Engineering Tuneable Gene Circuits in Yeast

CONTENTS

List of Figures

List of Tables

Abbreviations

Abstract

Declaration of Authorship

Copyright

Acknowledgements

Preface

1 Introduction
1.1 Aims and Objectives
1.2 The Yeast Saccharomyces cerevisiae
1.2.1 Yeast Mating
1.2.2 Pheromone Receptor-G-protein Coupling
1.2.3 Pheromone-Induced G-protein Activation
1.2.4 The MAP Kinase Cascade
1.2.4.1 Ste11, Ste7 and Fus
1.2.4.2 Ste12 and The Pheromone Response Element
1.3 Switching Off The Pheromone Response
1.4 Modelling The Mating Pathway
1.4.1 Chen et al (2000): Kinetic Analysis of Budding Yeast Cell Cycle Model
1.4.2 Yi et al G-Protein Model
1.4.3 Hao et al RGS Protein Pheromone Desensitization Model
1.4.4 The Kofahl and Klipp Yeast Pheromone Pathway Model
1.4.5 Modelling tools
1.4.5.1 Copasi
1.4.5.2 XPPAUT
1.4.5.3 Cytoscape
1.4.5.4 Mathematical Programming Languages
1.4.5.5 Scripting Languages
1.4.5.6 SBML
1.4.6 Metabolic Control Analysis
1.4.7 Parameter Estimation
1.4.8 Signal to Noise Ratio
1.5 Synthetic Biology
1.5.1 Transcription Cascades
1.5.2 Synthetic Oscillators
1.5.3 Synthetic Switches
1.5.4 Riboswitches
1.5.5 Application of Synthetic Biology
1.5.6 Project Overview

2 Materials and Methods
2.1 Plasmids
2.2 Primers
2.3 Yeast & Bacterial Strains
2.4 Yeast Growth Conditions
2.5 Bacterial Growth Conditions
2.6 Transformation of competent E. coli TOP10 cells
2.7 MINIPrep Plasmid Purification
2.8 Manual Miniprep Plasmid Purification Protocol
2.8.1 Reagents
2.8.1.1 25% sucrose
2.8.1.2 Lysozyme
2.8.1.3 Triton Lytic Mix
2.9 Plasmid DNA Restriction digest
2.9.1 Analytical Plasmid DNA Digest
2.9.2 Preparative Digest
2.10 Cranenburgh Ligation Method
2.11 Primer Design
2.12 PCR
2.13 Colony PCR Protocol
2.14 Genomic DNA Extraction
2.14.1 Extraction Buffer
2.15 Site Directed Mutagenesis Protocol
2.15.1 Site Directed Mutagenesis PCR Reaction Program
2.16 Phosphorylation and Annealing of Synthetic Oligonucleotides
2.17 Agarose Gel Electrophoresis
2.17.1 TAE buffer - 5 Litre, 10x stock
2.17.2 Preparation of DNA loading dye
2.18 Yeast Transformation
2.18.1 Preparation of Solutions and Growth Media for Yeast Transformation
2.18.1.1 Preparation of 10x LiAc and 10X TE solution for yeast transformation
2.18.1.2 Preparation of 20ml PEG/LiAc/TE solution
2.18.1.3 Preparation of YP agar
2.18.2 Yeast transformation protocol
2.19 Yeast Protein Extraction
2.19.1 Lysis buffer
2.19.2 SDS Sample buffer
2.19.3 Preparation of SDS PAGE Protein Gels
2.20 Western blotting
2.20.1 Polyacrylamide gel electrophoresis protocol
2.20.2 Western Blot Transfer protocol
2.20.3 Antibody binding
2.20.4 Western Blot Imaging
2.20.5 Alkaline Phosphatase Protocol
2.20.6 Quantification of Western Blot Images
2.21 DNA Sequence Alignment
2.22 DNA Primer Design
2.23 Pheromone Induction of Yeast Cells for Luminescence Assay
2.24 Optical Density Measurements
2.25 Cellometer Cell Measurements
2.26 Yeast Growth Rate Measurements
2.27 Yeast in situ Luciferase Assay
2.28 Real-time Quantitative PCR (RT-qPCR)
2.28.1 RT-qPCR Primer Design
2.28.2 mRNA extraction and purification
2.28.3 Turbo DNase protocol
2.28.4 Reverse Transcriptase protocol
2.28.5 RT-qPCR protocol
2.29 Mathematical Modelling
2.29.1 Metabolic Control Analysis
2.29.2 Sensitivity Analysis
2.29.3 Metabolic Control Analysis
2.29.4 Signal to Noise Ratio
2.29.5 Parameter Estimation
2.30 Dissertation

3 Results - Circuit Construction
3.1 Introduction
3.1.1 The Iron Responsive Element-Binding Protein
3.1.2 The LexA DNA Binding Protein
3.1.3 Yeast Promoters
3.2 Circuit Overview
3.2.1 Design overview
3.2.2 Component Interactions
3.2.3 Overview of Luciferase Gene Expression Tuning
3.3 Construction of the Reporter Plasmid
3.3.1 The Luciferase Reporter Gene
3.4 Insertion of the Iron Response Element
3.5 Construction of the Repressor Plasmid
3.5.1 Cloning the Iron Response Protein Gene
3.5.1.1 TRP1 promoter strategy
3.5.1.2 DCD1 promoter strategy
3.5.1.3 TEF1 promoter strategy
3.5.2 Insertion of LexA Operator Control Sequences
3.5.3 Cloning the IRP PEST Degradation Tag
3.6 Construction of the De-Repressor Plasmid
3.7 Conclusion

4 Results - Circuit Characterization
4.1 Introduction
4.2 Growth Rate Investigation
4.3 Luminescence Measurement
4.3.1 Luciferase Signal to Noise Ratio
4.4 Protein Quantification
4.5 mRNA Quantification
4.5.1 qPCR Housekeeping Gene Selection
4.5.2 Primer Validation
4.5.3 Sample Preparation
4.5.4 pDCD1 Circuit qPCR Analysis
4.5.5 pTEF1 Circuit qPCR Analysis
4.5.6 pDCD1-PEST Circuit qPCR Analysis
4.5.7 pTEF1 Circuit qPCR Analysis
4.5.8 qPCR Analysis Summary
4.6 Conclusion

5 Modelling
5.1 Introduction
5.2 Modelling Eukaryotic Signal Cascades
5.2.1 A Revised Mating Pathway Model
5.2.1.1 Simulation Results
5.3 Modelling the Gene Circuit
5.4 Model Parameterisation
5.4.1 Further Parameterisation and the Final Model
5.5 Stochastic Simulation of the Gene Circuit
5.6 Parameter Estimation

6 Discussion
6.1 Introduction
6.2 Design and Development
6.3 Characterisation
6.4 Noise
6.5 Modelling
6.6 Summary and Further Work
6.7 Conclusion

A Appendix
A.1 Sequences
A.1.1 Iron Response Element (IRE) Nucleotide Sequence
A.1.2 P FUS1 -IRE-Luciferase Nucleotide Sequence
A.1.3 P FUS1 -LexA Nucleotide Sequence
A.1.4 Cln2 Protein Sequence
A.1.5 PEST region nucleotide sequence
A.1.6 Iron Response Protein (IRP) Nucleotide Sequence
A.1.7 IRP PEST Nucleotide Sequence
A.1.8 IRP PEST protein sequence
A.1.9 LexA Operator, DCD1 promoter, and IRP Nucleotide Sequence
A.1.10 LexA Operator, TEF1 promoter, and IRP Nucleotide Sequence

B Appendix
B.1 Python script for processing Copasi stochastic data

LIST OF FIGURES

1.1 Diagram of the yeast mating process

1.2 Diagram of yeast Ste2 GPCR

1.3 Diagrammatic representation of the process of G-protein activation

1.4 Diagrammatic representation of the yeast pheromone response pathway

1.5 Schematic overview of yeast MAP kinase modules that share Ste

1.6 Hypothesis-driven research in systems biology

1.7 Pathway regulation by RGS and Gβγ proteins

1.8 Spatial diagram of the pheromone pathway in yeast

1.9 Diagrammatic representation of the Kofahl and Klipp model reactions

1.10 Diagrammatic representation of an oscillating gene circuit

1.11 Network diagram of the dual-feedback oscillator

1.12 Tsai (2008) negative feedback models

1.13 Gardner et al toggle switch design

1.14 Diagrammatic representation of the Becskei et al positive feedback genetic switch circuit

1.15 Ajo-Franklin (2007) circuit diagram

1.16 Diagrammatic representation of riboswitch mechanism

1.17 Gene circuit schematic diagram

3.1 Iron Response Element secondary structure

3.2 Crystal structure of the iron response protein

3.3 Unrefined crystal structure of the LexA-DNA complex

3.4 Diagrammatic representation of the strategy for the construction of the gene circuit

3.5 Firefly luciferase crystal structure

3.6 Map of the reporter plasmid

3.7 Nucleotide sequence of the Iron Response Element

3.8 Schematic diagram of the IRE position in the reporter plasmid

3.9 Restriction enzyme digest of the reporter plasmid to confirm insertion of the IRE

3.10 Map of the pJM6 hIRP plasmid

3.11 Map of the pTRPex plasmid

3.12 Map of the LexAop-pDCD1-IRP repressor plasmid

3.13 Colony PCR of P DCD1 -IRP plasmid construct

3.14 Map of the LexAop-pTEF1-IRP repressor plasmid

3.15 The LexA operator sequence

3.16 PCR amplification of the PEST degron tag from plasmid pSV

3.17 Colony PCR of the repressor plasmids containing the DCD1 and TEF1 promoters, following ligation with the PEST degradation tag

3.18 Map of the repressor plasmid P DCD1 -PEST

3.19 Map of the repressor plasmid P TEF1 -PEST

3.20 Map of the de-repressor plasmid

3.21 LexA PCR product amplified from E. coli

3.22 Ligation of LexA into the pRS313 plasmid

4.1 Growth rate of sst2 Δ and pTC5 strains of S. cerevisiae, with and without the gene circuit

4.2 luciferase expression for the P DCD1 and P DCD1 -PEST circuits

4.3 Baseline luciferase expression for the P DCD1 and P DCD1 -PEST circuits

4.4 Fold change in luciferase output from the P DCD1 and P DCD1 -PEST circuits

4.5 Luciferase expression for the P TEF1 and P TEF1 -PEST circuits

4.6 Baseline luciferase expression for the P TEF1 and P TEF1 -PEST circuits

4.7 Fold change in luciferase expression from the P TEF1 and P TEF1 -PEST circuits

4.8 Maximum luminescence fold change for each circuit

4.9 Schematic of the control luminescence experiment without de-repression

4.10 Fold change in luciferase output from the P DCD1 and P DCD1 -PEST circuits minus the de-repressor plasmid

4.11 Fold change in luciferase output from the P TEF1 and P TEF1 -PEST circuits minus the de-repressor plasmid

4.12 Signal to Noise Ratio (SNR) for the P DCD1 and P DCD1 -PEST circuits

4.13 Signal to Noise Ratio (SNR) for the P TEF1 and P TEF1 -PEST circuits

4.14 Signal to Noise Ratio (SNR) plotted as a function of luminescence for each of the circuits and the control

4.15 Signal to Noise Ratio (SNR) for the P DCD1 and P DCD1 -PEST circuits

4.16 Signal to Noise Ratio (SNR) for the P TEF1 and P TEF1 -PEST circuits

4.17 Representative western blots of the P DCD1 and P TEF1 gene circuits with and without pheromone-induction

4.18 P DCD1 and P TEF1 constitutive expression of luciferase

4.19 Western blot analysis of IRP expression for the P TEF1 circuit

4.20 Representative IRP western blot of the P TEF1 and P TEF1 -PEST circuits

4.21 Western blot analysis of the short half-life IRP PEST expression for the P TEF1 -PEST circuit

4.22 Percentage IRP expression from the P TEF1 and P TEF1 -PEST circuits, analysed by western blot

4.23 Representative western blot of LexA protein expression from the P DCD1 circuit

4.24 Analysis of LexA protein expression from the gene circuits by western blot

4.25 Base-line corrected LexA protein expression, comparing induced with non-induced cells

4.26 Micro-array gene expression fluctuation for the RT-qPCR housekeeping genes during the pheromone response

4.27 Representative RT-qPCR cycle primer validation results

4.28 Representative RT-qPCR cycle primer cDNA validation results

4.29 Graph of the mRNA expression data for the P DCD1 circuit

4.30 Graph of the mRNA expression data for the P TEF1 circuit

4.31 Graph of the mRNA expression data for the P DCD1 -PEST circuit

4.32 Graph of the mRNA expression data for the P TEF1 -PEST circuit, obtained by RT-qPCR

5.1 MAP kinase cascade outputs plotted with varying initial concentration of complexD

5.2 Flux through reaction v34 in minimal model

5.3 Diagrammatic representation of the revised MAPK model

5.4 Time course simulation of the revised MAPK model

5.5 Accumulation of the phosphorylated forms of the MAP kinases and active Ste12 in the revised MAPK model in response to varying levels of input

5.6 Schematic diagram of the gene circuit model

5.7 Concentration control coefficients for the gene circuit model

5.8 Transcriptional and translational bursting behaviour of the P DCD1 circuit

5.9 Stochastic simulation of the P DCD1 model

5.10 Stochastic simulation of the P TEF1 circuit

5.11 Stochastic simulation luciferase expression for the P DCD1 and P TEF1 models

5.12 Signal to noise ratio for the P DCD1 and P TEF1 models

5.13 Metabolic control analysis on the P DCD1 parameterised model

5.14 Metabolic control analysis on the P TEF1 parameterised model

5.15 Time course simulation of the gene circuit with the short half-life IRP PEST and the DCD1 promoter

5.16 time course simulation of the gene circuit with IRP PEST and the P TEF1 promoter

5.17 Time course simulation of the gene circuit P DCD1 and P TEF1 simulated promoters and IRP PEST

5.18 Signal to noise ratio for the P DCD1 -PEST and P TEF1 -PEST models

5.19 P DCD1 model parameter fitting

5.20 P TEF1 model parameter fitting

5.21 P DCD1 -PEST model parameter fitting

5.22 P TEF1 -PEST model parameter fitting

LIST OF TABLES

2.1 List of plasmids used in this study

2.2 List of primers used in this study

2.3 List of yeast strains used in this study

2.4 Copasi MCA parameters

3.1 Table of plasmid circuit strains

4.1 Growth calculation for yeast strains with and without the gene circuit

4.2 Table of housekeeping gene expression fluctuation during the yeast pheromone response

4.3 Table of RT-qPCR Primer gDNA validation data

4.4 Representative RT-qPCR data from P DCD1 circuit cDNA

5.1 The simplified MAPK model based on the yeast pheromone response pathway model by Kofahl and Klipp (2004)

5.2 Revised MAPK model reactions

5.3 Parameter values for the revised MAPK model

5.4 Gene circuit model reactions

5.5 steady-state number of particles for the un-parameterised circuit in the OFF-state

5.6 steady-state number of particles for the un-parameterised circuit in the ON-state

5.7 Table of generic parameter values from the published literature, used for the first round of parameterisation of the gene circuit model

5.8 Sensitivity analysis of the parameterised gene circuit model

5.9 Concentration control coefficients for the gene circuit model

5.10 Final gene circuit model parameter values

5.11 Concentration control coefficients for the DCD1 gene circuit model

5.12 Concentration control coefficients for the TEF1 gene circuit model

5.13 Fitted circuit model parameter values

ABBREVIATIONS

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Abstract

Synthetic biology is an emergent field incorporating aspects of computer science molecular biology-based methodologies in a systems biology context, taking naturally occurring cellular systems, pathways, and molecules, and selectively engineering them for the generation of novel or beneficial synthetic behaviour. This study described the construction of a novel synthetic gene circuit, which utilises the inducible downstream transcriptional activation properties of the pheromone-response pathway in the budding yeast Saccharomyces cerevisiae as the basis for initiation. The circuit was composed of three novel yeast expression plasmids; (1) a reporter plasmid in which the luciferase reporter gene was fused to the iron response element (IRE), and expressed under the control of the pheromone-inducible FUS1 promoter, (2) a repressor plasmid which constitutively expressed the mammalian iron response protein (IRP), which can bind to the IRE in the luciferase mRNA transcript, blocking translation, and (3) a de-repressor plasmid which also utilised the pheromone-inducible FUS1 promoter to express the bacterial LexA protein that represses transcription of the IRP gene, and thereby de- represses luciferase translation.

Yeast cultures were propagated in media that selected for cells containing all three plasmid components of the gene circuit. In these cells, during vegetative growth conditions, reporter gene translation is constitutively repressed by IRP until addition of pheromone. Upon pheromone-induction, the pheromone response pathway up- regulated the expression of the LexA protein which represses transcription of IRP, enabling the translation of luciferase, which is itself up-regulated by the pheromone response pathway. The combination of the repressors functioned to increase the ratio of induction of the reporter gene between pheromone-induced and un-induced states. Proteins and mRNA species expressed by each plasmid were semi-quantified using SDS-PAGE, Western blot, and RT-qPCR. Luciferase expression was measured using an in vitro whole cell luminescence assay, and the data used to define the circuit “output”.

Metabolic control analysis was used prior to building the circuit in silico, and identified the transcription of IRP, as well as the IRP protein half-life as significant control points for increasing the expression of luciferase in vivo. Modelling resulted in the development of multiple variations of the circuit, incorporating strong and weak constitutive promoters for the IRP. For the degradation rate, the IRP was fused with a degradation tag from the PEST rich C-terminal residue of the Cln2 protein, forming IRP PEST, with approximately a 10-fold reduced half-life compared to wild type. By varying the promoter strength and half-life of the IRP, the circuit could be tuned in terms of the amplitude and period of luciferase expression during pheromone induction.

Simulated annealing and Hooke-Jeeves algorithms were used to estimate model pa- rameter values from the experimental luminescence data, refining the modelling such that it produced accurate time course simulation of the circuit output. While further characterisation of the individual components would be advantageous, the construction of the system represents a completed cycle of extensive modelling, experimentation, and further model refinement.

Declaration of Authorship

I confirm that no portion of the work referred to in the thesis has been submitted in support of an application for another degree or qualification of this or any other university or other institute of learning.

Copyright Statement

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Acknowledgements

I would like to acknowledge the members of the McCarthy lab for their help throughout this project, particularly Sheona Drummond, John Hughes, Maja Firczuk, Abi Stevenson, John Hildyard, John Duncan, Naglis Malys, Paola Pietroni, Mary Ortmayer, and Zurin Tajul Arifin. I would also like to thank Jean-Marc Schwartz for his help with the final corrections for this document.

I would like to thank Professor Hans Westerhoff for giving me the opportunity to study at the University of Manchester, and thank Professor Gerold Baier for his time and patience in teaching me maths.

Finally I would like to acknowledge my supervisors, Professors John McCarthy and Pedro Mendes, for allowing me the opportunity to work on this project.

Dedicated to Kim,

for all of the years of encouragement and support.

“ What I cannot build, I cannot understand. ”

Richard Feynman

Preface

This work details investigationsinto synthetic gene circuitry by the parallel employment of both in vivo laboratory experiments and in silico computational modelling. The two approaches were employed in a simultaneous fashion, and indeed each approach frequently used information gained from the other to validate hypotheses, and aid rational experimental design. While it is hoped that this work thus demonstrates the power of such interdisciplinary methods, for illustrative clarity the author has largely segregated the descriptions of the two aspects of this work. As such, the computational modelling collected together in chapter five actually describes simulations developed over the course of this entire work, and can be cross-referenced with the laboratory experiments depicted in chapter four. The author has made efforts to indicate such cross-referencing in the text, wherever appropriate.

CHAPTER ONE INTRODUCTION

1.1 Aims and Objectives

The objective of this project was to build a novel gene circuit in the yeast Saccha romyces cerevisiae that could enable cells to respond to environmental stimuli with the expression of a quantifiable reporter gene. Published research has shown that reporter genes can be coupled to promoters that control the expression of genes involved in the yeast pheromone response pathway (or “mating pathway”) enabling cells to express a gene of interest in response to the presence of an extracellular stimulus. [1-3]. In this way, the project investigated the construction of a synthetic system that could be used to study features such as amplification, sensitivity, and noise.

Previous research in the McCarthy lab characterized the human iron response protein (IRP) and its interaction with genes containing the iron response element (IRE) as an effective repressor of translation in yeast[4]. Also research by Brent and Ptashne had shown that the LexA repressor from Escherichia coli functioned as a repressor of transcription in yeast[5].

In this project, a gene circuit was designed that utilized both of the IRP and LexA repressors, that resulted in repression at both transcription and translation levels, with a pheromone response pathway-inducible reporter gene. This circuit design is unique from previously published work linking reporter genes to the mating response, in that the circuit was designed to suppress the basal expression of the reporter gene in an OFF- state, and then simultaneously de-repress and trigger expression in an ON-state. The design of the circuit therefore reduces the level of background noise from the reporter gene through inhibition of basal expression, enabling a higher relative-fold increase in expression, compared with a pheromone response pathway-inducible reporter gene alone [1, 6, 7]. Also, at the time of writing this approach to boosting the output of a reporter gene, and combining transcriptional and translational inhibition in a gene circuit, had not been attempted.

To achieve these objectives, the project utilized a synthetic biology approach to building a system of interacting plasmids that function in combination as a module. The simultaneous interactions of multiple components produce complex, dynamic behaviours that are impossible to conceptualize without the aid of mathematical modelling and computer simulation [8, 9]. Synthetic biology incorporates aspects of computer science from systems biology to augment molecular biology with computer aided-design and enable the modelling of gene circuits as an engineer would design electronic devices [10-13]. Synthetic biology projects result in rounds of iterative design and development as models are constructed and used to guide experimental design. Parameter values are obtained experimentally and the model evolves alongside the engineered system [11, 14-16].

1.2 The Yeast Saccharomyces cerevisiae

The Saccharomyces cerevisiae genome was one of the first to be completely sequenced, and is a widely recognized model organism for studying the genetic systems of eukaryotes, providing rapid growth, dispersed cells, simple replica plating and mutant isolation, together with a well-defined genome [17-20]. S. cerevisiae is non-pathogenic,

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FIGURE 1.1: Diagrammatic representation of the yeast mating process. 1. Yeast cells produce mating pheromone that binds to receptors on cells of the opposite mating type.

2. Cells exhibit chemotaxis, and grow towards the opposite mating type. 3. The haploid cells fuse to form a diploid cell. Reproduced with permission from A. Fijalkowski[21]. can be handled with few precautions, and can be propagated easily and cheaply in large quantities giving rise to an ideal organism for biochemical studies[18].

1.2.1 Yeast Mating

Yeast cells exist in two distinct haploid forms, a and α with genotypes MATa and MATα respectively, which can mate to form a diploid a/α cell (figure 1.1). The mating between Mata and Matα enables genetic transfer within the yeast population and enables the colony to evolve through genetic recombination[20]. The diploid cells can continue to bud in vegetative growth until they encounter starvation conditions, at which point the cells undergo meiosis and sporulation, re-establishing the haploid phase [22-29].

Each cell type produces a 13 amino acid peptide pheromone protein that binds to specific receptors on the surface of the opposite mating type; MAT α cells produce α- factor (WHWLQLKPGQPMY) and binds to MAT a cells[26]. MAT a cells produce a-factor (YIIKGVFWDPAC) that binds MAT α cells [22, 25]. Binding of one of these pheromone proteins to a cell of the opposite mating type halts the cell cycle, induces changes in cell morphology, and prepare the cell for cytoplasmic and nuclear fusion [29-34]. This signalling system in yeast has become one of the most well characterized signal transduction and developmental systems, and nearly all of the pathway has now been extensively documented through molecular genetics, cell biology, and biochemistry studies [35-42].

Yeast are non-motile organisms and therefore require some mechanism to orient themselves into close proximity with cells of the opposite mating type[18]. In order to achieve this, yeast exhibit a chemotropic response to pheromone secreted by the opposite mating type through asymmetric cellular organization, directing their growth towards the mating partner [29, 32, 34, 43]. Yeast demonstrate the ability to polarize their actin cytoskeleton in the direction of the site of highest pheromone concentration [34]. The cells elongate towards the mating partner, forming a structure termed a “mating projection”, containing proteins involved in signalling, polarization, cell adhesion, and fusion, causing the cells to take on a “pear-like” morphology known as a “Shmoo” (figure 1.1) [34, 38, 43].

The yeast mating response involves a complex cascade of events that enable yeast to translate changes in environmental conditions into an appropriate genetic and metabolic response [31, 44]. The mating response is an intracellular signal transduction pathway comprising a trans-membrane spanning heterotrimeric G-Protein-coupled receptor, and a mitogen activated protein kinase (MAPK) cascade which activates transcription factors for genes that enable the appropriate genetic response in the nucleus to a particular input stimulus at the cell surface receptor [33, 45-47]. Understanding the interactions and dynamic behaviour of the cascade is important when building gene circuits that use the mating response pathway as a generic “signal processing module” [1, 2, 46].

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FIGURE 1.2: Diagram of the yeast Ste2 G-protein receptor demonstrating the 7- transmembrane domains (H1-H7,), 4 extracellular domains (E1-E4) and 4 intra-cellular domains (C1-C4), an intracellular loop for G-protein coupling, and a cytoplasmic carboxy-terminal domain.

1.2.2 Pheromone Receptor-G-protein Coupling

S. cerevisiae MAT a cells express the Ste2 α-factor binding receptor, and MAT α cells express Ste3 a-factor binding receptor [22, 25, 26, 32]. The pheromone receptors have a structural topology of seven trans-membrane domains, a third intracellular loop that is involved in G-protein coupling, and a cytoplasmic carboxy-terminal domain that mediates ligand-induced endocytosis and desensitization (figure 1.2)[38]. Hundreds of G-protein coupled receptors have been identified in eukaryotic cells, responding to a variety of stimuli such as hormones, neurochemicals, light, odours, and tastes [48, 49]. G-proteins constitute a large proportion of known drug targets, as the released G- proteins elicit biochemical responses, and changes in cellular physiology by stimulating a variety of target (effector) enzymes [50-52]. G-protein receptors share a common design consisting of 7 membrane spanning regions linked to the G-protein[33]. In yeast, the G-proteins are formed from three subunits - Gα (Gpa1), Gβ (Ste4), and Gγ (Ste18) [53, 54]. Gβ and Gγ act as a heterodimer Gβγ[48], and Gα subunit interacts Gβγ to form the inactive Gαβγ trimer (figure 1.3 1.) [33, 55]. A superfamily of G-protein subunits has been identified in eukaryotes comprising 17 distinct Gα, 5 Gβ, and 6 Gγ isoforms, allowing for many combinatorial possibilities for cell receptors[49]. G-proteins are activated when a ligand molecule binds to the linked surface receptor, in this case the mating pheromone from the opposite cell type, causing a conformational change in the receptor that is transmitted to the G-protein causing the Gα subunit to exchange

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FIGURE 1.3: Diagrammatic representation of the process of G-protein activation. 1 and 2. Pheromone binds to the extracellular Ste2 receptor and is internalized by the receptor. 3 and 4. GDP is exchanged for GTP and the α subunit disassociates from the Gβγ units, resulting in activation of the pheromone response pathway. 5 and 6. During the process of switching off the pheromone response pathway, the Gα subunit binds GDP in place of GTP and re-associates with the Gβγ subunits.

GTP for GDP and disassociate from Gβγ exposing the effector binding regions of Gβγ [38, 42, 56, 57] (figure 1.3). The released Gβγ is then able to participate in a 3 level (MAP) kinase cascade that quickly transmits the pheromone binding signal through the cell to the nucleus [48, 51, 54, 58, 59] (figure 1.3 5, and figure 1.4 right.). The Gα subunit is released from the inner membrane into the cytoplasm[38]. The Gβ subunit has been shown to be most significant in activation of the signal response, while Gγ has been found to contain a conserved cysteine-aliphatic-aliphatic-X motif at the carboxy terminus that is thought to localize the Gβγ subunits to the membrane[33].

1.2.3 Pheromone-Induced G-protein Activation

The free Ste4 Gβγ subunit interacts with three effectors: Ste5/Ste11 complex, Ste20 protein kinase, and Far1/Cdc24 complex via a binding site that was previously buried

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FIGURE 1.4: Diagrammatic representation of the main components of the yeast pheromone response pathway. Left is the inactive pathway prior to pheromone activation. Right is the pheromone stimulated, active pathway. The activated G- protein results in the phosphorylation of Ste20, subsequently resulting in the sequential phosphorylation of Ste11, Ste7, and Fus3, forming the MAPK cascade. The MAPK cascade communicates the pheromone receptor binding event through the cytosol to the nucleus where the appropriate mating response genes are up-regulated via the de- repression of the Ste12 transcription factor by the phosphorylated Fus3. (Image from yeastpheromonemodel.org[61])

within the Gα associated molecule [49, 55]. The Ste18-Gβγ complex anchors the βγ G-protein subunits to the inner cell surface by covalently attached lipid farnesyl and palmitoyl groups [54, 60]. The association of the Gβγ subunit with the inner cell membrane surface localizes the position of the mating response, and assists in orientating the cell towards the pheromone gradient, and the mating partner [25, 34, 54, 60]. Localization of the Gβγ subunit results in Ste20 moving in close proximity to Ste11 and Ste5, forming the initiating step in the signal cascade 1.4[38]. Ste20 exists in an inactive form in the cytoplasm and is activated by a small 21kD, Rho- like G-protein Cdc42[38]. Cdc42 in yeast has a similar amino acid sequence to members of the Ras super family and is known to be involved in the control of several morphogenetic events during the cell cycle, including the generation of cell polarity, development of normal cell shape, localization of secretion, and deposition of cell- surface material[62]. Cdc42 binds to the CRIB domain of the large N-terminal region of Ste20 that ordinarily sterically occludes and auto-inhibits the active kinase C-terminal

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FIGURE 1.5: Schematic overview of yeast MAP kinase modules that share Ste11, adapted from Drogen F.[51]. Yeast signalling pathways are capable of sharing components but maintaining signal specificity through the use of pathway specific scaffold proteins. Ste11 and Ste7 are shared pheromone, high osmolarity, and low nitrogen response pathways but differentiated through the use of the Ste5 and Pbs2 scaffolds that ensure signal specificity and prevent cross-talk between physiological responses[51].

region, thereby activating Ste20 by permitting auto-phosphorylation of the exposed activation loop[63]. Cdc42 is also permanently tacked to the inner leaflet of the plasma membrane, assisting in localizing Ste20 to the membrane[63].

Ste5 is a large, multi-functional scaffold protein that, whilst having no catalytic activity, serves as a scaffold and binding platform for components of the MAP kinase cascade [63-67]. In yeast, the pheromone pathway scaffold Ste5 binds Ste11, Ste7, and Fus3, whilst the high osmolarity glycerol pathway scaffold Pbs2p interacts with Ste11 and Hog1 (see figure 1.5)[51]. There are common components in each pathway (figure

1.5) and the scaffold serves to insulate the signal, preventing cross-activation between signalling pathways [51, 68-71]. Choi, 1994 demonstrated by yeast two-hybrid analysis and co-immunoprecipitation that Ste11, Ste7, and Fus3 associate with different domains of Ste5 implying, that Ste5 simultaneously binds the components of the MAP kinase reaction. Ste5 initially forms an adapter between Gβγ and Ste11, bringing Ste11 into proximity with Cdc42-bound Ste20 at the plasma membrane, resulting in immediate phosphorylation of Ste11 by Ste20 [64-66].

The third effector to bind Gβγ is Far1, complexed with Cdc24[55]. Far1 moves from the nucleus to the cytoplasm when cells are stimulated by pheromone, and interacts with Gβγ at the cell membrane transiently via the MAP kinase cascade[34]. The N- terminal domain of Far1 contains a RING H2 domain that interacts with Gβγ, while the C-terminal end binds Cdc24, a guanine nucleotide exchange factor (GEF) that promotes exchange of GTP for Cdc42[72]. GTP-bound Cdc42 is then able to bind to Ste20 and several other regulators of cell polarity and the actin cytoskeleton[43]. Far1 is a multi-functional regulator of the mating process. One function is to bind to Cdc24 and facilitate growth towards the mating partner, another function is to mediate pheromone- induced cell cycle arrest[32]. Chang demonstrated that Far1 (“factor arrest”) is a non-essential gene, induced 4 to 5 fold by pheromone-induced Ste12 which, in turn, interacts with Cdc28 cyclin-dependent kinase, the master regulator of the cycle growth phase[32]. This interaction provides the link between the signal transduction pathway and cell cycle arrest under pheromone stimulation[73]. The exact mechanism of how Far1 inhibits the cell cycle is unclear. However Pi and Gartner determined that Fus3- mediated phosphorylation of Far1 is required for cell cycle arrest [28, 72].

1.2.4 The MAP Kinase Cascade

The MAP kinase cascade is the most prominent signalling mechanism in yeast, facilitating a rapid response to extracellular stimuli [34, 40, 43]. MAP kinase cascades are found ubiquitously in eukaryotic organisms functioning in cell growth, differentiation, tumorigenesis, and stress responses [40, 46, 74]. MAP kinase pathways usually consist of three protein kinases that act in series: a MAP kinase kinase kinase (MAPKKK), a MAP kinase kinase (MAPKK), and a MAP kinase (MAPK) (figure 1.4) [39, 43, 75, 76]. When the cascade is activated, the MAPKKK phosphorylates the MAPKK, which in turn phosphorylates the MAPK[77]. In yeast, the MAPKKK is Ste11 and the MAPKK is Ste7, and there are two MAPKs: Kss1 and Fus3 [47, 74, 78] (figure 1.4 and figure 1.5 left). The MAPK usually serve to regulate transcription factors by MAPK-mediated phosphorylation, and many intracellular and extracellular signals modulate transcription of specific genes through activation or inhibition of MAPK cascades [28, 35, 79].

1.2.4.1 Ste11, Ste7 and Fus3

The MAPK cascade function is facilitated by Ste5 and Ste20 (figure 1.4) [39, 67]. Ste11 bound to Ste5 is activated by Ste20 and subsequently activates Ste7 by phosphorylating a threonine residue in the Ste7 activation loop[47]. Ste7 does not bind strongly to the Ste5 scaffold, but binds with high affinity to Fus3 and Kss1[64]. Ste7 contains a highly-conserved catalytic domain and a less conserved N-terminal domain, in which the first 20 amino acid residues form the MAPK-binding/docking site (D-site)[27]. Ste7 activates Fus3 and Kss1 by phosphorylating threonine and tyrosine residues in their activation loops [64, 65]. The MAPK’s Fus3 and Kss1 are proline-directed kinases and phosphorylate their targets on serine or threonine residues that are immediately followed by a proline and primarily target the Ste12/Dig1/Dig2 transcription factor complex as well as Far1, and both can activate Ste12, demonstrating functional redundancy[74]. Fus3, however can also activate Ste7 and Ste5, and can phosphorylate Far1, whereas Kss1 cannot[65]. Bardwell hypothesizes that this redundancy provides overlapping reinforcing contributions to the activation of the MAPKs so that a loss of the mating response is only observed when multiple links are severed simultaneously ([55]. A recent publication by Malleshaiah et al. revealed that a phosphatase Ptc5 competes with Fus3 for phosphorylation sites on Ste5, facilitating a switch-like response in the mating pathway and ultra-sensitivity to pheromone[80].

1.2.4.2 Ste12 and The Pheromone Response Element

Ste12 is a protein consisting of 688 amino acids with an N-terminal DNA-binding region providing its function as a transcriptional activator, enabling it to form a protein- DNA complex specifically with the genes it regulates [28, 81, 82]. Genes up-regulated following pheromone induction all contain a common pheromone response element (PRE) with sequence 5′ -ATGAAACA (or sometimes reported as 5′ TGAAACA)[81]. The PRE sequence is found in over 200 genes associated with cell mating [83, 84], of which over 100 are induced two-fold by the pheromone response pathway [28, 73, 82, 85, 86].

Yuan and Fields partially characterized the DNA binding domain of Ste12, localizing the minimum region to 164 amino acids near the N-terminus between amino acids 41 and 204[86]. They also found an N-terminal domain can bind cooperatively to two copies of the PRE in a manner independent of the orientation, binding head-to-tail or tail-to-tail with variable spacing between the two elements.[86]. Kirkman-Correia et al located the transcriptional activation domain at the C-terminus (residues 384-688), and it has been shown that deletion mutants lack the ability to activate basal and induced transcription of PRE genes, however, only region 255-354 is required for pheromone- induced transcription[87].

Ste12-dependent, pheromone-induced genes include positively-acting components of the mating pathway (Ste2, Fus3, and Far1), together with negative feedback regulators of the pathway (Sst2, Msg5, Ptc1, and Gpa1), as well as genes involved in the process of cell fusion (Fus1, Fus2, Fig1, Fig2, Aga1) [28, 80, 88]. Ste12 has been shown to up-regulate its own transcription during pheromone response and can also work in conjunction with other transcription factors, in particular Tec1p, forming a heteromultimer with Ste12 regulated by Kss1 [68, 89], and this complex guides Ste12 to specific genes in the filamentous growth pathway [85, 90].

1.3 Switching Off The Pheromone Response

A natural property of G-protein signalling systems is the ability to attenuate the response following prolonged stimulation[91]. Haploid cells that do not mate and form diploids must return to the vegetative growth state [92, 93]. It has been observed in many signalling systems, and particularly with G-protein-coupled receptors, that prolonged signal exposure results in desensitization of the response [91, 94-96]. This attenuation of signal response involves a number of complex mechanisms that are activated within minutes of receptor activation, and these mechanisms are thought to be responsible for attenuation in response to light, colours, odours, chemical stimulants and narcotics[91]. Unlike the detailed information that has been accumulated about the activation and response of the mating pathway, there is much less understanding of the mechanisms involved in switching it off [43, 90, 92, 97]. The yeast α-factor desensitization mechanism is similar to hormone desensitization in animal cells and receptor desensitization has been extensively studied in the vertebrate β-adrenergic and rhodopsin receptors[91]. In yeast, there are a number of negative feedback mechanisms that facilitate control of the mating response.

The four main mechanisms employed to attenuate the pheromone signal are: pheromone degradation, pheromone de-sensitization, phosphorylation of the Gβ subunit, and dephosphorylation of the Fus3 MAPK by a phosphatase encoded by Msg5[92]. Chan and Otte screened for genes involved in the desensitization and recovery from the mating response [98, 99]; by screening for haploid cells that were hyper-sensitive to pheromone-induced cell-cycle arrest, they discovered two classes of super-sensitive mutants designated Sst1 Δ and Sst2 Δ[98]. Sst1 Δ mutants are allelic for the gene Bar1 which encodes a 587 amino acid endoprotease and cleaves α-factor, inactivating the pheromone and forming a negative feedback loop in the pheromone response pathway [1, 99]. SST1 Δ mutants demonstrate hyper-sensitivity to pheromone and are slow to recover from G1 growth arrest[100].

SST2Δ mutants are unable to degrade α-factor pheromone and cannot recover from cell cycle arrest[99]. The SST2Δ mutants defined a novel gene that was the first discovery of the RGS (“regulator of G-protein signalling”) factor family. RGS factors are negative regulators of G-proteins, so called because they stimulate the hydrolysis of the GTP bound active form of the Gα subunit, back into inactive GDP bound Gα [49, 101]. Sst2 stability is increased by phosphorylation by Fus3 and has been shown to increase the rate of hydrolysis of active Gα by at least 20-fold[55]. The activity of Sst2 serves to complete the G-protein cycle by sequestering free Gβγ subunits thereby forming a second negative feedback loop, terminating signal response, and restoring the pool of inactive Gαβγ[52].

Chen reported in the absence of ligand, the Ste3 receptor is subject to rapid degradative endocytosis[56]. However, when bound to a-factor pheromone, the receptor transcrip- tion is up-regulated and subjected to a process of recycling, whereby the ligand is degraded prompting ligand disassociation and re-utilization at the membrane surface

in selected proteins[108]. Both Fus3 and Kss1 require tyrosine phosphorylation for activation, making them potential targets for Msg5, and a GST-Msg5 fusion protein has been shown to dephosphorylate and deactivate in vitro phosphorylated Fus3[108]. Doi et al went on to show that epistatic interactions imply that Msg5 functions between Ste11 and Ste12, disruption of the Msg5 gene enhances Fus3-dependent kinase activity, and over expression of Msg5 suppresses pheromone-induced modification of Fus3 [108].

In addition, studies by Straton et al demonstrated the Gα subunit functions as a slow negative feedback function on activation of the signal pathway by Gβγ and interacts with an effector molecule, stimulating an adaptive signal that decreases sensitivity to pheromone over time and eventually shuts off the mating response downstream of the receptor[92]. This signal is delayed relative to the mating signal and through observations using two-hybrid analysis, does not involve sequestration of Gβγ[92]. Zhou et al demonstrated how, under low pheromone conditions Gα interacts with the GTPase activating protein Sst2, stimulating Gβγ sequestration[109]; through pheromone concentrations sufficient to halt the cell cycle, Gα functions as an adaptive mechanisms to recover the cell from the mating response[109]. Metodiev et al using GST-tagged Gα protein with glutathione-agarose pull-down experiments, 2D-gel electrophoresis, and mass spectrometry, found Gα associated with the phosphorylated form of Fus3[110]. Histidine-tagged Fus3 applied to a nickel column also demonstrated binding to Gα[110]. A number of hypotheses were presented by Metodiev et al to explain the association of Gα with Fus3. Firstly, it is thought that Gα might anchor Fus3 to the membrane and restrict it from transmitting the mating signal to the nucleus, and secondly, the active form of Gα is targeted for degradation and interaction with Fus3 might include the kinase in this degradation process[110]. Finally, Metodiev et al. postulated that in cells exposed to a physiological gradient of pheromone, Gα recruits Fus3 to the mating projection site where the kinase phosphorylates Gβγ, which promotes assembly or stabilization of the Gβγ-Far1 complex required for chemotropic growth[110]. The function of Gα presents a paradox, in that Gα acts as both an effector and inhibitor of Fus3 activity in the mating pathway [106, 110, 111].

In conclusion, published research has revealed the mating pathway as not a simple linear chain of events from pheromone stimulation of the membrane receptor through the MAP kinase cascade to the transcription factors. Instead there is a subtle interplay of secondary messengers and auxiliary effectors fine tuning the interaction of the major components, ensuring an appropriate level of response and timely recovery from the mating process. [80, 90, 97, 106, 109, 110].

1.4 Modelling The Mating Pathway

Systems biology is an emerging scientific field that undertakes a holistic approach to understanding biological processes through the interactions of the component parts[14]. Systems biology seeks to gain an understanding of the functions of biological systems, using methods that cannot be described by studying the component macromolecules in isolation, and consequently requires interaction between diverse experimental fields and datasets to arrive at this understanding [9, 14, 112-114]. The physiological response of cells to internal and external stimuli is governed by a complex set of interacting genes and proteins with non-linear reaction kinetics and pathway fluxes [113, 115]. Recent advances in theoretical biology have shown that biological reaction networks can be accurately modelled using mathematics [116-118], and these models can provide understanding of the principles of biological control systems as well as predictions that can be varied experimentally in the laboratory [14, 115, 119]. Figure 1.6 illustrates the cycle of systems biology research, employing an iterative process of computational and experimental science to explore complex biological problems through modelling and systems analysis. The model provides hypotheses for experimental research, which produces data that feeds back into the model, driving new understanding and further hypothesis generation.

This iterative modelling and experimentation approach has been applied to the yeast mating pathway by a number of researchers [46, 75, 76, 120]. As mentioned earlier, the yeast mating pathway is a well-characterized system that is easily modified and has a number of discrete and accessible quantifiable behaviours making it a favourable

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FIGURE 1.6: Hypothesis driven research in systems biology, adapted from Kitano et al [14]. Hypotheses can be explored using “dry science” techniques of modelling and systems analysis. Models can be parameterised through experimentation and data analysis which leads to further knowledge and understanding, leading to further hypothesis.[14]

target for mathematical modellers [77, 121-125]. In the following sections the key publications in modelling budding yeast pathways will be discussed.

1.4.1 Chen et al (2000): Kinetic Analysis of Budding Yeast Cell

Cycle Model

Chen et al have developed a kinetic model of the cyclins Cln1-3 and Clb1-6 which have been shown to coordinate the events of the cell cycle: DNA synthesis, bud emergence, spindle formation, nuclear division, and cell separation in yeast[56]. Chen converted the established mechanisms of cyclin synthesis and degradation into a set of differential equations, describing the time courses of three major classes of cyclin- dependant kinase activities[56]. The model was then used to examine the molecular events controlling the initiation of chromosome replication, bud formation, and mitosis (the “start” of cell division) and also the transition through metaphase to anaphase (the “finish” steps of cell division) in both wild-type and a selection of mutants[56]. After refining the model based on laboratory experimental data, the model included 10 non-linear ordinary differential equations for the cyclins, and their associated proteins, three algebraic functions for transcription factors, three “integrators” to trigger DNA synthesis, budding, and spindle formation, and a simple rule for separating mother and daughter cells at division[56]. The model includes approximately 50 parameters that are fitted to the phenotypic behaviour of yeast and require further optimization, but are sufficient to account for the properties of cell cycle control in yeast[56].

1.4.2 Yi et al G-Protein Model

Yi et al quantitatively characterized the G-protein cycle in yeast, based on direct in vivo measurements using fluorescence resonance energy transfer (FRET)[126]. A cyan fluorescent tagged protein (CFP)-Gα, and yellow fluorescent protein (YFP) tagged Gβγ were used to observe a reduction in FRET when the receptor was stimulated with pheromone, causing the G-protein to disassociate[126]. Time course experiments were performed and data was obtained on how Sst2 and the C-terminal tail of the α- factor receptor, modulates the kinetics of G-protein signalling. The data used to build a quantitative model to estimate the in vivo rates of G-protein activation and deactivation in yeast[126].

The model validated existing observations that the majority of the control of the mating pathway resides at the G-protein cycle[126]. The work published by Yi et al also found that G-protein activation, transcriptional induction, and cell-cycle arrest responded with the same K0.5 value for pheromone dose response, and aligns with observations in mammalian G-proteins, where K d for receptor-antagonist binding and IC50 values for inhibiting the corresponding physiologic downstream processes overlap. The work by Yi et al provides quantitative evidence that the overall G-protein cycle determines the dose response of G-protein systems, not just the receptor ligand dynamics.

1.4.3 Hao et alRGS Protein Pheromone Desensitization Model

Hao et al published a model of the activation, desensitization, and re-sensitization steps of the mating pathway, following pheromone induction[127]. The study used a combination of experimental and mathematical techniques. Hao et al investigated how external signals produce responses inside the cell, specifically G-protein activation and desensitization by the pheromone receptor and the RGS proteins (Sst2 and Gα). Radio-ligand binding measurements were used to measure receptor expression, while quantitative immunoblotting on whole cell extracts was used to quantify Sst2 and Gα. Expression levels were measured for wild-type and also in mutants engineered to over-express Ste2, Gα, Gβγ, Sst2, and Ste18, and changes in protein level were measured with immunoblotting.[127]. The functional changes brought about by altered expression were investigated using a reporter transcription assay comprised of a pheromone-responsive promoter (FUS1) fused to LacZ (β-galactosidase)[127]. Experimental data was used to build a mathematical model of the pathway using differential equations (equation 1.1 and figure 1.7)

An overview of the model is presented in figure 1.7. Hao et al ’s model simulates the pathway activation and inactivation with two coupled ordinary differential equations, and assumes that free Gβγ activates the expression of pheromone response genes and RGS protein switches the pathway off by attenuating the amount of free Gβγ through recombination with Gα. The model provided predictions that could be compared with the experimental results and both correlated a sharp rise in Gβγ during pheromone stimulation and a slower increase in Sst2. A mathematical expression for the response of the signalling pathway was derived from the model using response R of the signalling pathway as a function of pheromone concentration [ L ], where R min is the response in the absence of pheromone and R max is the maximum response and C in terms of [ L ], steady state RGS concentration[127]. (equation 1.1).

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The model did not predict a reduction in the mating response when over-expressing Sst2 however, which prompted a second round of experimentation with a GFP-tagged LacZ reporter and individual cells assessed by flow cytometry to assess wild-type and mutant cells with over-expressed Sst2. Following 90 minutes exposure to α- factor, the wild-type displayed a small intensity peak in fluorescence, which diminished

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FIGURE 1.7: Pathway regulation by RGS and Gβγ proteins. Upon binding of the ligand (L) α-factor (αF) to its receptor (R, Ste2), the G-protein α subunit (Gpa1) releases GDP, binds to GTP, and liberates the G-protein βγ subunits (Ste4/Ste18). Sustained signalling requires activation of multiple effectors (not shown) by the dissociated Gβγ components. These effectors activate a pathway (dotted line) leading to transcription of several genes including the RGS protein Sst2. GTP hydrolysis is accelerated by the RGS protein, and this leads to subunit re-association and pathway inactivation. The model assumes that GTP hydrolysis is the rate-limiting step of subunit reassembly. A potential positive feedback loop leading to Sst2 degradation is indicated by a darker line. Adapted from Hao et al.

and was replaced by a second peak of higher intensity, however the lower intensity peak continued in the Sst2 mutant cells[127]. The authors hypothesize that when Sst2 is over-expressed, the graded response to α-factor is replaced with a binary response through positive feedback regulation where a second feedback loop promotes degradation of Sst2[127]. Implementing the experimental observations into the model, the author was able to explain the slow initial induction of Sst2, as seen in Sst2 over- expression mutants. The model was used to show that alterations in the expression of Sst2 occur slower than alterations in the active state of the G-protein such that the activation state of the G-protein adjusts rapidly to the slow change in Sst2 expression and is therefore in equilibrium, allowing the state of the system to be determined by Sst2 expression levels[127]. Degradation of Sst2 occurs at a constitutive rate when pheromone is absent and is proportional to expression (a “constitutive steady-state”). Following pheromone induction, the rate of Sst2 production exceeds the constitutive degradation rate and as Sst2 levels increase, expression becomes inhibited by increasing levels of inactive G-protein and the production rate reduces back to the constitutive rate, forming a positive feedback loop. In over-expression mutants the level of Sst2 degradation falls much more rapidly than the production rate and the rate of production rises until it reaches a new steady state, correlating with the experimental observations [127]. In addition, the model was modified with a stochastic term to account for random fluctuations in protein concentration. 10,000 simulations were run using the new random model, averaged for a mean time course and the results demonstrated the binary behaviour observed in the experimental work for the Sst2 over-expression mutant [127]. To confirm that pheromone stimulation promotes Sst2 degradation, cells were grown for an hour in presence of α-factor, treated with cyclohexamide to block further protein synthesis, and the remaining Sst2 protein was monitored with immunoblotting. Results demonstrated a faster reduction in Sst2 when pretreated with pheromone, as predicted by the model[127].

The work published by Hao et al demonstrates the iterative process of mathematical modelling combined with wet lab experimentation described by Kitano et al. The modelling component of the work provided unique insights into the biological inter- actions and hypothesis generation that could not be derived through experimentation alone, such as the positive feedback loop that facilitates re-activation of the pathway that had not been observed prior to the study. The model also developed from a simple mathematical derivation of the activation and de-activation of the signalling pathway, to an in vivo representative simulation of the mating response, eventually including the feedback loops that provide the timing and coordination for controlling the pathway response.

1.4.4 The Kofahl and Klipp Yeast Pheromone Pathway Model.

Kofahl and Klipp published a mathematical model of the dynamics of the pheromone pathway in haploid yeast cells of mating type MATa after stimulation with α-factor [128]. Yi et al and Hao et al modelled specific aspects of the yeast pheromone pathway to augment the specific areas of their research [126, 127]. Prior to Kofahl and Klipp there was no single model that attempted to simulate the complete pheromone pathway and concatenate the research conducted in this field. The Kofahl and Klipp model consists of a set of coupled differential equations that describe the transmission of the mating signal from the surface receptor, through the G-protein, to the MAP kinase cascade, and activation of the Ste12 transcription factor[128](see figure 1.8). The model includes:

- activation of the membrane-bound pheromone receptor.
- activation of the G-protein.
- formation and activation of the scaffold-bound MAP kinase cascade.
- activation of transcription factor Ste12.
- downstream effects on gene expression alteration and preparation for mating.
- down regulation of the signal process through Sst2 and Bar1.

The Kofahl and Klipp model was not part of a combined wet and dry experimental project as with the work by Yi et al and Hao et al, but the authors used parameter values obtained from published literature to fit the model behaviour to experimental observations of the changes in the relative levels of the mating response pathway components over time [126-128]. The model attempts to provide the most complete representation of the yeast mating pathway, in terms of including all of the interactions between the known components and the available kinetic data (figure 1.9).[128]. The model groups the reactions that comprise the yeast mating response into a series of complexes which represent the temporal order of events of the pathway including receptor activation, the G-protein cycle, Ste5 complex formation, and down stream effects of phosphorylated Fus3 and Far1 (figure 1.9). Using the model to investigate mutant phenotypes, Kofahl and Klipp were able to demonstrate the pheromone desensitization response of yeast cells to prolonged pheromone exposure. Cole et al showed that over expressing Gα resulted in five times the normal level of α- factor required to induce a mating response and can compensate for super sensitivity to pheromone observed in Sst2 and Ste2 mutant strains, resulting in pheromone desensitization[33]. Cole hypothesized that this was due to increased Gα mopping up available Gβγ and preventing progression of the mating signal through to the MAPK cascade[33]. This observation was also observed in the Kofahl and Klipp model where an increase in Gα creates a decrease in free Gβγ, resulting in shortened complex

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FIGURE 1.8: Spatial diagram of the pheromone pathway in yeast. Adapted from Kofahl et al [128]. The α-factor pheromone binds to the Ste2 receptor in the membrane, which is close to the heterotrimeric G-protein (middle). The G α subunit disassociates from the Gβ and Gγ sub-units. The Gβ and γ subunits are bound by Ste20 and to Ste5 which functions as a scaffold for the sequential phosphorylation of the MAPK cascade components Ste11, Ste7, and Fus3, as well as Cdc24 and Bem1 (right). Elements of the MAPK cascade shuttle to and from the nucleus (Fus3 and Bar1). Fus3pp phosphorylates Dig1 and Dig2 resulting in de-repression of the transcription factor Ste12 which initiates transcription of the mating response genes resulting in the up- regulation of over 200 genes (bottom).

formation, reduced Fus3 phosphorylation and Far1PP-Gβγ, and eventually reduced pheromone sensitivity[128]. The published role of the G-protein components Sst2, Ste12, Ste11, Ste20, Msg5, and Far1 were replicated in the model and used to validate its response to observed phenotypic changes[128].

The Kofahl and Klipp model also produces the same quantitative results as the Yi model for the G-protein cycle, however it does not include the feedback loops developed by Yi et al., but replicates the observed behaviour [126, 128]. The model incorporates

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FIGURE 1.9: Diagram of the reactions modelled in the Kofahl and Klipp model. The model includes reactions for G-protein cycling, assembly of the MAPK scaffold, and sequential phosphorylation of the Ste11, Ste7, and Fus3 kinases. The model results in the activation of the transcription factor Ste12, as well as the Sst2 and Bar1 negative feedback components[128].

regulatory control with several feedback loops. Phosphorylated Fus3 activates Sst2 which stimulates hydrolysis of GαGTP, closing the G-protein cycle[128]. Also, the transcription and activation of Bar1 results in the degradation of α-factor resulting in down regulation of the pathway and negative feedback under prolonged pheromone stimulation[128].

Although many models of MAP kinase cascades have been published, they are not parameterised with data from yeast, and do not include yeast mating pathway- specific features such as the Ste5 scaffold and the Dig1/Dig2-Ste12 activation complex. Parameters are often obtained from studies of MAP kinase cascades in Xenopus species [120, 122, 124] and focus on the phosphorylation of the three kinases in isolation. The models also do not incorporate more recently identified components of the pathway such as Ptc1, observed by Malleshaiah et al [80]. It was hypothesized that the non-linear behaviour of the yeast mating pathway may influence the experimentally observed behaviour of the gene circuit. The inclusion of an ultra-sensitive cascade relevant to the yeast cells in which the circuit is embedded may be more useful for predicting experimental observations than a simplified version of the Kofahl and Klipp model that does not incorporate any of the dynamic behaviours of the cascade.

The Kofahl and Klipp model disregards a number of important key features of the yeast mating response, particularly the central MAPK cascade that transfers the extra-cellular signal through the cytoplasm to the nucleus (figure 1.8). There has been a great deal of research conducted into MAPK cascades over the past 30 years, both experimentally and mathematically. A number of researchers have investigated why eukaryotic signalling systems are comprised of three sequentially activated kinases with multiple rounds of non-processive phosphorylation [77, 129]. Extensive modelling work by Goldbeter in the early 1970s, Kholodenko, Huang and Ferrell, and Markevich in the 1990s and early 2000’s, Xaio Wang, and Fernando Ortega in 2006, and O’Shaughnessey et al in 2011 have shown that the signalling cascades produce an ultra-sensitive response to input, converting a graded input signal to a binary output response through the action of nested feedback loops within the cascade and amplification through repeated phosphorylation of the kinases [76, 120, 122-124, 130-132]. The model by Kofahl and Klipp did not replicate any of the behaviours observed by other models of MAPlkinase cascades, and did not build on any of the previous research in this field. While the author has included all of the known components of the pathway, the relationship between them and the dynamic behaviour of the cascade was not replicated. The Kofahl and Klipp model did not produce a sigmoidal increase in the steady-state level of Fus3pp in response increasing initial concentrations of pheromone, characteristic of ultra-sensitivity[133]. The model also did not replicate the chronological order of events observed experimentally (as reported by Yu et al during time course simulations, in terms of the activation of the G-protein, followed by sequential phosphorylation of the kinases, and Ste12[121].

The Kofahl and Klipp model is capable of reproducing the change in the relative amounts of the components in mutants of the mating pathway[128], but cannot be used to study the systems-level behaviour of the signal cascade that underlines the pathway, such as ultra-sensitivity to pheromone, or potentially more complex behaviour, such as bi-stability and oscillation [77, 120, 131].

1.4.5 Modelling tools

Simulation and modelling is becoming a standard approach to understanding biological systems, and this requires software tools that enable researchers to access diverse mathematical modelling and simulation methods[134]. Fortunately there are a range of applications available that enable researchers to access these tools without a mathematics specialism, which will be discussed below[135].

1.4.5.1 Copasi

Copasi is a software application for the simulation and analysis of biological networks. The software is free for non-commercial use and runs on all major operating systems [134]. The Copasi project is an international collaboration between three groups at the Virginia Bioinformatics Institute, the University of Heidelberg, and the University of Manchester. Copasi has a number of unique features, including the criteria to switch between stochastic, deterministic, and hybrid modelling methods; flexible parameter [56]. This ensures that a suitable quantity of receptors are available throughout the mating response and, more importantly, receptor expression is focused at the point of pheromone contact, facilitating the chemotropic response up the pheromone gradient [56]. This response is not as prominent in the α-factor stimulated Ste2 receptor, where pheromone stimulation increases Ste2 vacuole-directed transport and degradation [96, 102]. Dohlman et al reports Ste2 desensitization occurs through binding of the RGS protein Sst2, such that it is positioned in close proximity to Gpa1[31].

Research suggests that the Gα subunit of the heterotrimeric G-protein has a positive signalling role and is responsible for pheromone desensitization and recovery back to the vegetative haploid growth stage [49, 92, 103, 104]. GTPase-deficient Gpa1 mutants demonstrate constitutive expression of pheromone response elements and morphological changes in the absence of pheromone [104, 105]. Kurjan, 1991 introduced mutations in the SCG1 gene, encoding the Gα subunit and observed defects in mating response, growth and cell morphology[105]. Dohlman and Thorner later found that inactivating mutations in the Gα gene Gpa1 do not block pheromone response, but result in constitutive signalling and it has been concluded that this is due to uncontrolled pathway activation by free Gβγ[49]. It was also found that over- expression of Gα leads to diminished signal transduction due to over-sequestration of Gβγ [33, 101, 106]. Cole et al also demonstrated how over expression of Gα subunit leads to suppression of the mating response, and represses the response even when over expressing the Gβ and Gγ subunits[33]. Deletions in either of the Gβ or Gγ genes results in pheromone insensitive sterile cells, whilst over-expression leads to constitutive activation of the mating pathway [33, 49, 106]. It has also been shown by Cole et al that over expression of Ste4 (Gβ) with expression of Ste18 (Gγ) promotes constitutive activation of the pheromone signalling pathway [33, 101].

Blackwell et al reported that Msg5 works in concert with Gα to down-regulate the mating signal by inhibiting the pheromone-induced increase of Fus3 in the nucleus [107]. Doi et al earlier reported that Gα may induce a post translational modification of Msg5 resulting in enhanced protein phosphatase activity or that Gα may induce transcription of Msg5.

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