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Control of gene expression for the study of neurodegenerative disorders: a proof-of-principle experimental study
6th IFAC Conference on 6th on Foundations of Systems 6th IFAC IFAC Conference Conference on Biology in Engineering 6th IFAC Conference on Foundations of Systems Biology in Engineering Available online at www.sciencedirect.com October 9-12, 2016. Magdeburg, Foundations of Systems Biology in Foundations of Systems BiologyGermany in Engineering Engineering October 9-12, 2016. Magdeburg, Germany October 9-12, 2016. Magdeburg, Germany October 9-12, 2016. Magdeburg, Germany
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Control of gene expression for the study Control Control of of gene gene expression expression for for the the study study neurodegenerative disorders: a neurodegenerative disorders: neurodegenerative disorders: a a proof-of-principle experimental study proof-of-principle proof-of-principle experimental experimental study study
of of of
∗∗ ∗∗ Perrino ∗,∗∗ ∗,∗∗ Cathal Wilson ∗∗ Marco Santorelli ∗∗ ∗,∗∗ ∗∗ Perrino Cathal Wilson Marco Santorelli ∗∗,∗∗∗ ∗,∗∗ Cathal ∗∗ Marco Santorelli ∗∗ ∗∗ Perrino Wilson Diego di Bernardo Perrino Cathal Wilson ∗∗,∗∗∗Marco Santorelli ∗∗,∗∗∗ Diego di Bernardo ∗∗,∗∗∗ Diego di di Bernardo Bernardo Diego ∗ ∗ Department of Information Technology and Electrical Engineering, ∗ Technology and Electrical ∗ Department Department of Information Technology and Electrical Engineering, University of of Information Naples Federico II, 80125 Naples, ItalyEngineering, (e-mail: Department of Information Technology and Electrical Engineering, University of Naples Federico II, 80125 Naples, Italy (e-mail: University of Naples Federico II, 80125 Naples, Italy (e-mail: [email protected]) University of Naples Federico II, 80125 Naples, Italy (e-mail: [email protected]) ∗∗ [email protected]) Telethon Institute of Genetics and Medicine, 80078 Pozzuoli, Italy [email protected]) ∗∗ ∗∗ Telethon Institute of Genetics and Medicine, 80078 Pozzuoli, Italy ∗∗ Telethon Institute of Genetics and Medicine, 80078 Pozzuoli, Italy (e-mail: {wilson, m.santorelli, dibernardo}@tigem.it) Telethon Institute of Genetics and Medicine, 80078 Pozzuoli, Italy (e-mail: {wilson, m.santorelli, dibernardo}@tigem.it) ∗∗∗ (e-mail: {wilson, m.santorelli, dibernardo}@tigem.it) Department of Chemical, Materials and Industrial Engineering, (e-mail: {wilson, m.santorelli, dibernardo}@tigem.it) ∗∗∗ ∗∗∗ of Chemical, Materials Industrial ∗∗∗ Department Department of Chemical, Materials and Industrial Engineering, University Naples Federico II,and 80125 Naples,Engineering, Italy Department of of Chemical, Materials and Industrial Engineering, University of Naples Federico II, 80125 University of of Naples Naples Federico Federico II, II, 80125 80125 Naples, Naples, Italy Italy University Naples, Italy
Giansimone Giansimone Giansimone Giansimone
Abstract: Abstract: Abstract: Neurodegenerative disorders are characterised by the progressive disruption of specific neuronal Abstract: Neurodegenerative disorders are characterised by the progressive disruption of specific Neurodegenerative disorders are by progressive disruption of neuronal population partly due to the formation of abnormal protein aggregates that interfere withneuronal normal Neurodegenerative disorders are characterised characterised by the the progressive disruption of specific specific neuronal population partly due to the formation of abnormal protein aggregates that interfere with normal population partly due to the formation of abnormal protein aggregates that interfere with normal cell functions. In Parkinson’s disease, the role of abnormal α-synuclein protein aggregates in population partly due to the formation of abnormal protein aggregates that interfere with normal cell functions. In Parkinson’s disease, the role of abnormal α-synuclein protein aggregates in cell functions. In Parkinson’s Parkinson’s disease, the the role of of abnormal abnormal α-synuclein protein aggregates in causing the disease is well established. Mutations in α-synuclein are known to cause familial cell functions. In disease, role α-synuclein protein aggregates in causing the disease established. Mutations in ofα-synuclein are known to cause familial causing the is well established. Mutations are to Parkinson’s disease.is Awell quantitative understanding the dynamics of α-synuclein protein causing the disease disease isA well established. Mutations in in ofα-synuclein α-synuclein are known known to cause cause familial familial Parkinson’s disease. quantitative understanding the dynamics of α-synuclein protein Parkinson’s disease. A quantitative understanding of the dynamics of α-synuclein protein aggregation in wild type and mutant form is however lacking. Here, we explore the feasibility of Parkinson’s disease. A quantitative understanding of the dynamics of α-synuclein protein aggregation in wild type and mutant form is however lacking. Here, we explore the feasibility of aggregation in wild type and mutant form is however lacking. Here, we explore the feasibility of using a microfluidics-based platform for automatic control of protein expression from a galactoseaggregation in wild type and mutantfor form is however lacking. Here, expression we explorefrom the feasibility of using a microfluidics-based platform automatic control of protein a galactoseusing a microfluidics-based microfluidics-based platform forand automatic control of protein protein expression from aa galactosegalactoseinducible promoter in yeast, to model study the human α-synuclein protein. using a platform for automatic control of expression from inducible promoter in yeast, to model and study the human α-synuclein protein. inducible inducible promoter promoter in in yeast, yeast, to to model model and and study study the the human human α-synuclein α-synuclein protein. protein. © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Synthetic Biology; Dynamics and control; Modelling; Model Predictive Control; Keywords: Biology; Keywords: Synthetic Synthetic Biology; Dynamics Dynamics and control; control; Modelling; Modelling; Model Model Predictive Predictive Control; Control; Microfluidics; Gene expression; Yeast. and Keywords: Synthetic Biology; Dynamics and control; Modelling; Model Predictive Control; Microfluidics; Gene expression; Yeast. Microfluidics; Gene expression; Yeast. Microfluidics; Gene expression; Yeast. 1. INTRODUCTION et al. (2011), Uhlendorf et al. (2012), Melendez et al. 1. INTRODUCTION INTRODUCTION et al. (2011), Uhlendorf et al. (2012), Melendez et al. 1. et al. (2014)). 1. INTRODUCTION et al. (2011), (2011), Uhlendorf Uhlendorf et et al. al. (2012), (2012), Melendez Melendez et et al. al. (2014)). (2014)). Neurodegenerative disorders are associated to the forma- (2014)). Here, we explore the feasibility of using a microfluidicsNeurodegenerative disorders are associated to the formaNeurodegenerative disorders are to formation of abnormal protein aggregates that interfere with the Here, explore the feasibility of aa microfluidicsNeurodegenerative disorders are associated associated to the thewith formaHere, we we explorefor theautomatic feasibility gene of using using microfluidicsbased platform expression control, tion of abnormal abnormal protein aggregates that interfere the Here, we explore the feasibility of using a microfluidicstion of protein aggregates that interfere with the normal functions of neurons, causing the progressive disbased platform for automatic gene expression control, tion of abnormal protein aggregates that interfere with the based platform platform for developed automaticingene gene expression control, which we recently Fiore et al. (2016), to normal functions of neurons, causing the progressive disbased for automatic expression control, normal of neurons, causing the progressive ruption functions of the neuronal population. The dysfunction ofdisα- which we recently developed in Fiore et al. (2016), to normal functions of neurons, causing the progressive diswhich we recently developed in Fiore et al. (2016), to control the expression of the human α-synuclein protein ruption of the neuronal population. The dysfunction of αwhich we recently developed in Fiore et al. (2016), to ruption the neuronal The dysfunction of αsynucleinof (α-syn) proteinpopulation. is involved in Parkinson’s disease control the expression of the human α-synuclein protein ruption of the neuronal population. The dysfunction of αcontrol the expression of the human α-synuclein protein in yeast cells. The aim is to attain a quantitative undersynuclein (α-syn) protein is involved in Parkinson’s disease control the expression of the human α-synuclein protein synuclein (α-syn) protein is involved in Parkinson’s disease (PD) and(α-syn) relatedprotein neurodegenerative disorders (Auluck aim aa quantitative undersynuclein is involved in Parkinson’s disease in in yeast yeast cells. cells. The aim is is to to attain quantitative understanding of theThe dynamics of attain α-syn protein’s aggregation, (PD) and related related neurodegenerative disorders (Auluck yeast cells. The aim is to attain a quantitative under(PD) and neurodegenerative disorders (Auluck et al. (2010)). Mutations in α-syn protein are also asso- in standing of the dynamics of α-syn protein’s aggregation, (PD) and related neurodegenerative disorders (Auluck standing of the dynamics of α-syn protein’s aggregation, by carefully regulating its expression and following its et al. (2010)). Mutations in α-syn protein are also assostanding of the dynamics of α-syn protein’s aggregation, et al. in associated with rareMutations forms of early-onset familialare PDalso (Outeiro carefully regulating its expression and following its et al. (2010)). (2010)). Mutations in α-syn α-syn protein protein are also asso- by by carefully regulating its expression and following its dynamics in real-time. Driving the expression of α-syn ciated with rare forms of early-onset familial PD (Outeiro by carefully regulating its expression and following its ciated with rare forms of early-onset PD (Outeiro and Lindquist (2003)). The human familial α-synuclein biology dynamics in real-time. Driving the expression of α-syn ciated with rare forms of early-onset familial PD (Outeiro dynamics in real-time. Driving the expression of α-syn protein at different values, we can assess quantitatively the and Lindquist (2003)). The human α-synuclein biology dynamics in real-time. Driving the expression of α-syn and Lindquist (2003)). The human α-synuclein biology has been extensively characterised (Auluck et al. (2010)). different we quantitatively the and Lindquist (2003)). The human α-synuclein biology protein protein at at that different values, we can can assess assess quantitatively the dynamics lead values, to the formation of protein aggregates. has been extensively characterised (Auluck et al. al. (2010)). (2010)). at different values, we can assess quantitatively the has been extensively characterised (Auluck et A yeast model expressing wild type and mutant human protein dynamics that lead to the formation of protein aggregates. has been extensively characterised (Auluck et al. (2010)). dynamics that lead to the formation of protein aggregates. A yeast model expressing wild type and mutant human dynamics that lead to the formation of protein aggregates. A yeast model expressing wild and human α-syn protein has been used totype qualitatively study its A yeast model has expressing wildto type and mutant mutant human α-syn protein beeninused study its 2. AN EXPERIMENTAL TESTBED TO STUDY THE α-syn protein has been used to qualitatively qualitatively study its aggregation properties Outeiro and Lindquist (2003). α-syn protein has been used to qualitatively study its 2. AN AN EXPERIMENTAL TESTBED TOPROTEIN STUDY THE THE aggregation properties in Outeiro and Lindquist (2003). 2. EXPERIMENTAL TO STUDY DYNAMICS OF THE TESTBED ALPHA-SYN 2. AN EXPERIMENTAL TESTBED TOPROTEIN STUDY THE aggregation properties in Outeiro and Lindquist (2003). However, α-synuclein overexpression is toxic also for yeast aggregation propertiesoverexpression in Outeiro and Lindquist (2003). DYNAMICS OF THE ALPHA-SYN However, α-synuclein is toxic also for yeast DYNAMICS OF THE ALPHA-SYN PROTEIN DYNAMICS OF THE ALPHA-SYN PROTEIN However, overexpression is for cells, thusα-synuclein making it difficult to study, if its also expression is However, overexpression is toxic toxic for yeast yeast cells, thusα-synuclein making it difficult difficult toastudy, study, if its its also expression is The toxicity of the α-syn protein has been characterised cells, thus making it to if expression is not carefully controlled. Indeed, quantitative study of the cells, thus making it difficult to study, if its expression is toxicity of the α-syn protein has been characterised not carefullydynamics controlled.ofIndeed, Indeed, quantitative study of the the The The toxicity of protein characterised several cell-based and organism-based models (Auluck not carefully controlled. aa study of The toxicity of the the α-syn α-syn protein has has been been characterised aggregation the α-syn protein is still lacking. not carefullydynamics controlled.ofIndeed, a quantitative quantitative study of the in in several cell-based and organism-based models (Auluck aggregation the α-syn protein is still lacking. in several cell-based and organism-based models (Auluck et al. (2010)). Yeast strains overexpressing normal and aggregation dynamics of the α-syn protein is still lacking. in several cell-based and organism-based models (Auluck aggregation dynamics the α-syn proteincan is still et al. (2010)). Yeast strains overexpressing normal and Automatic control of ofgene expression be lacking. used to et al. (2010)). Yeast strains overexpressing normal and mutant α-syn protein fused to a green fluorescent reporter et al. (2010)). Yeast strains overexpressing normal and Automatic controlthe of expression gene expression expression can be used usedin to toa mutant α-syn protein fused to a green fluorescent reporter Automatic control of gene be precisely regulate level ofcan a protein Automatic control of gene expression can be used to mutant α-syn protein fused to a green fluorescent reporter protein (α-syn-GFP) under the galactose responsive promutant α-syn protein fused to a green fluorescent reporter precisely regulate the expression level of a protein in a (α-syn-GFP) under theused galactose responsive proprecisely expression level aa protein in populationregulate of cells the (Fiore et al. (2016)). Several successful precisely regulate the expression level of of protein in aa protein protein (α-syn-GFP) under galactose responsive promoter have been successfully to dissect molecular protein (α-syn-GFP) under the theused galactose responsive propopulation of cells cells (Fiore et al. al. in (2016)). Several successful moter have been successfully to dissect molecular population of (Fiore et (2016)). Several successful attempts have been described literature to assess the population of cells (Fiore et al. (2016)). Several successful moter have been successfully used to dissect molecular pathways involved in α-syn biology (Outeiro and Lindquist moter have been successfully used to dissect molecular attempts have been described in literature to assess the involved in α-syn biology (Outeiro and Lindquist attempts been described in to the feasibility have of such technology using fluorescent reporter attempts have beentechnology described using in literature literature to assess assess the pathways pathways involved in (Outeiro and Lindquist (2003)). The overexpression of the human α-syn in pathways involved in α-syn α-syn biology biology (Outeiro and protein Lindquist feasibility of such such fluorescent reporter The overexpression of the human α-syn protein in feasibility of technology using fluorescent proteins (Menolascina et al. (2014), Danino et al.reporter (2010), (2003)). feasibility of such technology using fluorescent reporter (2003)). The overexpression of the human α-syn protein in yeast cells mimics the situation of the aging neurons when (2003)). The overexpression of the human α-syn protein in proteins (Menolascina et al. (2014), Danino et al. (2010), yeast cells mimics the situation of the aging neurons when proteins (Menolascina et al. (2014), Danino et al. (2010), Olson et al. (2014), Milias-Argeitis et al. (2011), Toettcher proteins (Menolascina et al. (2014), Danino et al. (2010), yeast cells mimics the situation of the aging neurons when the capacity of the quality-control (QC) system to cope yeast cells mimics the situation of the aging neurons when Olson et al. (2014), Milias-Argeitis et al. (2011), Toettcher the of quality-control system to Olson et al. Milias-Argeitis et (2011), Toettcher Olson al. (2014), (2014), Milias-Argeitis et al. al.Frontier (2011),Science Toettcher the capacity capacity of the themisfolded quality-control (QC) system(Outeiro to cope cope with accumulating proteins(QC) is exceeded the capacity of the quality-control (QC) system to cope This et work was supported by a Human Pro with accumulating misfolded proteins is exceeded (Outeiro This work was supported by a Human Frontier Science Pro with accumulating misfolded proteins is exceeded (Outeiro and Lindquist (2003)). One copy of the α-syn-GFP congram HFSP RGP0020/2011 to DdB and by the Italian Fondazione This work was supported by a Human Frontier Science Pro with accumulating misfolded proteins is exceeded (Outeiro ThisHFSP workRGP0020/2011 was supportedtoby a Human Frontier Science Proand Lindquist (2003)). One copy of the α-syn-GFP congram DdB and by the Italian Fondazione and Lindquist (2003)). One copy of the α-syn-GFP construct is not able to saturate the QC system of the yeast. Telethon. gram HFSP RGP0020/2011 to DdB and by the Italian Fondazione and Lindquist (2003)). One copy of the α-syn-GFP congram HFSP RGP0020/2011 to DdB and by the Italian Fondazione struct is not able to saturate the QC system of the yeast. Telethon. struct is not able to saturate the QC system of the yeast. Telethon. struct is not able to saturate the QC system of the yeast. Telethon. Copyright © 2016, 2016 IFAC 1 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright 2016 IFAC 1 Copyright © 2016 IFAC 1 Peer review© of International Federation of Automatic Copyright ©under 2016 responsibility IFAC 1 Control. 10.1016/j.ifacol.2016.12.095
2016 IFAC FOSBE October 9-12, 2016. Magdeburg, Germany Giansimone Perrino et al. / IFAC-PapersOnLine 49-26 (2016) 008–013
However, when inserting multiple copies of the α-syn-GFP construct in yeast, the α-syn protein causes the formation of protein aggregates that are toxic for yeast cells. Thus, the toxicity of the α-syn protein can be studied using yeast strains carrying multiple copies of the galactose-inducible α-syn-GFP construct. However, as soon as the promoter is activated by growing these cells in galactose enriched medium, α-syn toxicity causes cell death thus preventing a thorough investigation and quantification of aggregation dynamics.
the respective pYM27 construct using primers with a 50 bp overhang corresponding to the 5’ and 3’ sequences of the yeast dubious ORF YMR082C using the primers Gal.Syn.Fwd 5’ - TGATTATCTAAGCAGCAATCCCCTTGTCCTA CAAAACAGAAACTGGAAGAAGTACGGATTAGAA GCCGCCGAG - 3’ and S2.Syn.Rev 5’ - ACGCAGACCCATTCGAGGGGCTCATTGGAAA CACGTAGTCGACATTAGTTATCGATGAATTCGA GCTCGTT - 3’.
1
αSyn - GFP
0.75
A yeast strain with a constitutively expressed cytosolic marker (TEF2pr-mCherry; Breker et al. (2013)) was transformed with the amplicon and transformant was selected on kanamycin-containing plates. Insertion of the α-syn cassette into the YMR082C locus by homologous recombination was verified by PCR from genomic DNA prepared from the strain.
Active promoter (Galactose)
0.5
Yeast strain carrying the α-synA53T-GFP construct in single copy was grown at 30◦ C in Synthetic Complete (SC) medium, enriched with (i) raffinose (SC+RAF), (ii) glucose (SC+GLC), or (iii) galactose and raffinose (SC+GAL/RAF). The glucose enriched medium is used to repress the induction of the galactose promoter, conversely the galactose/raffinose enriched medium allows the induction of the α-synA53T-GFP construct. The raffinose enriched medium permits instead to grow the cells repressing the induction of the galactose promoter, but allowing faster induction of the construct when they are switched to the galactose enriched medium.
Repressed promoter (Glucose)
0.25
0
9
Time
Fig. 1. Proof of concept. Automatic control of the galactose-inducible promoter can overcome this limitation and enable quantitative analysis of α-syn dynamics in yeast strains carrying multiple copies of the α-syn-GFP construct. Specifically, as depicted in Fig. 1, automatic control of gene expression from the galactose-inducible promoter can be used to increase αsyn-GFP expression at discrete steps, starting from a fully repressed promoter (glucose), thus enabling precise quantification and comparison of the aggregation dynamics of α-syn-GFP wild type and mutant forms.
3.2 Microfluidics Real-time experiments were performed using the MFD0005a microfludics device (Ferry et al. (2011)) in a time-lapse fluorescent microscopy platform as described in Menolascina et al. (2014). Yeast cells are trapped inside a microchamber (height: 3.5 µm), allowing them to grow only in a monolayer, in order to perform accurate image analysis of their fluorescence. Microfluidic devices are fabricated according to the protocol published in Ferry et al. (2011), whereas the experimental setup is the same as in Fiore et al. (2016).
In this work, we proposed a pilot study on the strain carrying the galactose-inducible α-syn A53T (mutant form) construct in single copy, in order to assess the feasibility of controlling its expression at discrete steps in yeast cells. 3. MATERIALS AND METHODS 3.1 Yeast strain and cell culture
3.3 Microscopy and image analysis
α-Syn A53T construct fused to a Green Fluorescent Protein (GFP) under control of the Gal promoter was amplified by PCR from the plasmid pRS304-Syn-A53T (Outeiro and Lindquist (2003)), using the forward primer O.Gal.Fwd 5’ - CAGCTGAAGCTTCGTACGCTGCAGGTCGACA GTACGGATTAGAAGCCGCC - 3’ and reverse primer O.Cyc.Rev 5’ - GGCGGGGACGAGGCAAGCTAAACAGATCTCA AATTAAAGCCTTCGAGCGTCC - 3’ and cloned SalI/BglII into the vector pYM27 (Janke et al. (2004)).
Fluorescence was acquired by means of an inverted fluorescence microscope (Nikon Eclipse Ti) equipped with an automated and programmable stage, an incubator to guarantee fixed temperature (30◦ C) and gasses to cell environment, and a high sensitivity Electron Multiplying CCD (EMCCD) Camera (Andor iXON Ultra897). The microscope and the camera were programmed to acquire, at 5 minutes intervals, two types of images: (i) a bright field image (phase contrast), and (ii) two fluorescence images (with the appropriate filters) to monitor cell fluorescence due to GFP and mCherry proteins and to track a red dye, Sulforhodamine B (Sigma-Aldrich), added to one of the enriched medium in order to evaluate the control input administered to the cells. A custom image processing algorithm was developed to quantify the fluorescence signals
After sequencing, a cassette containing α-syn sequence together with the Kan resistance gene was amplified from 2
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being expressed by the entire population of yeast cells (Menolascina et al. (2014)). The measurement units for the fluorescence are considered arbitrary and, thus, a calibration phase at the beginning of each control experiment is needed to calculate a reference value for the fluorescence steady states.
sources of uncertainty, the optimal input computed by the MPC could, in principle, be applied to the yeast cells over the entire prediction horizon. However, in order to make the control action robust to any source of uncertainty and variability, the feedback loop is closed by applying only the first element of the calculated control input and at the next sampling time (k + 1) T when the entire procedure is repeated.
4. CONTROL STRATEGY
To reduce the computational effort to solve the optimal control problem, we decided to use a discrete-time dynamical model of the yeast strain as described in details in the next section.
To assess the dynamics of the α-syn protein, i.e. to control the value of the protein at different levels, we implemented a Model Predictive Control (MPC) strategy, which we previously used to control the galactose-inducible promoter (Fiore et al. (2016)). The MPC algorithm is a feedback optimisation-based technique, which uses a mathematical model of the system being controlled to predict the future values of the control error and to find the best value of the control input that minimises it (Morari and Lee (1999)).
5. MODELLING The MPC strategy needs a dynamical model of the system being controlled to compute the control input u. Thus, we derived a state-space linear model of the strain carrying the galactose-inducible α-synA53T-GFP construct in single copy. To this end, a system identification experiment was performed on the α-synA53T-GFP yeast strain, as depicted in Fig. 2. Cells were kept in galactose enriched medium in order to fully activate the galactose promoter. The identification experiment was carried out for 40 hours, and galactose and glucose enriched media were alternatively provided to the micro-chamber for 480 minutes (Fig. 2). The average fluorescence of the cell population was then quantified at each sampling time and taken as the system output (Fig. 2, Upper Panel; black line).
In designing the control strategy, two major control constraints were identified: (i) the sampling time and (ii) the admissible values of the control input. We set the sampling time T = 5 min as a compromise to minimise phototoxicity to the cell but maintain a reasonable timeresolution. The control input u can instead assume only two values (galactose = ON, glucose = OFF). Thus, at each sampling time kT , the control algorithm can only choose the duration tON of galactose pulse, which can vary from 0 min to 5 min, and it is defined as the duty-cycle: tON , (1) dk = T i.e. the percentage of the time interval during which the cells are fed with galactose. The control input u is mathematical described as follows, where ON means that cells are fed with galactose enriched medium, and conversely OFF with glucose enriched medium:
SSE
i=k+1
Fluorescence (n.u.)
GFPsimulated
0.6 0.4
kT ≤ t < (k + dk ) T (k + dk ) T ≤ t < (k + 1) T
0.2
(2)
0
The algorithm chooses, at each sampling time kT , the optimal control input, i.e. the duty-cycle values dk , that minimises the sum of the squared control error (SSE): k +N
GFPmeasured
1
0.8
Galactose (w/v%)
ON u(t) = OF F
1.2
2 N + 1 + k − i yˆi − ri ,
0
500
1000
1500
2000
0
500
1000
1500
2000
2
1.5 1
0.5 0
Time (min.)
(3) Fig. 2. Identification experiment. The gray line is the input u provided to the yeast cells inside the microchamber. The black line is the output y measured as an average fluorescence (GFP) on cell population. The blue line is the simulated output to the same stimuli provided for the identification experiment, using the identified discrete model.
where r is the reference signal, and yˆ is the output provided by the dynamical model of α-syn protein under the galactose-inducible promoter, which is computed by a Kalman state estimator able to reconstruct system states from the measured output y. The integer N = 24 (corresponding to 120 min) defines the length of the prediction horizon in terms of sampling intervals. The forgetting factor (N + 1 + k − i) weights the error samples more at the beginning of the prediction horizon than at the end; this guarantees faster corrections of output deviations from the reference. The optimisation was carried out by adopting the Matlab implementation of the Genetic Algorithm described in Goldberg (1989). The result of the optimisation is an array of N optimal duty cycles dk+i , i ∈ [1, N ]. In the absence of external disturbances and other
We decided to identify a two dimensional time-discrete state-space linear model from the input-output data shown in Fig. 2: xk+1 = A xk + B uk (4) yk = C xk where xk = [xk,1 xk,2 ]T is the vector of system state, uk is the control input, yk is the measured output, and 3
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promoter when the cells are fed with galactose. The calibration phase in this case lasts 15 min and the mean of the fluorescence emitted by a constitutively expressed mCherry fluorescent protein was used to estimate the fluorescence value associated to the full induction of the galactose promoter (Fig. 3d).
x0 = [x0,1 x0,2 ]T is the vector of the initial condition. We assumed that the input is piece-wise constant during the sampling period T (zero-order hold method as described in Franklin et al. (1997)). A state-space identification technique was used to fit the model parameters to the data set obtained from the identification experiment (Ljung (1999)). The control input u is the only external stimulus to the model, and it is arbitrarily assumed to be equal to 2 when yeasts are fed with galactose enriched medium, conversely, when yeasts are fed with glucose enriched medium, is assumed to be equal to 0. The estimated model matrices and the initial condition are:
0.9623 0.0095 A = 0.0067 0.9709
(6)
C = [9.569 −0.0424]
(7)
0.1190 x0 = 0.4466
The experimental results confirmed the numerical simulations, demonstrating the ability of the methodology to study quantitatively the dynamics of α-syn protein expression. 7. CONCLUSIONS Automatic control of gene expression is a key technology in synthetic biology and is mature enough to assess quantitatively the dynamics of gene expression. By means of yeast model for the study of the Parkinson’s disease, we demonstrated that a quantitative study of protein aggregation dynamics is possible using the automatic control platform here described.
(5)
−0.0001461 B = 0.006252
11
ACKNOWLEDGEMENTS We are thankful to Prof. Jeff Hasty for microfluidics device and Prof. Susan Lindquist for providing the plasmid carrying the galactose-inducible α-synuclein construct.
(8)
The identified model was able to predict the experimental data across the identification scenario, as depicted in Fig. 2 (Upper Panel; blue line).
REFERENCES Auluck, P.K., Caraveo, G., and Lindquist, S. (2010). α-synuclein: Membrane interactions and toxicity in parkinson’s disease. Annual Review of Cell and Developmental Biology, 26(1), 211–233. doi: 10.1146/annurev.cellbio.042308.113313. PMID: 20500090. Breker, M., Gymrek, M., and Schuldiner, M. (2013). A novel single-cell screening platform reveals proteome plasticity during yeast stress responses. The Journal of Cell Biology, 200(6), 839–850. doi: 10.1083/jcb.201301120. Danino, T., Mondragon-Palomino, O., Tsimring, L., and Hasty, J. (2010). A synchronized quorum of genetic clocks. Nature, 463(7279), 326–330. Ferry, M., Razinkov, I., and Hasty, J. (2011). Chapter fourteen - microfluidics for synthetic biology: From design to execution. In C. Voigt (ed.), Synthetic Biology, Part A, volume 497 of Methods in Enzymology, 295 – 372. Academic Press. doi:http://dx.doi.org/10.1016/B9780-12-385075-1.00014-7. Fiore, G., Perrino, G., di Bernardo, M., and di Bernardo, D. (2016). In vivo real-time control of gene expression: A comparative analysis of feedback control strategies in yeast. ACS Synthetic Biology, 5(2), 154–162. doi: 10.1021/acssynbio.5b00135. PMID: 26554583. Franklin, G.F., Workman, M.L., and Powell, D. (1997). Digital Control of Dynamic Systems. Addison-Wesley Longman Publishing Co., Inc., Boston, MA, USA, 3rd edition. Goldberg, D.E. (1989). Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley Longman Publishing Co., Inc., Boston, MA, USA, 1st edition.
6. EXPERIMENTAL RESULTS As we would like to increase the protein expression at discrete steps, we chose two reference signals: (i) a descending staircase function where each step lasts 750 min, beginning at 75% of the maximum fluorescence when cells are grown in galactose, then stepping down to 50% and then 25%; and (ii) an ascending staircase function where the first and the second step last 750 min, and the third 500 min, beginning at 25% of the maximum fluorescence value, then stepping up to 50% and then 75%. Numerical simulations of the control experiments confirmed the ability of the controller to follow the desired time-varying reference signals (Fig. 3a-b). We thus decided to perform the control experiments invivo, whose results are shown in Fig. 3c-d. Before each control experiment started, cells were inoculated in proper enriched medium to induce, or repress, the expression of the α-syn-GFP construct, depending on the reference signal. In the case of the descending staircase, cells were inoculated in galactose/raffinose enriched medium, and then the culture was repeatedly diluted to achieve a desired concentration on the day the cells were injected into the microfluidics device. A calibration phase lasting 180 min was performed at the beginning of each experiment to normalize the measured fluorescence value during the control experiment (Fig. 3c). Conversely, in the case of ascending reference signal, cells were inoculated in raffinose enriched medium, and then repeatedly diluted to achieve the desired concentration. The raffinose enriched medium allows a faster induction of the galactose-inducible 4
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a
b 1
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Fig. 3. Simulated and experimental staircase control tasks. The black line is the reference signal. The blue line is the simulated (a-b) and measured (c-d) value of the green fluorescent reporter. The gray line is the administered control input. Control tasks were achieved by MPC controller. a) Control experiment simulated on the mathematical model of the strain carrying α-synA53T-GFP construct in single copy with a descending staircase reference signal. The initial level of fluorescence is assumed to be equal to 1. The control action starts at t = 0 min and ends at t = 2250 min. b) Control experiment simulated on the mathematical model of the strain carrying α-synA53T-GFP construct in single copy with an ascending staircase reference signal. The initial level of fluorescence is assumed to be equal to 0. The control action starts at t = 0 min and ends at t = 2250 min. c) Control experiment performed on the strain carrying α-synA53T-GFP construct in single copy with a descending staircase reference signal. The calibration phase lasts 180 min, and the mean value of the measured green fluorescence across the cell population is set equal to 1. The control action starts at t = 0 min and ends at t = 2250 min. d) Control experiment performed on the strain carrying α-synA53T-GFP construct in single copy with an ascending staircase reference signal. The calibration phase lasts 15 min, and the mean value of the measured green fluorescence across the cell population is set equal to 0, whereas the high steady state is set to a fluorescence value proportional to the mean of measured mCherry fluorescent protein across the cell population. The control action starts at t = 0 min and ends at t = 2000 min. Janke, C., Magiera, M.M., Rathfelder, N., Taxis, C., Reber, S., Maekawa, H., Moreno-Borchart, A., Doenges, G., Schwob, E., Schiebel, E., and Knop, M. (2004). A versatile toolbox for pcr-based tagging of yeast genes: new fluorescent proteins, more markers and promoter substitution cassettes. Yeast, 21(11), 947–962. doi: 10.1002/yea.1142. Ljung, L. (ed.) (1999). System Identification (2Nd Ed.): Theory for the User. Prentice Hall PTR, Upper Saddle River, NJ, USA. Melendez, J., Patel, M., Oakes, B.L., Xu, P., Morton, P., and McClean, M.N. (2014). Real-time optogenetic
control of intracellular protein concentration in microbial cell cultures. Integr. Biol., 6, 366–372. doi: 10.1039/C3IB40102B. Menolascina, F., Fiore, G., Orabona, E., De Stefano, L., Ferry, M., Hasty, J., di Bernardo, M., and di Bernardo, D. (2014). In-Vivo real-time control of protein expression from endogenous and synthetic gene networks. PLoS Comput Biol, 10(5), e1003625. doi: 10.1371/journal.pcbi.1003625. Milias-Argeitis, A., Summers, S., Stewart-Ornstein, J., Zuleta, I., Pincus, D., El-Samad, H., Khammash, M., and Lygeros, J. (2011). In silico feedback for in vivo 5
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regulation of a gene expression circuit. Nat Biotech, 29(12), 1114–1116. Morari, M. and Lee, J.H. (1999). Model predictive control: past, present and future. Computers I& Chemical Engineering, 23(4–5), 667 – 682. doi: http://dx.doi.org/10.1016/S0098-1354(98)00301-9. Olson, E.J., Hartsough, L.A., Landry, B.P., Shroff, R., and Tabor, J.J. (2014). Characterizing bacterial gene circuit dynamics with optically programmed gene expression signals. Nat Meth, 11(4), 449–455. Outeiro, T.F. and Lindquist, S. (2003). Yeast cells provide insight into alpha-synuclein biology and pathobiology. Science, 302(5651), 1772–1775. doi: 10.1126/science.1090439. Toettcher, J.E., Gong, D., Lim, W.A., and Weiner, O.D. (2011). Light-based feedback for controlling intracellular signaling dynamics. Nat Meth, 8(10), 837–839. Uhlendorf, J., Miermont, A., Delaveau, T., Charvin, G., Fages, F., Bottani, S., Batt, G., and Hersen, P. (2012). Long-term model predictive control of gene expression at the population and single-cell levels. Proceedings of the National Academy of Sciences, 109(35), 14271– 14276. doi:10.1073/pnas.1206810109.
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Control of gene expression for the study Control Control of of gene gene expression expression for for the the study study neurodegenerative disorders: a neurodegenerative disorders: neurodegenerative disorders: a a proof-of-principle experimental study proof-of-principle proof-of-principle experimental experimental study study
of of of
∗∗ ∗∗ Perrino ∗,∗∗ ∗,∗∗ Cathal Wilson ∗∗ Marco Santorelli ∗∗ ∗,∗∗ ∗∗ Perrino Cathal Wilson Marco Santorelli ∗∗,∗∗∗ ∗,∗∗ Cathal ∗∗ Marco Santorelli ∗∗ ∗∗ Perrino Wilson Diego di Bernardo Perrino Cathal Wilson ∗∗,∗∗∗Marco Santorelli ∗∗,∗∗∗ Diego di Bernardo ∗∗,∗∗∗ Diego di di Bernardo Bernardo Diego ∗ ∗ Department of Information Technology and Electrical Engineering, ∗ Technology and Electrical ∗ Department Department of Information Technology and Electrical Engineering, University of of Information Naples Federico II, 80125 Naples, ItalyEngineering, (e-mail: Department of Information Technology and Electrical Engineering, University of Naples Federico II, 80125 Naples, Italy (e-mail: University of Naples Federico II, 80125 Naples, Italy (e-mail: [email protected]) University of Naples Federico II, 80125 Naples, Italy (e-mail: [email protected]) ∗∗ [email protected]) Telethon Institute of Genetics and Medicine, 80078 Pozzuoli, Italy [email protected]) ∗∗ ∗∗ Telethon Institute of Genetics and Medicine, 80078 Pozzuoli, Italy ∗∗ Telethon Institute of Genetics and Medicine, 80078 Pozzuoli, Italy (e-mail: {wilson, m.santorelli, dibernardo}@tigem.it) Telethon Institute of Genetics and Medicine, 80078 Pozzuoli, Italy (e-mail: {wilson, m.santorelli, dibernardo}@tigem.it) ∗∗∗ (e-mail: {wilson, m.santorelli, dibernardo}@tigem.it) Department of Chemical, Materials and Industrial Engineering, (e-mail: {wilson, m.santorelli, dibernardo}@tigem.it) ∗∗∗ ∗∗∗ of Chemical, Materials Industrial ∗∗∗ Department Department of Chemical, Materials and Industrial Engineering, University Naples Federico II,and 80125 Naples,Engineering, Italy Department of of Chemical, Materials and Industrial Engineering, University of Naples Federico II, 80125 University of of Naples Naples Federico Federico II, II, 80125 80125 Naples, Naples, Italy Italy University Naples, Italy
Giansimone Giansimone Giansimone Giansimone
Abstract: Abstract: Abstract: Neurodegenerative disorders are characterised by the progressive disruption of specific neuronal Abstract: Neurodegenerative disorders are characterised by the progressive disruption of specific Neurodegenerative disorders are by progressive disruption of neuronal population partly due to the formation of abnormal protein aggregates that interfere withneuronal normal Neurodegenerative disorders are characterised characterised by the the progressive disruption of specific specific neuronal population partly due to the formation of abnormal protein aggregates that interfere with normal population partly due to the formation of abnormal protein aggregates that interfere with normal cell functions. In Parkinson’s disease, the role of abnormal α-synuclein protein aggregates in population partly due to the formation of abnormal protein aggregates that interfere with normal cell functions. In Parkinson’s disease, the role of abnormal α-synuclein protein aggregates in cell functions. In Parkinson’s Parkinson’s disease, the the role of of abnormal abnormal α-synuclein protein aggregates in causing the disease is well established. Mutations in α-synuclein are known to cause familial cell functions. In disease, role α-synuclein protein aggregates in causing the disease established. Mutations in ofα-synuclein are known to cause familial causing the is well established. Mutations are to Parkinson’s disease.is Awell quantitative understanding the dynamics of α-synuclein protein causing the disease disease isA well established. Mutations in in ofα-synuclein α-synuclein are known known to cause cause familial familial Parkinson’s disease. quantitative understanding the dynamics of α-synuclein protein Parkinson’s disease. A quantitative understanding of the dynamics of α-synuclein protein aggregation in wild type and mutant form is however lacking. Here, we explore the feasibility of Parkinson’s disease. A quantitative understanding of the dynamics of α-synuclein protein aggregation in wild type and mutant form is however lacking. Here, we explore the feasibility of aggregation in wild type and mutant form is however lacking. Here, we explore the feasibility of using a microfluidics-based platform for automatic control of protein expression from a galactoseaggregation in wild type and mutantfor form is however lacking. Here, expression we explorefrom the feasibility of using a microfluidics-based platform automatic control of protein a galactoseusing a microfluidics-based microfluidics-based platform forand automatic control of protein protein expression from aa galactosegalactoseinducible promoter in yeast, to model study the human α-synuclein protein. using a platform for automatic control of expression from inducible promoter in yeast, to model and study the human α-synuclein protein. inducible inducible promoter promoter in in yeast, yeast, to to model model and and study study the the human human α-synuclein α-synuclein protein. protein. © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Synthetic Biology; Dynamics and control; Modelling; Model Predictive Control; Keywords: Biology; Keywords: Synthetic Synthetic Biology; Dynamics Dynamics and control; control; Modelling; Modelling; Model Model Predictive Predictive Control; Control; Microfluidics; Gene expression; Yeast. and Keywords: Synthetic Biology; Dynamics and control; Modelling; Model Predictive Control; Microfluidics; Gene expression; Yeast. Microfluidics; Gene expression; Yeast. Microfluidics; Gene expression; Yeast. 1. INTRODUCTION et al. (2011), Uhlendorf et al. (2012), Melendez et al. 1. INTRODUCTION INTRODUCTION et al. (2011), Uhlendorf et al. (2012), Melendez et al. 1. et al. (2014)). 1. INTRODUCTION et al. (2011), (2011), Uhlendorf Uhlendorf et et al. al. (2012), (2012), Melendez Melendez et et al. al. (2014)). (2014)). Neurodegenerative disorders are associated to the forma- (2014)). Here, we explore the feasibility of using a microfluidicsNeurodegenerative disorders are associated to the formaNeurodegenerative disorders are to formation of abnormal protein aggregates that interfere with the Here, explore the feasibility of aa microfluidicsNeurodegenerative disorders are associated associated to the thewith formaHere, we we explorefor theautomatic feasibility gene of using using microfluidicsbased platform expression control, tion of abnormal abnormal protein aggregates that interfere the Here, we explore the feasibility of using a microfluidicstion of protein aggregates that interfere with the normal functions of neurons, causing the progressive disbased platform for automatic gene expression control, tion of abnormal protein aggregates that interfere with the based platform platform for developed automaticingene gene expression control, which we recently Fiore et al. (2016), to normal functions of neurons, causing the progressive disbased for automatic expression control, normal of neurons, causing the progressive ruption functions of the neuronal population. The dysfunction ofdisα- which we recently developed in Fiore et al. (2016), to normal functions of neurons, causing the progressive diswhich we recently developed in Fiore et al. (2016), to control the expression of the human α-synuclein protein ruption of the neuronal population. The dysfunction of αwhich we recently developed in Fiore et al. (2016), to ruption the neuronal The dysfunction of αsynucleinof (α-syn) proteinpopulation. is involved in Parkinson’s disease control the expression of the human α-synuclein protein ruption of the neuronal population. The dysfunction of αcontrol the expression of the human α-synuclein protein in yeast cells. The aim is to attain a quantitative undersynuclein (α-syn) protein is involved in Parkinson’s disease control the expression of the human α-synuclein protein synuclein (α-syn) protein is involved in Parkinson’s disease (PD) and(α-syn) relatedprotein neurodegenerative disorders (Auluck aim aa quantitative undersynuclein is involved in Parkinson’s disease in in yeast yeast cells. cells. The aim is is to to attain quantitative understanding of theThe dynamics of attain α-syn protein’s aggregation, (PD) and related related neurodegenerative disorders (Auluck yeast cells. The aim is to attain a quantitative under(PD) and neurodegenerative disorders (Auluck et al. (2010)). Mutations in α-syn protein are also asso- in standing of the dynamics of α-syn protein’s aggregation, (PD) and related neurodegenerative disorders (Auluck standing of the dynamics of α-syn protein’s aggregation, by carefully regulating its expression and following its et al. (2010)). Mutations in α-syn protein are also assostanding of the dynamics of α-syn protein’s aggregation, et al. in associated with rareMutations forms of early-onset familialare PDalso (Outeiro carefully regulating its expression and following its et al. (2010)). (2010)). Mutations in α-syn α-syn protein protein are also asso- by by carefully regulating its expression and following its dynamics in real-time. Driving the expression of α-syn ciated with rare forms of early-onset familial PD (Outeiro by carefully regulating its expression and following its ciated with rare forms of early-onset PD (Outeiro and Lindquist (2003)). The human familial α-synuclein biology dynamics in real-time. Driving the expression of α-syn ciated with rare forms of early-onset familial PD (Outeiro dynamics in real-time. Driving the expression of α-syn protein at different values, we can assess quantitatively the and Lindquist (2003)). The human α-synuclein biology dynamics in real-time. Driving the expression of α-syn and Lindquist (2003)). The human α-synuclein biology has been extensively characterised (Auluck et al. (2010)). different we quantitatively the and Lindquist (2003)). The human α-synuclein biology protein protein at at that different values, we can can assess assess quantitatively the dynamics lead values, to the formation of protein aggregates. has been extensively characterised (Auluck et al. al. (2010)). (2010)). at different values, we can assess quantitatively the has been extensively characterised (Auluck et A yeast model expressing wild type and mutant human protein dynamics that lead to the formation of protein aggregates. has been extensively characterised (Auluck et al. (2010)). dynamics that lead to the formation of protein aggregates. A yeast model expressing wild type and mutant human dynamics that lead to the formation of protein aggregates. A yeast model expressing wild and human α-syn protein has been used totype qualitatively study its A yeast model has expressing wildto type and mutant mutant human α-syn protein beeninused study its 2. AN EXPERIMENTAL TESTBED TO STUDY THE α-syn protein has been used to qualitatively qualitatively study its aggregation properties Outeiro and Lindquist (2003). α-syn protein has been used to qualitatively study its 2. AN AN EXPERIMENTAL TESTBED TOPROTEIN STUDY THE THE aggregation properties in Outeiro and Lindquist (2003). 2. EXPERIMENTAL TO STUDY DYNAMICS OF THE TESTBED ALPHA-SYN 2. AN EXPERIMENTAL TESTBED TOPROTEIN STUDY THE aggregation properties in Outeiro and Lindquist (2003). However, α-synuclein overexpression is toxic also for yeast aggregation propertiesoverexpression in Outeiro and Lindquist (2003). DYNAMICS OF THE ALPHA-SYN However, α-synuclein is toxic also for yeast DYNAMICS OF THE ALPHA-SYN PROTEIN DYNAMICS OF THE ALPHA-SYN PROTEIN However, overexpression is for cells, thusα-synuclein making it difficult to study, if its also expression is However, overexpression is toxic toxic for yeast yeast cells, thusα-synuclein making it difficult difficult toastudy, study, if its its also expression is The toxicity of the α-syn protein has been characterised cells, thus making it to if expression is not carefully controlled. Indeed, quantitative study of the cells, thus making it difficult to study, if its expression is toxicity of the α-syn protein has been characterised not carefullydynamics controlled.ofIndeed, Indeed, quantitative study of the the The The toxicity of protein characterised several cell-based and organism-based models (Auluck not carefully controlled. aa study of The toxicity of the the α-syn α-syn protein has has been been characterised aggregation the α-syn protein is still lacking. not carefullydynamics controlled.ofIndeed, a quantitative quantitative study of the in in several cell-based and organism-based models (Auluck aggregation the α-syn protein is still lacking. in several cell-based and organism-based models (Auluck et al. (2010)). Yeast strains overexpressing normal and aggregation dynamics of the α-syn protein is still lacking. in several cell-based and organism-based models (Auluck aggregation dynamics the α-syn proteincan is still et al. (2010)). Yeast strains overexpressing normal and Automatic control of ofgene expression be lacking. used to et al. (2010)). Yeast strains overexpressing normal and mutant α-syn protein fused to a green fluorescent reporter et al. (2010)). Yeast strains overexpressing normal and Automatic controlthe of expression gene expression expression can be used usedin to toa mutant α-syn protein fused to a green fluorescent reporter Automatic control of gene be precisely regulate level ofcan a protein Automatic control of gene expression can be used to mutant α-syn protein fused to a green fluorescent reporter protein (α-syn-GFP) under the galactose responsive promutant α-syn protein fused to a green fluorescent reporter precisely regulate the expression level of a protein in a (α-syn-GFP) under theused galactose responsive proprecisely expression level aa protein in populationregulate of cells the (Fiore et al. (2016)). Several successful precisely regulate the expression level of of protein in aa protein protein (α-syn-GFP) under galactose responsive promoter have been successfully to dissect molecular protein (α-syn-GFP) under the theused galactose responsive propopulation of cells cells (Fiore et al. al. in (2016)). Several successful moter have been successfully to dissect molecular population of (Fiore et (2016)). Several successful attempts have been described literature to assess the population of cells (Fiore et al. (2016)). Several successful moter have been successfully used to dissect molecular pathways involved in α-syn biology (Outeiro and Lindquist moter have been successfully used to dissect molecular attempts have been described in literature to assess the involved in α-syn biology (Outeiro and Lindquist attempts been described in to the feasibility have of such technology using fluorescent reporter attempts have beentechnology described using in literature literature to assess assess the pathways pathways involved in (Outeiro and Lindquist (2003)). The overexpression of the human α-syn in pathways involved in α-syn α-syn biology biology (Outeiro and protein Lindquist feasibility of such such fluorescent reporter The overexpression of the human α-syn protein in feasibility of technology using fluorescent proteins (Menolascina et al. (2014), Danino et al.reporter (2010), (2003)). feasibility of such technology using fluorescent reporter (2003)). The overexpression of the human α-syn protein in yeast cells mimics the situation of the aging neurons when (2003)). The overexpression of the human α-syn protein in proteins (Menolascina et al. (2014), Danino et al. (2010), yeast cells mimics the situation of the aging neurons when proteins (Menolascina et al. (2014), Danino et al. (2010), Olson et al. (2014), Milias-Argeitis et al. (2011), Toettcher proteins (Menolascina et al. (2014), Danino et al. (2010), yeast cells mimics the situation of the aging neurons when the capacity of the quality-control (QC) system to cope yeast cells mimics the situation of the aging neurons when Olson et al. (2014), Milias-Argeitis et al. (2011), Toettcher the of quality-control system to Olson et al. Milias-Argeitis et (2011), Toettcher Olson al. (2014), (2014), Milias-Argeitis et al. al.Frontier (2011),Science Toettcher the capacity capacity of the themisfolded quality-control (QC) system(Outeiro to cope cope with accumulating proteins(QC) is exceeded the capacity of the quality-control (QC) system to cope This et work was supported by a Human Pro with accumulating misfolded proteins is exceeded (Outeiro This work was supported by a Human Frontier Science Pro with accumulating misfolded proteins is exceeded (Outeiro and Lindquist (2003)). One copy of the α-syn-GFP congram HFSP RGP0020/2011 to DdB and by the Italian Fondazione This work was supported by a Human Frontier Science Pro with accumulating misfolded proteins is exceeded (Outeiro ThisHFSP workRGP0020/2011 was supportedtoby a Human Frontier Science Proand Lindquist (2003)). One copy of the α-syn-GFP congram DdB and by the Italian Fondazione and Lindquist (2003)). One copy of the α-syn-GFP construct is not able to saturate the QC system of the yeast. Telethon. gram HFSP RGP0020/2011 to DdB and by the Italian Fondazione and Lindquist (2003)). One copy of the α-syn-GFP congram HFSP RGP0020/2011 to DdB and by the Italian Fondazione struct is not able to saturate the QC system of the yeast. Telethon. struct is not able to saturate the QC system of the yeast. Telethon. struct is not able to saturate the QC system of the yeast. Telethon. Copyright © 2016, 2016 IFAC 1 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright 2016 IFAC 1 Copyright © 2016 IFAC 1 Peer review© of International Federation of Automatic Copyright ©under 2016 responsibility IFAC 1 Control. 10.1016/j.ifacol.2016.12.095
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However, when inserting multiple copies of the α-syn-GFP construct in yeast, the α-syn protein causes the formation of protein aggregates that are toxic for yeast cells. Thus, the toxicity of the α-syn protein can be studied using yeast strains carrying multiple copies of the galactose-inducible α-syn-GFP construct. However, as soon as the promoter is activated by growing these cells in galactose enriched medium, α-syn toxicity causes cell death thus preventing a thorough investigation and quantification of aggregation dynamics.
the respective pYM27 construct using primers with a 50 bp overhang corresponding to the 5’ and 3’ sequences of the yeast dubious ORF YMR082C using the primers Gal.Syn.Fwd 5’ - TGATTATCTAAGCAGCAATCCCCTTGTCCTA CAAAACAGAAACTGGAAGAAGTACGGATTAGAA GCCGCCGAG - 3’ and S2.Syn.Rev 5’ - ACGCAGACCCATTCGAGGGGCTCATTGGAAA CACGTAGTCGACATTAGTTATCGATGAATTCGA GCTCGTT - 3’.
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Yeast strain carrying the α-synA53T-GFP construct in single copy was grown at 30◦ C in Synthetic Complete (SC) medium, enriched with (i) raffinose (SC+RAF), (ii) glucose (SC+GLC), or (iii) galactose and raffinose (SC+GAL/RAF). The glucose enriched medium is used to repress the induction of the galactose promoter, conversely the galactose/raffinose enriched medium allows the induction of the α-synA53T-GFP construct. The raffinose enriched medium permits instead to grow the cells repressing the induction of the galactose promoter, but allowing faster induction of the construct when they are switched to the galactose enriched medium.
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Fig. 1. Proof of concept. Automatic control of the galactose-inducible promoter can overcome this limitation and enable quantitative analysis of α-syn dynamics in yeast strains carrying multiple copies of the α-syn-GFP construct. Specifically, as depicted in Fig. 1, automatic control of gene expression from the galactose-inducible promoter can be used to increase αsyn-GFP expression at discrete steps, starting from a fully repressed promoter (glucose), thus enabling precise quantification and comparison of the aggregation dynamics of α-syn-GFP wild type and mutant forms.
3.2 Microfluidics Real-time experiments were performed using the MFD0005a microfludics device (Ferry et al. (2011)) in a time-lapse fluorescent microscopy platform as described in Menolascina et al. (2014). Yeast cells are trapped inside a microchamber (height: 3.5 µm), allowing them to grow only in a monolayer, in order to perform accurate image analysis of their fluorescence. Microfluidic devices are fabricated according to the protocol published in Ferry et al. (2011), whereas the experimental setup is the same as in Fiore et al. (2016).
In this work, we proposed a pilot study on the strain carrying the galactose-inducible α-syn A53T (mutant form) construct in single copy, in order to assess the feasibility of controlling its expression at discrete steps in yeast cells. 3. MATERIALS AND METHODS 3.1 Yeast strain and cell culture
3.3 Microscopy and image analysis
α-Syn A53T construct fused to a Green Fluorescent Protein (GFP) under control of the Gal promoter was amplified by PCR from the plasmid pRS304-Syn-A53T (Outeiro and Lindquist (2003)), using the forward primer O.Gal.Fwd 5’ - CAGCTGAAGCTTCGTACGCTGCAGGTCGACA GTACGGATTAGAAGCCGCC - 3’ and reverse primer O.Cyc.Rev 5’ - GGCGGGGACGAGGCAAGCTAAACAGATCTCA AATTAAAGCCTTCGAGCGTCC - 3’ and cloned SalI/BglII into the vector pYM27 (Janke et al. (2004)).
Fluorescence was acquired by means of an inverted fluorescence microscope (Nikon Eclipse Ti) equipped with an automated and programmable stage, an incubator to guarantee fixed temperature (30◦ C) and gasses to cell environment, and a high sensitivity Electron Multiplying CCD (EMCCD) Camera (Andor iXON Ultra897). The microscope and the camera were programmed to acquire, at 5 minutes intervals, two types of images: (i) a bright field image (phase contrast), and (ii) two fluorescence images (with the appropriate filters) to monitor cell fluorescence due to GFP and mCherry proteins and to track a red dye, Sulforhodamine B (Sigma-Aldrich), added to one of the enriched medium in order to evaluate the control input administered to the cells. A custom image processing algorithm was developed to quantify the fluorescence signals
After sequencing, a cassette containing α-syn sequence together with the Kan resistance gene was amplified from 2
2016 IFAC FOSBE 10 Giansimone Perrino et al. / IFAC-PapersOnLine 49-26 (2016) 008–013 October 9-12, 2016. Magdeburg, Germany
being expressed by the entire population of yeast cells (Menolascina et al. (2014)). The measurement units for the fluorescence are considered arbitrary and, thus, a calibration phase at the beginning of each control experiment is needed to calculate a reference value for the fluorescence steady states.
sources of uncertainty, the optimal input computed by the MPC could, in principle, be applied to the yeast cells over the entire prediction horizon. However, in order to make the control action robust to any source of uncertainty and variability, the feedback loop is closed by applying only the first element of the calculated control input and at the next sampling time (k + 1) T when the entire procedure is repeated.
4. CONTROL STRATEGY
To reduce the computational effort to solve the optimal control problem, we decided to use a discrete-time dynamical model of the yeast strain as described in details in the next section.
To assess the dynamics of the α-syn protein, i.e. to control the value of the protein at different levels, we implemented a Model Predictive Control (MPC) strategy, which we previously used to control the galactose-inducible promoter (Fiore et al. (2016)). The MPC algorithm is a feedback optimisation-based technique, which uses a mathematical model of the system being controlled to predict the future values of the control error and to find the best value of the control input that minimises it (Morari and Lee (1999)).
5. MODELLING The MPC strategy needs a dynamical model of the system being controlled to compute the control input u. Thus, we derived a state-space linear model of the strain carrying the galactose-inducible α-synA53T-GFP construct in single copy. To this end, a system identification experiment was performed on the α-synA53T-GFP yeast strain, as depicted in Fig. 2. Cells were kept in galactose enriched medium in order to fully activate the galactose promoter. The identification experiment was carried out for 40 hours, and galactose and glucose enriched media were alternatively provided to the micro-chamber for 480 minutes (Fig. 2). The average fluorescence of the cell population was then quantified at each sampling time and taken as the system output (Fig. 2, Upper Panel; black line).
In designing the control strategy, two major control constraints were identified: (i) the sampling time and (ii) the admissible values of the control input. We set the sampling time T = 5 min as a compromise to minimise phototoxicity to the cell but maintain a reasonable timeresolution. The control input u can instead assume only two values (galactose = ON, glucose = OFF). Thus, at each sampling time kT , the control algorithm can only choose the duration tON of galactose pulse, which can vary from 0 min to 5 min, and it is defined as the duty-cycle: tON , (1) dk = T i.e. the percentage of the time interval during which the cells are fed with galactose. The control input u is mathematical described as follows, where ON means that cells are fed with galactose enriched medium, and conversely OFF with glucose enriched medium:
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(3) Fig. 2. Identification experiment. The gray line is the input u provided to the yeast cells inside the microchamber. The black line is the output y measured as an average fluorescence (GFP) on cell population. The blue line is the simulated output to the same stimuli provided for the identification experiment, using the identified discrete model.
where r is the reference signal, and yˆ is the output provided by the dynamical model of α-syn protein under the galactose-inducible promoter, which is computed by a Kalman state estimator able to reconstruct system states from the measured output y. The integer N = 24 (corresponding to 120 min) defines the length of the prediction horizon in terms of sampling intervals. The forgetting factor (N + 1 + k − i) weights the error samples more at the beginning of the prediction horizon than at the end; this guarantees faster corrections of output deviations from the reference. The optimisation was carried out by adopting the Matlab implementation of the Genetic Algorithm described in Goldberg (1989). The result of the optimisation is an array of N optimal duty cycles dk+i , i ∈ [1, N ]. In the absence of external disturbances and other
We decided to identify a two dimensional time-discrete state-space linear model from the input-output data shown in Fig. 2: xk+1 = A xk + B uk (4) yk = C xk where xk = [xk,1 xk,2 ]T is the vector of system state, uk is the control input, yk is the measured output, and 3
2016 IFAC FOSBE October 9-12, 2016. Magdeburg, Germany Giansimone Perrino et al. / IFAC-PapersOnLine 49-26 (2016) 008–013
promoter when the cells are fed with galactose. The calibration phase in this case lasts 15 min and the mean of the fluorescence emitted by a constitutively expressed mCherry fluorescent protein was used to estimate the fluorescence value associated to the full induction of the galactose promoter (Fig. 3d).
x0 = [x0,1 x0,2 ]T is the vector of the initial condition. We assumed that the input is piece-wise constant during the sampling period T (zero-order hold method as described in Franklin et al. (1997)). A state-space identification technique was used to fit the model parameters to the data set obtained from the identification experiment (Ljung (1999)). The control input u is the only external stimulus to the model, and it is arbitrarily assumed to be equal to 2 when yeasts are fed with galactose enriched medium, conversely, when yeasts are fed with glucose enriched medium, is assumed to be equal to 0. The estimated model matrices and the initial condition are:
0.9623 0.0095 A = 0.0067 0.9709
(6)
C = [9.569 −0.0424]
(7)
0.1190 x0 = 0.4466
The experimental results confirmed the numerical simulations, demonstrating the ability of the methodology to study quantitatively the dynamics of α-syn protein expression. 7. CONCLUSIONS Automatic control of gene expression is a key technology in synthetic biology and is mature enough to assess quantitatively the dynamics of gene expression. By means of yeast model for the study of the Parkinson’s disease, we demonstrated that a quantitative study of protein aggregation dynamics is possible using the automatic control platform here described.
(5)
−0.0001461 B = 0.006252
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ACKNOWLEDGEMENTS We are thankful to Prof. Jeff Hasty for microfluidics device and Prof. Susan Lindquist for providing the plasmid carrying the galactose-inducible α-synuclein construct.
(8)
The identified model was able to predict the experimental data across the identification scenario, as depicted in Fig. 2 (Upper Panel; blue line).
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6. EXPERIMENTAL RESULTS As we would like to increase the protein expression at discrete steps, we chose two reference signals: (i) a descending staircase function where each step lasts 750 min, beginning at 75% of the maximum fluorescence when cells are grown in galactose, then stepping down to 50% and then 25%; and (ii) an ascending staircase function where the first and the second step last 750 min, and the third 500 min, beginning at 25% of the maximum fluorescence value, then stepping up to 50% and then 75%. Numerical simulations of the control experiments confirmed the ability of the controller to follow the desired time-varying reference signals (Fig. 3a-b). We thus decided to perform the control experiments invivo, whose results are shown in Fig. 3c-d. Before each control experiment started, cells were inoculated in proper enriched medium to induce, or repress, the expression of the α-syn-GFP construct, depending on the reference signal. In the case of the descending staircase, cells were inoculated in galactose/raffinose enriched medium, and then the culture was repeatedly diluted to achieve a desired concentration on the day the cells were injected into the microfluidics device. A calibration phase lasting 180 min was performed at the beginning of each experiment to normalize the measured fluorescence value during the control experiment (Fig. 3c). Conversely, in the case of ascending reference signal, cells were inoculated in raffinose enriched medium, and then repeatedly diluted to achieve the desired concentration. The raffinose enriched medium allows a faster induction of the galactose-inducible 4
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Fig. 3. Simulated and experimental staircase control tasks. The black line is the reference signal. The blue line is the simulated (a-b) and measured (c-d) value of the green fluorescent reporter. The gray line is the administered control input. Control tasks were achieved by MPC controller. a) Control experiment simulated on the mathematical model of the strain carrying α-synA53T-GFP construct in single copy with a descending staircase reference signal. The initial level of fluorescence is assumed to be equal to 1. The control action starts at t = 0 min and ends at t = 2250 min. b) Control experiment simulated on the mathematical model of the strain carrying α-synA53T-GFP construct in single copy with an ascending staircase reference signal. The initial level of fluorescence is assumed to be equal to 0. The control action starts at t = 0 min and ends at t = 2250 min. c) Control experiment performed on the strain carrying α-synA53T-GFP construct in single copy with a descending staircase reference signal. The calibration phase lasts 180 min, and the mean value of the measured green fluorescence across the cell population is set equal to 1. The control action starts at t = 0 min and ends at t = 2250 min. d) Control experiment performed on the strain carrying α-synA53T-GFP construct in single copy with an ascending staircase reference signal. The calibration phase lasts 15 min, and the mean value of the measured green fluorescence across the cell population is set equal to 0, whereas the high steady state is set to a fluorescence value proportional to the mean of measured mCherry fluorescent protein across the cell population. The control action starts at t = 0 min and ends at t = 2000 min. Janke, C., Magiera, M.M., Rathfelder, N., Taxis, C., Reber, S., Maekawa, H., Moreno-Borchart, A., Doenges, G., Schwob, E., Schiebel, E., and Knop, M. (2004). A versatile toolbox for pcr-based tagging of yeast genes: new fluorescent proteins, more markers and promoter substitution cassettes. Yeast, 21(11), 947–962. doi: 10.1002/yea.1142. Ljung, L. (ed.) (1999). System Identification (2Nd Ed.): Theory for the User. Prentice Hall PTR, Upper Saddle River, NJ, USA. Melendez, J., Patel, M., Oakes, B.L., Xu, P., Morton, P., and McClean, M.N. (2014). Real-time optogenetic
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