Faculty of Electrical Engineering and Informatics
Modeling, Realization and Characterization of Microreactors in Lab-on-a-Chip Devices
PhD Thesis
Author: Ferenc Ender
Advisor: Prof. Vladimír Székely, member of HAS
Department of Electron Devices
Budapest, 2016.
átvételéről
Alulírott Ferenc Ender kijelentem, hogy ezt a doktori értekezést magam készítettem és abban csak a megadott forrásokat használtam fel. Minden olyan részt, amelyet szó szerint, vagy azonos tartalomban, de átfogalmazva más forrásból átvettem, egyértelműen, a forrás megadásával megjelöltem.
Budapest, 2016. május 19.
Alulírott Ferenc Ender hozzájárulok a doktori értekezésem Interneten történő nyilvánosságra hozata- lához az alábbi formában:
• korlátozás nélkül
• elérhetőség csak magyarországi címről
• elérhetőség a fokozat odaítélését követően 2 év múlva, korlátozás nélkül
• elérhetőség a fokozat odaítélését követően 2 év múlva, csak magyarországi címről
Budapest, 2016. május 19.
1 Introduction 6
1.1 Objectives . . . 7
2 Principles 9 2.1 Microfluidics and related technologies . . . 9
2.1.1 Introduction to microfluidics . . . 9
2.1.2 Technology overview . . . 11
2.1.3 Systems . . . 12
2.1.4 System level modelling of microsystems . . . 13
2.2 Theory and modelling of two phase flows . . . 14
2.2.1 Classification of two phase flows . . . 14
2.2.2 Segmented flow in microfluidics . . . 16
2.2.3 Droplet formation . . . 17
2.2.4 Droplet merging . . . 18
2.3 Modelling of heat transfer in microchannels . . . 18
2.3.1 Convective heat transfer in tubes . . . 18
2.3.2 Thermal compact modeling . . . 20
2.4 Catalytic reactions in microscale . . . 22
2.4.1 Interaction between macromolecules and ligands . . . 22
2.4.2 Enzyme kinetics . . . 23
2.4.3 Enyzmes in packed bed microreactors . . . 26
2.4.4 Phenylalanine ammonia-lyase (PAL) . . . 27
2.5 Analysis methods of reaction kinetics . . . 28
2.5.1 Analysis of the reaction kinetics by calorimetry . . . 28
2.5.2 Spectroscopic analysis of reaction kinetics . . . 28
2.6 Magnetic nanoparticles . . . 31
2.6.1 Magnetic properties of MNPs . . . 32
2.6.2 Sphere packing theory . . . 33
3 State-of-the-art 34 3.1 Thermal design of microreactors . . . 34
3.2 Nanoparticle counting . . . 36
3.2.1 Ensemble methods . . . 37
3.2.2 Single particle counting . . . 39
3.3 Microreactors . . . 41
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4 Thermal compact model for droplet microreactors 46
4.1 Introduction . . . 47
4.2 Modelling methods . . . 47
4.2.1 Governing equations . . . 48
4.2.2 Switched capacitor approach . . . 48
4.2.3 Simplifications . . . 50
4.2.4 Setting up the model solver . . . 52
4.2.5 Building the AEN model . . . 54
4.2.6 CFD simulation settings . . . 55
4.3 Results . . . 56
4.3.1 Performance analysis . . . 56
4.3.2 Model validity range analysis . . . 57
4.3.3 CFD comparison for constant heat flux boundary . . . 58
4.3.4 Comparing FEM and AEN solutions . . . 59
4.4 Application example . . . 59
4.4.1 Modelling the enzyme reaction . . . 59
4.4.2 Temperature profile analysis . . . 61
4.5 Conclusion . . . 61
4.6 Summary of scientific results . . . 62
5 Equipment 63 5.1 Microfluidic testbench . . . 63
5.1.1 uFLU Studio Framework . . . 63
5.1.2 Controller . . . 66
5.1.3 Fluid Control Unit . . . 66
5.2 MagneChip . . . 67
5.2.1 Characteristics . . . 68
5.3 Construction methods of microfluidic chips . . . 69
5.3.1 4 cell MagneChip . . . 69
5.3.2 2 cell MagneChip with integrated magnetosensor . . . 69
5.4 Unit operations of MagneChip . . . 71
5.4.1 Filling of the Magne-Chip microreactors with MNPs . . . 71
5.4.2 Cleaning the chip . . . 72
5.5 Method of single parameter experiments in-chip . . . 72
5.6 Method of multi parameter experiments in-chip . . . 73
5.6.1 Calibration . . . 74
5.6.2 Fluid handling during the Experiment Cycles . . . 74
5.6.3 Variants of experiment cycles . . . 74
6 In-situ quantification of magnetic nanoparticles in a microchamber 76 6.1 Introduction . . . 76
6.2 Materials and Methods . . . 77
6.2.1 Magnetic nanoparticle suspensions . . . 77
6.2.2 Immobilization PcPAL onto MNPs . . . 78
6.2.3 Oscillator circuit and frequency measurement . . . 78
6.2.4 Calibration of the sensors . . . 79
6.2.5 Measurement of the entrapped particle quantity . . . 80
6.3 Results . . . 81
6.3.1 Characterization of the sensors . . . 81
6.3.2 Measurements of the MNP quantity in the chamber . . . 82
6.3.3 Particle volume fraction . . . 83
6.4 Conclusions . . . 84
6.5 Summary of scientific results . . . 85
7 Lab-on-a-Chip microreactor platform 86 7.1 Introduction . . . 87
7.2 Materials . . . 87
7.2.1 Phenylalanine ammonia-lyase from parsley (Petroselinum crispum) . . . 87
7.2.2 Chemicals . . . 88
7.3 Methods . . . 88
7.3.1 UV characterization of the substrates . . . 88
7.3.2 Reference measurements . . . 88
7.3.3 Chip selection and fluid handling methods . . . 88
7.3.4 Summary of MagneChip parameter settings for enzymatic reactions . . . 89
7.3.5 Optical inspection of the chambers . . . 89
7.3.6 Numerical modeling of the chambers . . . 90
7.3.7 Calculation of kinetic parameters . . . 90
7.4 Results . . . 91
7.4.1 General assumptions on the reliability of MagneChip experiments . . . 91
7.4.2 Failures of MNP layers detected by visual inspection . . . 92
7.4.3 Assessment of the reliability of multiparameter measurements . . . 94
7.4.4 Reference measurements . . . 94
7.4.5 Effect of particle size on the enzymatic activity . . . 96
7.4.6 Influence of the flow rate on biotransformation with1a . . . 98
7.4.7 Calculation of the kinetic parameters of the transformation of l-1ato2a. . . . 98
7.4.8 Substrate screening with MNP biocatalyst in the MagneChip system . . . 100
7.5 Conclusion . . . 101
7.6 Summary of the scientific results . . . 102
8 Utilization of the results 104 8.1 Compact model for the nutrient transport in blood capillary vessels . . . 104
8.2 Finding a new operation mechanism of PAL enzyme . . . 104
Köszönetnyilvánítás
Szeretném köszönetemet kifejezni mindazoknak, akik segítettek a disszertációban bemutatott tudo- mányos munkám során. Elsősorban köszönettel tartozom Poppe László professzornak a BME Szerves Kémia és Technológia Tanszékről, akitől rengeteg szakmai támogatást kaptam az enzimes kísérletek kidolgozása és eredményeim publikálása során. Köszönöm a segítséget Weiser Diánának a BME Szerves Kémia és Technológia Tanszékről, hogy úgy mint kiváló szakember és mint barát, mellettem állt és minden helyzetben támogatott. Köszönöm hallgatóimnak, különösen Drozdy Andrásnak, Pálovics Péter- nek, Vitéz Andrásnak és Sallai Gábornak a lelkes munkájukat és a rutinmérések során nyújtott segít- ségüket. Köszönöm a szakmai és emberi támogatást a BME Elektronikus Eszközök Tanszéke vezetőinek, Dr. Rencz Mártának és Dr. Poppe Andrásnak. Köszettel tartozom Dr. Sántha Hunornak az Elektronikai Technológia Tanszékről, aki elindított a tudományos pályán. Végül tiszteletemet fejezem ki konzu- lensemnek Dr. Székely Vladimírnek, akinek a tudományos életművét példaértékűnek tekintem. Kö- szönöm az MTA-EK-MFA a mikrofluidikai chipek elkészítésében nyújtott támogatását.
Köszönöm a támogatást családomnak. Köszönöm Édesapámnak, hogy mindig mögöttem állt és támog- atott a legnehezebb döntésekben. Végül köszönöm páromnak, hogy példát mutatott munkabírásból és kitartásból.
List of Abbreviations AEN Analogous Elecrical Network
CCD Charge Coupled Device
CFD Computational Fluid Dynamics
CTM Compact Thermal Model
DLS Dynamic Light Scattering FEM Finite Element Model
HOMO Highest Occupied Molecular Orbital
LoC Lab-on-a-Chip
LUMO Lowest Unoccupied Molecular Orbital MEMS Micro Electromechanical Systems MNP Magnetic Nanoparticle
MNP-PAL MNP immobilized with PAL MOR Model Order Reduction NMR Nuclear Magnetic Resonance PCR Polymerase Chain Reaction PDE Partial Differential Equation PDM Physical Device Models
PoC Point-of-Care
RCM Resonant Coil Magnetometer ROM Reduced Order Modelling SNR Signal to Noise Ratio
SPICE Simulation Program with Integrated Circuit Emphasis SQUID Superconducting Quantum Interference Device SVR Surface to Volume Ratio
UV-Vis Ultraviolet and Visible Spectral Range (also∼spectroscopy)
VHDL Very High Speed Integrated Circuit Hardware Description Language VHDL-AMS Analog and Mixed Signal Library for VHDL
Materials COC Cyclic Olefyn Copolymer GOD Glucose Oxidase Enzyme IPA Isopropyl Alcohol
PAL Phenylalanine Ammonia Lyase PDMS Polydimethylsiloxane
PEG Polyethylene Glicol PTFE Polytetrafluoroethylene TEOS Tetraethyl orthosilicate
Introduction
Gordon Moore’s prediction on the development of integrated circuits [1] became a standard measure in the technology progress of microsystems. This unbroken development in the recent50years led to a technology breakdown in the related fields such as microtechnology and precision engineering. Short after the first presented micro-electromechanical systems (MEMS) e.g. pressure sensors in the 70’s, chip-scale manipulation of biological samples became reality, establishing the basics of Lab-on-a-Chip technology. Microscale working with biosamples and bio related data, such as DNA, have undergone a steady development that nowadays requires a specialized and devoted infrastructure of robotics, bioin- formatics, computer databases and instrumentation [2]. In the progress of its development, the cost per reaction of DNA sequencing has fallen with a Moore’s Law precision, and, most recently, has been developing even faster [3].
Microfluidics and Lab-on-a-Chip technology have its own role in chemical and especially in biochem- ical analysis and became even more significant in microreactor technology where small size makes enzymatic processes more effective and economical [4, 5, 6].
Microreactors are usually defined as miniaturized reaction systems fabricated by using methods of microtechnology and precision engineering. The term ’microreactor’ is the proposed name for a wide range of devices, having typically sub millimetre channel dimensions which can be further divided into submicron sized components e.g. micro and nanoparticle carriers[7].
Before the evolving of microreactor technology, the traditional way to conduct solution phase syn- thesis and analysis was the conventional batch mode in stationary reactors with stirring or shaking as the only means of mix reactants. Today, micro structured devices offer greatly enhanced performance compared to conventional batch systems due to effects arising from the microscale domain:
• pBatch processes arespace-resolvedtherefore the process must be readjusted in each demand for larger product quantities. In contrast, flow-microreactor processes are time-resolved therefore the output of the reaction is determined by the flow rate and the operation time and no further optimization is needed. This also leads to accelerated process development and enhanced safety due to smaller reactor volumes.[8]
• Microreactors with high surface to volume ratios (SVR) are able to absorb heat created from a reaction more efficiently than any batch reactor. Therefore the reactions are subjected to a homogeneous temperature distribution inside the reactor volume. In contrast, small SVR usually leads to uneven temperature distribution in large scale batch reactors, decreasing the product yield.[8]
• Mixing quality is crucial for many reactions where the molar ratio between the reactants needs to be controlled precisely. Short diffusion paths provide efficient mixing in microreactors, which
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overrides the achievable mixing efficiency of batch reactors. [8]
• In biocatalytic applications, the efficiency of the microreactor can be further improved by immob- ilization of enzymes on nanoscale carriers accommodated in the reactor volume. Re-usability of the biocatalyst makes the process economical and more environmental friendly.
• The possibility of performing similar analyses in shorter reaction time-scale even in parallel is an attractive feature for screening and routine use [9] in protein and enzyme research. A desir- able goal is the high throughput screening of enzymes and their substrates and inhibitors. The prospective fields of application of microreactors are quite wide, include biotechnology, as well as combinatorial chemistry and enzyme targeted drug search [10].
• Analytical systems which comprise microreactors are characterized by outstanding repeatability and reproducibility, due to replacing batch iterative steps and discrete sample treatment by flow injection systems [10]. Benefiting from system automation, this also eliminates errors associated with manual protocols.
• The above benefits lead to a more flexible response to market demands gaining a high poten- tial of using microreactors in industry, as the development results can be faster transferred into production at lower costs.
Despite of the rapid development of enzymatic microreactors in the recent decade, important design questions still need to be answered.
Reaction kinetics is a key parameter of device design. Widely used kinetic parameters are deduced from the Michaelis-Menten model, which has a limited validity to batch reactions only. In flow systems the effects introduced by the flow itself should be also considered. Further complication in modelling can be expected from the immobilized enzymes. On one hand, immobilization may affect the kinetic parameters, on the other hand, the kinetic model should also be changed as the liquid and solid phases are moving related to each other.
Microreactors are built of a reaction chamber which may be filled by an appropriate carrier of the catalyst. The reproducible loading of this carrier is not always straightforward especially in micro scale.
Even more challenging the determination of the actual loaded quantity of the carriers and biocatalysts Long-time stability of the reactor and the reproducibility of the measurements may be affected by the flow rate, the substrate concentration, the immobilized biocatalyst morphology etc.
Micro scale may arise issues also in thermal design as the effects of axial heat conduction, viscous dissipation and low Reynolds numbers should be also considered.
1.1 Objectives
Principles of related fields such as single and two phase microfluidics, heat transfer, enzyme kinetics and nanoparticles are summarized in the next chapter. Recent developments and the state-of-the art are summarized; the challenges are also identified in each related field. The following objectives of this dissertation work intend to make an impact in relation with the challenges outlined below.
• Thermal aspects of device design may play a key role in some bioMEMS devices such as droplet polymerase chain reaction (PCR) microreactors and nanocalorimeters. Approaches on thermal modelling have been demonstrated recently but no general solution has been presented so far for effective assistance of droplet based LoC devices design.
Objective 1: To construct a thermal compact model which provides direct input for a subsequent
transient analysis and handles transient chemical (e.g. enzyme) reactions taking place inside the droplets and resulting in a temperature field as output.
• Possible applications of packed bed microreactors were demonstrated in biocatalysis and in en- zyme screening, however, some questions still need to be clarified. An ever arising question is the accurate determination of the biocatalyst concentration in the reactor. Although several ad- hoc methods were already presented, there is no standardized method to measure the quantity of immobilized enzymes in micro chambers.
Objective 2: To implement a method for accurate, in-situ and on-line determination of the amount of biocatalyst particles in a microfluidic reaction chamber.
• A layer built up of biocatalyst carriers (e.g. nanoparticles) may change its fine structure due to viscous effects caused by the flowing medium in the reactor. Changes in the layer structure may affect the activity of the biocatalyst.
Objective 3: To analyse the effects of structural changes in the layer structure on the biocatalytic activity. Furthermore, to create a measure to describe the structural changes and investigate the requirements of making reproducible measurements with enzyme biocatalysts.
• Particle size and distribution undoubtedly affect the achievable enzyme activity in microreactors.
However, the effect of different particle sizes or using a mixture of different particles have not been analysed before.
Objective 4: To investigate the effect of using different particle sizes on the enzymatic activity and on the possible loading capacity of the microchambers.
• Due to their re-usability, working with enzymes in microreactors makes the process environ- mentally friendly and economical.
Objective 5: To analyse the kinetics of immobilized enzymes in a chip sized microreactor sys- tem and to present a method to carry out multi-parametric measurements providing that the biocatalyst is reused during the measurements.
Principles
2.1 Microfluidics and related technologies
2.1.1 Introduction to microfluidics
At themicroscale, the forces which may be negligible in macroscale (everyday life), can become dom- inant and vice versa. Because of downscaling, shrinking existing large devices and expecting them to function well at the microscale is often counter-productive, although proper design enables function- alities which are unreachable at macroscale [11].
Microfluidics has the potential to change the way modern biology is performed due to the possibility of working with small reagent volumes, shorter reaction times, excellent controllability and the pos- sibility of parallel operation and therefore gaining higher throughput. Efficient technologies may be utilized for the cheap and economical mass production of microfluidics devices.
In the past decade two main areas have prevailed in microfluidics research and development. One is related to the precise handling of biological liquid samples and detecting analytes. The field ofLab-on- a-Chip(LoC) devices [12] has emerged from in-line or on-chip detection. The other field has emerged from the enhanced heat transport in microscale, which created the possibility to design and devise cooling deviceson-chipfor integrated circuits [13].
A general aim of microfluidics design is the intended use of the scaling effects in order to achieve the above mentioned functionalities. Such effects becoming dominant in microfluidics include laminar flow, diffusion, fluid resistance, high surface area to volume ratio and surface tension [11].
Reynolds Number is defined as the ratio of the inertial and viscous forces of a fluid flow. Reis a dimensionless property which describes the flow pattern of the flow. One of the basic concept related to Reynolds number is thedynamic similarity theorem of fluid mechanics. It states that two vessels with the same boundary conditions and sameRewill exhibit the same fluid flow. Besides the fluid flow velocityv, the Reynolds NumberRedepends on geometry and material properties only.
Re= ρvDh
µ (2.1)
whereρis the density and µis the dynamic viscosity of the fluid. Geometry constraint is defined by theDh hydraulic diameter which is related to the cross sectional geometry of the channel. At highRe (typically greater than Re > 2500) inertial forces override viscous forces and the flow may turn into turbulent which is a complicated flow structure of interacting vortices. Taking the typical geometry and flow considerations of microfluidic devices, viscous forces become dominant resulting in lowRe.
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In this caselaminar flowdevelops which is smooth and predictable [14].
Laminar Flow is a condition in which the velocity distribution of a fluid flow, far enough from the fluid entrance is invariant in space and time. One important consequence of this invariability is that the analytical solution of the velocity profile can be obtained directly by solving theNavier-Stokes equations [15]. In case of circular pipes the velocity profile is parabolic and depends on the geometry and the axial pressure gradient only. This follows to theHagen–Poiseuille equation
∆P = 32µLv
d2 = 128µLQ
πd4 =QR (2.2)
where∆P is the pressure gradient between the ends of the pipe,L is the length, d is the diameter, R = 128µLπd4 is the fluid resistance of the pipe, respectively. The fluid flow can be characterized even by the flow velocityvor by the volumetric flow rateQ. The above approach suggests the electrical circuit analogy (Ohm’s Law) therefore basic fluid flow calculations can be done with ease.
Diffusion is the dominating radial mass transfer method in laminar flow. Note that viscous forces constrain the fluid’s molecules to move on the axial direction only, according to the direction of the pressure gradient. Taking the derivation of theFick’s equationin one dimension the moving distanced of a particle overttime is given by
d =p
2Dtdif f (2.3)
whereDis the diffusion constant of the particle. By rearranging, the diffusion time can be deduced tdif f = d2
2D (2.4)
Surface Area to Volume Ratio (SV R) is another factor that becomes important at the microscale and defined as
SV R= A
V (2.5)
Table 2.1. Scaling effect of some related physical quantities Quantity Scaling factor (of size)
Microscale example (d= 50µm)
Macroscale example (d= 5 mm)
Re [L1] Re= 0.5 Re= 50
∆P [L−2] 6.4 kPa 0.64Pa
tdif f [L2] 5 s 14days
SV R [L−1] 2.7·105 m−1 842 m−1
Scaling of the related quantities A comparison of two similar but different sized devices is shown in Table 2.1.
Themacroscopicdevice is a circular duct with a diameter of5 mmand length of5 cm. Water is flowing through the duct with a flow rate ofv = 1 cm s−1.
Themicroscopicdevice is a circular duct with a diameter of50µmand length of5 cm. Water is flowing
through the duct with a flow rate ofv = 1 cm s−1.
Relevant quantities such as Re, ∆P,tdif f andSV R are calculated for both devices. Scaling factor is denoted by the Trimmer’s notation[Ls][16].
Diffusion mixing time is considered as the homogeneous mixing of a solution of30bp DNA strands.
Taking typical geometry sizes of microchannels,Recertainly falls into the laminar flow regime, how- ever high driving pressures are expected in the range ofkPas. Pressure drop found to be an important design parameter of blood plasma separator devices using the Zweinfach-Fung effect [17]. The squared scaling of diffusion time provides the using diffusion mixers in microscale. Efforts had been made in the recent decade to improve mixing efficiency by using zig-zag channel layouts [18, 19]. Surface to volume factor increases linearly as the size reduces, which provides more effective surface reactions and also reduced reaction time compared to the macroscale e.g. in growing complex organisms, such as bacteria [20].
2.1.2 Technology overview
The current technologies used for fabricating microfuidic devices include micromachining (a.k.a. MEMS technology), soft lithography, embossing, injection moulding and laser ablation [11].
Micromachining is originated from the integrated circuit technology and typically uses silicon as the construction material [21]. Distinguishable to surface and bulk micromachining, the technology is widely used to construct micro-electromechanical systems (MEMS) and one of the first approaches to fabricate microfluidic devices. Using bulk micromachining, which defines the structures using selective etching, microchannels can be constructed. Nanopillars were formed in silicon microchannels by using DRIE (Deep Reactive Ion Etching) method [22]. Microchannels were formed in a microcooler struc- ture by anisotropic wet chemical etching using potassium hydroxide (KOH) [23]. In contrast, surface micromachining relies on the deposition of structural thin films on the wafer surface, resulting in relat- ively easy integration of the micromachined structures with on-chip electronics. SU-8 is a typical choice to construct thin film layers for microfluidics [24]. As a supplementary technique, substrate bond- ing can be used either for integrating functionalities or for packaging. Wafer bonding (silicon–silicon, silicon–glass, and glass–glass) is frequently used to fabricate complex 3-D structures. The two most important bonding techniques are silicon–silicon fusion (or silicon direct bonding) and silicon–glass electrostatic (or anodic) bonding [21].
Soft lithography is faster, less expensive, and more suitable for most biological applications than glass or silicon micromachining [11].
PDMS (polydimethylsiloxane) is a popular material of choice for microfluidic devices due to its low cost, ease of fabrication, oxygen permeability and optical transparency [25]. PDMS microchips can be fabricated through microscale moulding processes. For laboratory use, a silicon wafer with patterned photo resist can be used as a mould master. To have a relatively thick structure of microchannels and mi- crochambers for transportation and/or incubation of the reagents and samples, an ultra thick photores- ist, SU-8 was adopted. After the patterning, prepolymer of PDMS is poured into the mould master. Cured PDMS is peeled off from the master to be pasted on a flat plate, i.e. PMMA (polymethylmethacrylate), glass, etc. On PDMS channel body access ports for introduction of the reagents and samples should be drilled in advance [26]. Ports can be also created by punching the PDMS body. The flat plate and the PDMS body can be bonded through free standing siloxane bonds. The process is initiated by oxygen or air plasma treatment [27]. However PDMS is generally treated to be biocompatible, in some cases biocompatibility has to be improved by surface modifications such as covalent linking of hyaluronic
acid on the PDMS surface [28]. PDMS’s hydrophobicity and fast hydrophobic recovery after surface hydrophilization is a general issue in many bioMEMS applications therefore attempts have been made by many research groups to devise longer lasting surface modifications of PDMS [25].
Other techniques Injection moulding is a very promising technique for low cost and production of microfluidic devices [29]. Thermoplastic polymer materials are heated past their glass transition temperature to make them soft and pliable. The molten plastic is injected into a cavity that contains the master. Because the cavity is maintained at a lower temperature than the plastic, rapid cooling of the plastic occurs, and the moulded part is ready in only a few minutes [11]. Similarly, hot embossing is a flexible, low-cost microfabrication method for polymer microstructures, which uses the replica- tion of a micromachined embossing master to generate microstructures on a polymer substrate [30].
Another method of forming microfluidic devices is laser ablation of polymer surfaces such as PMMA (poly(methyl methacrylate)) or COC (cyclic olefin copolymer) [31].
2.1.3 Systems
The ultimate goal of microfluidic systems is a “Lab-on-a-Chip” (LoC) — the incorporation of multiple aspects of modern biology or chemistry labs on a single microchip. One of the first mention of the term
’Lab-on-a-Chip’ was found in the work of Ramsey et. al. (1995) [32]. In the state-of-the-art of LoC tech- nologysemiconductor sequencinghad one of the greatest impact [3] and stands here as an example of the cutting edge but already commercialized LoC technology. This remarkable method broke through the$1,000limit of genome sequencing cost for the first time and therefore opened up the perspectives of next-generation sequencing. The device is the clever integration of semiconductor technology, mi- crofabrication, electrochemical sensing and microfluidics in a chip-sized device and uses a variety of the advances of microtechnology discussed so far.
Figure 2.1. a) Simplified drawing of a well of the semiconductor sequencer, a bead containing DNA tem- plate, and the underlying sensor and electronics. Protons (H+) are released when nucleotides (dNTP) are incorporated on the growing DNA strands, changing the pH of the well (∆pH). This induces a change in surface potential of the metal-oxide-sensing layer, and a change in potential (∆V) of the source terminal of the underlying field-effect b) Die in ceramic package wire bonded for electrical con- nection, shown with moulded fluid lid to allow addition of sequencing reagents. Figure reprinted from [3]
DNA-template is prepared using droplet microreactor based PCR on high surface-to-volume ratio poly- mer micro-beads which are spread homogeneously in the micromachined well array of a silicon chip.
Ion-sensitive (ISFET) chemical sensors are integrated below the wells, together with the seamlessly in- tegrated CMOS readout electronics in the same silicon substrate (Figure 2.1,a). Highly parallel reaction occurs in each well (microreactor) when the mixture of a selected dNTP and polymerase enzyme is driven through the chip (’nucleotide flow’) chamber which is designed to maintain laminar flow on the whole chip surface. The process is repeated sequentially using different nucleotide in the flow, en- abling the detection of the polymerisation of the forthcoming nucleotide bind in each well (depending on the chip size, 1.1 million-11 million wells per chip). Due to short diffusion times each cycle is car- ried out within 5 seconds. One of the first demonstration attempt of the usage the new device was the sequencing of Gordon Moore’s genome, author of Moore’s law [3].
2.1.4 System level modelling of microsystems
System level modelling is a top-downdesign methodology which became one of the common design methods of complex microsystems [34]. The basic concept of system modelling is to provide the beha- vioural description of the system using a high level language e.g. System-C [35] or VHDL-AMS1[36].
Design steps follow each other [33] from the higher level downwards as follows (Figure 2.2)
• Device (LoC) description lies at the highest, ’system’ level and represents the highest level of abstraction as a pure behavioural model [37, 38]. The structural part of the system description is aschematic, a textual (e.g. System C [35]) or graphical (e.g. LabVIEW, SimuLink) representation of the interconnection network of system components. Thelayoutof the device can be generated directly from the description.Detailed simulationprovides information to validate if the system fulfils the design constraints and layout modifications can be done on request. In contrast, system
1VHDL-AMS stands for Very High Speed Integrated Circuit Hardware Description Language for Analog and Mixed Signals
LoC description
Schematic (RTL)
Behavioral simulation
Meet the Spec?
Fabrication Outputs Element
Library
Layout generation
Detailed simulation
Meet the Spec?
No No
Figure 2.2. An integrated top-down design automation environment for microfluidic biochips (after [33]). Compact models and behavioural description provides a shorcut in the design process (red path)
components may be represented by the library elements ofcompact models, which are connected to each other through algebraic equations.
• Compact modelsor Reduced Order Models (ROMs) are derived fromPhysical Device Models(PDMs) by negligating, approximating or linearising secondary physical effects act on the device while the primary effects are described by partial differential equations or algebraic equations. Com- pact models are considered as a behavioural description of the device, therefore even multi do- main functionalities can be handled together at a high level of abstraction. Detailed numerical modelling usually provides high accuracy, requires high computation times, though. In contrast, reduced order models focus on the key behaviour of the device and require only moderate com- putation time. Therefore bypassing the numerical modelling step the design iteration time can be significantly reduced. Figure 2.2, red track shows a possible shortcut in the design flow by utilizing compact models. Different methods were developed for ROM generation.
– Set of Algebraic Equations can describe the device’s behaviour with a given accuracy. The equations can be solved directly or by numerical methods [39]. Initial values are coming from preceding calculations, even from other models. Calculated values are passed towards to subsequent simulations.
– Model Order Reduction (MOR) is an automated method to generate a set of Ordinary Dif- ferential Equations from the original set of Partial Differential Equations e.g. by the Modal Superposition Method [40], used especially for mechanical systems. These models are usu- ally sharing a common interface with FEM elements.
– Analogous electrical network representation. Components of electrical networks may rep- resent analogous quantities in mechanical [36], flow [33, 41] or thermal systems [42]. An important advance of this models is the straightforward integration with electrical subdo- mains of the modelled system.
• Detailed simulation, also referred as Finite Element Analysis (FEM) module, deals with the 2D or 3D geometrical representation of the device which is discretized into elements defined by the
’mesh’ grid. After defining the boundary conditions, loadings and initial values, a set of partial differential equations (PDEs) describe the corresponding physics domain (mechanics, fluidics, thermal, electrostatics etc) are solved numerically [43, 44, 45]. Coupling of the fields (e.g. electro- thermal) is also possible. The result of the analysis is a set of Degree of Freedom (DoF) values (e.g. temperature, displacement etc.) in each finite element.
2.2 Theory and modelling of two phase flows
2.2.1 Classification of two phase flows
Multiphase flows provide several mechanisms for enhancing the performance and extending the func- tionalities of single phase microfluidic systems. Even the shorter diffusion times related to microscale often limits the throughput of single-phase flow systems. Diffusion time can be reduced by adding a second, immiscible, fluid stream that enhances mixing and transverse channel transport by inducing a recirculation motion in the liquid [48]. The resulting multiphase system can also prevent a liquid from direct contact with microchannel walls and thereby eliminate or reduce the unwanted deposition of material on wall surfaces. Multiphase flows are created when two of more partially or immiscible fluids (liquids or a liquid and a gas phase) are brought in contact[49, 50, 44].
(a) (b) (c) (d) (e) (f) (g) (h)
Slug or Annular
Annular Bubble Slug
ReGs ReLs
ReLs Ca
10−3 10−2 10−1 100 101 102 103 107
106
105
104
Figure 2.3. Left: Sketch of observed flow patterns in capillary channels. (a,b): bubbly flow, (c,d) segmen- ted flow (a.k.a. bubble train flow, Taylor flow, capillary slug flow), (e) transitional slug/churn flow, (f ) churn flow, (g) film flow (downflow only), (h) annular flow. Right: ’Flowmap’ from Jayawardena et al.
(after Jayawardena et al., 1997) [46]. Figures reprinted from [47]
Multiphase microflows are characterized by the ratio of viscous to surface forces, the capillary number (Ca), and by the ratio of the Reynolds numbersReof the fluids [46]. Capillary number is the ratio of interfacial tension and viscous forces.Cacan be defined as follows:
Ca= µv
γ (2.6)
whereγis the surface tension between the two fluids. Based on the ratio of the Reynolds number of the carrier liquid and the capillary number (ReLs
Ca ) and the ratio the Reynolds numbers of the two immiscible fluids (ReGs
ReLs
) different flow patterns may develop [47] as it it shown in (Figure 2.3).
• In bubbly flow, when small bubbles dispersed in the continuous, wetting liquid (Figure 2.3,a,b).
In this regimeCa <1therefore the interfacial tension dominates resulting in spherical bubbles.
• Taylor flow, sometimes called plug flow, slug flow, bubble train flow, segmented flow or inter- mittent flow is the flow pattern of large long bubbles that span most of the cross-section of the channel. The relevant lengths are mainly determined by the inlet conditions [51] (Figure 2.3,c,d).
In this regionCais typically larger than1resulting in elongated and asymmetric bubbles.
• At higher velocities, small satellite bubbles appear at the rear of the slug, the pattern is called churn flow. (Figure 2.3,e,f ).
• At high velocities and low liquid fraction, the annular flow pattern exists only of a thin liquid film flowing along the wall, while the core volume is occupied by the flowing gas (Figure 2.3,g,h).
Bond numberBois the ratio of gravitational and surface forces and defined as follows Bo= ∆ρgL2
γ (2.7)
In microfluidic devices Bo 1 can be found indicating gravitational forces can be neglected and should be not considered in device design.
FinallyWeber number W eis the ratio of inertial to surface forces and defined as follows W e= ρv2L
γ (2.8)
Typical W e in microfluidic devices tends to zero indicating the predomination of surface forces. In deed, fine tuning of surface forces is the key point of droplet manipulation device design.
2.2.2 Segmented flow in microfluidics
In the Lab-on-a-Chip usage of such reactors the term ’microdroplets’ usually refers to the above men- tioned second type (Figure 2.3,b,c). Note, that droplets can be also manipulated based on theelectrowet- ting effect, sometimes referred asdigital microfluidics.
The key features of microdroplets in microfluidics are as follows [50]. Microdroplets, forming a mi- croreactor
1. provide a compartment in which species or reactions can be isolated,
2. are monodisperse and therefore potentially suitable for carrying out quantitative studies, 3. provide the possibility to work with extremely small volumes and single cells or molecules and, 4. offer the ability to perform very large numbers of experiments.
Taking this approach, each droplet is analogous to the traditional chemist’s flask [54], with the added physical advantages of reduced reagent consumption, rapid mixing, automated handling, and continuous rather than batch processing [50]. Multiphase microchemical systems (Figure 2.5) take ad- vantage of the large interfacial areas (SVR), fast mixing and reduced mass transfer limitations to achieve
0 0.2 0.4 0.6 0.8 1
0 0.5 1 1.5 2 2.5 3 3.5 4
r/R
z/R
Figure 2.4. Bubble shape (bold line) of gas-liquid segmented flow and relative streamlines. Solid line, clockwise circulation; dashed line, anti-clockwise circulation. Figure reprinted from [52]
Figure 2.5. Droplets formed within microfluidic channels can serve as microreactors. The reactions are performed within aqueous droplets, which contain reagents (A and C), and a separating stream containing buffer (B). The droplets are encapsulated by a layer of a carrier fluid (D) and transported through the microchannels. Figure reprinted from [53]
increased performance compared to conventional bench scale systems [48]. The use of isolated, well mixed droplets enables kinetic studies of organic reactions at millisecond time scales [55], synthesis of nanoparticles [56], biological applications include DNA analysis [57], droplet-based PCR [58], cell encapsulation, and cell stimulus and lysis [48]. Manipulation techniques like well controlled droplet formation, merging, splitting and incubation of the droplets were worked out to build up a complete set of functions for Lab-on-a-Chip usage [59].
The velocity stream structure of the segmented flow was first investigated by Taylor (Taylor, 1961) [60], advancing the development of high performance numeric methods, CFD analysis was done later by others [43, 61, 44, 45, 52] and optical investigation was done by Micro-Particle Image Velocimetry (µPIV) [62, 49].
In Figure 2.4 the typical streamlines can be seen developed inside the bubbles and droplets. The elong- ated anti-clockwise circulation is analogous to a caterpillar track and significantly enhance the mass and heat transfer inside the segmented compartments [52]. Enhanced mixing inside of liquid droplets was proved experimentally [63, 64]. Enhanced heat transfer was investigated experimentally [65] and by CFD analysis [44, 43].
2.2.3 Droplet formation
Droplet formation is the process of in-situ production of monodisperse droplets within the microfluidic device. Droplet formation can bepassiveand activeby means of alternate external field is applied on the device corresponding the droplet generation frequency.
a
b
c
d
e
f
Figure 2.6. Droplet formation techniques: a) T-Junction dripping b) T-junction squeezing c) flow-focus dripping d) flow-focus squeezing; Droplet merging techniques: e) merging in wide channels f ) merging with pillars
The review article of Gu et al. [59] summarized the most common techniques utilized nowadays:
• Passive T-junction devices utilize a T-shaped channel junction where the fluid phase to be dis- persed is brought into the microchannel while the immiscible carrier fluid is driven independ- ently through the other branch. These two phases meet at the junction, where the interface of the two immiscible fluids is deformed by the forces dictated by the flow conditions and geometry.
The competion between the viscous shear stress and capillary pressure results in the pinch-off of the droplet, i.e. viscous shear stress override interfacial tension. Based on the ratio of these forces the following scenarios could be developed:
– In case of dripping, typically develops at higher Ca droplet breakup happens before the droplet would obstruct the channel (Figure 2.6,a).
– Alternatively, in thesqueezing regime, the growing droplet may reach the channel wall and restricts the carrier fluid resulting in rapid pressure increment. This induces the pinch-off of the droplet (Figure 2.6,b).
• Passive Flow-Focusing (FF) devicesconsist of three inlet channels converging into a main channel via a narrow orifice. The dispersed phase is squeezed by the continuous phase flows from the sides. The laminar stream of the two phases flow through the orifice than the narrowed dispersed phase breaks apart into droplets. The droplet size is entirely determined by the flow rate ratio and the orifice geometry. Similarly to T-junction devices, droplet breakup can develop also in the dripping andsqueezing, furthermore injettingregimes (Figure 2.6,c,d).
• Active devicesutilize external fields to affect interfacial forces on demand e.g. by electrowetting.
2.2.4 Droplet merging
Merging of droplets is a key step for triggered start of chemical reactions. The perquisite of merging is the touch of the two droplets and the overcome of stabilizing forces by surface tension and lubrication.
Gu et. al. differentiated the following types [59]:
• Inpassive mergingthe channel is widened at a certain section. In this geometry the droplet velo- city decreases in the widening channel because of drainage of the continuous phase. Due to this changing flow field, two subsequent droplets are allowed to come close and coalescence happens (Figure 2.6,e).
• Droplets can be also merged by slowing down or stopping the leading droplet at widening channel with an array of pillar elements, where the carrier phase is drained letting the subsequent droplet come close (Figure 2.6,f ).
• Droplets can be mergedactively e.g. by applying voltages with opposite sign to the droplets. The oppositely charged surfaces will attract each other as soon as the droplets come close to each other and merging occurs.
2.3 Modelling of heat transfer in microchannels
2.3.1 Convective heat transfer in tubes
Convective heat transfer in tubes The Navier-Stokes equation describes the general energy, mo- mentum and continuity relations of the fluid flow. The following deduction of the energy equation is strongly built on the 9th chapter of Convective Heat and Mass Transfer by W. M. Kays [15]. In case of laminar flow, after a transient section where the velocity profile is space dependent and referred as
r0 r
x
u q''.
u
t0 t
Hydrodyamic entry region
Figure 2.7. Development of the velocity profile in the hydrodynamic entry region of a circular pipe, the fully developed velocity profile and the fully developed temperature profile under constant wall heat flux condition. (After [15])
hydrodynamic entry region, a parabolic velocity distribution is developed along the radial axis of the channel (Figure 2.7). Assuming circular pipe with a radius of r, laminar flow with a flow velocity of u, symmetrical and constant heat flux from the walls, hydrodynamically fully developed flow and no axial conduction the following equation describes the energy state of the flow:
1 r
∂
∂r
r∂t
∂r
= uρc k
dtm
dx (2.9)
wherecis the specific heat andkis the thermal conductivity of the fluid, respectively.tmis themixed mean fluid temperatureand defined as
tm = 1 AcV
Z
Ac
utdAc (2.10)
whereAcis the cross sectional area of the tube.
The fluid temperature is necessary equals to the wall temperature at the wall i.e.
t=t0at r =r0 (2.11)
As the temperature profile must be symmetrical once the heat flux is also symmetrical, the local max- imum of the temperature profile is at the centreline of the channel
∂t
∂r = 0at r = 0 (2.12)
After a transient section where the temperature profile may vary along the tube axis, the profile be- come invariant with the tube length and thereafter is called fully developed temperature profile. The hydrodynamic and thermal development regions are not necessarily the same.
Heat transfer coefficient (h) is defined as
h= q˙00
t0 −tm (2.13)
whereq˙00is the heat flux andt0 is the local (axial position dependent) wall temperature. A heat current will be also developed due to the temperature gradient along the radial axis of the pipe:
˙
q00=−k ∂t
∂r
r=r0
(2.14) Nusselt Number Assuming fully developed velocity and temperature profile and by combining the equations 2.9, 2.13 and 2.14, the following can be deduced for the ratio ofhandk:
N u= 2hr0
k = 4.364 (2.15)
where N uis the Nusselt number, which is simply the non-dimensional version of the heat-transfer coefficient. For non-fully developed flows,N umay be different. Note, that by usingN u, the fluid and wall temperatures can be easily calculated at any length of the channel. The theoretical values ofN u were determined for a great variety of boundary conditions and geometries. Empirical data is also available for N u(x) plots for the thermal development region. On one hand, despite its simplicity theN umodel is quite well usable for engineering calculations. On the other hand, by increasing the Reynolds number or decreasing the channel size, experimental heat transfer values show great deviance from the theoretical values.
100−1 100 101 102 103 104 1
2 3 4 5 6 7 8
Re
Nu
Conjugate effects
Entrance effects
Viscous dissipation Nu0
Figure 2.8. Scaling effects on the mean value of the Nusselt number for water, based on [66]
Scaling effects Several special problems related to heat transfer in micro-channels were observed and analysed in depth: the effect of axial conduction in the channel wall [67], entrance effects and the viscous dissipation effect (Figure 2.8) [68].
• at low Reynolds numbers the heat conduction along the solid wall of the channel is coupled to the convection heat transfer inside the channel: this effect tends to reduce the mean Nusselt number and is referred to as axial conduction or conjugate heat transfer. Due to small hydraulic diameters of the channels and thick walls compared to the channel diameter, axial heat conduction in the walls has to be taken into consideration. This phenomenon is generally neglected in the standard macro-analysis stems from the small size of the systems. Disregarding this effect can lead to a very large bias in the experimental estimation of heat transfer coefficients. [67]. Consequently, modelling of small scale fluid systems requires the introduction of heat conductive shell regions around the channel volume.
• Although this dissertation intends to focus on flows with small Reynolds numbers, entrance ef- fects and viscous dissipation should be undoubtedly mentioned here. Entrance effects become important at high values of the Reynolds numbers and tend to increase the mean value of the Nusselt number [69]. In contrast, viscous heat generation at high Reynolds numbers [68] tends to reduce the mean value of the Nusselt number.
2.3.2 Thermal compact modeling
Transient behaviour of electrical systems The transient behaviour of an electrical transmission line can be described using thetelegrapher’s equation [70]. Each infinitesimally short segment of the distributed system can be modelled by theoretical elementary components, represented by a two-port circuit (Figure 2.9,a):
∂
∂xu(x, t) =−Ri(x, t)−L∂
∂ti(x, t) (2.16)
u(x, t) Cdx Rdx i(x, t) L dx
Gdx i(x+dx, t)
u(x+dx, t)
u(x, t) i(x, t) Rdx
Cdx i(x+dx, t)
u(x+dx, t) T(x, t) Rth
q(x, t)
Cth
a)
b) c)
Figure 2.9. Schematic representation of the elementary component of a transmission line a) detailed model b) simplified model c) analogous representation of the elementary thermal model
∂
∂xi(x, t) =Gu(x, t)−C∂
∂tu(x, t) (2.17)
If the effect of the distributed magnetic field and shunt conductance between the lines should not be considered then a simplifying boundary condition can be applied i.e.L= 0andG= 0(Figure 2.9,b)
∂
∂xu(x, t) =−Ri(x, t) (2.18)
∂
∂xi(x, t) = −C ∂
∂tu(x, t) (2.19)
Transient behaviour of thermal systems The distribution of heat in given region over time is described by theheat equation. Assuming one dimensional problem
k ∂2
∂x2T(x, t)−ρc∂
∂tT(x, t) = 0 (2.20)
wherekis the thermal conductivity,cis the specific heat,ρis the density andT is the temperature.
Temperature gradient causes heat current ofqas described byFourier’s law: q=−k ∂
∂xT(x, t) (2.21)
where, again, the problem is assumed to be one dimensional. Substituting Eq. 2.21 into Eq. 2.20
− ∂
∂xq(x, t)−ρc∂
∂tT(x, t) = 0 (2.22)
by rearranging
∂
∂xT(x, t) =−(1
k)q(x, t) (2.23)
∂
∂xq(x, t) =−(ρc)∂
∂tT(x, t) (2.24)
The formal analogy is obvious between Eqs. 2.18 and 2.23 and similarly Eqs. 2.19 and 2.24. The analogy can be summarized as follows and also represented as an elementary component in Figure 2.9,c.
Table 2.2. Electrical-thermal analogy of lumped thermal models
Electrical quantity Symbols Units Thermal equivalent Symbols Units
Electrical voltage u [V] Temperature T [◦C,K]
Electrical current i [A] Heat current q [W]
Electrical resistance R [Ω] Thermal resistance Rth = k1 [K W−1] Electrical capacitance C [F] Thermal capacitance Cth =ρc [J K−1]
2.4 Catalytic reactions in microscale
2.4.1 Interaction between macromolecules and ligands
This and the following Section 2.5 are merely based on chapters 1.2, 2.1 and 2.2, 3.3, 3.4 of H. Biss- wanger’s Enzyme Kinetics book [71].
Chemical reactions are initiated by the collision of molecules having sufficient energy to react with each other, resulted in conversion into products. In living matter this process is strictly controlled by enzymesand only those compounds (theligands)are converted into products, which were previously selected from others. Selectivity is provided by the binding site of the enzyme and the ligand is a so calledsubstrate. The latter is selectively bond to the binding site and the enzyme catalyses the trans- formation of the substrate toproduct.
In an arbitrary system, the substrate molecules are free to move by diffusion obeying the Fick’s law, characterized by theD diffusion constant. Enzymes can be also free to move (free enzyme system) or they can be attached to a fix surface (immobilized enzyme system). In both cases, the probability of the event that the substrate meets the macromolecule is characterized by theassociation rate constant,ka. Assuming that both the enzyme and and the substrate are spherical and their distance is r, and the binding site is regarded as a circular area, forming angleαwith the center of the enzyme, the following relationship can be written toka(known asSmoluchowski limit)
α r
Enzyme
Binding center
Substrate
[E]+[S] [ES] [E]+[P]
Figure 2.10. Schematic illustration of the interaction of a substrate molecule with its binding site on the enzyme, and the three steps of the catalytic reaction sequence of the product formation. ?: non- substrate,: substrate,/: product
ka = 4πrDsinα (2.25) This approach suggests that every ligand should react whichever once met the binding site. Such un- specific binding could not distinguish between the specific ligand and other metabolites. The gating model, however assumes the binding site opened or closed like a gate by changing the physical con- formation of the enzyme, thus modulating the accessibility of the binding site.
Taking the gating mechanism also into account, the kaassociation constant is limited bykcat, the so calledturnover number.
2.4.2 Enzyme kinetics
Theorderof a chemical reaction with respect to the individual components is defined as the power of the component concentration included in the rate equation.
Zero order reaction is a reaction which is independent on the reactant concentrations. In this case the reaction rate is dictated solely by the very limited amount of free enzyme which remains unchanged during the reactions
v =−d[S]
dt = d[P]
dt =k (2.26)
Integration with respect to time gives a linear relationship
[S] = [S0]−kt (2.27)
Therefore zero order reactions can be identified by the linear progression of the substrate decay and subsequent product formation (Figure 2.11).
0 5 10 15 20 25 30 35
0 1 2 3 4 5 6 7
Time [s−1]
Concentration
[S]
[E]
[ES]
[P]
1 2 3
Figure 2.11. Time-related changes of the reactants of an enzyme-catalysed reaction. 1) Pre-steady phase 2) steady-state phase 3) substrate depletion phase. (kinetic parameters: k1 = 2 mol−1s−1 k−1 = 0.15 s−1k2 = 0.5 s−1)
First order reaction is the conversion of a substrateSinto a productP
A−k→1 P (2.28)
The reaction ratev can be determined either from the time-dependent decrease ofSor the increase of P formed fromS by thek1 rate constant
v =−d[S]
dt = d[P]
dt =k1[S] (2.29)
As one can noticek1 has a dimension ofs−1i.e. independent on the concentration. By integration, the decrease of the substrate can be written as
[S] = [S0]e−k1t (2.30)
Where[S0]is the initial substrate concentration. Decrease in substrate or increase in product proceeds exponentially with time (Figure 2.11).
Let us assume that product P is formed irreversibly from substrate S by the enzymeE in a steady system with diffusion limited mass transfer, and with no compound in - and outflow.
E+S−−)k−−1*
k−1
ES −−→k2 E+P (2.31)
The time-dependent variations of the individual reactants are expressed by the following differential equations:
d[S]
dt =−k1[S][E] +k−1[ES] (2.32) d[E]
dt =−k1[S][E] + (k−1+k2)[ES] (2.33) d[ES]
dt =k1[S][E]−(k−1+k2)[ES] (2.34) d[P]
dt =k2[ES] =v (2.35)
The turnover rate v is defined as the product formation. This depends on, and is therefore directly proportional to the amount of the enzyme-substrate complex ES. Moreover, [ES] depends on the concentration of the reactants.
By solving Eqs. 2.32-2.35 the time-dependent concentration changes of the reactants can be calculated.
This solution merely describes the batch reaction, where initial concentrationsS0andE0are given. For solution in flow systems, see Section 2.4.3. Figure 2.11 shows the solution of changes of concentrations done in MATLAB. Three phases can be differentiated:
1. A short initial (pre-steady) phase, where the [ES]complex is formed and free enzyme [E]de- creases.The turnover rate is low in this region
2. A medium (steady-state) phase, where the concentration of [ES] is nearly constant. Here the turnover ratev attains its highest value.
3. Depletion phase, where the substrate [S] becomes exhausted, the [ES] complex decays and turnover ratev tends to zero
Stability
Temperature stability pH stability
Ingredient/byproduct stability
Solvent stability
Specificity Substrate range
Substrate Specificity (Κm,kcat/Κm Substrate regioselectivity and
enantioselectivity Substrate conversion (%) yield Producibility/expression yield
Byproduct/ingredient inhibition Product inhibition Efficiency
Space-time yield PH profile
Activity
Turnover frequency (kcat) Specific activity (kat/kg, U/mg)
Temperature profile
)
Figure 2.12. Construction of a multi-parameter decision matrix for an efficient candidate enzyme selec- tion. Catalytic reaction rate (kcat), Michaelis-Menten constant (Km), Biocatalytic activity (U) [72]
Since in the steady-state [ES]is nearly constant, the zero order kinetics can be applied therefore
d[ES]
dt = 0and d[E]
dt = 0. The corresponding rate equations can be simplified therefore the turnover rate can be written as
v = d[P]
dt =k2[ES] = k2[E0][S]
k−1+k2
k1 + [S]
(2.36) In practical cases the individual rate constants are not directly accessible by measurement, therefore they are converted intokinetic constants:
• Michaelis-Menten constantKm, units m ormm, gives and indication of the affinity of the substrate, lowKm values indicating high affinities andvica-versa
• Catalytic constantkcat, unitss−1, is a measure of the turnover rate of the enzyme i.e. the maximum number of chemical conversions of substrate molecules per second,kcat =Vmax/[E]0
• Maximum velocity Vmax, units ms−1 is the saturation turnover rate of the reaction
• Catalytic efficiency, the ratio of kcat
Km
, dimension m−1s−1, large values indicate high specificity Using the kinetic constants, the turnover rate can be written as
v = Vmax[S]
Km+ [S] (2.37)
Therefore by knowing the kinetic constants from measurements, the product quantity can be calculated assuming a given substrate concentration[S]and conversely, measuring the product concentration[P] with respect to the initial substrate concentration[S0], the kinetic constants can be determined. For the determination of the constants, several graphical representations are widely used e.g. direct diagram
(a.k.a. Michaelis-Menten plot), Eadie-Hofstee diagram, Lineweaver-Burk diagram etc.
Taking enzymatic reactions, the trade-off betweenactivity,stability,specificity andefficiency have to be taken into consideration. (Figure 2.12). This decision matrix reveals the strengths and weaknesses of every candidate enzyme, so that the most promising candidate enzymes from diverse enzyme lib- raries can be selected for further process development by re-screening, protein engineering or directed evolution methods [72]. For instance, immobilization of enzymes may increase their stability but the activity may be reduced [73]. Specificity of enzymes or enzyme-cascades could improve by genetic modification (mutation) of the protein, however stability and activity could be affected as well [74].
2.4.3 Enyzmes in packed bed microreactors
The kinetics of enzyme catalysed reactions in reactor columns filled with enzymes linked to insoluble carriers were first studied by Lilly and Hornby[75] and their proposed method is referred as Lilly- Hornby method thereafter. The reactor has an initial volume ofVtand as a given space is occupied by the carrier, the void volume isVl(Figure 2.13).
The insoluble enzyme constituting the microreactor chambers may be considered as a suspension of enzyme in a volume equal to the total volume of the reactor:
[E] = E
Vt (2.38)
Let us consider an enzymatic catalysis where the substrate flows through the reactor by a flow rate of Q˙ and spendstresidence time in the reactor. The initial substrate concentration[S0]has been changed to[St]as[S0]−[St]concentration was transformed to product over the residence timet=Vl/Q˙ (Figure 2.13). Let us assume that the reaction obeys the Michaelis-Menten kinetics, therefore the amount of the reacted substrate can be obtained by integration the Michaelis-Menten equation:
[S0]−[St] =kcat[E]t−Kmlog([St]/[S0]) (2.39) The model assumes that a horizontal cross-section of the liquid moves like an imaginary piston in the column and the flow may be referred to as ’piston flow’. Under these conditions Eq. 2.39 applies to each infinitesimal cross-sectional piston volume and therefore expresses the total reaction taking place in
log(1−P)
*
Ps 0
*
s0 Q
st Q Vt
Vl P =s0s−st
0
P s0= Kmlog(1−P∗) + R/ Q
Figure 2.13. Interpretation of enzyme kinetics in filled reactors and the plot of Lilly-Hornby method to determine the kinetic constants
each such volume during its passage through the column [75].
LetP∗ be the fraction of the substrate reacted in the column:
P∗ = [S0]−[St]
[S0] (2.40)
Using the above notations Eq. 2.39 can be written as
P s0 =Kmlog(1−P∗) +R/Q (2.41) whereR = kcatEVl/Vt. If the values ofP are measured when reacting with different initial[S0]con- centrations of the substrate, thenP∗[S0]plotted againstlog(1−P∗)will give a straight line ifKm,Q˙ andRare constants. The slope of the line will be equal toKm and the intercept on theP∗s0 axis will be equal toR/Q.
2.4.4 Phenylalanine ammonia-lyase (PAL)
PAL enzyme was used as a model biocatalyst in the experiments presented in this work. PAL is a member of the ammonia-lyase family, which catalyses non-oxidative deamination of it natural sub- strate (l-phenylalanine , denoted by l-1ahereinafter). In nature phenylalanine ammonia-lyase (PAL;
E.C.4.3.1.24) catalyses the biotransformation of l-1ato(E)-cinnamic acid (denoted by l-2ahereinafter), a precursor for the lignin and flavonoid biosynthetic pathways [76]. The reaction scheme including the subsequent steps can be described as follows:
[E]+[l−1a]−−)k−−1*
k−1
[E.l−1a]−−)k−−2*
k−2
[E.N H3−l−2a]−−)k−−3*
k−3
[E.N H3]+[l−2a]−−)k−−4*
k−4
[E]+[l−2a]+[N H3] (2.42) Here ’.’ denotes the primary, strong bonds while ’-’ denotes weaker, secondary bonds. During the meas- urements, only the concentration of l-2a was measured directly therefore there was no information collected regarding the2nd and3nd reaction steps.
Figure 2.14 illustrates the ammonia elimination of l-1aand the formation of l-2aby the biocatalyst.
Here, the termbiocatalystis referred as the biofunctionalized particle (MNP), carrying the PAL enzyme.
MNP-PAL
L-phenylalanine trans-cinnamic acid PcPAL
MNP
L-1a L-2a
Figure 2.14. Schema of ammonia elimination of l-phenylalanine by MNP-PAL biocatalyst Since its discovery, much knowledge has been gathered with reference to the enzyme’s catabolic role in micro-organisms and its importance in the phenylpropanoid pathway of plants[77]. PAL has
