WO2006005371A1 - Microfluidic device for performing a plurality of reactions and uses thereof - Google Patents

Abstract

The present invention relates to a microfluidic device for performing a plurality of reactions. In particular, the present invention features a method and device for performing a plurality of chemical and/or biological reactions in parallel by providing an array of releasable reagents into the inner surface of a capillary. The present invention is exemplified by performing a large number of polynucleotide amplification reactions using the capillary array. In addition, the present invention features a method and device for coupling the amplification of polynucleotides and the detection and/or analysis of the amplified products.

Description

MICROFLUIDIC DEVICE FOR PERFORMING A PLURALITY OF REACTIONS AND USES THEREOF

The present invention relates to a microfluidic device for perforrning a plurality of reactions. In particular, the present invention features a method and device for performing a plurality of chemical and/or biological reactions in parallel by providing an array of releasable reagents into the inner surface of a capillary. The present invention is exemplified by performing a large number of polynucleotide amplification reactions using the capillary array. In addition, the present invention features a method and device for coupling the amplification of polynucleotides and the detection and/or analysis of the amplified products.

BACKGROUND OF THE INVENTION

The draft sequences currently available for a large number of genomes can serve as reference sequences for assays that are being developed to compare individual sample sequences to such a reference. As an example, in the medical field, such comparative analyses between a reference sequence and a sequence obtained from a person displaying a disorder, or having a predisposition to such a disorder or to a disease, should allow the diagnosis, the prognosis and/or the provision of appropriate treatment of said human disorder or disease. Analytical tools of nucleic acid sequences are thus required to study the genetic diversity especially based on single or polynucleotide polymorphisms as compared to the sequences generated by the sequencing of entire genomes.

A general prerequisite for nucleic acid detection and/or analysis is the amplification of the target nucleic acid sequence according to protocols such as the polymerase chain reaction (PCR) protocol. The polymerase chain reaction (PCR) has proven to be a phenomenal success for genetic analysis, largely because it is simple and very versatile, and requires relatively low cost instrumentation. The methodology of the polymerase chain reaction is more fully described in US Pat Nos 4,683,202 and 4,683,195.

Basically, the first step of PCR consists in heating the reaction mixture containing the target DNA, a large excess of primers, the four nucleotide bases, and DNA polymerase, such that the paired strands of all of the DNA in the sample denature, or separate. The single strands are thus accessible for the primers. Next, the sample is cooled to allow doύble-strands to form again. Because of the large excess of primers, the two strands of the denatured or separated strands of the target DNA templates bind to the complementary primers instead of with each other. In the third step, the temperature is adjusted to obtain maximum activity for the DNA polymerase enzyme. For each DNA sequence that is annealed to a short primer, the enzyme will extend the primer's sequence such that the original double helix for the DNA sequence is replicated.

This process is repeated several times, usually between 20 to 30 times, each time approximately doubling the amount of DNA present. The result is an exponential increase in the concentration target DNA, known as

"amplification" of the target DNA.

Nucleic acid amplification technologies have been developed in various fields including, for example, the food industry or agro-industry for contaminant detection, or the medical field for disease diagnostic or genetic testing.

PCR is typically performed in disposable reaction tube such as small, plastic, microcentrifuge tubes or test tubes which are placed in an instrument containing a thermally controlled heat exchanger. PCR reaction volume is generally comprised between 10 microliters and 1.5 milliliters in conventional heat block or liquid bath heat exchanger PCR instrument designs where the reaction mixture has been stored in microcentrifuge tubes.

For complete diagnostic or analytical purposes, multiple amplification reactions performed on the same sample are often required. Ideally, the procedures for performing in parallel a plurality of amplifications should be carried out with a small volume of sample and a small volume of reaction mixture for each amplification reaction, without loss of sensitivity.

The procedures should also be easy to carry out, i.e., requiring a minimum of manual steps to be performed by a technician.

There is a thus a need to develop new procedures allowing to perform in parallel a plurality of amplification assays having recourse to small volumes of the same sample.

One solution is the multiplex amplification, which is widely used in the Art, especially for genotyping analysis. Multiplex amplification consists in performing multiple PCR amplifications in the same reaction tube by mixing different pairs of primers, said pairs of primers being designed so that they do not interact each other. The different amplified products mixed in the same reaction tube can be detected, for example, by size separation through capillary electrophoresis.

However, for different reasons, including competitive inhibition between the different pairs of primers when the target sequences are overlapping or hybridisation between the different primers, some amplification reactions may not occur, leading to false negative and decreasing the sensitivity of the multiplex amplification.

PCT patent application WO 01/27327 (Protogene, October 6, 2000) describes a device for performing multiplex amplification by bringing two arrays into close apposition and allowing reagents on the surfaces of the two arrays to come into contact. However, such array-based devices are hampered by their format: planar arrays are indeed difficult to handle and do not allow complex enzymatic reactions to take place.

There is therefore a need in the Art to provide alternative and sensitive method suitable for performing a plurality of polynucleotide amplifications.

A first object of the present invention is thus to provide methods and device to perform a plurality of polynucleotide amplifications in parallel in a single reaction volume.

More generally, one object of the present invention is to provide methods and device to perform a plurality of reactions in a single reaction volume, especially a plurality of chemical reactions.

The method and device of the invention are indeed capable of generating large amounts of products per unit time by carrying out large numbers of reactions using a single reaction volume. Furthermore the present invention is amenable to full automation.

It is shown in the present invention that single capillary can be advantageously used to perform different reactions in a single reaction volume, wherein corresponding reagents for each reaction are released in a discrete area of the capillary. Indeed, it is shown in the present invention that products present in a discrete region of a capillary have an axial controllable diffusion capacity which can be used to allow them to mix with other products present in the discrete region of the capillary and to prevent them from mixing with other products present in other distinct regions.

A microfluidic device comprising a PCR amplification reaction chamber coupled with capillary electrophoresis is described in US patent 6,372,484. The capillary allows electrophoresis of the amplified product and further analysis.

Device for performing PCR amplifications comprising reaction chambers for the reception of the reaction solution and capillaries in close proximity to heating and cooling elements, thereby accelerating the temperature setting in the reaction solution, are also described in the Art (see for example US 5,176,203; US 5,827,480).

A device for performing PCR amplifications in capillary, comprising a system to control temperature is also commercialised from Roche Diagnostics (the Lightcycler©, F. Hoffmann-La Roche Ltd, Basel,

Switzerland).

The above-mentioned capillaries are used either as a means for moving small PCR reaction volumes from different reaction chambers or as a means for optimising efficient heat transfer to small PCR reaction volumes, thereby limiting the time of the reaction.

None of these devices provides solutions to perform multiplex amplification.

A first object of the invention thus concerns a capillary suitable for performing a plurality of reactions, wherein said capillary comprises a plurality of functional rings (FR₁-FR_n) designed in its inner surface, each functional ring having an inner surface which comprises at least a first area

(R) and a second area (F), and each functional ring having a first releasable reagent releasably attached to said first area (R) within the inner surface of the functional ring of the capillary and a second releasable reagent releasably attached to said second area (F) within the inner surface of the functional ring of the capillary, and wherein in each determined ring, said area (F) is overlapping or is close enough to said area (R) for allowing their respective reagents to mix after their release and for performing a reaction involving at least the two released reagents as substrates. As used herein, the term "capillary" refers to a single tube or a single channel having a diameter less than 1 millimeter.

In the above definition, the inner surface of the functional ring is a part of the inner surface of the capillary, identical to or smaller than the whole surface of the functional ring, which comprises the areas R and F.

Any suitable material for capillary may be used in the present invention. These materials include glass, silicon, quartz, metal, among others, and more preferably glass, silicon or quartz.

In one embodiment, the capillary is rigid, and is preferably made of glass, as illustrated in examples 1 and 2.

Examples of diameters of a capillary according to the invention are given in Table 1. In one preferred embodiment, the capillary of the invention has a diameter of between 1 and 500 μm, preferably between 1 and 200 μm, and more preferably between 1 and 100 μm.

Table 1

As used herein, the term "functional ring" refers to a functional unit of the capillary which corresponds to the section of the inner surface of the capillary wherein, at least two releasable reagents are attached in a releasable manner, one first reagent being attached to a first area and one second reagent being attached to a second area, said second area overlapping or being close enough to the first area for allowing the reagents to mix especially by diffusion, after their release, and for performing at least one reaction involving at least the two released reagents as substrates.

While it is convenient to describe a capillary for performing reactions triggered by the mixing of two reagents released in each functional ring, many variations of said capillary are within the contemplation of the present invention. Optionally, more than two reagents can be attached to the same functional ring allowing to perform one reaction using more than two reagents or to perform multiple reactions in the same reaction volume, such as multiplex amplifications.

Each reagent occupies a definite area when attached to the inner surface of the capillary, which area may extend after the release of said reagent in such a manner that the reagents of one functional ring are allowed to react together after mixing as a result of the controlled diffusion.

As understood by those skilled in the Art, molecular diffusion of released reagents and reaction products in a confined reaction region is based on the Einstein law depending upon the viscosity of the fluid, the temperature and hydrodynamic radius of the reagents and reaction products.

In a capillary, where ratios surface/volume are high, it is shown in the present invention that interactions of the reagents with the internal walls impact the axial diffusion coefficients.

More specifically, the following have been shown: If the ratio between the size of functional ring and the radius of the capillary is high enough, in the first seconds, the reagents occupies the capillary section delimited by the initial functional ring and, surprisingly, the axial diffusion is weak in this first period of time. Axial diffusion is becoming more important in broader range of time. This result has two causes: geometrical and biochemical. The diffusion coefficient is isotropic so that the speed of diffusion is the same in the radial and axial directions. However, due to the largely anisotropic geometry of the capillary, the characteristic time for diffusion in the radial direction on a distance equal to the capillary radius is smaller than that in the axial direction on a distance equal to the spacing between the functional rings. Besides, the primers can be recaptured on the wall in the functional rings and this leads to a slower diffusion in the axial direction.

Taking into account the advantageous properties of molecular diffusion in the capillary, the one skilled in the Art will thus determine the structure of the capillary, the density of the attached reagent to the inner surface of the capillary, and the dimensions of each area for obtaining locally a concentration of both reagents after their release equal to or above the critical minimum concentration necessary for the reaction to take place, while avoiding mixing of the other reagents from distinct functional rings.

According to one embodiment, said definite area is a cylindrical section of said inner surface as shown in figure 1.

In one embodiment, the two reagents of a functional ring can be mixed and attached to the inner surface in the same cylindrical section, the first area (R) and the second (F) being thus indistinguishable. In another embodiment, the two reagents can be attached to distinct areas which correspond to neighbour sections of the capillary as shown in figure 1.

One advantage of the capillary of the invention is that no specific mechanical methods such as microfabricated reaction wells or chemical methods such as chemical barrier including hydrophobic chemicals are necessary to prevent reagents of one functional ring from entering another functional ring after release.

According to one preferred embodiment of the capillary, each functional ring has an axial length of between 20 μm and 10 mm, preferably between

100 μm and 1 mm.

Depending upon the axial length of functional ring, the length of the capillary and the type of reagents attached to the inner surface of the capillary, the number of functional rings in the capillary-for performing may vary between about 2 to 1000, preferably between about 2 to 100, and more preferably between 10 to 50.

Optionally, in order to prevent reagents or products of one reaction to mix with reagents or products of another reaction, the capillary can comprise a region forming a spacer (S) between two functional rings, wherein no reagent is attached to the inner surface of the capillary in said spacer region, wherein the spacer prevents the reagents released from two distinct functional rings to mix together, as shown in figure 1.

The reactions which are compatible with the present device and method are very broad, encompassing all non-unimolecular reactions, preferably chemical reactions involving two or more reagents, provided that the reactions can be performed in the same reaction solution comprising optionally one or more reagent in common.

The reagents can thus be selected, but are not limited to, among the peptides, polysaccharides, carbohydrates, lipids, proteins, cells, viruses, and nucleic acids.

The reaction is triggered by releasing of the reagents attached to the inner surface of the capillary, at least for one functional ring and their mixing. The reagents and the reaction products remain confined to a discrete region in the functional ring according to the limited axial diffusion in the capillary.

Methods for immobilizing the releasable reagents in the capillary are described in the Art. Especially, the releasable reagents can be synthesized and attached to the capillary in situ or can be synthesized in a first step and attached to the capillary in a second step.

The reagents are immobilized via a releasable site, for example, by tethering to an immobilized molecule with a cleavable moiety. Methods for attaching releasable reagents at a specific area to the inner surface of the capillary are described in the Art, and in particular in US patent application

2003-0032035-A1 (Chatelain et al., CEA, 2003).

In one preferred embodiment of the invention, the capillary is suitable for performing one or several polynucleotide amplifications.

Especially, the capillary is suitable for performing a plurality of polynucleotide amplifications in parallel.

In a preferred embodiment, each functional ring has an inner surface which comprises at least a first area (R) and a second area (F), wherein a first releasable oligonucleotide as the forward primer of one polynucleotide amplification, is releasably attached to said first area (R) within the inner surface of the capillary, and a second releasable oligonucleotide suitable for use as the reverse primer is releasably attached to said second area (F) within the inner surface of the capillary.

According to the invention, a forward primer is a primer which can prime extension after hybridisation to the one strand (+) of a target DNA. A reverse primer is a primer which can prime extension after hybridisation to the complementary strand (-) of said target DNA. Each functional ring comprises at least one couple of reverse and forward primers for amplifying one specific nucleic acid sequence. Different primer sequences specific for different regions of the same target sequence can be attached to the same capillary, allowing multiple amplifications of different fragments of the same target sequence to perform.

Primers can be released using any usual known methods in the Art, including, enzymatic, chemical, thermal or photolytical treatment.

For example, primers may be initially hybridised to immobilized polynucleotides and subsequently released by strand separation from the inner surface of the capillary. In another example of primer release, one or more primers for polynucleotide amplification reactions may be covalently immobilized on an array via a cleavable site. A cleavable site may be introduced in a moiety, bound to the inner surface of the capillary, during in situ synthesis. Alternatively, the immobilized moieties containing releasable sites may be prepared before they are covalently or noncovalently immobilized on the capillary.

In one specific embodiment, said cleavable moiety is cleavable by photolysis.

Typically, the density of oligonucleotides attached within the inner surface of the capillary in each functional ring is between about 1 and 1000 fentomoles per square mm, preferably between 10 and 100 fmoles/mm².

In a preferred embodiment, each functional ring is divided into two cylindrical sections comprising respectively the reverse primer and the forward primer for one amplification reaction.

Some dimensions of the capillaries and the corresponding number of functional rings are given in the following table 2. The values listed herein are merely illustrative and do not limit the scope of the invention. TABLE 2

In one embodiment, the number of functional rings on the capillary is between about 2 to 100, preferably between 10 and 50.

One other advantage of the capillaries of the invention is that they can be easily integrated in a microfluidic device.

It is thus another object of the present invention to provide a microfluidic device for performing a plurality of chemical reactions, comprising: a) one or several capillaries of the invention as herein above defined, b) means for circulating the reaction solution, c) means for controlling the flow rate of the reaction solution through the capillary, d) means for releasing the releasable reagents attached to the inner surface of the capillary, and, e) optionally, means for quantitating the reaction products.

The device should provide means for circulating the reaction solution, i.e., to move the reaction solution into the capillary (where the reaction takes place), after its introduction into the device, to immobilize the solution flow during the reaction period, and to remove the solution containing the reaction products from the capillary, before, during or after analysis of said reaction products. In one embodiment of said device, solution flow in the capillary is pressure- induced, and said means for circulating the reaction solution comprises pressure-driven syringe pump.

The skilled artisan is aware of the fact that pressure injection devices are commercially available; having been developed for numerous automates

[computer controlled syringe pumps by Carvo (Applied Biosystems, Foster City, CA, USA), Hamilton Company (Reno, NV, USA), Tecan Group Ltd. (Mannedorf, Switzerland), P/ACE™ Series system from Beckman Coulter Inc.]. A wide range of volumes and flow rates are thus achievable.

According to other embodiments, solution flow is, for instance, electro- kinetically induced, and/or induced by shear forces, gravimetrical forces, capillary action, and the like.

The device should also provide means for releasing the releasable reagents. Such means can be based for example on thermal methods or photochemical methods initiated by irradiation.

When photochemical methods are used, said means may comprise irradiation sources which include, but are not limited to, laser light, CRTs, LEDs, Resonant Microcavity Anodes, photodiodes, broad wavelength lamps, and the like. Irradiation can be focused to discrete sites, for example, some specific functional rings along the capillary length using optical or physical methods. In this embodiment, the capillary is preferably made of optical clear material, such as glass or quartz, allowing the light to cross the capillary walls.

For allowing in situ synthesis using photochemical methods, the device may also advantageously comprise means for producing collimated light beams, including for instance, individual lasers, masks, arrays of mirrors, and TV screens. Several methods have been developed to detect biochemical products in capillaries. Detection of the reaction products in the capillary can be performed by methods including, without limitation, photochemical, electrochemical, electrophoretic, fluorescent, UV/VIS absorbance, MS, IR, and/or chromatographic methods.

Optical detection methods are usually used since they alleviate the problem posed by the necessity to detect the products at the capillary end. Suitable methods are for instance UV-VIS spectrophotometry, direct fluorescence, and time-resolved fluorescence.

In one specific embodiment, the device comprises means for carrying out optical detection, including an excitation light source associated to a detector of fluorescent emission such as a PMT, a scanner or a linear charged coupled device (CCD) to generate a quantitative fluorescent image of the capillary as a means for quantitating the reaction products labelled with fluorescent material.

Moreover, as far as most biochemical reactions and/or analyses require the temperature to be precisely controlled, the microfluidic device according to the invention can further comprise means for controlling the temperature in the capillary. As an example, when PCR is used to amplify target DNA, the device temperature is usually cycled between 40 and 95⁰C. Systems were developed and are commercially available to enable PCR to be performed in capillaries. Such a system, for instance, the Lightcycler from Roche Diagnostics (F. Hoffmann-Laroche Ltd, Basel, Switzerland) (PCR in capillaries), the P/ACE™ Series system from Beckman Coulter, Inc. (Brea, Fullerton, CA, USA) (capillary electrophoresis with thermostated capillary compartment), can be adapted the skilled person to perform temperature- controlled experiments (not only for PCR) in the microfluidic device of the invention as described herein. In one specific embodiment, the device may comprise a plurality of capillaries.

Another aspect of the invention relates to a method for performing a plurality of reactions, comprising the use of a capillary according to the invention as above-defined or the microfluidic device of the invention comprising such capillary as above defined.

More specifically, the invention concerns a method for performing a plurality of reactions, comprising the steps of: a) providing a capillary according to the invention as above-defined or the microfluidic device of the invention comprising such capillary as above defined; b) filling the capillary with a reaction solution comprising one or more reagent(s) in common to all reactions and an appropriate buffer; and, c) releasing reagents attached to the inner surface of the capillary; thereby allowing one or several reactions to perform in said capillary, each reaction occurring in the discrete region where appropriate reagents are released and mix.

According to one embodiment of the method, the reagents from distinct functional rings of the capillary are released simultaneously, thereby allowing multiple reactions to perform in parallel in a single reaction volume.

The invention thus also concerns a method for performing a plurality of polynucleotide amplifications, comprising the use of a capillary appropriate for performing multiple polynucleotide amplifications according to the invention as above-defined or the microfluidic device of the invention comprising such capillary as above defined.

More specifically, the invention concerns a method for performing a plurality of polynucleotide amplifications, comprising the steps of: a) providing a capillary appropriate for performing multiple polynucleotide amplifications according to the invention as above-defined or the microfluidic device of the invention comprising such capillary as above defined; b) filling said capillary with a reaction solution appropriate for polynucleotide amplifications and an appropriate buffer; and, c) releasing primers attached to the inner surface of the capillary; thereby performing one or several polynucleotide amplifications in said capillary, each amplification reactions occurring in the discrete region where appropriate reverse and forward primers are released and mix.

According to one embodiment of the method, the primers from distinct functional rings of the capillary are released simultaneously, thereby allowing multiple polynucleotide amplifications to perform in parallel in a single reaction volume.

A reaction solution appropriate for polynucleotide amplifications may comprise at least one of the following components:

- the target DNA, in particular, genomic DNA or cDNA;

- salts such as KCI or NaCI solution and/or other appropriate PCR buffers, typically a mixture of NaCI and MgCI₂; - dATP, dCTP, dTTP, dGTP;

- one primer used in common for all the amplification reactions;

- MgCb; and/or,

- DNA polymerase.

The target might be mRNA as well, the first step is then a reverse transcription to generate cDNA.

The solution can also comprise DNA binding dye such as the SyBR green dye, labelled probes containing fluorophores, allowing detection of the amplicons in real time. The reaction solution might include fluorescent dXTP for use in appropriate detection methods. The reaction solution may also further comprise fluorescent-quencher probes type TaqMan, or fluorescent intercalating agents such as SyBR Green.

The reaction solution may comprise DNA extracted from a biological sample. Especially, the DNA may be extracted from a biopsy, from biological fluid including blood, urine, saliva ...

The DNA may be extracted from a biopsy or a biological fluid of an animal, a non-human mammal or a human. It can also be extracted from a cell culture, eucaryotic cells or prokaryotic cells, bacteria, fungi or yeasts.

It can also be extracted from cereals, fruits, meat and food in general.

A large variety of polynucleotide amplification reactions known to those skilled in the Art may be suitable for the instant invention. The most common form of polynucleotide amplification reaction, known as the PCR reaction is well known in the Art. The polymerase used to direct the nucleotide synthesis may include, for example, E. coli DNA polymerase I₁ Klenow fragment of E. coli DNA polymerase, polymerase muteins, heat- stable enzymes, such as Taq polymerase, Vent polymerase and the like.

One of skill in the Art will appreciate that many other polynucleotide amplification reactions may also be carried out using the instant method and apparatus (For reviews, see lsaksson and Landegren, Curr. Opin. Biotechnol. 10: 11-15 (1999)). Typically, amplification of either or both strand of the target nucleic acid comprises the use of one or more nucleic acid-modifying enzymes, such as DNA polymerase, a ligase, an RNA polymerase, or an RNA-dependent reverse transcriptase. For example, polynucleotide amplification reactions may include self-sustained sequence replication (S3R), nucleic acid sequence-based amplification (NASBA), strand displacement activation (SDA), ligase chain reaction (LCR), and Qp replicase system, among others. The present invention may be used to couple the amplification and detection procedures of the amplified products, thus providing an environment for simultaneously carrying out a plurality of amplification reactions followed by simultaneous detection of the amplified products.

In some embodiments of the method of the invention, the method further comprises the step (d) of capturing the amplified products by a plurality of immobilized polynucleotide probes on the inner surface of the capillary through hybridization.

The invention is thus directed to a method of detecting and analysing nucleic acid in a sample, comprising the use of a capillary suitable for performing multiple polynucleotide amplifications according to the invention as above-defined or the microfluidic device of the invention comprising such capillary as above defined.

For example, a fraction of immobilized polynucleotides may contain non- releasable polynucleotides designed to probe (capture) amplification products. The non-releasable probes can be attached to an area of the inner surface of the capillary, located in the corresponding functional ring containing the releasable primers for amplifying the products to be captured by said probes. For example, in one embodiment, the non-releasable probe is attached to the inner surface of the capillary located between the (F) area containing the forward primer and the (R) area containing the reverse primer.

Alternatively, the probes can be attached to a different area than the functional ring containing the corresponding primers for amplifying the sequence to be captured.

After the amplified products of a target nucleic acid are captured, they may also be directly or indirectly analysed by detecting polynucleotide sequence variations. Strategies for identification and detection of polynucleotide sequence variations in a capillary are described in the Art and in particular in US patent application 2003-0032035 (Chatelain et a/., CEA, 2002) or in WO 02/18949 (University of California, 2001).

According to one embodiment of the method of the invention, said method further comprises the step of detecting polynucleotide sequence variations by detecting hybridisation complexes obtained at step (c).

The invention also concerns the use of a capillary as above-defined or a microfluidic device comprising such capillary, for protein detection and/or analysis.

The one skilled in the Art will better appreciate the invention and its advantages when reading the examples set forth below. Of course, these examples only illustrate certain preferred embodiments of the invention and should not be considered as limiting the scope of the claimed invention.

LEGENDS OF THE FIGURES

Figures 1: illustrates the body structure of a capillary according to the invention. The capillary tube comprises functional rings (FR1,

FR2), each functional ring having an inner surface which comprises at least a first area (F 1 or F2) and a second area

(R1 and R2) comprising releasable reagents, and wherein F area is closer to R area for allowing the respective reagents of a functional ring to mix together. A spacer is placed between FR1 and FR2 in order to prevent mixing of reagents F1 and R1 with F2 and R2 by diffusion.

Figure 2: illustrates the release of reacting moieties and the approximate diffusion of the moieties in the capillary. The upper diagram represents relative concentration of primers F and R in the capillary. PCR reactions occur at the boundaries between the zones F1 and R1, F2 and R2, etc; an optimal design is when the rings are sufficiently spaced so that PCR products do not mix together but not to much spaced in order to satisfy a criteria of minimal length of the system. The lower diagram represents the relative concentration of the reaction product in the capillary.

EXPERIMENTAL PART

A. Modeling of the diffusion of released primers in a capillary.

Schematically, the method of multiplex amplification is achieved by a capillary tube comprising functional rings with forward (F) and reverse (R) primers on its inner surface (fig.1).

A capillary tube comprising functional rings was prepared according to the invention. Each functional ring contains forward or reverse primers according to figure 1. The carrier fluid containing the DNA to be amplified is injected inside the capillary. After it has been injected inside the capillary, the carrier fluid is at rest and the primers are released from the different rings and diffuse in the capillary. In volumic zones where the concentrations of primers F1 and R1, F2 and R2 , etc., the PCR reactions PCR1, PCR2, etc. are performed by a series of about 30 cycles of an adequate temperature transient, each transient being of the order of 30 seconds.

Optimal configuration is described in figure 2, where the different rings are sufficiently spaced to have distinct PCR areas and no mixed PCR products - for detection reasons - but not to far from each other in order to have a compact system.

The couple of rings - containing forward and reverse primers - may be spaced by a spacer, as it is shown in the figure 2.

The goal of the modelling is to add to the feasibility of the method in numerically calculating the physical characteristics that allow for a satisfactory functioning of the device.

More specifically, one wants to know if, when carrying out the PCR cycles, the arrangement of the rings satisfies the following requirements:

(1) an efficient concentration of primers F and R, (2) an efficient distance between the PCR rings, and

(3) a compact design of the rings.

The problem was tackled in two steps: the first step consists in modelling only the molecular diffusion inside the capillary; the second step includes the effect of the association/dissociation on the walls. In the first step, it is assumed that the primers are instantaneously released from the wall and that they have no adherence to the walls. In the second step, it is allowed for the primers to temporarily associate on the walls, this phenomenon is supposed to follow a langmuiran kinetics.

The first case over-estimates the speed of diffusion along the capillary axis, because there are no delays due to adherence on the walls. In the second case, it is assumed that the different primers do not interact, which is translated in the model by a unique diffusion coefficient for each of the components.

Nomenclature

a VT. length of functional rings [m]

C Concentration [mole/m³]

Co Initial concentration [mole/ m³] c_w Concentration at the wall [mole/m³]

D Diffusion coefficient [m²/s]

Da Dammkόlher number H

Da_0n Adsorption Dammkόlher number H

Da_off Desorption Dammkδlher number H

J Mass flux [mole/m²/s]

Adsorption coefficient [m³/mole/s] ^koff Desorption coefficient [1/⁸]

L Total length of capillary [m]

Lf Length of a function ring [m] r Radial coordinate [m] r* Normalized radial coordinate H

R Radius of the capillary [m]

SpCR Concentration threshold for PCR [mole/m³] t Time [S]

Z Axial coordinate [m]

Z* Normalized axial coordinate H δ Diffusion distance [m] τ Normalized time H r Surface concentration [mole/m²]

Γ₀ Surface concentration of available sites [mole m²] A.1 Modelling of the diffusion of the primers, assuming that these primers do not adhere to the walls

In a first step, we analyze the diffusion of the primers inside the capillary of the invention, assuming that these primers do not adhere to the walls. This model gives an over-estimate of the speed of diffusion because there are no delays due to the association/dissociation of the primers with complementary sequences at the walls. In other words, the primers are considered as particles bouncing elastically on the walls.

A.1.1 Diffusion model

Diffusion of a chemical or biochemical species is determined by its molecular diffusion coefficient, usually taken from Einstein's relation: k_KT

D = -

6 π η R_H

(1) where D is the molecular diffusion coefficient (m²/s), kβ Bolzmann's constant (k_B = 1.38 10^"23 JJK), 7 the temperature (K), η the viscosity of the carrier fluid (kg/m/s) and RH the hydraulic radius of the particle. In the present case, the dynamic viscosity of the carrier fluid is close to that of water 77=10^"3 kg/m/s, the hydraulic radius of the order of 3 to 10 nm and the temperature is the ambient temperature, approximately 300 K; the coefficient D is then comprised between 2. 10^'11 and 6. 10^"11 m²/s. The equation for diffusion in an axisymmetric, cylindrical coordinate system (r,z) is

dt [dz² r dr{ dr

(2)

In this problem, the dimensions of the capillary are such that the ratio between the inner radius and the total length of the capillary R/L is very small (this ratio is smaller than 5. 10^'3): from this ratio, a difficulty in the meshing of the system stems : a good numeric solution requires an almost equal size of the meshes in the axial and radial directions r and z. If one chooses 20 meshes along the r direction, meaning a mesh size of about 2.5 μm in this direction, it is necessary to have more than 8000 meshes in the axial z direction. To avoid this drawback, the following change in the variables can be made ∑→∑^* = z— , which changes the computational domain to an axisymmetric domain with R = L Thus, it is now possible to choose the same number of meshes in both directions r and z. However this change of variable induces a change in equation (2)

(3)

The diffusion coefficient is now anisotropic in the new coordinate system, the diffusion coefficient in the z direction IsD₂ = D^₁- ^anc* D_Γ = D . The

anisotropy ratio ^- is equal to ^- .

D_r L

To provide for more versatility, the diffusion equation has been written under a fully non-dimensional form by the change of variable: _z→z' and

_r→r' = — . The computational domain is enclosed in a « square box » of dimensions R*=1 and L*=1, and we have the same number of meshes in the axial and radial directions. A reference concentration Co is defined by the number of primers initially immobilized on a ring divided by the corresponding annular volume:

_{c =} 2x RL, T_{0 =} 2r₀ ⁰ UR¹L₁ R Denoting c^* = — and t' = - = ~, where r is the characteristic scale for time, ^co ^{τ RL}

D equation (2) can be rewritten under the form

(4)

The diffusion coefficient is again anisotropic, with D₂ =- R and D_r =— L . : We

L R can verify that the ratio ^- is still equal to ^₁-. In all the following, we will

D_r L make use of equation (4).

A.1.2 Numerical solution and results Data

The data required for the calculation are given in the table 3:

Table 3 : reference data

We used the numerical computational program FEMLAB [1] to calculate the diffusion of a species (here, a primer) in the capillary. More precisely, we have programmed the diffusion equation under the version 2.3 in order to create an equation similar to that of the modulus « chemical engineering ». To take into account the release of primers from the wall, we have set up regions of very small width along the walls. The axial dimension of such a region is 1 mm and the radial dimension 2.5 μm. The meshing was refined along the wall to provide for an accurate calculation of the first time steps during which there is the release of the primers.

In the present calculation, the functionalized length is 1 mm and no spacing has been introduced between the rings.

Diffusion of the primers was then analysed.

Schematically, the results show that the primers are released at time t = 0 and fill the entire section of the capillary in 5 to 10 seconds, then diffuse axially in the capillary. After 500 seconds, the approximate distance of propagation is about 0.5 mm.

Brownian model

Another approach can be done, using direct simulation of the Brownian motion. This approach is more detailed than the "continuous media" approach but much more demanding in computational resources (calculation time and memory). Besides, a 2D axisymmetric geometry requires a 3D treatment.

The computational method is the Monte Carlo method where each primer executes a random walk in the prescribed domain. Statistically, diffusion is determined by the calculation of a great number of random walks. In each time step, each particle follows a straight line, and then at the next time step, its direction is randomly changed. When impacting a wall, the particle is supposed to bounce back.

Theoretically, two parameters are needed: (1) the distance along the straight line run by the particle in a time step, (2) the changing of direction at each time step. The first parameter is constant and is given by the relation

λ = 2^DAt

The second parameter is the result of a random choice of uniform probability between 0 and 360.

The starting point is that of a great number of primers initially immobilized at the wall and randomly distributed along the wall in the functional ring.

Brownian motion begins with the release of the primers. After 5 and 10 seconds, we verified that the primers fill very quickly the annular regions in front of the initial rings and that there is not much axial diffusion at these times. After 2 seconds, the primers are not yet uniformly distributed in the cross section of the capillary.

The results reveal that there is a weak axial propagation of the particles before 10 seconds.

The Brownian model is in agreement with the numerical « continuous » (4).

Because of the very important computational time required to treat the Brownian case, we have not performed any calculation at larger times.

Analytical model

Introduction After a few seconds, « slugs » of concentration in primers occupy the volume in front of the initial rings. Then, it is possible to consider that the diffusion of concentration is 1 D in the axial direction. The diffusion equation for component / is

(5)

The solution to this equation is known [2], it is the error function « erf »; and if we take into account the initial and boundary conditions, the solution can be cast under the form

(6)

where a,- is the V≥ length of a ring and the function « erf » is defined by

Comparison with the numerical model

The agreement between the results of the analytical model and those of the numerical model is the better when the ratio between the length of a ring (Lf) and the radius (R) is the larger, in such a case, the characteristic time of radial diffusion is small compared to that of the axial diffusion.

One of the requirement enounced in the introduction of this work - the one that concerns the separation of the different PCR zones - leads us to look at the concentration in F1 (« forward 1 ») and R2 (« reverse 2 »), because if these concentrations mix the requirement will not be satisfied. We present now a comparison of the concentration distribution of species F1 and R2 at time t=500 seconds, calculated by both the analytical formulation and the numerical model, for the case of a ring length of L_f=1 mm and f?=50 μm. The results obtained with analytical and numerical model reveals similar concentration distribution. As long as the ratio ^- is large in respect to 1 , the analytical model is a

R good approximation of the diffusion in the capillary.

Results of the analytical model

We show here how the different primers axially diffuse depending on their specific diffusion coefficient. We present results for 2 primers that initially occupy neighbouring rings on the wall (F1 and R1 or R1 and F2 or F2 and R2) at different times. One of the advantages of the analytical calculation is the possibility of adding new species.

The function of the device for multiplex amplification requires areas where « forward » and « reverse » primers are present in a sufficient amount (the threshold is 25 nM - or 25 10^'6 mole/m³). We can define 2 criteria approximately equivalent to quantify the joint concentration, i.e. a concentration of « forward » and « reverse » primers mixed in an elementary fluid volume. We can define the function

_L_ l_

Cp C_R

(7)

is a good criterion for the joint concentration of primers F et R. If one of the 2 species is not present, then c =o. If the 2 species are present with the same concentration, then Έ = C_F = C_Λ . This function (7) was implemented, at times 1 , 200, 500 and 900 seconds. In this calculation, the initial concentration in primers are the same, as well as the 2 diffusion coefficients. The results show that the mass of the "joint concentration" increases in time, due to inter-diffusion of the species.

Another criterion for the « joint concentration » is c = min (c_F,c_R)

(8)

This second function for the « joint concentration » was also implemented. The similarity of the 2 criteria is clear. The results have shown that the criteria are similar.

According to the obtained results, the 2 PCR zones have a non-void intersection after 900 seconds. A more detailed picture of the intersection of the intersection is obtained, where the intersection of the 2 "joint concentration" is defined by any of the 2 following formuJas

c_{1 2} = mm(min(c_Fl,c_m),min(c_F2,c_R2))

(9)

or

C <^>Fp-2, C,

(10)

We consider a threshold concentration defined by a value of 1/10 of the threshold concentration for PCR (0.1* SPCR). This threshold is considered as the limit beyond which the PCR products are getting mixed together, preventing an accurate detection. For reference values taken here for the calculation, and for this value of the threshold, we find that the concentrations in PCR1 and PCR2 are overlapping above threshold after

500 seconds. Parametric study

Influence of the diffusion coefficient

We show here that the value of the diffusion coefficient is very important in our problem. The reference value of D = 1. 10^'10 m²/s is very likely a maximum value. When considering the smaller value D = 2. 10 ^"11 m²/s, the threshold value (2.5 10^"6 mole/m³) is not reached at 2700 seconds for adjacent functional rings of 1 mm.

Influence of the length of the rings

For a diffusion coefficient smaller than that of reference, it is possible to reduce the length of the functional rings. With D= 2. 10 ^~11 m²/s and L_f= 500 μm, a detectable intersection appears shortly after 600 seconds and the threshold is reached at 700 seconds.

Influence of the 2 parameters D and L

The advantage of the analytical formulation is that we can easily search the influence of the parameters. Assuming only one ring, with the help of equation (6), we determine the distance reached by the primers at t= 900 s

(=30 cycles x 30seconds) as a function of the V≥ ring length a-U2 and of the diffusion coefficient D and of the initial concentration cø - or, the density of initial fictionalization G, which is equivalent to Co. The threshold value of 2.5 10^"6 mole/m³ is taken as a criterion for the propagation distance. We have implemented the propagation length as a function of D and a.

We find that the diffusion coefficient D and the functionalized length (ring length) L_f have a noticeable impact on the results. If we want to reduce the axial dimensions, it is necessary to reduce the diffusion coefficient. If the diffusion coefficient can be reduced (by increasing the viscosity of the carrier fluid for example) below 10^'11 m²/s, the length of the rings can be reduced to 200 μm. A.1.3 Discussion / Conclusion

If the ratio between the functioπalized length (ring length) and the radius^ is large enough, during the 10 first seconds, the primers occupy

R progressively that part of the capillary corresponding to the ring. Axial propagation is not important at small times. The axial diffusion is visible only later.

When slugs of concentration are formed, diffusion is axial, approximately 1 D inside the capillary. Under the hypothesis that the different primers do not interact, it is possible to superpose the different distributions of concentration as functions of their diffusion coefficient, their initial concentration and their initial location.

The design of the device is satisfactory until 500 seconds for functional rings of 1 mm, diffusion coefficients of 1. 10^"10 m²/s and initial surface concentrations of 50 femtomoles/mm²). But after 500 seconds, overlapping of PCR areas occurs. If the diffusion coefficients are closer to 2.10^"11 m²/s, the design is satisfactory until 2700 seconds. In such situation, it is possible to reduce the size of the rings to less than 500 μm and not to have overlapping before 900 seconds.

A general rule is that the propagation distance is approximately ΔX≡ IJDΪ

and the axial speed of propagation is approximately ^^ ≤ J— .

We then analyse the more complete case where interactions of the primers with the walls are taken into account.

A.2 Modeling of diffusion and adherence of primers

We first analysed the diffusion of the primers. If diffusion is the only cause for the transport of primers, a speed of diffusion has been determined.

Because the association/dissociation reactions have been neglected, this velocity can be seen as an upper bound of the real speed of transport in the capillary. We now show that interactions of primers with the walls result in a slower speed of axial propagation. Thus, the axial dimensions can be further reduced.

We analyse now the coupling between diffusion in the capillary and the temporary binding of the primers on the functionalized walls. Interactions with the walls are complex and, in this study, we assume that they obey Langmuiran reactions, with an association coefficient (Zc_0n) and a dissociation coefficient (k_Ofd-

For the numerical solution, we will follow the approach of Ligler [4] and

Hibbert [5] who have solved numerically the coupled system diffusion in a volume/Langmuiran reaction at the walls. In the present case, there is no fluid advection, unlike the 2 compartments model of Mason [6], which renders the conservation equation simpler. However, it will not require much work to incorporate advection in our model. More generally, the present model can handle the capture of antigenes on immobilized antibodies [7], [8].

A.2.1 Model

Coupled system (reduced coordinates)

Inside the capillary, « far » from the walls, the hypotheses are the same as before, i.e. the primers do not interact. The equation for diffusion is then exactly the same as before (2) and we have

after dimensional scaling, this equation boils down to (4)

At the walls, we assume we have Langmuir type reactions [4]:

^ = k_Mc_w{r₀-τyk_ojrr

(11 )

where k_on and k_off are respectively association and dissociation constants, F₀ is the initial concentration in available association sites on the walls and

/"the surface concentration of immobilized primers on the walls. In (11) w stands for « wall ».

The two preceding equations are coupled via Fick's law. If we use primary coordinates (with the real dimensions) Fick's law can be written

dc_

J = -D Br dt

(12)

where J is the mass flux at the wall in mole/m²/s.

As we have to use dimensionless coordinates (because of the very elongated geometry), we need render the whole system dimensionless. So the approach is to use first the diffusion equation under its dimensionless form

dc R d²C L 1 d ( .3c^*

_ • _ _ _* dt L d∑ ^■ R r' δr' dr^*

where the reduced diffusion coefficient is anisotropic : z>^*_ =— in the z*

direction and D\ = — in the r* direction ; the dimensionless flux at the walls

R is J _r = -D_r' • dc dr

(13)

Equation (13) can be cast under the form

_ D c₀ dc\ ^{r ~} R dr' ^U

(14)

Then, after substitution of (11) and (12) in (14) and denoting r = —

(15)

After looking at equations (4) and (15), we remark that the physics of the phenomena depends only on 4 dimensionless numbers:

1. The geometric ratio — between the length of the capillary and its

R. radius, which appears in the diffusion equation

2. The ratio EL between the number of available association sites on

C₀ R the wall and the product of the radius and the initial free concentration. This ratio can be cast under the form : , if we assume that the

association sites are uniformly disposed in each ring.

3. The ratio ^{km T}°^L is the Dammkόlher number for association

(adsorption) and represents the ratio between the speed of adsorption and the speed of axial diffusion, because ^k°° ^r° ^L = ^Es. 4. The ratio ^kojrT° ^L is the Dammkόlher number of dissociation

Dc₀

(desorption) and represents the ratio between dissociation speed and axial diffusion, because Kff ^ro^L_ {^kojr ^ro^/co)

Dc₀ DIL

In fact, if we make use of the Buckingham's π theorem, we could have seen that the whole system is depending on four dimensionless numbers [3]: this theorem proves that, if a physical system is depending on N parameters based on M different units, then the system is determined by N- M dimensionless numbers. In the following table, we have listed the parameters connected to the physical systems (diffusion only and diffusion plus reaction at the wall) and the units of these parameters and finally, the dimensionless numbers that we have found. We verify that the dimension analysis is in agreement with Buckingham's theorem.

Table 4: verification of the π theorem

The geometry and the meshing of the domain were evaluated.

The equations system (4), (13) and (15) has been implemented in the FEMLAB numerical program. The first equation (4) is described under the form « coefficient », equation (13) is a boundary condition for the mass flux and equation (15) is a differential equation coupled to the pde and described under the « weak » form. Values of the reference data are given in table 5

Table 5. Reference data

Values of association and dissociation constants are not well known. The association constant is taken from the work from the published work of Ligler [7]; thus the primers can be successively captured at the walls and released.

The dimensionless reference values are given in table 6 :

Table 6. Dimensionless values of the reference numbers

A.2.2 Results and discussion

Parametric study

We examine here the role of the dimensionless parameters that we have produced in the last paragraph. To simplify, we note Da_m = *°"^r°^z and

Da. Λi off - . It seems intuitive that association (even temporary) will reduce

Dc_n the axial speed of diffusion through immobilization and release processes. The larger the association constant, the longer the primers will stay immobilized; on the other hand, large dissociation constants results in small retention at the wall. This is the reason why we analyze first the behaviour of the system for different values of Da_0n and Da_off . Influence of Da_0n (Dammkδlher adsorption number)

In this paragraph, the adsorption Dammkδhler number Da_0n

j_s

changed. The other parameters are always that of the reference case (see table 6). We will focus on the diffusion distance at time t = 1000 seconds; this distance is determined by a threshold of concentration equal to 0.1

(SPCF/CO). We implemented axial concentration profiles. Concentration distribution has still the same gaussian shape, but is more spread when the Dammkohler adsorption number decreases. As expected, the profile based only on diffusion is always the most spread out.

The diffusion distance at 1000 seconds was evaluated as a function of

_{Da =} KJO^L _ A_{S more} primers are immobilized at the wall when the

D adsorption Dammkδhler number increases, the concentration in free primers in the capillary decreases. A decrease of the maximum concentration in the capillary is observed as the Dammkohler number increases.

Axial diffusion is slowed down when the adsorption Dammkohler increases. Physically, it is explained by temporary immobilization of the primers on the walls. This phenomenon is confirmed by the decrease of free primers in the capillary.

Influence o\Da_off (desorption Dammkδlher number)

In the last paragraph, we show that adsorption (or association or immobilization) decreases the speed of axial diffusion. Primers located at the diffusion front are captured so that the diffusion front progresses slower in the capillary. In this paragraph, we analyse desorption. We have investigated the relation between the diffusion distance and the desorption number Da_off at /=1000 seconds. We find that desorption (or dissociation or release) has the opposite effect when compared with association. The larger Da₀^ (or k_off), the faster the axial diffusion. Immobilized primers are released in a very short time when the desorption coefficient is large. The larger the desorption, the larger the free concentration in the capillary. However, the axial speed of diffusion is always slower than that of pure diffusion.

Influence of the radius R

When the radius is changed, the ratio aspect — and the ratio -ϋ- .are

R C₀ R changed. In this paragraph, we vary the radius from 10 a 1000 μm. As long as UR > 50 (Lf /R > 5) there are no visible changes in the diffusion of primers. For smaller values of this ratio, like UR = 10 or L_f /R =1 , profiles are that of diffusion only. This was expected since the influence of the wall is reduced when the aspect ratio decreases.

Calculation with 4 rings

In the last paragraphs, we have shown that speed of propagation can be reduced by temporary immobilization on the wall. We comment here 2 calculations encompassing 4 rings. The first calculation uses the reference geometry and tries to slow down the axial diffusion process by a convenient choice of the parameters Da_0n = ^kmT°^L and Da_ojr = -V°£ . Using these values,

a second calculation is performed in a more compact geometry.

Calculation with 2x2 rings and no spacers (D = 1. 10^"10 m²/s)

In this calculation, the association coefficient k_on is large, equal to 500 m³/moles/s and the dissociation coefficient k_Off is also relatively large, equal to 4. 10^"2 1/s. The data for the calculation are given in table 7:

Table 7. Data for the calculation

The dimensionless values of the parameters are given in table 8:

Table 8. Values of the dimensionless parameters

Concentration profiles are implemented for the sum of the four concentrations — = ^{CF1 +Cffl +CF2 +Cj?2} and the « joint concentration » in primers

of type 1 and type 2, defined by c = at t =500, 900 et

1000 seconds.

On the one hand, the axial diffusion is very much reduced by the choice of the 2 Dammkhδler numbers (a very strong association constant and a somewhat less strong dissociation constant, the ratio that

characterizes the relative importance of the two mechanisms is equal to 2). Axial propagation is nearly stopped because primers successively associate, then dissociate at the wall. The free concentration is relatively small but still enough for the PCR reactions to take place. On the other hand, the PCR products do not mix even at f=1000s.

A comparison with the « diffusion only » case was done. On one hand, there is a decrease of the "free concentration" in the capillary; on the other hand, the PCR products do not mix, contrary to the case of the "free diffusion".

Calculation using 2 x 2 zones of 500 μm with a 500 μm spacer.

This calculation is aimed at estimating the possibility of compacting fhe size of the rings, using the advantageous Dammkδhler numbers found during the previous calculation. The data for the calculation are given in the table 9.

Table 9. Data for the calculation

The corresponding dimensionless parameters are given in table 10 :

Table 10. Dimensionless parameters

Here the rings have an axial extent of 0.5 mm and they are separated by spacers of 0.5 mm. The contour plot of the sum of the 4 concentrations was determined at t= 0.5, 10 and 1000 seconds. At t = 0.5 seconds, the initial rings appear very clearly. At t= 10 seconds, the results show that the primers have filled the interior of the rings.

« Joint concentrations)) was investigated at t = 0.5

and 10 and 500 seconds. An overlapping of the PCR zones seems to begin at 500 seconds. This is confirmed with the concentration C_{1 2} = min(πmi(e_n,c_Λ1),min(c_F2,c_Λ2)) at t = 900 s. A mixture of the PCR zones can be seen at t = 500s thus this extension is very limited even at 900 seconds.

A.3 Conclusion

In the present work, we have solved the problem of diffusion of primers in a cylindrical volume coupled with reaction of association and dissociation on functionalized walls.

Axial speed of diffusion is a key factor for the feasibility of the capillary PCR device. Transport of primers inside the capillary has to be slow enough if we want to incorporate many functional rings inside the capillary and still have a compact device.

The first part of the present study considers only the diffusion process (and excludes the interactions between the primers and the wall). This approach produces an upper bound for the speed of diffusion of the primers in the capillary. It shows that each couple of « forward » and « reverse » ring has to be separated from the next one by a distance of at least 1 mm in order not to have overlapping of PCR products during the 900 seconds required for the 30 cycles of PCR, assuming that the diffusion coefficient is D =10^"10 m²/s. If the diffusion coefficient is less, for example D = 2. 10^"11 m²/s the spacing between the couples of rings can be reduced to 500 μm.

The second part of this study takes into account association and dissociation of the primers on the functional rings, resulting in a more accurate estimate of the axial transport of the primers. A very important conclusion is that the physical mechanisms depend only on 4 dimensionless numbers (thus verifying Buckingham's πtheorem). Another conclusion is that the axial speed of transport decreases when the adsorption Dammkδlher number Da_0n = ^S^ increases, and increases with the desorption Dammkδlher number Da_oS = ^k°^sY°^L . The influence of the

Dc₀ capillary radius on the axial speed of propagation of the primers is weak as long as the ratio L_f /R of the functionalized length to the radius is larger than 5.

If we want to reduce the axial speed of propagation, it is best to satisfy to the following "theoretical" conditions:

1. A adsorption Dammkδlher number large enough to slow down the advancing front of diffusing primers, but a very important adsorption will result in a complete depletion of the primers.

2. A value of the desorption Dammkόhler number about Yz of that of the adsorption Dammkδlher number,

3. A ratio between the length of a functional ring and the radius of about 5,

4. A spacing between the couples of rings (F1 , R1), (F2, R2), etc., to constitute a diffusion « barrier ». For example, this spacer could be functionalized with oligonucleotide complementary to the R1 and F2 type of oligonucleotides.

An important point here is that the speed of propagation of primers in the capillary can be very much reduced if we can choose an optimal ratio between the 2 Dammkhόler numbers . it has been shown in this

report that a slow axial diffusion regime could be obtained when this ration is close to 2. If such a ratio is physically obtainable, then the device can be rendered very compact by the reduction of the size of the rings. References

[1] http://www.femlab.com/chem/ : module "Chemical engineering" du code FEMLAB.

[2] H.S. Carslaw, J. C. Jaeger. Heat conduction in solids. Oxford Press 1959.

[3] R. Moreau. Cours de Mecanique des fluides. INPG. 1973.

[4] RA. Vijayendran, F. Ligler, D. E. Leckband. A computational reaction-diffusion model for the analysis of transport-limited kinetics. Analytical Chemestry, 1999, 71, pp 5405-5412.

[5] D.B. Hibbert, J.J. Goodm^' g, P. Erokhin. Kinetics of irreversible adsorption with diffusion: application to biomolecule immobilization. Langmuir, 2002,18. pp 1770-1776.

[6] T. Mason, A. Pineda, C. Wofsy, B. Goldstein. Effective rate models for the analysis of transport dependent biosensor data . Mathematical Biosciences, 1999, 159, pp 123-144.

[7] K.E. Sapsford, Z. Liron, Y.S. Shubin, F.S. Ligler. Kinetics of antigen bindings to arrays of antibodies in different sized spots. Analytical Chemestry, 2001, 73, pp 5518-5524.

[8] M. F. Templin, D. Stoll, M. Schrenk, P.C. Traub, CF. Vohringer, T.O. Joos. Protein microarray technology. Tren B. EXAMPLES

Example 1: Preparation of a capillary for performing a plurality of nucleotide amplifications in parallel

Capillaries preparation

Capillaries are purchased from SGE, Milton Kaynes UK. The inside diameter is 100 μm and the diameter including the inner wall but excluding the Teflon jacket is 300 μm. These capillaries are made of fused silica and are UV transparent.

In order to address specifically the internal surface of the capillary, benzophenone (Bz) was used to create a photo-reactive surface. The benzophenone was chosen because its photo chemical properties are well- known. In particular, it reacts with C-H under UV irradiation in a wide range of different chemical environments. Furthermore, benzophenone is chemically inert in the absence of light and stable in aqueous solutions. Capillaries were cleaned using a 3.6N NaOH solution in 50% ethanol and then washed with bi-distilled water. They were dried using a stream of air, and then treated with a 5% solution of aminopropylsilane in pure ethanol. The reaction was performed overnight. Capillaries were rinsed, first with 95 % ethanol, then with bi-distilled water, and again with 95% ethanol. The silane layer was reticulated by baking the capillaries at 115°C during 3 hours. The resulting amino-surface was then reacted with 20OmM Bz- isothiocyanate in DMF overnight. The capillaries are washed twice with DMF and twice with 95% ethanol.

Attachement of releasable primers

The Bz-modifιed capillary was filled with the first oligonucleotide solution and a section of the capillary was UV365nm irradiated. Non-immobilized oligonucleotides were washed out of the capillary. The array was formed by repeating these steps for each oligonucleotide.

The light generator was an inverted microscope with a mercury lamp. The irradiation was performed orthogonally to the capillary through a 160μm slot with 4 mW/mm² intensity. The capillary was moved under the device to create an oligonucleotide array.

Primers in hybridization buffer (25μM in PBS 1X, NaCI 0.5M, EDTA 1OmM, Salmon sperm DNA 100μg/ml, formamide 50%) were injected in the capillary and the hybridization is carried out for one hour at 42°C.

After hybridization, the capillaries were washed twice with SSC 2X, SDS

0.1%.

Example 2: Release of reagents attached to the surface of the capillary

The capillaries were prepared as described in example 1. After immobilization of the complementary oligonucleotides, the capillaries were hybridized with Cyanine 3 labelled primers following the above protocol: After washes, the hybridized labelled primers are detected through the wall of the capillary using a standard DNA chip scanner. The fluorescence intensities for each primer were recorded.

The capillaries were filled with the hybridization buffer and the temperature increased to 65°C for 1 hour. The capillaries were flushed with fresh hybridization buffer and scanned. The fluorescence intensities corresponding to each primer were recorded and showed a decrease to less than 30% of the intensities recorded before the release. We conclude that 70% of the hybridized primers were released in the capillary, suitable for PCR amplification. Example 3: Amplification of the NAT2 gene

This example illustrates the general approach to amplify any DNA sequence of any species, including any artificially created sequence. Illustrated here is the amplification of a part of the human NAT2 gene. The amplification product includes the coding region of the human N- acetyltransferase 2 (NAT2) gene which spans 872 basepairs (GenBank accession number NM_000015).

A capillary is created to generate a PCR product for the NAT2 gene from human genomic DNA using a forward (5'- GTCACACGAGGAAATCAAATGC-3', sequence ID no. 1 ) and reverse (5'-

GTTTTCTAGCATGAATCACTCTGC-3', sequence ID no. 2) primers.

These primers can be pre-synthesized and attached via a cleavable linker to the surface of the capillary or in situ synthesized in the capillary on a cleavable linker. Different types of linkers can be used depending on the release mechanism. In example, the cleavage can be achieved upon light irradiation (photocleavable linker), with a reagent (chemical cleavage) or using a restriction enzyme (DNA sequence linker).

Alternatively, the primers complementary sequences can be pre- synthesized and covalently and permanently attached to the surface of the capillary or in situ synthesized in the capillary. The capillary is then "loaded" by hybridization with a large excess of primers in solution. The primers are released by a denaturation step at 94°C.

Before the PCR amplification reaction, the capillary is washed in 1x PCR buffer (5OmM KCI, 1.5mM MgCI2, 1OmM Tris-HCI pH 8.0). Then, for PCR amplification, PCR reagents containing 10ng human genomic DNA, PCR buffer, 200μM deoxynucleotide triphosphates, and 1 unit DNA polymerase are added to the capillary. Primers are released (as described earlier) and allowed to mix with the PCR reagents. The capillary is then subjected to temperature cycling using a temperature cycling apparatus dedicated to accommodate capillaries. The resulting amplification product (amplicon) has a length of approx. 1.2kb, containing the 872 base pair long coding sequence of the NAT2 gene, plus 5' and 3' flanking sequences. The PCR product is analyzed using standard technologies known to the skilled in the art, e.g. using agarose gel electrophoresis.

Example 4: Genotyping of polymorphisms in the NAT2 gene by allele- specific extension

The coding region of interest of the human N-acetyltransferase 2 (NAT2) gene spans 872 basepairs (GenBank accession number NM_000015). Numerous alleles are found in the population which can be associated with decreased function, determining slow, intermediate, and fast metabolism. The enzyme has been shown to play a role in the inactivation of aromatic and heterocyclic compounds including carcinogens. Carriers of certain alleles are likely to be more susceptible to certain cancers, i.e. colorectal and bladder cancer. A list of the alleles can be found in table 11.

TABLE 11 : The seven most common polymorphisms (G191A, C282T, T341 C, C481T, G590A, A803G, and G857A) with their associated alleles,

(the *4 allele refers to the wildtype sequence: GenBank accession number NM_000015).

Ph: phenotype; R: rapid; S: slow; Fr: frequency; AA: amino acid.

The low complexity, well understood genetics, and clinical relevance makes the NAT2 gene a good candidate to develop a proof-of-principle assay. The assay described below is adapted from F. Chatelain and F.- Frueh, PCT/EP02/05459, US No. 60/288,526. Homozygous and heterozygous genotypes are determined at each polymorphic site and allele assignments are made according to the genotypes identified which ensures and improves the assay as each allele is defined by more than one SNP.

First, a capillary is created to generate a PCR product from human genomic DNA using a forward (5'-GTCACACGAGGAAATCAAATGC-S', sequence

ID no. 1) and reverse (5'-GTTTTCTAGCATGAATCACTCTGC-3^I, sequence

ID no. 2) primer. These primers can be presynthesized and attached via a cleavable linker to the surface of the capillary or in situ synthesized In addition to the primers used for generating the NAT2 amplicon, probes are attached to the surface of the capillary, or in situ synthesized, to be used for the identification of the sequence of the NAT gene at the positions described in table 11. These probes are allele-specific containing allele- specific nucleotides (representing the positions of the nucleotides outlined in table 11) at their 3' end. These ends are exposed and can be elongated by (performing an enzymatic reaction known to the skilled in the art as

"primer extension"). Details have been described earlier (F. Chatelain and

F. Frueh, PCT/EP02/05459, US No. 60/288,526).

Next, the capillary is pre^washed in 1x PCR buffer (5OmM KCI, 1.5mM MgCI2, 1OmM Tris-HCI pH 8.0). Next, PCR reagents containing 10ng human genomic DNA, PCR buffer, 200 μM dATP, 200μM dGTP, 175μM dTTP, 25μM labeled dUTP (i.e. Cy3-dUTP), 175μM dCTP, 25μM labelled dCTP (i.e. Cy3-dCTP), and 1 unit DNA polymerase are added to the capillary. Primers are released (as described in example 2) and allowed to mix with the PCR reagents. The capillary then is subjected to temperature cycling using a temperature cycling apparatus dedicated to accommodate capillaries. After completion of the temperature cycling, the capillary is washed in a solution of triethylamine and alcohol (1 :1) for 15 minutes and rinsed several times with water, and analyzed during the PCR reaction, the template DNA is initially amplified by the primers (sequence ID nos. ϊ and

2). When a sufficient amount of amplicon is present, the allele-specific probes containing allele-specific nucleotides at their 3' end (representing the positions of the nucleotides outlined in table 1 and described above) are being extended. These probes remain attached to the surface of the capillary at known locations, allowing the identification of allele-specific amplification products based on their location on the surface of the capillary.

Alternatively, non allele-specific probes can be used. These probes are ending precisely one base short (upstream) of the polymorphic site. To visualize the identity of the polymorphic site, differently labelled di-deoxy nucleotide terminators (ddNTPs) replace the dNTPs for the extension reaction. Ideally, the four different ddNTPs are labelled in a different colour which can be distinguished by a colour detection device. The use of such terminators allows extending the allele-specific probe by only one base. The label which is characteristic for each of the four possible bases identifies attached nucleotide at each of the probe locations and, hence, identifies the sequence at the polymorphic site.

Claims

1. A capillary suitable for performing a plurality of reactions, wherein said capillary comprises a plurality of functional rings (FRrFR_n) designed in its inner surface, each functional ring having an inner surface which comprises at least a first area (R) and a second area

(F), and each functional ring having a first releasable reagent releasably attached to said first area (R) within the inner surface of the functional ring of the capillary and a second releasable reagent releasably attached to said second area (F) within the inner surface of the functional ring of the capillary, and wherein in each determined ring, said area (F) is overlapping or is close enough to said area (R) for allowing their respective reagents to mix after their release and for performing a reaction involving at least the two released reagents as substrates.

2. The capillary according to Claim 1 , wherein the functional rings are separated by a region forming a spacer (S), wherein no reagent is attached to the inner surface of the capillary in said spacer region, wherein the spacer prevents the reagents released from two distinct functional rings to mix together.

3. The capillary according to Claim 1 or Claim 2, wherein said capillary is rigid, and is preferably made of glass.

4. The capillary according to any of Claims 1 to 3, wherein said capillary has a diameter of between 1 and 500 μm, preferably between 1 and 200 μm, and more preferably between 1 and 100 μm.

5. The capillary according to any of Claims 1 to 4, wherein each functional ring has an axial length of between 20μm and 10mm, preferably between 100μm and 1mm.

6. The capillary according to any of Claims 1 to 5, suitable for performing one or several polynucleotide amplifications, wherein each functional ring has an inner surface which comprises at least a first area (R) and a second area (F), wherein a first releasable oligonucleotide suitable for use as the forward primer of one polynucleotide amplification, is releasably attached to said first area (R) within the inner surface of the capillary, and a second releasable oligonucleotide suitable for use as the reverse primer is releasably attached to said second area (F) of the same functional ring within the inner surface of the capillary.

7. The capillary according to claim 6, wherein said releasable oligonucleotide is covalently linked to a cleavable moiety, bound to the inner surface of the capillary.

8. The capillary according to claim 7, wherein said cleavable moiety is cleavable by photolysis.

9. The capillary according to Claim 6, wherein said releasable oligonucleotide is releasable by strand separation.

10. The capillary according to any one of the claims 6 to 9, wherein the density of oligonucleotides attached within the inner surface of the capillary in each functional ring is between 1 and 1000 femtomoles per square mm.

11. The capillary according to any one of the claims 6 to 10, wherein the number of functional rings on the capillary is between about 2 to 100, preferably between 10 to 50.

12. A microfluidic device for performing a plurality of reactions, comprising a. one or several capillaries according to any of Claims 1 to 11 , b. means for circulating the reaction solution; c. means for controlling the flow rate of the reaction solution through the capillary, d. means for releasing the releasable reagents attached to the inner surface of the capillary e. optionally, means for quantitating the reaction products.

13. The microfluidic device according to Claim 12, wherein said means for circulating the reaction solution comprises pressure-driven syringe pump.

14. The microfluidic device according to Claim 12 or 13, wherein said device comprises an excitation light source associated to a detector of fluorescent emission such as a PMT, a scanner or a linear charged coupled device (CCD) to generate a quantitative fluorescent image of the capillary as a means for quantitating the reaction products labelled with fluorescent material.

15. A method for performing a plurality of chemical reactions in parallel, comprising the use of a capillary according to any of Claims 1 to 11 or a microfluidic device according to any of Claims 12 to 14.

16. The method according to Claim 15, comprising the steps of: a. providing a capillary according to any of Claims 1 to 11 or a microfluidic device according to any of Claims 12 to 14, b. filling said capillary with a reaction solution comprising one or more reagent(s) in common to all reactions and an appropriate buffer; c. releasing the reagents attached to the inner surface of the capillary; thereby performing a plurality of reactions in parallel in said capillary, each reactions occurring in the discrete region where appropriate reagents are mixed.

17. The method according to any of Claims 15 to 16, for performing a plurality of polynucleotide amplifications, comprising the use of the capillary according to any of Claims 6 to 11.

18. The method according to Claim 17, wherein said method. further comprises the step (d) of capturing through hybridization the amplified products by a plurality of polynucleotide probes attached the inner surface of the capillary.

19. The method according to 15, wherein said method further comprises the step of detecting polynucleotide sequence variations by detecting hybridisation complexes obtained at step (d).

20. Use of the capillary according to any of Claims 1 to 11 or the microfluidic device according to any of Claims 12 to 14, for protein detection and/or analysis.