% o

f to

tal G

EP

s

Fulfill all criteria of HS performance:• SIMULATION: 0.06% of GEPs (4238 ) • All experimental databases

Eisen et al. at 10 min (BD1 10’) Causton et al. at 15’ (BD2 15’) Gasch et al. at 10’ (DB3 10’) Gasch et al. at 15’ (DB3 15’) Gasch et al. at 20’ (DB3 20’)

►29Abril 2008 CRG

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

►30Abril 2008 CRG

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 ►31

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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?



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A coordinated rearrangement of fluxes and metabolites is required for an adaptive response.

Evolution of specific gene expression profiles allow to fulfill these requirements.


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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


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39 72 G RE 3

0 10 20 30 40 50 600

10 00

20 00

30 00

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47 30 un kn ow n

0 10 20 30 40 50 600

10 00

20 00

30 00

40 00

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48 16 H SP 7 8

0 10 20 30 40 50 600

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20 00

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50 74 P RX1

0 10 20 30 40 50 600

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56 69 Y G P 1

ORF that are almost undetectable a t=0 and that reach high values after heat shock

Out[168]/ /TableF orm =

YGL037C PNC1 nicotinamidase chromatin silencing at ribosomal DNA rDNA, chromatin silencing at telomere, nicotinate nucleotide biosynthesis, salvageYNL006W LST8 unknown signal transduction, transportYOR120W GCY1 aldoketo reductase activity salinity responseYER150W SPI1 unknown unknownYMR105C PGM2 phosphoglucomutase activity glucose 1phosphate utilization, glucose 6phosphate utilizationYFL014W HSP12 heat shock protein activity cell adhesion, hyperosmotic response, response to dessication, response to heat, response to oxidative stressYBL075C SSA3 heat shock protein SRPdependent, cotranslational membrane targeting, translocation, protein folding, response to stressYLR438W CAR2 ornithineoxoacid aminotransferase arginine catabolismYPR154W PIN3 unknown unknownYBR169C SSE2 heat shock protein protein foldingYHR104W GRE3 aldehyde reductase activity arabinose metabolism, response to stressYHR087W unknown unknown unknownYDR258C HSP78 ATPdependent peptidase activity, chaperone activity, heat shock protein activity protein folding, mitochondrial genome maintenance, response to stress, mitochondrial translocationYBL064C PRX1 thioredoxin peroxidase activity regulation of redox homeostasisYNL160W YGP1 unknown response to nutrients, response to stressYKL035W UGP1 UTPglucose1phosphate uridylyltransferase activity UDPglucose metabolism, protein amino acid glycosylationYNL274C unknown oxidoreductase activity, acting on the CHOH group of donors, NAD or NADP as acceptor metabolism


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

0 10 20 30 40 50 600

10 00

20 00

30 00

40 00

Time

14 P N C1

Which is the connection of these changes with survival after heat shock?

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


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


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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

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


Albert Sorribas Rui Alves Ester Vilaprinyó Grup de Bioestadística i Biomatemàtica

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