Method and apparatus for determining the amount of an analyte in a fluid using a periodic waveform

Abstract

A method is provided for interrogating an aptamer-based electrochemical sensor using square wave voltammetry. A redox reporter is attached to each aptamer. The current resulting from the interrogation is measured and used to determine the initial distribution of the redox reporter on the surface of the aptamer-coated working electrode of the sensor. The measured current is used to determine the location or distribution of the redox-active species relative to the surface, which is then used to determine the amount of analyte around the electrode.

Description

[Technical Field]

[0001] The present invention relates generally to electrochemical sensors useful for determining the amount of an analyte in a fluid, including biological fluids such as blood and interstitial fluid. More particularly, the present invention provides electrochemical sensors operated by improved methods that provide more reliable analyte determination and extended sensor life. [Background technology]

[0002] Several classes of electrochemical sensors are selective and capable of real-time continuous detection of target analytes as well as single-point measurements, including exogenous agents (e.g., pharmaceutical compounds and toxins) and also endogenous agents (e.g., metabolites, proteins, hormones, etc.).

[0003] Electrochemical sensors show great promise in the fields of human and animal health. In that context, sensors can be embodied in the form of a microneedle-based patch applied to the skin. The microneedle forms a working electrode that is inserted into the skin to contact interstitial fluid. The tip of the microneedle functions as the sensor electrode, and an analyte recognition element (such as an aptamer) is associated with the tip. This arrangement provides a minimally invasive platform for real-time, continuous in vivo target analyte detection that is sensitive and selective enough to function in the complex matrix of interstitial fluid.

[0004] Electrochemical sensors typically include a working electrode coated with an analyte recognition element that undergoes a conformational change upon analyte binding. A redox reporter (such as methylene blue) can be covalently attached to the analyte recognition element. The conformational change of the analyte recognition element alters the accessibility of the redox reporter to the electrode surface, thereby resulting in an analyte-induced change in the level of electron transfer between the redox reporter and the electrode. In some situations, analyte binding brings the redox reporter closer to the electrode surface, thereby increasing the level of electron transport and subsequently increasing the current through the electrode. In other situations, binding displaces the reporter distal to the electrode surface, resulting in the opposite effect. Nevertheless, analyte binding results in a detectable change in the electrode current.

[0005] Electrochemical sensors are typically interrogated by applying a potential between the working and counter electrodes and then measuring the current after the potential is removed or changed.

[0006] One method of sensor interrogation is square-wave voltammetry, in which a potential is applied to the working electrode in the form of a square wave. A voltammogram (i.e., current vs. voltage) is generated, and the peak current through the working electrode is determined. The amount of analyte is determined by a previously constructed calibration curve, which defines the relationship between analyte amount and peak current. Square-wave voltammetry can be customized for specific applications to provide an increase ("signal on") or decrease ("signal off") in peak current in the presence of the target analyte. Signal drift and loss of signal gain can be problematic, and these are addressed by taking measurements at two square-wave frequencies and then using these to generate a kinetic difference measurement (KDM) value. The KDM value is calculated by subtracting the normalized peak currents measured at the signal on and signal off frequencies and then dividing by their average. Average KDM values ​​were collected over a range of target concentrations to create a calibration curve fitted using a Hill-Langmuir isotherm.

[0007] Another method used to interrogate electrochemical sensors is cyclic voltammetry. In this method, the voltage between the working and reference electrodes is modulated at a constant rate between two values ​​(V1 and V2). When the voltage reaches V2, the scan is reversed and the voltage is modulated back to V1. The voltage is measured between the reference and working electrodes, and the current is measured between the working and counter electrodes. The resulting measurements are plotted as a voltammogram. With square-wave voltammetry, the peak current is used to determine the amount of analyte around the working electrode.

[0008] Another prior art interrogation method is chronoamperometry, which has been shown to achieve drift-free, subsecond resolution aptamer-based sensing. The difference in electron transfer rate between bound and unbound analytes can be measured as a difference in current decay lifetimes. Such lifetimes can be related to the concentration of the target in the sample. Because chronoamperometric lifetimes are a function of the subpopulation of bound versus unbound receptors, they are less sensitive to gradual changes in the sensor interface compared to the total current amplitude, which depends on the total number of aptamers. A variation called intermittent pulse amperometry can be used to achieve millisecond-resolved measurements of analyte binding kinetics. Each periodic pulse output generates one forward chronoamperogram and one reverse chronoamperogram, which can be subtracted to generate a differential current directly proportional to the concentration of the target analyte.

[0009] Another prior art interrogation method is electrochemical impedance spectroscopy (EIS). EIS is a technique that has been found useful in analyzing interfacial properties associated with biorecognition events, such as aptamer-target folding, that occur due to target analyte binding. EIS biosensing is based on changes in electron transfer resistance using redox probe pairs such as [Fe(CN)6]. Dynamic impedance measurements are typically performed at a single frequency, and a calibration curve is used to convert the impedance measurements to analyte quantities.

[0010] Prior art methods for analyte quantification using square-wave voltammetry or chronoamperometry present several challenges. For example, the determination of KDM by square-wave voltammetry is temperature dependent. This method requires normalization in the absence of the target analyte, making it unsuitable for in situ use in humans to determine the amount of endogenous analytes, such as hormones. Chronoamperometry is strongly affected by capacitive currents and any potential shifts at the reference electrode.

[0011] Sensor degradation is an additional problem that can arise when the sensor is repeatedly interrogated, such as in the case of continuous real-time monitoring of a target analyte.

[0012] There are also issues with sensor accuracy, repeatability, and the time required to make a measurement.

[0013] When the sensor is configured as a portable device, including a wearable device, power consumption of the device electronics may limit operation time due to battery capacity, and therefore, reducing power consumption is desirable in such situations. Summary of the Invention [Problem to be solved by the invention]

[0014] One aspect of the present invention is to provide improvements in the operation of electrochemical sensors to ameliorate or overcome any one or more of the problems described herein. A further aspect of the present invention is to provide a useful alternative to prior art methods of interrogating electrochemical sensors.

[0015] The discussion of documents, acts, materials, devices, articles and the like is included in this specification solely for the purpose of providing a context for the present invention. No suggestion or representation is made that any or all of these matters formed part of the prior art or were common general knowledge in the art relevant to the present invention as they existed prior to the priority date of each provisional claim in this application. [Means for solving the problem]

[0016] In a first aspect, not necessarily its broadest aspect, the present invention provides a method for determining the amount of an analyte in a fluid, the method comprising: providing an electrochemical sensor working electrode having a plurality of analyte recognition elements associated therewith, each of the plurality of analyte recognition elements having a redox-active species associated therewith; applying a potential to the working electrode according to a periodic waveform; and measuring the current value resulting from the application of the potential.

[0017] In one embodiment of the first aspect, each of the plurality of analyte recognition elements is associated with a surface of a working electrode, and the measured current value is used to determine the location or distribution of the redox-active species relative to the surface.

[0018] In an embodiment of the first aspect, the positions or distributions are initial positions or initial distributions.

[0019] In one embodiment of the first aspect, the location or distribution of the redox-active species is used to determine the extent to which the redox-active species migrates toward the surface of the working electrode and, therefore, the amount of analyte recognized by the plurality of analyte recognition elements.

[0020] In one embodiment of the first aspect, the measured current value is used to determine the extent to which the redox-active species migrates toward the surface of the working electrode and, therefore, the amount of analyte recognized by the plurality of analyte recognition elements.

[0021] In one embodiment of the first aspect, the measured current values ​​are used to generate one or more current-potential relationships.

[0022] In an embodiment of the first aspect, each of the one or more current-potential relationships is a differential current-potential relationship.

[0023] In one embodiment of the first aspect, the one or more current-potential relationships each provide a peak current, and the peak currents are used to calculate one or more f-values, each f-value indicative of the fraction of redox-active species at or proximate to the surface of the working electrode.

[0024] In one embodiment of the first aspect, the f value is calculated according to equation (3).

[0025] In one embodiment of the first aspect, the periodic waveform has a substantially fixed frequency, and the periodic waveform is superimposed on an underlying sweep potential.

[0026] In an embodiment of the first aspect, the underlying sweep potential has a step shape.

[0027] In one embodiment of the first aspect, the periodic waveform has a duty cycle of about 50%.

[0028] In one embodiment of the first aspect, the periodic waveform is stepped to provide a substantially instantaneous change in potential.

[0029] In an embodiment of the first aspect, the periodic waveform is a substantially square waveform.

[0030] In an embodiment of the first aspect, the periodic waveform is applied for multiple cycles.

[0031] In an embodiment of the first aspect, the periodic waveform is applied for at least about 3, 4, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 1000, 10000, or 100000 cycles.

[0032] In an embodiment of the first aspect, the periodic waveform has a substantially fixed frequency.

[0033] In one embodiment of the first aspect, the substantially square waveform is applied according to a square wave voltammetry method.

[0034] In one embodiment of the first aspect, the measured current values ​​are used to provide a time-current relationship.

[0035] In an embodiment of the first aspect, the time-current relationship defines a change in current over time.

[0036] In an embodiment of the first aspect, the change in current over time is a transient current.

[0037] In one embodiment of the first aspect, the current transient depends on the rate of electron transfer between the redox active species and the surface of the working electrode.

[0038] In one embodiment of the first aspect, the rate of transfer depends on the accessibility of the redox active species to the surface of the working electrode.

[0039] In one embodiment of the first aspect, the accessibility of the redox active species to the surface of the electrode depends on the proximity of the reporter to the surface of the working electrode.

[0040] In one embodiment of the first aspect, the time-current relationship is used to determine the distribution of the redox active species, taking into account the proximity of the redox active species to the surface of the working electrode.

[0041] In one embodiment of the first aspect, the method includes measuring the current at two, three, or more different points in time within a cycle of the periodic waveform.

[0042] In an embodiment of the first aspect, the method includes measuring current at two, three, or more different frequencies of the periodic waveform.

[0043] In an embodiment of the first aspect, the method includes calculating one or more current ratios from the measured currents.

[0044] In one embodiment of the first aspect, the time-current relationship is processed to determine the amount of the analyte.

[0045] In an embodiment of the first aspect, the processing comprises determining a rate of current decay that occurs after application of the potential.

[0046] In one embodiment of the first aspect, the time-current relationship is used as an input to a method for determining the amount of an analyte by chronoamperometry.

[0047] In an embodiment of the first aspect, the periodic waveform has a first frequency, and the method further comprises: Applying the potential using the periodic waveform at the first frequency and measuring the resulting current at a late point in the periodic waveform cycle and at one or two earlier points.

[0048] In one embodiment of the first aspect, the time-current relationship is a transient current or is used to determine a peak current.

[0049] In one embodiment of the first aspect, a waveform having only a single frequency is applied to the working electrode.

[0050] In one embodiment of the first aspect, each of the plurality of analyte recognition elements is an aptamer or functional equivalent thereof that has binding specificity for the analyte.

[0051] In one embodiment of the first aspect, the redox-active species is linked to an analyte recognition element.

[0052] In a second aspect, the present invention provides a method for producing a medicament for the treatment of a pulmonary arthritis, comprising: a working electrode having associated therewith (i) an analyte recognition element and (ii) an associated redox-active species spatially confined within a layer adjacent to the electrode surface; a microprocessor-based controller; and The microprocessor-based controller provides an electrochemical sensor device or system configured to carry out the method of any embodiment of the first aspect.

[0053] In one embodiment of the second aspect, the microprocessor-based controller is in electrical communication with the working electrode or in wired or wireless network communication with another microprocessor-based controller that is in electrical communication with the working electrode.

[0054] In one embodiment of the second aspect, the microprocessor controller is configured to access and execute program instructions to perform the method of any embodiment of the first aspect.

[0055] In an embodiment of the second aspect, the electrochemical sensor device or system comprises a variable power supply electrically connected to the working electrode, and the program instructions direct the power supply to apply a potential to the working electrode according to the method of any embodiment of the first aspect.

[0056] In one embodiment of the second aspect, the program instructions direct application of the electrical potential in a periodic waveform or a substantially square waveform.

[0057] In an embodiment of the second aspect, the electrochemical sensor device or system comprises a current measurement circuit configured to measure a current through the working electrode.

[0058] In one embodiment of the second aspect, the electrochemical sensor device or system comprises an electronic memory operatively associated with the microprocessor-based controller and the current measurement circuit, the electronic memory configured to store one or more currents measured by the current measurement circuit.

[0059] In one embodiment of the second aspect, the microprocessor-based controller is configured to process the one or more currents measured by the current measurement circuit to provide an amount of the analyte.

[0060] In a third aspect, the present invention provides a computer readable medium comprising program instructions configured to carry out the method of any embodiment of the first aspect. [Brief explanation of the drawings]

[0061] With the exception of graphs, the drawings are not made to any particular scale or dimensions, and are not intended to be entirely accurate representations of various embodiments.

[0062] [Figure 1] A preferred method of the present invention is shown in which square wave potentials at three frequencies are applied to the working electrode of an aptamer-based electrochemical sensor, and the current output is measured and used to calculate the f value according to equation (3) herein. [Figure 2] 2 is a graph illustrating the implementation of the method of FIG. 1 showing the f value response using peak currents at Fon, Fnr, and Foff instead of i(t1), i(t2), and i(t3) in the context of a working electrode having a vancomycin-sensitive aptamer with a methylene blue redox reporter. [Figure 3] FIG. 2 is a graph illustrating the implementation of the method of FIG. 1 showing the response of an aptamer-based vancomycin-sensitive electrode to various concentrations of vancomycin (2 μm, 10 μm, and 200 μm) over a 24-hour period using square wave voltammetry to query and equation (3) to calculate the f value. [Figure 4] An alternative to the method of Figure 1, whereby a single-frequency square-wave potential is applied to the working electrode of an aptamer-based electrochemical sensor and the current output is measured and used to calculate the f value according to equation (3) herein. DETAILED DESCRIPTION OF THE INVENTION

[0063] After considering this description, it will be apparent to those skilled in the art how the present invention may be implemented in various alternative embodiments and applications. However, while various embodiments of the present invention are described herein, it is understood that these embodiments are presented by way of example only, and not by way of limitation. Accordingly, this description of various alternative embodiments should not be construed as limiting the scope or breadth of the present invention. Furthermore, statements of advantages or other aspects apply to particular exemplary embodiments and not necessarily to all embodiments, or indeed to any embodiments encompassed by the claims.

[0064] Throughout the description and claims of this specification, the word "comprise" and variations of this word such as "comprising" and "comprises" are not intended to exclude other additives, ingredients, integers, or steps.

[0065] Throughout this specification, reference to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the invention. Thus, the appearances of the phrase "in one embodiment" or "in an embodiment" in various places throughout this specification do not necessarily all refer to the same embodiment, but may.

[0066] When the terms "determine," "determining," and "determined" are used, these terms are not intended to be construed as necessarily implying any completely precise determination, although that meaning is not excluded. These terms may be construed to include estimation, approximation, or even indication.

[0067] The term "aptamer" is intended to include DNA and RNA aptamers. "Functional equivalents" of aptamers include related species such as heterologous nucleic acids (XNA) and peptide nucleic acids (PNA).

[0068] In a first aspect, not necessarily its broadest aspect, the present invention provides a method for determining the amount of an analyte in a fluid, the method comprising: providing an electrochemical sensor working electrode, the working electrode having a plurality of analyte recognition elements associated therewith, the plurality of analyte recognition elements having redox-active species associated therewith; applying a varying potential to the working electrode according to a periodic waveform; measuring the current resulting from the application of the potential; and using the measured current to provide a time-current relationship.

[0069] It has been found that a viable or advantageous interrogation method for electrochemical sensors is provided, in one embodiment, in which an interrogation potential is applied to the working electrode as a periodic waveform (such as a square waveform). The current resulting from the applied potential is taken as a function of time and used in a time-based methodology (e.g., as utilized in chronoamperometry) to determine the amount of target analyte.

[0070] In some embodiments of the method, the potential applied to the working electrode of the device as a periodic waveform (e.g., a square waveform) is varied from a potential sufficient to convert and maintain redox species in one redox state to another potential sufficient to substantially immediately change the redox state of any redox-active species close enough to the electrode to allow electron transfer across the electrode / solution interface. Expressed another way, the potential (applied as a periodic waveform, such as a square waveform) is varied to a potential such that the current flowing through the electrode surface as a result of the redox-active species changing redox state is controlled primarily or substantially by mass transfer of the redox-active species toward the electrode. As a result of the change in potential, a net current flows through the electrode surface, and the magnitude of the current typically varies over time.

[0071] While not wishing to be bound by theory in any way, it is proposed that redox-active reporters tethered to the working electrode surface (e.g., by aptamers) and therefore capable of limited movement only within the layer adjacent to the electrode, nevertheless, the redox-active species diffuse substantially freely within the layer. Therefore, the movement of redox-active species can be modeled with some accuracy (though not necessarily complete accuracy) based on Fick's first and second laws of diffusion. Thus, despite being bound, redox-active species can move from regions of high concentration to regions of low concentration, with the magnitude of the flux being proportional to the difference in concentration, as expected for a freely diffusible (i.e., unbound) species. Furthermore, the concentration gradient of the redox-active species in the layer changes over time, as expected for a freely diffusible species.

[0072] Fick's first and second laws were applied to systems in which redox-active species were spatially constrained to be in a layer adjacent to the electrode surface but were free to diffuse within that layer. It was therefore possible to model the diffusion of the constrained redox species and, therefore, the change in current (called a "current transient") due to the movement of the redox-active species relative to the electrode surface, taking into account that electron transfer increases as the redox-active species moves closer to the surface.

[0073] The resulting modeled transient currents resulting from the migration of redox-active species revealed a dependence on (i) the surface area of ​​the electrode, (ii) the thickness of the layer adjacent to the electrode, (iii) the diffusion coefficient of the redox species in the layer adjacent to the electrode, (iv) the overall concentration of the redox species in the layer adjacent to the electrode, and (v) the distribution of the redox species within the layer adjacent to the electrode when a potential step is applied. These changes have been found to have practical consequences for methods for interrogating electrochemical sensor devices, determining the distribution of redox-active species, and determining the amount of analyte recognized by an analyte recognition element.

[0074] Further investigations were performed to demonstrate the practical relevance of a single current measurement and the current ratio determined during the period immediately following the application of a potential change. Surprisingly, at longer times after the potential change was applied, the ratio of the two measured currents was found to depend strongly on the thickness of the layer adjacent to the electrode and the diffusion coefficient of the redox species, but only weakly on the initial distribution of the redox species. Meanwhile, the ratio of the currents at shorter times after the potential step was applied was more strongly dependent on the initial distribution of the redox species compared to the currents at longer times, and similarly, strongly dependent on the thickness of the layer adjacent to the electrode and the diffusion coefficient of the redox species. Furthermore, both of these current ratios were modeled to be insensitive to the overall concentration of the redox species and the electrode area.

[0075] These modeled behaviors suggested that the later current ratios may be useful in combination with the thickness of the layer adjacent to the electrode to obtain a combined measure of the redox species diffusion coefficient, which can be applied to the earlier current ratios to obtain an estimated measure of the initial distribution of the redox species, where the estimate is largely insensitive to changes in the overall concentration of the redox species in the layer adjacent to the electrode, the thickness of the layer adjacent to the electrode, and the diffusion coefficient of the redox species in the layer adjacent to the electrode and the area of ​​the electrode.

[0076] The equation for the current over time derived from the model is shown below as equation (1).

number

[0077] Thus, f can be used to determine the distribution of redox-active species when an initial potential is applied and at the moment before a change in potential is applied. The distribution of redox-active species can be used to determine the amount of analyte recognized by the analyte recognition element of the sensor.

[0078] Note from equation (1) that by taking the ratio of the currents at two different times, the electrode area and redox species concentration terms cancel out. Furthermore, at sufficiently long times, the exponential term for n>0 is small enough relative to the exponential term for n=0, and equation (1) can be approximated by equation (2) as follows:

number

[0079] Therefore, by taking the ratio of the currents at two different times to which equation (2) applies, only the exponential terms do not cancel, resulting in D / l 2 An estimate of can be obtained.

[0080] According to this method, the current at at least three different times during the current transient can be determined: i(t1), i(t2), and i(t3). Optionally, the current at a fourth time, i(t4), can be determined. Time t1 is selected to be a short time after the potential step change is applied, t3 and optionally t4 are longer times after the potential step is applied, and t2 is selected to be between t1 and t3 or optionally between t1 and t4.

[0081] At least two current ratios can then be determined. In preferred embodiments of the invention, the ratios i(t1) / i(t3) and i(t2) / i(t3) are determined. In other embodiments of the invention, the ratios i(t1) / i(t4) and / or i(t2) / i(t4) are determined. In some embodiments of the invention, current ratios at additional times can be calculated and used to improve the method by providing additional estimates of the derived parameters.

[0082] In a further embodiment of the method, the second change in electrode potential is implemented in the context of a periodic waveform (e.g., a square waveform), with the second change occurring after the first change in electrode potential. In this embodiment, the electrode is held at a potential resulting from the first potential change by application of the periodic waveform for a time sufficient to electrochemically oxidize or reduce substantially all redox-active species present in the tether layer. The electrode potential is then changed in the direction of the initial potential. For example, if the electrode potential was initially held at a value at which the redox-active species is reduced, the second potential change is in the direction of a stronger reduction potential. If the electrode potential was initially held at a value at which the redox-active species is oxidized, the second potential change is in the direction of a stronger oxidation potential. The current resulting from the second potential change is used to obtain an estimate of non-faradaic currents flowing through the electrode, for example, due to capacitive double layer charging, as well as any faradaic currents from redox species not confined in layers adjacent to the electrode, which can be subtracted from the currents used to calculate the current ratios disclosed above to improve the accuracy of the results.

[0083] The potentials achieved by the first, second, and third changes in potential may occur in the context of a periodic waveform, such as a square waveform, and may correlate to the minimum potential value of the waveform, the maximum potential value of the waveform, and the minimum potential value of the square waveform, respectively (each potential being added to the underlying sweep potential).

[0084] The required inputs for the chronoamperometric method involving equation (3) are the values ​​of three different times t1, t2, and t3 after the step potential is applied, along with the corresponding currents i(t1), i(t2), and i(t3) at those times.

[0085] It has been found that the peak current resulting from square wave voltammetry provides a step potential and can therefore generate an f value according to equation (3), which can be used to determine the concentration of a target analyte. In square wave voltammetry, the potential is slowly swept from one potential to another using a square wave, with the potential slowly rising or falling over the sweep. When the potential is swept over an appropriate window, a current peak is generated at the potential in the sweep. The baseline currents on either side of the peak are subtracted from the current value at the peak to generate what is referred to as a "peak current" value. When using square wave voltammetry, the current flow is completely or nearly completely electron transfer rate controlled; that is, the current is limited by the potential applied to the electrode rather than by mass transfer of redox species to the electrode. Therefore, it is unexpected that the peak current measured in this manner would be useful in the context of a chronoamperometric approach to determining analyte concentration (e.g., involving calculating f according to equation (3)). This approach may be considered to violate the assumptions used to derive the equation for f, as outlined herein.

[0086] The use of square-wave voltammetry to generate input values ​​for the equation for f is potentially useful because subtracting a baseline current to calculate the square-wave voltammetry peak current allows for correction of the charging current contribution as well as background faradaic current not associated with the redox species of interest. The time used when using square-wave voltammetry to generate i(t1), i(t2), and i(t3) is also typically longer than the time required when using prior art chronoamperometric approaches, potentially reducing the charging current contribution and allowing slower electronic components to be used, making the potential application and current measurement tasks easier and / or less expensive.

[0087] The present invention can be practiced by at least two different methods for obtaining peak currents by square wave voltammetry for use in calculating f:

[0088] The first method involves performing square wave voltammetry at three different frequencies to obtain three peak currents, one from each frequency sweep. This method is shown in Figure 1 and described in detail in Example 1 below.

[0089] The second method is a variation of the first method, requiring that the square wave voltammogram be generated at only one frequency, typically the lowest frequency necessary to generate data from the input to the equation. Instead of repeating the voltammogram sweep three times at different frequencies, the current is sampled at three different times during the square wave cycle at the lowest frequency of interest. This method is shown in Figure 4 and described in detail in Example 2 below.

[0090] The advantage of the second method over the first method is that it requires only one frequency sweep instead of three, which saves time and battery life in battery-powered sensing devices.

[0091] An advantage of some embodiments of the present invention is that a method is provided that allows for estimation of the distribution of redox species without specific knowledge of the electrode area, the thickness of the tethered redox layer, the total amount of redox species, or the number of electrons transferred per mole of redox species. Additionally or alternatively, application of a potential in the context of a periodic waveform (such as a square waveform) provides lower fluctuations in the charging current. Furthermore, it allows for scanning a range of potentials to identify the optimal potential for a given redox-active species (such as methylene blue) and accurately subtract this from the non-redox-active species current.

[0092] Another advantage of some embodiments of the present invention is that they provide a method that is significantly faster than prior art interrogation methods, which can take seconds to minutes to execute. The methods described herein, in some embodiments, can execute in tens of milliseconds. For example, an electrode is optionally held at an initial potential for a short period of time (on the order of tens of milliseconds to a second), and then the potential is stepped and held at a second potential for a period of time, typically up to tens of milliseconds. Due to the speed of execution and the fact that a redox species is tethered to the electrode, the potential stepping can be repeated multiple times over a short period of time to obtain multiple estimates of the desired parameter, which can be averaged or otherwise combined to reduce random fluctuations in the results.

[0093] The present invention may be embodied in the form of an apparatus or system configured to facilitate the performance of the methods described herein.

[0094] The devices of the present invention may be embodied in the form of a wearable device that is substantially self-contained, allowing measurements to be taken while a subject is undergoing normal activity and / or over an extended period of time. The wearable device may be a collar, bracelet, strap, adhesive, or patch. The wearable device may include transdermal microneedles, one of which functions as the working electrode of the sensor by contacting the subject's interstitial fluid and detecting an analyte therein.

[0095] The wearable device may further include a housing structure that encloses one or more other components, such as a processor-based microcontroller configured to electrically communicate with at least one electrode and generally including a power source, a data processing unit, an electronic memory, and a wireless transmitter / receiver.

[0096] When embodied as a system, the components may operate in an integrated manner but be distributed across different physical locations. For example, software instructions may be stored and executed by a smartphone or other remote process in data communication with a microprocessor-based controller within the wearable device.

[0097] As will be appreciated, the methods described herein may be deployed, in part or in whole, via one or more microprocessors executing computer software, program code, and / or instructions thereon. A microprocessor may be any type of computing or processing device capable of executing program instructions, code, binary instructions, etc.

[0098] Any microprocessor can access a storage medium (such as electronic memory) through an interface that can store the methods, codes, and instructions described herein. The storage medium is associated with the processor for storing methods, programs, codes, program instructions, or other types of executable instructions.

[0099] Computer software, program code, and / or instructions may be stored and / or accessed on computer-readable media, which may include computer components, devices, and recording media that hold digital data used for computations for some interval of time, semiconductor memory devices known as random access memory (RAM), and typically mass storage devices for more permanent storage, e.g., non-volatile memory such as read-only memory (ROM).

[0100] The methods described herein can transform physical and / or intangible items from one state to another. The methods and systems described herein can also transform data representing physical and / or intangible items from one state to another.

[0101] Software products may be created using structured programming languages ​​such as C, object-oriented programming languages ​​such as C++, or any other high-level or low-level programming languages ​​(including assembly languages, hardware description languages, and database programming languages ​​and techniques) that can be stored, compiled, or interpreted for execution on a microprocessor, as well as heterogeneous combinations of processors, processor architectures, or combinations of different hardware and software, or any other machine capable of executing program instructions.

[0102] Thus, in one aspect, any method may be embodied in computer-executable code that, when executed on one or more microprocessors, performs its steps. In another aspect, the method may be embodied in a system that performs its steps, may be distributed in some manner across devices, or all of the functionality may be integrated into a dedicated, stand-alone device or other hardware. In another aspect, the means for performing the steps associated with the processes described above may include any of the hardware and / or software described above. All such permutations and combinations are intended to fall within the scope of the present disclosure.

[0103] The present invention may be embodied in a set of program instructions executable on one or more microprocessors. Such an instruction set may include any one or more of the following instruction types:

[0104] Data processing and memory operations may include instructions to set a register to a fixed constant value or copy data from a memory location to a register or vice versa, to store the contents of a register, the result of a calculation, or to retrieve stored data to perform calculations on it at a later time, or to read or write data from a hardware device.

[0105] Arithmetic and logical operations may include instructions to add, subtract, multiply, or divide the values ​​of two registers; to place the result in a register; possibly to set one or more condition codes in a status register; to perform bitwise operations, such as ANDing and ORing corresponding bits in a pair of registers, negating each bit in a register, or comparing two values ​​in registers (e.g., to determine if one is less than or if they are equal).

[0106] A control flow operation may include an instruction that branches to another location in a program and executes an instruction there, conditionally branches to another location if a particular condition is true, indirectly branches to another location, or calls another block of code while saving the location of the next instruction as a point to return to.

[0107] Coprocessor instructions may include instructions that load / store data to / from the coprocessor, exchange with CPU registers, or perform coprocessor operations.

[0108] The processors of the computers in this system may include "complex" instructions in their instruction sets. A single "complex" instruction does something that would take many instructions on other computers. Such instructions are typified by instructions that take multiple steps, control multiple functional units, or appear on a larger scale than most of the simple instructions implemented by a given processor. Some examples of "complex" instructions include storing many registers on the stack at once, moving large blocks of memory, complex integer and floating-point arithmetic (sine, cosine, square root, etc.), SIMD instructions, a single instruction that performs operations on many values ​​in parallel, performing atomic test-and-set instructions or other read-modify-write atomic instructions, and instructions that perform ALU operations with operands from memory rather than registers.

[0109] An instruction may be defined according to its parts. According to more traditional architectures, an instruction includes an opcode that specifies an operation to perform, such as adding the contents of memory to a register, and zero or more operand specifiers, which may specify registers, memory locations, or literal data. Operand specifiers may have addressing modes that determine their meaning, or may be in fixed fields. In very long instruction word (VLIW) architectures, which include many microcode architectures, multiple simultaneous opcodes and operands are specified in a single instruction.

[0110] Some types of instruction sets have no opcode field (such as the Transport Trigger Architecture (TTA) or Force Virtual Machine), but only operands. Other unusual "zero operand" instruction sets lack the operand specifier field, such as some stack machines including NOSCs.

[0111] Conditional instructions often have a few bits in a predicate field that encode a particular condition that causes an operation to be executed rather than not executed. For example, a conditional branch instruction may be executed; if the condition is true, the branch is taken, resulting in execution proceeding to a different part of the program; if the condition is false, the branch is not executed and the branch is not taken, resulting in execution continuing sequentially. Some instruction sets also have conditional moves, resulting in if the condition is true, the move is executed and data is stored to a target location; if the condition is false, the move is not executed and the target location is not modified. Similarly, the IBM z / Architecture has conditional stores. Some instruction sets include a predicate field in each instruction, called the branch predicate.

[0112] The instructions that make up a program are rarely specified using their internal numeric form (machine code); they may be specified using assembly language, or more commonly, generated from a programming language by a compiler.

[0113] The present invention will now be more fully described by reference to the following non-limiting examples.

[0114] Example 1: Square wave voltammetry method using three different frequencies

[0115] Referring to FIG. 1, which details a preferred embodiment of the method of the present invention, the working electrode is excited with a potential applied as a square waveform. The potential is applied using square waveforms at three different frequencies (250 Hz, 25 Hz, and 10 Hz). The differential current vs. potential relationship is then derived for each frequency (shown as a voltammogram in FIG. 1), and the peak current (i) in each case is defined. The f value is calculated by inputting the values ​​of i(250 Hz), i(25 Hz), and i(10 Hz) into Equation (3) (derived from Equations (1) and (2) and shown below), substituting i(250 Hz), i(25 Hz), and i(10 Hz) for i(t1), i(t2), and i(t3) at t1, t2, and t3, respectively, in Equation (3).

number

number

[0116] Note that the ratio i(t2) / i(t3) is present in the calculation of f, although it is not explicitly shown. To further explain, the variable r2 is actually given by

number

[0117] In equation (3), terms up to n=10, or even larger terms can be used to approximate an infinite series of exponents.

[0118] Multiple separate calculations for f can be performed and averaged.

[0119] Considering the method of Figure 1 in more detail, square wave voltammograms were generated using peak currents measured at three different frequencies: the signal-on frequency, the non-response frequency, and the signal-off frequency for three time points. The currents were sampled immediately before the square wave flip, as is accepted practice in the art.

[0120] The peak current from the highest frequency scan (250 Hz) is used to obtain the value corresponding to i(t1), the peak current from the middle frequency scan (25 Hz) is used to obtain the value corresponding to i(t2), and the peak current from the lowest frequency scan (10 Hz) is used to obtain the value corresponding to i(t3). The times t1, t2, and t3 required to calculate the f values ​​are given by ½F1, ½F2, and ½F3, respectively, where F1, F2, and F3 are the three frequencies used to generate the three square wave voltammograms.

[0121] According to this method, the following equation is used to generate input data for the equation to solve for f: i(t1)=ip(F1) and t1=1 / 2F1 i(t2)=ip(F2) and t2=1 / 2F2 i(t3)=ip(F3) and t3=1 / 2F3 where ip(F) denotes the square wave voltammetry peak current when frequency F is used.

[0122] For EAB sensors, three frequencies found to be useful in the present invention are: F1, in the range where the peak current responds in one direction (increases) when the target analyte is present in solution; F3, in the range where the peak current responds in the opposite direction (decreases) when the target analyte is present in solution; and F2 (which is between F1 and F3), in the range where the peak current is relatively insensitive to the presence or absence of the target analyte. The frequency at which the peak current increases in the presence of the target analyte is often referred to in the art as the "signal-on" frequency. This can be either higher or lower depending on the aptamer used. The frequency at which the peak current decreases with the presence of the target analyte is referred to as the "signal-off" frequency. This can be either higher or lower depending on the aptamer used, but is always the opposite frequency to the signal-on frequency. The frequency that is relatively unresponsive to the presence of the target is referred to as the "non-responsive frequency" or "minimum responsive frequency." This frequency is between the signal-on and signal-off frequencies. Although the invention need not be limited to using these three frequencies, high, medium, and low frequencies are commonly used. For example, the three frequencies can be determined empirically by trial and error using different frequencies and observing the effectiveness of the resulting f-values ​​in determining analyte concentration.

[0123] For the vancomycin-sensitive aptamer used in this example, the higher frequency is the signal-on frequency, and the lower frequency is the signal-off frequency. Examples of suitable frequency ranges for EAB sensors constructed using this aptamer, corresponding to the signal-on, signal-off, and non-responsive frequencies, are 100-300 Hz for F1, 20-50 Hz for F2, and 5-20 Hz for F3. A suitable potential sweep window for this aptamer with methylene blue as the redox reporter is, for example, -0.45 V to -0.15 V, with the sweep starting at either -0.45 V or -0.15 V.

[0124] These observations regarding frequency selection and potential sweeps can also be applied to methods performed using a single frequency, as detailed in Example 2.

[0125] See Figure 2, which shows the correlation between the f-values ​​calculated above and vancomycin concentration. A direct correlation, which appears to fit a Langmuir isotherm, is evident regardless of vehicle (i.e., PBS at neutral pH vs. HEPES at pH 8 vs. TAPS at pH 9). A correlation was also found before and after 7 days of storage.

[0126] See Figure 3, which shows the results of an experiment to quantify the drift in f-values ​​over a 26-hour period and across a range of vancomycin concentrations. It is easy to see that for each concentration, there was little drift in the f-values ​​determined by the above method. Therefore, this method may be useful for interrogating electrodes placed in situ within the human body for continuous, real-time monitoring of analytes over extended periods of time.

[0127] Example 2: Single Frequency Square Wave Voltammetry Method

[0128] Referring to FIG. 4, an outline of a method for determining the f value from the peak current value is shown. The difference from Example 1 is how the i(t1), i(t2), and i(t3) currents are generated. According to this method, a single square-wave voltammogram is performed at a frequency of F3. This results in the current transients seen in the upper graph of FIG. 4. Instead of performing separate square-wave voltammetry at a higher frequency, additional current samples are taken from both the forward and reverse portions of the applied square-wave potential. Using the example shown in FIG. 4, a voltammogram is constructed using the difference in current sampled t1 seconds after the forward and reverse potential steps to obtain the peak current corresponding to i(t1). A second voltammogram is constructed using the difference in current sampled t2 seconds after the forward and reverse potential steps to obtain the peak current corresponding to i(t2). A third voltammogram is constructed using the difference in current sampled t3 seconds after the forward and reverse potential steps to obtain the peak current corresponding to i(t3). The selected current sampling times typically correspond to ½F1, ½F2, and ½F3, where F1, F2, and F3 are as described above, but again can be determined empirically to obtain the most effective f value.

[0129] Those skilled in the art will appreciate that the invention described herein is susceptible to further variations and modifications other than those specifically described, and it is to be understood that the invention includes all such variations and modifications that are within its spirit and scope.

[0130] Accordingly, the spirit and scope of the present invention is not intended to be limited by the foregoing examples, but is to be understood in the broadest sense permitted by law.

Claims

1. 1. A method for determining an amount of an analyte in a fluid, the method comprising: providing an electrochemical sensor working electrode having a plurality of analyte recognition elements associated therewith, each of the plurality of analyte recognition elements having a redox-active species associated therewith; applying a potential to the working electrode according to a periodic waveform; and measuring a current value resulting from the application of the potential at one or more points in a cycle of the periodic waveform.

2. 10. The method of claim 1, wherein each of the plurality of analyte recognition elements is associated with a surface of the working electrode, and measured current values ​​are used to determine the location or distribution of the redox-active species relative to the surface.

3. The method of claim 2 , wherein the positions or distributions are initial positions or initial distributions.

4. 3. The method of claim 2, wherein the location or the distribution of the redox-active species is used to determine the extent to which the redox-active species migrates toward the surface of the working electrode and, therefore, the amount of the analyte recognized by the plurality of analyte recognition elements.

5. 10. The method of claim 1, wherein the measured current value is used to determine the extent to which the redox-active species migrates toward the surface of the working electrode and, therefore, the amount of the analyte recognized by the plurality of analyte recognition elements.

6. The method of claim 1 , wherein the measured current values ​​are used to generate one or more current-potential relationships.

7. 7. The method of claim 6, wherein each of the one or more current-potential relationships is a differential current-potential relationship.

8. 7. The method of claim 6, wherein the one or more current-potential relationships each provide a peak current, the peak currents being used to calculate one or more f-values, each f-value indicative of a fraction of the redox-active species at or proximate to a surface of the working electrode.

9. The f value is calculated by the following formula (3): [Equation 1] The method of claim 8, wherein the calculated value is calculated according to:

10. The method of claim 1 , wherein the periodic waveform has a substantially fixed frequency, and the periodic waveform is superimposed on an underlying sweep potential.

11. The method of claim 10 , wherein the underlying sweep potential has a step shape.

12. The method of claim 1 , wherein the periodic waveform has a duty cycle of approximately 50%.

13. The method of claim 1 , wherein the periodic waveform is shaped to provide a substantially instantaneous change in potential.

14. The method of claim 1 , wherein the periodic waveform is a substantially square waveform.

15. The method of claim 1 , wherein the periodic waveform is applied for multiple cycles.

16. 10. The method of claim 1, wherein the periodic waveform is applied for at least about 3, 4, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 1000, 10,000, or 100,000 cycles.

17. The method of claim 1 , wherein the periodic waveform has a substantially fixed frequency.

18. 15. The method of claim 14, wherein the substantially square waveform is applied according to a square wave voltammetry method.

19. The method of claim 1 , wherein the measured current values ​​are used to provide a time-current relationship.

20. The method of claim 19 , wherein the time-current relationship defines a change in current over time.

21. 21. The method of claim 20, wherein the current change over time is a transient current.

22. 22. The method of claim 21, wherein the transient current depends on the rate of electron transfer between the redox-active species and the surface of the working electrode.

23. 23. The method of claim 22, wherein the rate of electron transfer depends on the accessibility of the redox-active species to the surface of the working electrode.

24. 24. The method of claim 23, wherein the accessibility of the redox-active species to the surface of the working electrode depends on the proximity of a reporter to the surface of the working electrode.

25. 20. The method of claim 19, wherein the time-current relationship is used to determine the distribution of the redox-active species, taking into account the proximity of the redox-active species to the surface of the working electrode.

26. The method of claim 1 , comprising measuring current at two, three, or more different points in a cycle of the periodic waveform.

27. The method of claim 1 , comprising measuring current at two, three, or more different frequencies of the periodic waveform.

28. The method of claim 1 , comprising calculating one or more current ratios from the measured currents.

29. 20. The method of claim 19, wherein the time-current relationship is processed to determine the amount of the analyte.

30. 30. The method of claim 29, wherein processing comprises determining a rate of current decay that occurs after application of the potential.

31. 20. The method of claim 19, wherein the time-current relationship is used as an input to the method for determining the amount of the analyte by chronoamperometry.

32. The periodic waveform has a first frequency, and the method includes:

10. The method of claim 1, comprising applying the potential using the periodic waveform at the first frequency and measuring the resulting current at a late point in a cycle of the periodic waveform and at one or two earlier points.

33. 33. The method of claim 32, wherein a waveform having only a single frequency is applied to the working electrode.

34. 20. The method of claim 19, wherein the time-current relationship is a transient current or is used to determine a peak current.

35. The method of claim 1 , wherein each of the plurality of analyte recognition elements is an aptamer or functional equivalent thereof having recognition specificity for the analyte.

36. The method of claim 1 , wherein the redox-active species is linked to the analyte recognition element.

37. a working electrode having associated therewith (i) an analyte recognition element and (ii) an associated redox-active species spatially confined within a layer adjacent to the electrode surface; a microprocessor-based controller; and 10. An electrochemical sensor device or system, wherein the microprocessor-based controller is configured to perform the method of claim 1.

38. 38. The electrochemical sensor device or system of claim 37, wherein the microprocessor-based controller is in electrical communication with the working electrode or in a wired or wireless network connection with another microprocessor-based controller that is in electrical communication with the working electrode.

39. 38. The electrochemical sensor device or system of claim 37, wherein the microprocessor-based controller is configured to access and execute program instructions to carry out the method of claim 1.

40. 38. The electrochemical sensor device or system of claim 37, comprising a variable power supply electrically connected to the working electrode, wherein program instructions direct the variable power supply to apply the potential to the working electrode in accordance with the method of claim 1.

41. 41. The electrochemical sensor device or system of claim 40, wherein the program instructions direct application of the potential in a periodic waveform or a substantially square waveform.

42. 38. An electrochemical sensor device or system according to claim 37, comprising a current measurement circuit configured to measure the current through the working electrode.

43. 43. The electrochemical sensor device or system of claim 42, comprising an electronic memory operatively associated with the microprocessor-based controller and the current measurement circuitry, the electronic memory configured to store one or more currents measured by the current measurement circuitry.

44. 44. The electrochemical sensor device or system of claim 43, wherein the microprocessor-based controller is configured to process the one or more currents measured by the current measurement circuit to provide a quantity of an analyte.

45. A computer readable medium comprising program instructions configured to carry out the method of any one of claims 1 to 36.

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