WO2003031962A2 - Apparatus and method for determining the complex permittivity of a test solution - Google Patents

Abstract

A method for accurately detemining the complex permittivity of a test solution to detect molecular or cellular events occurring therein includes selecting a plurality of calibration solutions, each of which has a predetermined complex permittivity comprising a real component and an imaginary component, whereby the real or imaginary component of the complex permittivities of the calibration solutions collectively extend above and below the expected real or imaginary component of the complex permittivity of the test solution. Measurement parameters are obtained for each of the calibration solutions. A respective number of complex coefficients corresponding to the number of calibration standards are computed, each complex coefficient comprising a term in a rational function for converting measurement parameters to a complex permittivity. Measurement parameters are obtained for the test solution and applied to the rational function to determine the complex permittivity of the test solution.

Description

SYSTEM AND METHOD FOR CREATING A SOLUTION WITH

DESIRED DIELECTRIC PROPERTIES USEFUL FOR DETERMINING

THE COMPLEX PERMITTIVITY OF A TEST SOLUTION

COPYRIGHT NOTICE [0001] A portion of the disclosure of this patent document contains material that is subject to copyright protection. The copyright owner has no objection to the facsimile reproduction by anyone of the patent document or patent disclosure, as it appears in the Patent and Trademark Office patent file or records, but otherwise reserves all copyright rights whatsoever.

CROSS REFERENCE TO RELATED APPLICATIONS [0002] This application claims the benefit of U.S. Provisional Application no. 60/268,401, entitled "System and Method for Characterizing the Permittivity of Molecular Events," filed February 11, 2001, herein incorporated by reference in its entirety for all purposes.

BACKGROUND OF THE INVENTION [0003] The present invention relates to systems and methods for creating test solutions having desired dielectric properties and a method for using those solutions to accurately determine the complex permittivity of a test solution suspect of containing molecular or cellular events.

[0004] The applicant has previously described systems and methods for detecting structures, activity, and interactions on the molecular and cellular level (generally referred to as "molecular events" and "cellular events" respectively) using a form of dielectric spectroscopy referred to as multiplole coupling spectroscopy. Generally, multipole coupling spectroscopy involves illuminating a sample containing a molecular or cellular event with an electromagnetic signal. The electromagnetic signal interacts with the molecular or cellular event occurring within the sample, producing in response, a modulated electromagnetic signal. Because the dielectric properties of most molecular and cellular events are unique, each modulates the electromagnetic signal differently. The modulated signal is then recovered and analyzed to determine what type of event is present in the sample. These measurements are typically accomplished using network analyzers or similar test system which are configured to launch a signal at one or over a range of frequencies, and subsequently recover the resulting modulated signal.

[0005] S -parameters or other such similar measurement parameters are disadvantageous in that they are test system dependent, i.e., the configuration of the test system itself influences the measurement to some extent. This effect can be minimized by calibrating the test system; these effects cannot be completely removed, however. Characterizing solution-based molecular and cellular events using a system independent quantity, such as permittivity, would be more advantageous as it would enable direct comparison of data obtained across diverse measurement platforms. However, because of the expected low concentration of molecular and cellular events in the sample, permittivity characterization of the sample requires an extremely high degree of measurement accuracy.

[0006] Conventional permittivity measurement instruments, such as the model no. 85070 manufactured by Agilent Technologies (Palo Alto, CA), are typically configured to measure permittivity of samples over a wide range of permittivity values. To achieve this, measurement standards used to calibrate the instrument usually vary over a wide permittivity range; a typical set of calibration standards including an air standard d ε | ~ 1), a short-circuit standard (| ε | ~ ∞), and a deionized water standard fl ε | ~ 80). While the use of widely varying permittivity standards permits a broad permittivity measurement range, measurement accuracy for these instruments is also limited, typically being on the order of 2-5% of the measured permittivity value. This degree of accuracy is insufficient to detect or sufficiently characterize molecular and cellular events occurring within a test solution.

[0007] What is therefore needed is a method of measuring the permittivity of a test solution with higher accuracy in order to detect molecular and cellular events occurring within a test solution.

SUMMARY OF THE INVENTION [0008] The present invention provides systems and methods for accurately determining the complex permittivity of a test solution to detect molecular or cellular events occurring therein. In one embodiment, the method includes selecting a plurality of calibration solutions, each of which has a predetermined complex permittivity comprising a real component and an imaginary component, whereby the real or imaginary component of the complex permittivities of the calibration solutions collectively extend above and below the expected real or imaginary component of the complex permittivity of the test solution. The method further includes obtaining measurement parameters for each of the calibration solutions and computing a respective number of complex coefficients, each comprising a term in a rational function for converting measurement parameters to a complex permittivity. The method further includes obtaining measurement parameters for the test solution, and applying these measurement parameters to the rational function to determine the complex permittivity of the test solution.

[0009] The aforementioned method for determining the complex permittivity of a test solution further includes a method for creating one or more calibration solutions having a desired complex permittivity. The method includes providing a reference solution having an initial complex permittivity at one or more frequencies, the initial complex permittivity comprising a real component and an imaginary component at each of the one or more frequencies, and subsequently changing the initial complex permittivity of the calibration solution to the predefined value by adding a first agent to, or diluting the first agent from a reference solution.

[0010] The present invention will be better understood in light of the following drawings and detailed description.

BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Fig.1 A illustrates a measurement system for obtaining s-parameters of the calibration and test solutions in accordance with the present invention.

Fig. IB illustrates a permittivity measurement system operable to make an initial permittivity measurements in accordance with the present invention.

Fig. 2A illustrates a simplified block diagram of a computer system operable to execute a software program designed to perform each of the described methods.

Fig. 2B illustrates the internal architecture of the computer system shown in Fig. 4A.

Fig. 3 illustrates a method for determining the complex permittivity of a test solution in accordance with one embodiment of the present invention.

Fig. 4A illustrates graphical programming language operable to compute bilinear coefficients A*, B*, and C* in accordance with one embodiment of the present invention.

Fig. 4B illustrates graphical programming language operable to compute the complex permittivity of a test solution in accordance with one embodiment of the present invention. Fig. 5 A illustrates a method for varying the permittivity of a calibration solution to a desired value in accordance with one embodiment of the present invention.

Fig. 5B illustrates a method for selecting three calibration solutions in accordance with one embodiment of the present invention.

Fig. 6A illustrates a graph showing the measured real permittivity components of three PBS-based calibration solutions in accordance with the present invention.

Fig. 6B illustrates broadband permittivity measurements of the three PBS- based calibration solutions shown in Fig. 6A.

Fig. 7 illustrates broadband permittivity measurements of three sucrose- based calibration solutions created in accordance with the present invention.

For clarity, like numerals identify like parts throughout the drawings.

DESCRPTION OF THE SPECIFIC EMBODIMENTS

Definitions

[0012] As used herein, the term "molecular event" refers to the interaction of a molecule of interest with another molecule (e.g., molecular binding) and to all structural properties of molecules of interest. Structural molecular properties include the presence of specific molecular substructures (such as alpha helix regions, beta sheets, immunoglobulin domains, and other types of molecular substructures), as well as how the molecule changes its overall physical structure via interaction with other molecules (such as by bending or folding motions), including the molecule's interaction with its own solvation shell while in solution. The simple presence of a molecule of interest in the region where detection/analysis is taking place is not considered to be a "molecular event," but is referred to as a "presence."

[0013] Examples of molecular binding events are (1) simple, non-covalent binding, such as occurs between a ligand and its antiligand, and (2) temporary covalent bond formation, such as often occurs when an enzyme is reacting with its substrate. More specific examples of binding events of interest include, but are not limited to, ligand/receptor, antigen/antibody, enzyme/substrate, DNA/DNA, DNA/RNA, RNA/RNA, nucleic acid mismatches, complementary nucleic acids and nucleic acid/proteins. Binding events can occur as primary, secondary, or higher order binding events. A primary binding event is defined as a first molecule binding (specifically or non-specifically) to an entity of any type, whether an independent molecule or a material that is part of a first surface, typically a surface within the detection region, to form a first molecular interaction complex. A secondary binding event is defined as a second molecule binding (specifically or non- specifically) to the first molecular interaction complex. A tertiary binding event is defined as a third molecule binding (specifically or non-specifically) to the second molecular interaction complex, and so on for higher order binding events.

[0014] Examples of relevant molecular structures are the presence of a physical substructure (e.g., presence of an alpha helix, a beta sheet, a catalytic active site, a binding region, or a seven-trans-membrane protein structure in a molecule) or a structure relating to some functional capability (e.g., ability to function as an antibody, to transport a particular ligand, to function as an ion channel (or component thereof), or to function as a signal transducer). Molecular structure is typically detected by comparing the signal obtained from a molecule of unknown structure and/or function to the signal obtained from a molecule of known structure and/or function. Molecular binding events are typically detected by comparing the signal obtained from a sample containing one of the potential binding partners (or the signals from two individual samples, each containing one of the potential binding partners) to the signal obtained from a sample containing both potential binding partners.

[0015] The term "cellular event" refers in a similar manner to reactions and structural rearrangements occurring as a result of the activity of a living cell (which includes cell death). Examples of cellular events include opening and closing of ion channels, leakage of cell contents, passage of material across a membrane (whether by passive or active transport), activation and inactivation of cellular processes, as well as all other functions of living cells. Cellular events are commonly detected by comparing modulated signals obtained from two cells (or collection of cells) that differ in some fashion, for example by being in different environments (e.g., the effect of heat or an added cell stimulant) or that have different genetic structures (e.g., a normal versus a mutated or genetically modified cell). Morpholic changes are also cellular events. Other examples of cellular events are illustrated in applicant's concurrently filed application entitled "Methods for Analyzing Cellular Events," (Atty. Docket No. 23 US) herein incorporated by reference in its entirety for all purposes.

[0016] The same bioassay systems can be used for molecular and cellular events, differing only in the biological needs of the cells versus the molecules being tested. Accordingly, this specification often refers simply to molecular events (the more difficult of the two measurements under most circumstances) for simplicity, in order to avoid the awkwardness of continually referring to "molecular and/or cellular" events, detection, sample handling, etc., when referring to an apparatus that can be used to detect either molecular events or cellular events. When appropriate for discussion of a particular event, the event will be described as, for example, a cellular event, a molecular binding event, or a molecular structure determination.

[0017] When a molecular event (e.g., binding of a potential drug with a receptor) is being detected in a biological sample capable of undergoing biological functions (e.g., a cell or a cell-free enzyme system), the molecular event can be amplified by the biological function and, if desired to increase sensitivity, the change resulting from the function can be detected rather than the molecular event itself. Examples of detectable amplified signals include the permittivity change of a cell resulting from the opening or closing of an ion channel when a molecular binding event occurs and a physiological reaction (e.g., synthesis of a protein) of a cell when a drug interacts with a cellular receptor. When working with cells, such binding event detection can be referred to as detection of a "cellular molecular event" (as opposed to a "non-cellular molecular event," which is one that occurs in the absence of cells). Similar language can be used to describe cell-free enzyme-system molecular events.

[0018] As used herein, the term "test solution" refers to the molecular or cellular event being investigated and the medium/buffer in which the analyte is found. The medium can include solid, liquid or gaseous phase materials; the principal component of most physiological media/buffers is water. Solid phase media can be comprised of naturally occurring or synthetic molecules including carbohydrates, proteins, oligonucleotides, SiO₂, GaAs, Au, or alternatively, any organic polymeric material, such as Nylon^®, Rayon^®, Dacryon^®, polypropylene, Teflon^®, neoprene, delrin or the like. Liquid phase media include those containing an aqueous, organic or other primary components, gels, gases, and emulsions. Exemplary media include celluloses, dextran derivatives, aqueous solution of d- PBS (phosphate buffered saline), Tris, Tween^®, deionized water, blood, cerebrospinal fluid, urine, saliva, water, and organic solvents. The test solution may include both liquid and solid phase materials. For example, the test solution may contain micro-carriers (e.g., micro- beads) having molecular or cellular events occurring along the surfaces thereof.

[0019] As used herein, the term "calibration standard" refers to a material which exhibits a desired complex permittivity. The calibration standard may exist in a gas phase, a solid phase, a liquid phase, or include a combination of two or more of these materials. For example in one embodiment, the calibration standard may consist of a solution in which a solute is either concentrated or diluted in order to achieve the desired complex permittivity. In another embodiment, the calibration standard may consist of a solution containing non- soluble constituents such as micro-carriers, which are added to solution to obtain the desired complex permittivity of the solution. In still a further exemplary embodiment, the calibration standard may consist of a solid material such as a dielectric rod having a known complex permittivity. These represent only a few of the possible examples of the calibration standards used in the present invention and variations to these will be apparent to those of skill in the art.

[0020] As used herein, the term "test signal" refers to a sub-optical, time-varying electromagnetic signal below 1000 GHz (GHz = 10⁹ Hz). A preferred operating frequency range is from 10 KHz to 110 GHz, and more particularly from 100 KHz to 20 GHz. "Test signal" can refer to a range of frequencies rather than a single frequency, and such a range can be selected over any terminal frequencies, including frequency ranges bounded by the specific frequencies named in this paragraph. When referring to the detected range (or multiple) of modulated signals obtained after a range of frequencies has been coupled to a test solution, the term "spectrum" is sometimes used. An "incident test signal" is a test signal that originates from the signal source and is destined for the detection region for interaction with the test solution. A "modulated test signal" is a test signal that has previously interacted with the test solution and is destined for a signal detector that can recover the modulation imparted by the signal interaction with the test solution.

[0021] As used herein, the term "measurement parameter" refers to any quantity which can be ascertained from, or output by a measurement system in which an incident test signal is transmitted to a device under test and a reflected signal is recoverable from the device under test. A non-exhaustive list of measurement parameters include g-parameters, h- parameters, s-parameters, y-parameters, or z-parameters, all known in the art of electronic circuit design.

[0022] As used herein, the term "electromagnetically coupled" refers to the transfer of electromagnetic energy between two objects, e.g., the signal transmission structure and molecular or cellular event events occurring within the test solution. The two objects can be electromagnetically coupled when the objects are in direct or indirect physical contact, (e.g., molecular events attached along the surface of the signal line or on a physical intervening layer or structure), or when the objects are physically separated from each other (e.g., molecular or cellular events suspended within solution flowing through a flow tube, the flow tube positioned within the detection region). As a modification, the term "electromagnetically couples" will indicate the interaction of an electromagnetic signal (e.g., the incident test signal) with an object (e.g., molecular or cellular events occurring within the test solution).

Overview

[0023] One of the methods of the present invention relates to the determining the complex permittivity of a test solution. Generally, this process is accomplished by obtaining a measured response of the test solution (the "measurement parameters" of the test solution) and subsequently converting those measurement parameters to a corresponding complex permittivity. The measurement parameters may consist of a variety of forms such as hybrid (g- or h-) parameters, scattering ("s") parameters, impedance ("z") parameters, and admittance ("y") parameters to name a few.

[0024] Conversion of the measurement parameters to a complex permittivity is accomplished through the use of a rational function which relates the measurement parameters to complex permittivity values. An example of such a rational function is the conventionally-known bilinear equation which translates measurement (scattering) parameters of a test solution S(ω) to the test solution's complex permittivity ε(ω)*:

_{r 1} . _!k A ( ω ) * S ( ω ) + B ( ω ) *

E q . 1 ^{: £} ( fl> ) = - C ( ω ) * S ( ω ) + 1 where: A(ω)*, B(ω)*, and C(ω)* are complex coefficients solved during a calibration process (described below); S(ω) is an s-parameter measurement at frequency ω; and ε(ω)* is the corresponding complex permittivity at frequency u)

[0025] As expressed in eq. (1), each s-parameter measurement occurring at frequency ω is transformed into a complex permittivity value ε(ω)* (referred to as permittivity ε* for brevity) at measurement frequency ω. For example, the computation of a test solution's permittivity at frequency a involves measuring the test solution's s- parameters at cøi, and applying these s-parameters to a set of coefficients A*, B*, and C* computed at The set of complex coefficients (referred to as A*, B*, and C* for brevity) are computed at cθι by creating three calibration solutions which exhibit desired permittivity values, and measuring their corresponding s-parameters at ω₁. This process is further illustrated and described below.

[0026] The illustrated bilinear equation is but one of a variety of possible rational functions that may be used to convert the test solution's measurement parameters to a corresponding complex permittivity. In another embodiment for instance, a bi-quadratic equation, consisting of a quotient of two expressions having a total of six coefficients may be used. Generally, any rational function (i.e., any polynomial divided by another polynomial) may be used in the method of the present invention to determine the complex permittivity of a test solution.

[0027] Fig.lA illustrates a measurement system 100 for obtaining measurement parameters of the calibration and test solutions in accordance with the present invention. In a specific embodiment, the measurement system 100 is configured to output s-parameters known in the art of high frequency circuit analysis, although other measurement parameters (for example, g-, h-, y, or z-parameters) may be used and converted to complex permittivity in the present invention.

[0028] The measurement system 100 includes a signal source 110a and a signal detector 120a connected to a first port of a bio-assay device 150 (referred to as "biosensor"). In this configuration, the signal source and detector can be used to obtain a one-port (i.e., a reflection) signal response. Alternatively, or in addition to the signal detector 120a, the measurement system 100 may include a signal detector 120b connected a second port 158 of the biosensor 150. When so configured, the signal source 110a and the signal detector 120b can be used to provide a two-port (i.e., a "through") signal response of the biosensor 150. A second signal source 110b may be further included to provide a reflection measurement capability at the second port 158 of the biosensor 150.

[0029] The signal sources 110 are operable to generate and launch an electromagnetic signal 160 ("incident test signal") at one or more amplitudes and/or frequencies. The signal detectors operate to recover the test signal after it has interacted with (i.e., after electromagnetically coupling to) the test solution in the biosensor 150. In a specific embodiment, the signal source 110 and the signal detector 120 are included within an automated network analyzer, such as model number 8714 manufactured by Agilent Technologies (Palo Alto, CA). Other measurement systems such as vector voltmeters, scalar network analyzers, time domain reflectometers, and the like that use signal characteristics of incident, transmitted, and reflected signals to evaluate an object under test may be used in alternative embodiment under the apparatus. Specific embodiments of the measurement system 100 are illustrated in applicant's co-pending applications listed below.

[0030] The sample handling assembly 130 includes a sample handling device 132 and a sample delivery apparatus 134. The sample handling device 132 may include sample preparation, mixing, and storage functions that may be integrated on a micro-miniature scale using, for instance, a microfluidic platform. The sample delivery apparatus 134 may consist of a tube, etched or photolithographcially formed channel or capillary, or other similar structure that delivers a volume of test solution to a location proximate to the signal path, such that the incident test signal propagating along the signal path will electromagnetically couple to the test solution. In another embodiment, the sample handling assembly 130 consists of a robotic or automated sample processor. Specific embodiments of the sample handling and delivery structures are illustrated in applicant's co-pending applications listed below. In a particular embodiment, a computer system 210 (shown and described below) is used to control the source(s) 110, detector(s) 190, and the solution flow from the sample handling assembly 130.

[0031] The biosensor 150 operates as a bioelectrical interface that detects molecular or cellular events occurring within the solution using electromagnetic signals. The biosensor 150 includes a signal path that is configured to support the propagation of electromagnetic signals over the desired frequency range. Electrical engineers will appreciate that the signal path may consist of a variety of different architectures, for instance a waveguide, transverse electromagnetic (TEM) mode structures such as coaxial cable, coplanar waveguide, stripline, microstrip, suspended substrate, and slotline, as well as other structures such as twisted pair, printed circuits, and the like. In a specific embodiment, the biosensor 150 consists of an open-ended coaxial resonant probe, an example of which is described in applicant's co- pending patent application no. 09/687,456 entitled "System and Method for Detecting and Identifying Molecular Events in a Test Sample," herein incorporated by reference. Other embodiments of the biosensor 150 are illustrated in applicant's co-pending applications listed below.

[0032] During operation, an incident test signal 160 is generated by the signal source 110a and launched along the signal path where it electromagnetically couples from the signal path to the supplied test solution. One or more signal characteristics (amplitude, phase, frequency, group delay, etc.) of the incident test signal 160 are modulated by its interaction with the molecular or cellular events occurring within the test solution. In a one- port measurement system, a portion of the modulated signal 180 is reflected back along the signal path and recovered by the signal detector 120a. In a two-port measurement system, a portion of the modulated signal is transmitted through to the second port and recovered by the second signal detector 120b. The modulation caused by the electromagnetically coupling may consist of a change in the amplitude, phase, frequency, group delay, or other signal parameters.

[0033] The modulated test signal 180 (and/or 170) is recovered and its signal characteristics (amplitude, phase, etc.) are compared to signal characteristics of the corresponding incident test signal 160. In a particular embodiment, changes in the amplitude and phase of the modulated reflected signal 180 relative to the incident test signal 160 are computed at each test frequency and a response plotted over the test frequencies as an s- parameter return loss ("Sπ") response. In another embodiment, changes in the amplitude and phase of the modulated transmitted signal 170 relative to the incident test signal 160 are computed at each test frequency and a response plotted over the test frequencies as an s- parameter transmission loss ("S₂₁") response.

[0034] Fig. IB illustrates a permittivity measurement system 190 used to make initial permittivity measurements in accordance with the present invention. The system 190 employs a conventional permittivity measurement instrument 192, consisting of model no. 85070 manufactured by Agilent Technologies (Palo Alto, CA) in one embodiment. The system 190 further includes a measurement probe 195 consisting of an open-ended coaxial type probe when the aforementioned model no. 85070 permittivity measurement instrument is employed. The probe 195 is operable to electromagnetically couple an incident test signal to the test solution 196. In a specific embodiment , the probe is immersed in approximately 25 ml of the subject solution A sample handling assembly 130, such as the above-described sample handling device 132 and sample delivery apparatus 134 may be used to provide the solution to the probe 195. A computer system 210 may be used to control the operation of the permittivity measurement instrument 192 and control the flow of the sample handling assembly 130. In a specific embodiment, a general purpose instrument bus (GPIB) or similar wired or wireless bus 197 is operable to communicate data, command, and/or control signals between the computer system 210 and the permittivity measurement instrument 192 and/or the sample handling assembly 130.

[0035] Fig. 2A illustrates a simplified block diagram of the computer system 210 operable to execute a software program designed to perform one or more of the methods described below. In a particular embodiment, the computer system 210 consists of Optex GX110 computer available from Dell Computers (Dallas, TX), and is programmed using LabNLEW^® graphical programming language available from National Instruments Corporation (Austin, TX). The computer system 210 also includes a monitor 214, screen 212, cabinet 218, and keyboard 234. A mouse (not shown), light pen, or other I/O interface, such as virtual reality interfaces can also be included for providing I/O commands. Cabinet 218 houses a CD-ROM drive 216, a hard drive (not shown) or other storage data mediums which can be utilized to store and retrieve digital data and software programs incorporating the present method, and the like. Although CD-ROM 216 is shown as the removable media, other removable tangible media including floppy disks, tape, and flash memory can be utilized. Cabinet 218 also houses familiar computer components (not shown) such as a processor, memory, and the like.

[0036] Fig. 2B illustrates the internal architecture of the computer system 210. The computer system 210 includes monitor 214, which optionally is interactive with the I/O controller 224. Computer system 210 further includes subsystems such as system memory 226, central processor 228, speaker 230, removable disk 232, keyboard 234, fixed disk 236, and network interface 238. Other computer systems suitable for use with the described method can include additional or fewer subsystems. For example, another computer system could include an additional processor 228 (i.e., a multi-processor system). Arrows such as 240 represent the system bus architecture of computer system 210. However, these arrows 240 are illustrative of any interconnection scheme serving to link the subsystems. For example, a local bus could be utilized to connect the central processor 228 to the system memory 226. In a specific embodiment, the network interface 238 includes a PCI slot for accepting a GPIB card for connection to the aforementioned GPIB cable 197. Further specifically, the network interface 238 also includes a RS-232 bus for controlling the operation of the sample handling assembly 130. Computer system 210 shown in Fig. 2B is but an example of a computer system suitable for use with the present invention. Other configurations of subsystems suitable for use with the present invention will be readily apparent to those of skill in the art.

Formulation of Calibration Solutions and Determination of Test Solution Permittivity

[0037] Fig. 3 illustrates a method for determining the complex permittivity of a test solution in accordance with the present invention. Initially at 302, a permittivity measurement instrument is provided and calibrated. In a specific embodiment, the permittivity measurement instrument used is model no. 85070 permittivity measurement instrument manufactured by Agilent Technologies (Palo Alto, CA) which outputs real and imaginary components of the solution's complex permittivity at each measurement frequency. Other instruments which measure complex permittivity directly, or output measurement parameters (e.g., s-parameters) convertible to permittivity components may be used in alternative embodiments under the present invention.

[0038] Next in process 310, a plurality of calibration standards are selected. In the preferred embodiment, the calibration standards are selected from a group of measured standards, the selected calibration standards having complex permittivity values which collectively extend above and below the expected complex permittivity value of the test solution. In the exemplary embodiment in which the three coefficient term bilinear eq. (1) is employed as the rational function relating s-parameters to complex permittivity, three calibration standards (solutions) are selected. Other embodiments in which the rational function uses a larger or smaller number of coefficients will accordingly require a larger or smaller number of calibration standards. Specific embodiments of the process of 310 are shown and described below.

[0039] Next at 320, measurement parameters are obtained for each of the calibration standards. In the illustrated embodiment, the measurement system illustrated in Fig. 1 A provides the measurement parameters in the form of s-parameters, although other forms of measurement parameters may be used in alternative embodiments. In a specific embodiment, the biosensor employed in is an open-ended resonant coaxial probe, described above. Other biosensors may be used to obtain s-parameters of the calibration solutions. For example, a two-port biosensor such as the coplanar waveguide biosensor described in applicant's co-pending patent application no. 09/929,521 can be used to obtain a two-port set of s-parameters. In any of these embodiments, scattering parameters may be obtained over a narrow or broad frequency range as the user desires, the measurement band being substantially consistent with the frequency range over which the complex permittivity was either measured or known to extend in process 310 above.

[0040] At 330, a plurality of coefficients corresponding to the number of calibration standards are computed, each of the coefficients comprising a term in the aforementioned rational function relating measurement parameters to complex permittivity values. In a specific embodiment, the rational function is as presented in eq. (1) and consists of three coefficients A*, B* and C*. These coefficients represent three unknowns which are solved by simultaneously solving for three versions of eq.(l) when the measured permittivity values (&ι*, ε₂*, and ε₃*) and the measured s-parameters (Sι(ω), S₂(ω), and S₃(ω)) are input to eq. (1). This process may be completed using software programming, for example the graphical programming code illustrated in Fig. 4A. Other programming languages such as C, C++, lava^®, Visual Basic^®, PERL, COBOL, FORTRAN, as well as other programming languages may be used and function equally as well in alternative embodiments under the present invention.

[0041] In the preferred embodiment, the permittivity of a given calibration solution is measured under the same conditions (i.e., temperature, pH, concentration, event activity, etc.) in process 310 as the s-parameters of the same solution measured in process 330. Should the calibration solution undergo an actual or suspected change in its condition, the permittivity and s-parameter measurement processes 310 and 330 may be repeated, and the coefficients A*, B* and C* recomputed. In an alternative embodiment, only the s-parameter measurement process in 330 is repeated, and the coefficients A*, B*, and C* are recomputed based thereon.

[0042] Further alternatively, one or more additional calibration solutions may be used, when for instance, one or more calibration solutions provide a desired permittivity response only over a specific frequency range. In this instance, processes 310, 320, and 330 are repeated for the new calibration solution(s). The permittivity and s-parameter measurements for the new solution(s) are made over that desired frequency range in processes 310 and 330, and the resulting coefficients being computed in 330, those coefficient being valid over the specific frequency range. As can be imagined, different sets of calibration solutions can be used to cover different test frequency ranges.

[0043] Test solution permittivity characterization begins at 340, at which point the measurement parameters of the test solution are obtained. In the preferred embodiment, the measurement set up employed in process 320 is used. Next at 350, the test solution's measurement parameters, measured over a set of frequencies, are used as arguments in the rational function, with the coefficients already computed for each frequency, to compute a set of permittivities, one at each frequency. At a particular measurement frequency, the permittivity of the test solution is obtained directly. At frequencies between measurement points, the permittivity of the test solution may be obtained by interpolating between adjacent data points. In this instance, a linear interpolation, polynomial fit, or other curve fitting algorithms may be applied to the measured data to compute the permittivity at a particular frequency. In another embodiment, a broadband permittivity value of the test solution may be computed by taking, for instance, the average value of the computed permittivity values computed over a portion (or all) of the measured frequency range. These processes are preferably executed using computer programming, one possible example being Lab VIEW^® graphical programming code illustrated in Fig. 4B. The test solution permittivity computed at 350 will be highly accurate since the calibration solutions used to compute the coefficients A*, B*, and C* have permittivity values which closely approximate (above and below) the permittivity of the test solution.

[0044] While the aforementioned calibration standards are described in terms of solutions, solid phase material may be used in conjunction with, or alternative to these solutions. In particular, a solid material (perhaps in the form of a rod, sphere, or other geometry) consisting of polyethylene, polystyrene, polypropylene, of similar materials which has either a known permittivity value over frequency or is calculable over a desired frequency, may be used as a calibration standard in alternative embodiment under the present invention.

[0045] Fig. 5 A illustrates an exemplary embodiment of process 310 in which calibration solutions are selected. In a specific embodiment of this process, three calibration solutions are selected, a first calibration solution which emulates the permittivity (real and/or imaginary components) of the test solution buffer, and two additional calibration solutions which collectively bracket the expected permittivity (real and or imaginary components) of the test solution. Other embodiments in which the calibration solutions exhibit permittivities only above or only below the test solution buffer permittivity are also possible under the present invention.

[0046] Initially at 502, the permittivity of the test solution buffer is determined. In one embodiment, the permittivity (real and/or imaginary components) of the test solution buffer is measured using the permittivity measurement instrument illustrated in Fig. IB. In another embodiment, the test solution buffer permittivity is calculable from known mathematical permittivity models such as the Debye model, the Cole-Cole model, the Cole- Davidson model, the Havriliak -Negami model, or variations thereof.

[0047] Next at 504, the first calibration solution is selected. In the preferred embodiment, the calibration solution selected is one having a permittivity value (real and/or imaginary components) which closely approximates the real and/or imaginary permittivity component values of the test solution buffer over the desired test frequency range. This can be accomplished by initially selecting a reference solution having substantially the same major agent concentration as present in the test solution buffer. For example, when measuring a test solution having a IX PBS buffer, a IX (150 mM) saline solution may be initially selected as a reference solution. [0048] Once the reference solution is selected, the process continues at 506 where the solution's permittivity is measured. In the preferred embodiment, this process is achieved using the aforementioned permittivity measurement instrument illustrated in Fig. IB. Next at 508 the measured permittivity of the calibration solution is compared to the permittivity of the test solution buffer to determine if it is within an acceptable range of the test solution buffer. In embodiments in which the calibration solution is well characterized (e.g., through known mathematical models such as the Debye model, Cole-Cole Model, Cole-Davidson, Havriliak -Negami, and variations thereof), measurement of the solution's permittivity may not be required. Instead, its known permittivity value is computed and compared to the permittivity value of the test solution buffer.

[0049] If the permittivities of the selected calibration and buffer solutions are not within a predefined window of agreement, the process continues at 510 where the permittivity (real and/or imaginary components) of the calibration solution is adjusted by adding an agent or diluting the concentration of an agent within the calibration solution. For example, the permittivity of the reference calibration solution may be adjusted by either diluting or concentrating the major agent's presence within the calibration solution. The process may further include adding additional agents present in the test solution to the calibration solution to more closely emulate its permittivity.

[0050] The added or diluted agent may be comprise a solute, such as sodium chloride, sucrose, glucose, HEPES, KC1, CaCl₂, MgCl₂, MgSO , and the like. Alternatively, the agent may comprise non-soluble materials such as micro-beads or micro-bubbles. Other solutes and non-soluble agents may be used in alternative embodiments under the present invention.

[0051] After the agent's concentration in the calibration solution has been adjusted, the processes of 506 and 508 are repeated to measure and compare the adjusted permittivity to the desired value. These steps may be repeated multiple times in order to dial in the measured permittivity to the desired value. Once the desired value of the permittivity of the calibration standard is reached within the predefined range, the process continues at 512 at which point a determination is made as to whether additional calibration standards are selected and their respective permittivities adjusted using the aforementioned processes. If so, the processes of 504-512 are repeated to ascertain the required number of calibration solutions having the desired permittivity values. When all of the calibration standards have been selected and their respective permittivities adjusted to the desired values, the process concludes at 514. In an exemplary embodiment, the predefined offset value is ± 1 unit for each of the real and imaginary component values, e.g., if the first calibration solution has a permittivity of εi* = 75 - j2 (real component value of + 75 and an imaginary component value of -2), calibration solution no. 2 may be selected to exhibit a permittivity ε₂* having a real component at ± 1 of εi* (i.e., ε₂* = 76 - j2, or 74 -j2), an imaginary component at ± 1 of εi* (i.e., ε₂* = 75 - jl, or 75 -j3), or a combination of both (e.g., ε_* = 74 -jl, or 74 -j3, or 76 - j 1, or 76 -j3). Specific embodiments of these processes are shown and described below.

[0052] Fig. 5B illustrates another embodiment of the process of 310 for selecting calibration solutions in accordance with the present invention. Initially at 522, a stock solution is provided which contains the major agent of the test solution buffer. As an example, a stock solution containing NaCl solute is provided to formulate calibration solutions for a test solution having PBS as a buffer. Solutions containing other solutes or non-soluble material may be employed as well under the present invention.

[0053] Next at 524, the agent in the stock solution is diluted or concentrated as needed, to approach the agent concentration in the test solution buffer, the diluted or concentrated solution comprising the first calibration (reference) solution. Using the aforementioned example, a stock solution of 3X NaCl is successively diluted to a IX NaCl solution, which is used as the reference solution for a test solution buffer of IX PBS. At 526, the permittivity of the reference solution is measured and compared to the permittivity of the test solution buffer. If the two permittivities are not within a desired range of agreement, the concentration of the first agent may be adjusted, or additional agents added to the reference solution in order of their presence in the test solution.

[0054] Next at 528, two additional calibration solutions are prepared, each formulated to exhibit a permittivity (real and/or imaginary component values) having a predefined offset from the permittivity (real and/or imaginary component values) of the test solution buffer. This process may be performed by adjusting the agent concentration within a predefined volume of the stock solution. One or more agents may be added to further adjust the solution's permittivity to the desired offset. In a specific embodiment, one of the two solutions provides a positive offset and the other solution provides a negative offset to the permittivity of the reference solution. In another embodiment, the two solutions provide an offset on the same side of the reference solution's permittivity, i.e., both exhibiting higher or lower permittivity values in relation thereto. The permittivities of the two additional calibration solutions are measured and compared to their respective desired offsets, the composition of the solutions being modified as described above if the measured permittivities are not within a predefined range of the desired offset.

[0055] In a specific example (further illustrated below), the second and third calibration solutions may be prepared by successively diluting the stock solution of 3X NaCl down to 1.2X NaCl for the second calibration solution, and further diluting the stock solution down to .5X NaCl for the third calibration solution. Permittivity measurements are made at each dilution or concentration step until the desired offset is achieved. An additional solute, 3% w/w glucose is added to the 1.2X NaCl solution in order to provide the desired permittivity offset as confirmed by a permittivity measurement of the solution.

[0056] The methods of Fig. 5 A and 5B are not limited to the formulation of calibration standards for use only with the bilinear equation. More generally, both methods may be used to create one or more calibration solutions of a desired permittivity, which would be useful in calibrating a high frequency measurement system such as a network analyzer, capacitance meter, or vector voltmeter. In a specific embodiment, the method is used to formulate a calibration solution having a desired permittivity as described above. The calibration solution is subsequently placed proximate to a biosensor (the aforementioned open-ended resonant coaxial probe in one example) connected to a network analyzer, and the Sπ of the biosensor is carefully tuned such that magnitude of the Si \ response is tuned to it minimum point. In this state, the resonant frequency (frequency at which the magnitude of Sπ is minimum) and the quality factor (ratio of energy retained within the resonant probe to the energy dissipated in the within the resonant probe at the resonant frequency) of the biosensor are determined. Next, the test solution is located proximate to the open-ended resonant coaxial probe and the Sπ response is monitored. The exchange of the calibration solution with the test solution will cause a change in the Sπ response, resulting in a change in the resonant frequency and q-factor of the biosensor. The change in resonant frequency and q-factor can then be translated into a change in the real and imaginary parts of the permittivity. This magnitude of the change ("delta") in the resonant frequency and/or q- factor values will be indicative of the presence or absence of molecular or cellular events and these figures themselves can be used as metrics to detect and identify molecular or cellular events. Alternatively, the complex permittivity can be compute directly as the complex permittivity of the calibration solution is known and the change therefrom can be computed using the change in the resonant frequency and q-factor. Examples

[0057] The method for creating calibrating calibration solutions is now illustrated by way of several examples. The foregoing examples are not exhaustive, and variation or modification of the presented processes, solutions, agents, and test systems will be apparent to those skilled in the art.

Saline Based Reference Solution

[0058] In the first example, three saline-based calibration solutions were prepared for a test solution having a IX PBS buffer (Gibco Industries, Grand Island, NY). The three calibration solutions were formulated to provide a ± 1 unit window around the real permittivity component of the IX PBS buffer. The permittivity measurement system 190 illustrated in Fig. IB using model no. 85070 permittivity measurement instrument was used to measure the real permittivity component of the IX PBS and the three calibration solutions.

[0059] The three calibration solutions were prepared from a stock solution of 3X (450 mM) NaCl. A solution of IX NaCl was initially chosen to emulate the real permittivity component of the PBS buffer. A 0.5X NaCl solution was prepared to provide the +1 upper boundary of the IX PBS solution, and a 1.2X NaCl + 3% w/w glucose solution was created to provide the -1 lower boundary to the IX PBS solution. The real part of the solutions' permittivity was measured at a single frequency, 1.3 GHz, at 27° C, 28° C, and 29° C, respectively, to determine temperature dependence.

[0060] Fig. 6A illustrates a graph of the measured real permittivity components of all four solutions at 27° C, 28° C, and 29° C, respectively, at a test frequency of 1.3 GHz. As shown, the real permittivity components of the IX PBS buffer and IX NaCl (response traces 610 and 620, respectively) are closely matched and trend in the same direction with increasing temperature. The solution of 1.2X NaCl +3% w/w glucose solution (response trace 630) provides a lower boundary of approximately 1.2 units below the PBS IX solution, and the 0.5x NaCl solution (response trace 640) provides an upper boundary of 0.95 units above the IX PBS solution.

[0061] Fig. 6B illustrates broadband measurements made from 500 MHz to 13.5 GHz of the aforementioned solutions at 27° C. The vertical axis represents the difference in the real permittivity component relative to the reference solution, and the horizontal axis represents frequency in GHz. Trace 622 indicates that the relative difference between the .5X and the reference solutions is +1 over the majority of the measured frequency range. Trace 632 indicates that the relative difference between the 1.2X + 3% and reference solutions decreases from -1 to between -2 and -2.5 units with increasing frequency. The above- described processes may be repeated to obtain calibration solutions having a predefined offset from the imaginary permittivity component of the reference solution.

IX Sucrose Buffer as a Reference Solution

[0062] In the second example, a solution of IX sucrose buffer was formulated and used as the reference around which an offset of ± 3 units was desired for the real permittivity component. This buffer is especially advantageous for the detection of cellular events in the methods and structures of the present invention as it has a similar ionic content to conventional buffers commonly used for cell-based assays, such as PBS. This low in ionic content enables signal interrogation over a wider range of frequencies. The buffer is also optimized for ability to measure a calcium flux using fluorescent dyes in living cells. HEPES was used as the buffering system so as to not precipitate out with the calcium, as occurs in the case when using sodium bicarbonate to buffer the solution.

[0063] The formulated sucrose buffer consisted of 230 mM sucrose (7.54 % w/w) 16 mM glucose (.288% w/w), 10 mM HEPES, 5 mM NaCl, 5.37 mM KC1, 1.26 mM CaCl₂, 1 mM MgCl₂, and 0.81 mM MgSO₄. Larger or smaller concentrations of these solutes may also be used. For example, the amount of CaCl₂ in the solution may be varied from 0 to 5 mM in order to optimize calcium signaling in cells. The concentration of sucrose may be varied to optimize the osmolarity of the solution. The amount of glucose may be changed to optimize for cellular health. The buffering system may be changed from HEPES to some other buffering system such as sodium bicarbonate or the like. In addition, EGTA or BAPTA may be added to chelate the calcium in the buffer should formulation of a calcium-free solution be deemed necessary. Concentrations of the sucrose buffer at .5X and 1.5X were chosen as the other two calibration solutions.

[0064] Fig. 7 illustrates broadband permittivity measurements made from 500 MHz to 13.5 GHz of the .5X and 1.5X buffers solutions at 27° C. The vertical axis represents the difference in the real permittivity component of the .5X and 1.5X buffers relative to the IX sucrose buffer, and the horizontal axis represents frequency in GHz. Trace 722 indicates that the relative difference in the real permittivity component between the .5X and the IX buffers increases from + 0.8 to between +2.5 and +3.0 units with increasing frequency. Trace 732 indicates that the relative difference between the 1.5X and IX buffers decreases from -1.2 to between -3.2 and -2.9 units with increasing frequency. [0065] While the above is a complete description of possible embodiments of the invention, various alternatives, modification and equivalents may be used to which the invention is equally applicable. For example, other calibration solutions may be formulated using the methods of the present invention. Other modifications will be apparent to the reader as well. Accordingly, the above description should be viewed as only a few possible embodiments of the present invention, the boundaries of which is appropriately defined by the metes and bounds of the following claims.

[0066] The following commonly owned, co-pending applications are herein incorporated by reference in their entirety for all purposes:

Serial No. 09/243,194 entitled "Method and Apparatus for Detecting Molecular Binding Events, filed February 1, 1999 (Atty Dkt No. 19501-000200US);

Serial No. 09/365,578 entitled "Method and Apparatus for Detecting Molecular Binding Events," filed August 2, 1999 (Atty Dkt No. 19501-000210);

Serial No. 09/243,196 entitled "Computer Program and Database Structure for Detecting Molecular Binding Events," filed February 1, 1999 (Atty Dkt No. 19501- 000300);

Serial No. 09/480,846 entitled "Resonant Bio-assay Device and Test System for Detecting Molecular Binding Events," filed lanuary 10, 2000 (Atty Dkt No. 19501- 000310);

Serial No. 09/365,978 entitled "Test Systems and Sensors for Detecting Molecular Binding Events," filed August 2, 1999 (Atty Dkt No. 19501-000500);

U.S. Patent No. 6,287,776 entitled "Method For Detecting and Classifying Nucleic Acid Hybridization";

U.S. Patent No. 6,287,874 entitled "Methods for Analyzing Protein Binding Events";

Serial No. 09/687,456 entitled "System and method for detecting and identifying molecular events in a test sample," filed October 13, 2000 (Atty Dkt No. -12US);

Serial No. 60/248,298 entitled "System and method for real-time detection of molecular interactions," filed November 13, 2000 (Atty Dkt No. -14P);

Serial No. 09/775,718 entitled "Bioassay device for detecting molecular events," filed February 1, 2001 (Atty Dkt No. -15US);

Serial No. 09/775,710 entitled "System and method for detecting and identifying molecular events in a test sample using a resonant test structure," filed February 1, 2001 (Atty Dkt No. -16US); Serial No. 60/268,401 entitled "A system and method for characterizing the permittivity of molecular events," filed February 12, 2001 (Atty Dkt No. -17P);

Serial No. 60/275,022 entitled "Method for detecting molecular binding events using permittivity," filed March 12, 2001 (Atty Dkt No. -18P);

Serial No. 60/277,810 entitled "Bioassay device for Detecting Molecular Events," filed March 21, 2001 (Atty Dkt No. -19P);

Serial No 09/837,898 entitled "Method and Apparatus for Detection of Molecular Events Using Temperature Control of Detection Environment," filed April 18, 2001 (Atty Dkt No. -20US)

Serial No. 09/880,331 entitled "Reentrant Cavity Bioassay for Detecting Molecular or Cellular Events," filed June 12, 2001 (Atty. Dkt. No. -21US);

Serial No. 09/880,746 entitled "Pipette-Loaded Bioassay Assembly for Detecting Molecular or Cellular Events," filed June 12, 2001 (Atty Dkt. No. -22)

Serial No. 09/929,513, entitled "Method for Analyzing Cellular Events," filed August 13, 2001 (Atty Dkt. No. 23 US);

Serial No. 09/929,520, entitled "Well-Based Biosensor for Detecting Molecular or Cellular Events," filed August 13, 2001 (Atty Dkt. No. 24 US); and

Serial No. 09/929,521, entitled "Coplanar Waveguide Biosensor for Detecting Molecular or Cellular Events," filed August 13, 2001 (Atty Dkt. No. 25 US).

Claims

WHAT IS CLAIMED IS:

1. A method for creating a solution having a desired complex permittivity, comprising: providing a reference solution having an initial complex permittivity at one or more frequencies, the initial complex permittivity comprising a real component and an imaginary component at each of the one or more frequencies; and changing the initial complex permittivity of the reference solution to the desired complex permittivity at the one or more frequencies by either adding a first agent to the reference solution, or diluting the presence of a first agent within the reference solution.

2. The method of claim 1, wherein changing the complex permittivity of the reference solution comprises changing only the real component of the complex permittivity.

3. The method of claim 1, wherein changing the complex permittivity of the reference solution comprises changing only the imaginary component of the complex permittivity.

4. The method of claim 1, wherein changing the complex permittivity of the reference solution comprises changing both the real and imaginary components of the complex permittivity.

5. The method of claim 1, wherein changing the complex permittivity of the reference solution comprises changing the real component of the complex permittivity ±1 unit.

6. The method of claim 1, wherein changing the complex permittivity of the reference solution comprises changing the imaginary component of the complex permittivity ±1 unit.

7. The method of claim 1, wherein the reference solution comprises a phosphate buffered solution.

8. The method of claim 1, wherein the first agent comprises sodium chloride.

The method of claim 8, wherein the first agent further comprises glucose.

10. The method of claim 1, wherein the first agent comprises sucrose.

11. The method of claim 10, wherein the first agent further comprises glucose, HEPES, sodium chloride, potassium chloride, calcium chloride, magnesium chloride, and magnesium sulfate.

12. A method for determining the complex permittivity of a test solution, comprising: selecting a plurality of calibration solutions, each of the plurality of calibration solutions having a predetermined complex permittivity comprising a real component and an imaginary component, wherein the real or imaginary component of the predetermined complex permittivities of the plurality of calibration solutions collectively extend above and below the expected real or imaginary component of the complex permittivity of the test solution; obtaining measurement parameters for each of the plurality of calibration solutions; computing a respective plurality of complex coefficients, each of the plurality of complex coefficients comprising a term in a rational function for converting measurement parameters to a complex permittivity; obtaining measurement parameters for the test solution; and applying measurement parameters of the test solution to the rational function to determine the complex permittivity of the test solution.

13. The method of claim 12, wherein selecting a plurality of calibration solutions comprises: providing first, second, and third volumes of a solution having an initial complex permittivity at one or more frequencies, the initial complex permittivity comprising a real component and an imaginary component; and changing the initial complex permittivity of the second volume of reference solution to a predefined value by either adding a first agent to the second volume of reference solution, or diluting the presence of a first agent within the second volume of reference solution.

14. The method of claim 13, wherein changing the initial complex permittivity of the second volume of reference solution comprises changing the real component value of the reference solution's complex permittivity.

15. The method of claim 13, wherein changing the initial complex permittivity of the second volume of reference solution comprises changing the imaginary component value of the reference solution's complex permittivity.

16. The method of claim 13, wherein changing the initial complex permittivity of the second volume of reference solution comprises changing both the real and imaginary component values of the reference solution's complex permittivity.

17. The method of claim 13, wherein the first agent comprises sodium chloride.

18. The method of claim 13, wherein the first agent further comprises glucose.

19. The method of claim 13, wherein the first agent comprises sucrose.

20. The method of claim 19, wherein the first agent further comprises glucose, HEPES, sodium chloride, potassium chloride, calcium chloride, magnesium chloride, and magnesium sulfate.

21. The method of claiml3, further comprising changing the initial complex permittivity of the third volume of reference solution to a predefined value by either adding a second agent to the third volume of reference solution, or diluting the presence of a second agent within the third volume of reference solution.

22. The method of claim 12, wherein obtaining measurement parameters for each of the plurality of calibration solutions comprises obtaining scattering parameters for each of the plurality of calibration solutions.

23. The method of claim 12, wherein computing a respective plurality of complex coefficients comprises simultaneously solving a respective plurality of the rational equations, each of the respective plurality of rational equations comprising the measurement parameters and the permittivity value corresponding to one of the respective plurality of calibration solutions.

24. The method of claim 12, wherein obtaining measurement parameters for the test solution comprises obtaining scattering parameters for the test solution.

25. The method of claim 12, wherein: selecting a plurality of calibration coefficients comprises selecting three calibration solution, each having a predefined complex permittivity; obtaining measurement parameters for each of the plurality of calibration solutions comprises obtaining scattering parameters of each of the plurality of calibration solutions; the rational equation comprises a bilinear equation having complex coefficients terms A*, B*, and C*; and computing a respective plurality of complex coefficients comprises simultaneously solving three bilinear equations in which each equation comprises scattering parameters and the predetermined complex permittivity associated with each of calibration solutions.

26. The method of claim 25, wherein: obtaining measurement parameters for the test solution comprises obtaining scattering parameters for the test solution; and applying the measurement parameters of the test solution to the rational function comprises applying the scattering parameters of the test solution to the bilinear equation having complex coefficients terms A*, B*, and C*.

27. A computer program product stored on a computer readable medium for creating a solution having a desired complex permittivity, the computer program product comprising: programming for adding a predefined amount of a first agent to a reference solution; and programming for diluting, to a predefined amount, the presence of the first agent within the reference solution.

28. A computer program product stored on a computer readable medium for computing the complex permittivity of a test solution, the computer program product comprising: programming for selecting a plurality of calibration solutions, each of the plurality of calibration solutions having a predetermined complex permittivity comprising a real component and an imaginary component, wherein the real or imaginary component of the predetermined complex permittivities of the plurality of calibration solutions collectively extend above and below the expected real or imaginary component of the complex permittivity of the test solution; programming for obtaining measurement parameters for each of the plurality of calibration solutions; programming for computing a respective plurality of complex coefficients, each of the plurality of complex coefficients comprising a term in a rational function for converting measurement parameters to a complex permittivity; programming for obtaining measurement parameters for the test solution; and programming for applying measurement parameters of the test solution to the rational function to determine the complex permittivity of the test solution.

29. The computer program product of claim 28, wherein the programming for computing a respective plurality of complex coefficients comprises a graphical programming language.

30. The computer program product of claim 28, wherein the programming for computing a respective plurality of complex coefficients comprises C++ programming language.

31. The computer program product of claim 28, wherein for applying measurement parameters of the test solution to the rational function to determine the complex permittivity of the test solution comprises a graphical programming language.

32. The computer program product of claim 28, wherein for applying measurement parameters of the test solution to the rational function to determine the complex permittivity of the test solution comprises C++ programming language.

33. A system for creating a solution having a desired complex permittivity, comprising: means for providing a reference solution having an initial complex permittivity at one or more frequencies, the initial complex permittivity comprising a real component and an imaginary component at each of the one or more frequencies; and means for changing the initial complex permittivity of the reference solution to the desired complex permittivity at the one or more frequencies by either adding a first agent to the reference solution, or diluting the presence of a first agent within the reference solution.

34. A system for measuring the complex permittivity of a test solution, comprising: means for selecting a plurality of calibration solutions, each of the plurality of calibration solutions having a predetermined complex permittivity comprising a real component and an imaginary component, wherein the real or imaginary component of the predetermined complex permittivities of the plurality of calibration solutions collectively extend above and below the expected real or imaginary component of the complex permittivity of the test solution; means for obtaining measurement parameters for each of the plurality of calibration solutions; means for computing a respective plurality of complex coefficients, each of the plurality of coefficients comprising a term in a rational function for converting measurement parameters to a complex permittivity; means for obtaining measurement parameters for the test solution; and means for applying measurement parameters of the test solution to the rational function to determine the complex permittivity of the test solution.