WO2013052837A1

WO2013052837A1 - Signal correction for multiplexer cross-talk in chemical sensor arrays

Info

Publication number: WO2013052837A1
Application number: PCT/US2012/059014
Authority: WO
Inventors: Todd Rearick
Original assignee: Life Technologies Corporation
Priority date: 2011-10-05
Filing date: 2012-10-05
Publication date: 2013-04-11

Abstract

Method for processing signals from an integrated circuit device comprising a sensor array and a multiplexer that receives output signals from sensors of the sensor array. The method includes initiating one or more chemical reactions in proximity to sensors in the sensor array. The method further includes receiving a first output signal from a first sensor of the sensor array via a first channel of the multiplexer. The method further includes receiving a second output signal from a second sensor of the sensor array via a second channel of the multiplexer. The method further includes calculating an adjusted second output signal to compensate for cross-talk from the first channel of the multiplexer due to the received first output signal from the first sensor. Corresponding apparatus. Computer readable storage medium storing instructions for operating the apparatus.

Description

SIGNAL CORRECTION FOR MULTIPLEXER CROSS-TALK IN

CHEMICAL SENSOR ARRAYS

BACKGROUND

[0001] The present disclosure relates to sensors for chemical analysis, and more particularly to methods for low-noise operation of sensor arrays for nucleic acid sequencing.

[0002] A variety of types of sensors have been used in the detection of various chemical and/or biological processes. One type of sensor is a chemically-sensitive field effect transistor (chemFET). A chemFET includes a source and a drain separated by channel region, and a chemically sensitive area coupled to the channel region. The operation of the chemFET is based on the modulation of channel conductance due to a chemical reaction which causes changes in charge near the sensitive area. The modulation of the channel conductance affects the threshold voltage of the chemFET, and the threshold voltage can be measured to indicate characteristics of the chemical reaction. The threshold voltage may for example be measuring by applying appropriate bias voltages to the source and drain of the chemFET, and measuring a current through the chemFET. As another example, the threshold voltage may be measured by applying appropriate bias voltages and driving a known current through the chemFET, and measuring a voltage at the source or drain of the chemFET.

[0003] An ion-sensitive field effect transistor (ISFET) is a type of chemFET that includes an ion-sensitive layer at the sensitive area. The presence of ions in an analyte solution alters the surface potential at interface of the ion-sensitive layer and the analyte solution, usually due to the dissociation of oxide groups by the ions in the analyte solution. The change in surface potential at the sensitive area of the ISFET affects the threshold voltage of the device, which can be measured to indicate the presence of ions within the analyte solution.

[0004] Arrays of ISFETs may be used for monitoring chemical reactions, such as DNA sequencing reactions, based on the detection of ions present, generated, or used during a reaction. See, for example, U.S. Patent No. 7,948,015 to Rothberg et al., which is incorporated by reference herein. More generally, large arrays of chemFETs or other types of chemical sensors may be employed to detect and measure static and/or dynamic amounts or concentrations of a variety of analytes (e.g. hydrogen ions, other ions, compounds, etc.) in a variety of chemical and/or biological processes, through which valuable information may be obtained based on such analyte measurements. The processes may for example be biological or chemical reactions, cell or tissue cultures or monitoring, neural activity, nucleic acid sequencing, etc.

[0005] A specific issue that arises in the operation of sensor arrays is the susceptibility of the output signals from the sensors to noise. Specifically, the noise affects the accuracy of downstream signal processing used to determine the characteristics of the chemical and/or biological process being detected by the sensors.

[0006] It is therefore desirable to provide a system including a chemical sensor array with reduced susceptibility to noise, and methods for operating such systems.

SUMMARY

[0007] In one implementation, a method is described for processing signals from an integrated circuit device comprising a sensor array and a multiplexer that receives output signals from sensors of the sensor array. The method includes initiating one or more chemical reactions in proximity to sensors in the sensor array. The method further includes receiving a first output signal from a first sensor of the sensor array via a first channel of the multiplexer. The method further includes receiving a second output signal from a second sensor of the sensor array via a second channel of the multiplexer. The method further includes calculating an adjusted second output signal to compensate for cross-talk from the first channel of the multiplexer due to the received first output signal from the first sensor.

[0008] This method and other implementations of the technology disclosed can each optionally include one or more of the following features.

[0009] The calculating can include multiplying the second output signal by a correction coefficient based on an amount of cross-talk contributed by the first channel of the multiplexer due to the received first output signal.

[0010] The calculating can include multiplying the second output signal by multiple correction coefficients, each correction coefficient based on an amount of cross-talk contributed by output signals received via corresponding channels of the multiplexer.

[0011] The method can further include, between receiving the first output signal and the second output signal, receiving a third output signal from a third sensor of the sensor array via a second multiplexer.

[0012] The integrated circuit device can further include a third multiplexer that receives outputs of the first multiplexer and the second multiplexer, wherein the third multiplexer has a first channel for the output of the first multiplexer and a second channel for the output of the second multiplexer. The calculation can further compensate for cross-talk contributed by the second channel of the third multiplexer from the receipt of the output from the second multiplexer.

[0013] The first output signal can be received from a first array line that is connected to the first sensor of the sensor array, and the second output signal can be received from a second array line that is connected to the second sensor of the sensor array.

[0014] The array lines can be column lines on the sensor array.

[0015] The sensor array can be a chemFET sensor array.

[0016] The chemFET sensors of the sensor array can detect hydrogen ions, and the chemical reactions can release hydrogen ions.

[0017] The method can further include performing a calibration step that characterizes the behavior of the multiplexer.

[0018] Other implementations may include a non-transitory computer readable storage medium storing instructions executable by a processor to perform a method as described above. Yet another implementation may include a system including memory and one or more processors operable to execute instructions, stored in the memory, to perform a method as described above.

[0019] Particular aspects of one more implementations of the subject matter described in this specification are set forth in the drawings and the description below. Other features, aspects, and advantages of the subject matter will become apparent from the description, the drawings, and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

[0020] FIG. 1 illustrates a block diagram of components of a system for nucleic acid sequencing according to an exemplary embodiment.

[0021] FIG. 2 illustrates cross-sectional and expanded views of a portion of the integrated circuit device and flow cell of FIG. 1.

[0022] FIG. 3 is a simplified block diagram of a portion of the integrated circuit device of FIG. 1.

[0023] FIG. 4 illustrates a block diagram of an example multiplexer configuration that can be used for the sensor array 205. [0024] FIG. 5 illustrates a block diagram of example of a data processing system for processing output signals from sensors in the sensor array.

[0025] FIG. 6 illustrates a plot of the output signals in two different channels of a multiplexer demonstrating the effect of cross-talk on the output signals.

[0026] FIG. 7 is a flow chart of an example process for processing output signals from a sensor array to compensate for multiplexer cross-talk.

DETAILED DESCRIPTION

[0027] Techniques are described herein for correcting or compensating for cross-talk in multiplexer channels of sensor arrays used for chemical analysis, so that the values of the output signals of the sensors can be more accurately determined. The sensors in the sensor arrays may be chemically-sensitive field effect transistors (chemFETs), such as ion-sensitive field effect transistors (ISFETS). Examples of sensor arrays are described in U.S. Patent Application Publication No. 2010/0300559, No. 2010/0197507, No. 2010/0301398, No. 2010/0300895, No. 2010/0137143, and No. 2009/0026082, and U.S. Patent No. 7,575,865, each which are incorporated by reference herein.

[0028] Individual sensors (e.g. individual chemFETs or individual chemFETs with associated circuits) arranged in an array configuration may sometimes be referred to as "pixels." The output signals of individual sensors can be acquired by selecting the appropriate rows and/or columns in the sensor array, so that the output signals from the selected sensors appear on array lines (e.g. column lines) of the array.

[0029] The sensor array may have many more array lines than output ports on the integrated circuit. For example, the sensor array may have millions of sensors arranged in thousands of rows or columns that simultaneously detect distinct analytes or reaction properties of interest, but only a few output ports due to size limitations or other constraints. Thus, in embodiments described herein, the output signals on the array lines are provided to output lines for the output ports through multiplexers, which allows for the sharing of multiple array lines with a single output line coupled to a corresponding output port on the integrated circuit.

[0030] The output signals at the output ports of the integrated circuit are collected and processed and/or analyzed by a computer (not shown) or other data processor external to the integrated circuit. This processing includes correcting for multiplexer cross-talk using the techniques described herein. [0031] In various exemplary embodiments, the methods, systems, and computer readable media described herein may advantageously be used to process and/or analyze data and signals obtained from electronic or charged-based nucleic acid sequencing, including correction of multiplexer cross-talk. In electronic or charged-based sequencing (such as, pH-based sequencing), a nucleotide incorporation event may be determined by detecting ions (e.g., hydrogen ions) that are generated as natural by-products of polymerase-catalyzed nucleotide extension reactions. This may be used to sequence a sample or template nucleic acid, which may be a fragment of a nucleic acid sequence of interest, for example, and which may be directly or indirectly attached as a clonal population to a solid support, such as a particle, microparticle, bead, etc. The sample or template nucleic acid may be operably associated to a primer and polymerase and may be subjected to repeated cycles or "flows" of deoxynucleoside triphosphate ("dNTP") addition (which may be referred to herein as "nucleotide flows" from which nucleotide incorporations may result) and washing. The primer may be annealed to the sample or template so that the primer's 3' end can be extended by a polymerase whenever dNTPs complementary to the next base in the template are added. Then, based on the known sequence of nucleotide flows and on measured output signals of the sensors indicative of ion concentration during each nucleotide flow, the identity of the type, sequence and number of nucleotide(s) associated with a sample nucleic acid present in a reaction confinement region coupled to a sensor can be determined.

[0032] FIG. 1 illustrates a block diagram of components of a system for nucleic acid sequencing according to an exemplary embodiment. The components include a flow cell 101 on an integrated circuit device 100, a reference electrode 108, a plurality of reagents 114 for sequencing, a valve block 116, a wash solution 110, a valve 112, a fluidics controller 118, lines 120/122/126, passages 104/109/111, a waste container 106, an array controller 124, and a user interface 128. The integrated circuit device 100 includes a micro well array 107 overlying a sensor array that includes sensors arranged in rows and columns. The flow cell 101 includes an inlet 102, an outlet 103, and a flow chamber 105 defining a flow path of reagents over the micro well array 107.

[0033] The reference electrode 108 may be of any suitable type or shape, including a concentric cylinder with a fluid passage or a wire inserted into a lumen of passage 111. The reagents 114 may be driven through the fluid pathways, valves, and flow cell 101 by pumps, gas pressure, or other suitable methods, and may be discarded into the waste container 106 after exiting the outlet 103 of the flow cell 101. The fluidics controller 118 may control driving forces for the reagents 114 and the operation of valve 112 and valve block 116 with suitable software. [0034] The microwell array 107 may include an array of defined spaces or reaction confinement regions, referred to herein as microwells, which are operationally associated with corresponding sensors in the sensor array. For example, each microwell may be coupled to a sensor suitable for detecting an analyte or reaction property of interest within that microwell. The microwell array 107 may be integrated in the integrated circuit device 100, so that the microwell array 107 and the sensor array are a single device or chip.

[0035] The flow cell 101 may have a variety of configurations for controlling the path and flow rate of reagents 114 over the microwell array 107. The array controller 124 provides bias voltages and timing and control signals to the integrated circuit 100 for reading the sensors of the sensor array. The array controller 124 also provides a reference bias voltage to the reference electrode 108 to bias the reagents 114 flowing over the microwell array 107.

[0036] The array controller 124 also collects and processes output signals from the sensors of the sensor array received through output ports on the integrated circuit device 100 via bus 127. This processing includes correcting for multiplexer cross-talk of the output signals using the techniques described herein. The array controller 124 may be a computer or other computing means. The array controller 124 may include memory for storage of data and software applications, a processor for accessing data and executing applications, and components that facilitate communication with the various components of the system in FIG. 1.

[0037] The user interface 128 may display information about the flow cell 101 and the output signals received from the integrated circuit device 100, as well as instrument settings and controls, and allow a user to enter or set instrument settings and controls.

[0038] In an exemplary embodiment, the fluidics controller 118 may control delivery of the individual reagents 114 to the flow cell 101 and integrated circuit device 100 in a predetermined sequence, for predetermined durations, at predetermined flow rates. The array controller 124 can then collect and store the output signals of the sensors due to reactions occurring in response to the delivery of the reagents 114. The output signals indicate physical and/or chemical parameters of one or more reactions taking place in the corresponding microwells in the microwell array 107. In operation, the system may also monitor and control the temperature of the integrated circuit device 100, so that reactions take place and measurements are made at a known predetermined temperature.

[0039] The system may be configured to let a single fluid or reagent contact the reference electrode 108 throughout an entire multi-step reaction. The valve 112 may be shut to prevent any wash solution 110 from flowing into passage 109 as the reagents 114 are flowing. Although the flow of wash solution may be stopped, there may still be uninterrupted fluid and electrical communication between the reference electrode 108, passage 109, and the microwell array 107. The distance between the reference electrode 108 and the junction between passages 109 and 111 may be selected so that little or no amount of the reagents flowing in passage 109 and possibly diffusing into passage 111 reach the reference electrode 108. In an exemplary embodiment, the wash solution 110 may be selected as being in continuous contact with the reference electrode 108, which may be especially useful for multi-step reactions using frequent wash steps.

[0040] FIG. 2 illustrates cross-sectional and expanded views of a portion of the integrated circuit device 100 and flow cell 101. During operating, the flow chamber 105 of the flow cell 101 defines a reagent flow 208 of delivered reagents across open ends of the microwells in the microwell array 107. The volume, shape, aspect ratio (such as base width-to-well depth ratio), and other dimensional characteristics of the microwells may be selected based on the nature of the reaction taking place, as well as the reagents, byproducts, or labeling techniques (if any) that are employed.

[0041] The expanded view of FIG.2 illustrates a representative microwell 201 in the microwell array 207, and a corresponding sensor 214 in the sensor array 205. The sensor 214 can be a chemical field-effect transistor (chemFET), more specifically an ion-sensitive FET (ISFET), with a floating gate 218 having a sensor plate 220 separated from the microwell interior by an ion-sensitive layer 216. The sensor plate 220 may for example include multiple layers of conductive material. The ion-sensitive layer 216 may for example be an oxide of an upper layer of conductive material of the sensor plate 220.

[0042] The sensor 214 can be responsive to (and generate an output signal related to) the amount of a charge 224 present on ion-sensitive layer 216 opposite the sensor plate 220.

Changes in the charge 224 can cause changes in the threshold voltage of the chemFET. The change in threshold voltage can be measured by measuring the current between a source 221 and a drain 222 of the chemFET. As a result, the chemFET can be used directly to provide a current- based output signal on an array line connected to the source 221 or drain 222, or indirectly with additional circuitry to provide a voltage-based output signal. Reactants, wash solutions, and other reagents may move in and out of the microwells by a diffusion mechanism 240.

[0043] In an embodiment, reactions carried out in the microwell 201 can be analytical reactions to identify or determine characteristics or properties of an analyte of interest. Such reactions can generate directly or indirectly byproducts that affect the amount of charge adjacent to the sensor plate 220. If such byproducts are produced in small amounts or rapidly decay or react with other constituents, multiple copies of the same analyte may be analyzed in the micro well 201 at the same time in order to increase the output signal generated. In an embodiment, multiple copies of an analyte may be attached to a solid phase support 212, either before or after deposition into the microwell 201. The solid phase support 212 may be microparticles, nanoparticles, beads, solid or porous comprising gels, or the like. For simplicity and ease of explanation, solid phase support 212 is also referred herein as a particle. For a nucleic acid analyte, multiple, connected copies may be made by rolling circle amplification (RCA), exponential RCA, or like techniques, to produce an amplicon without the need of a solid support.

[0044] FIG. 3 is a simplified block diagram of a portion of the integrated circuit device 100, including the sensor array 205 of sensors arranged in rows and columns which can be operated as described herein. The integrated circuit device 100 includes a row select register 328 and output circuitry for reading the output signals from the sensors in the sensor array 205 via array lines (e.g. row and/or column lines). The row select register 328 and the output circuitry read the sensors in response to timing and control signals provided by the array controller 124.

[0045] The output circuitry is coupled to array lines of the sensor array 220 which contain the output signals from the selected sensors in the sensor array 220. The array lines may for example be column lines that are arranged along columns in the sensor array 220.

[0046] In the illustrated embodiment, the output circuitry includes a channel circuit 220, column multiplexer 248, output multiplexer 224, and output buffer 240. The channel circuit 220 may include sample and hold (S/H) circuits for sampling and holding the output signals of the sensors provided on the array lines. The sampled output signals supplied from the channel circuit are provided to the column multiplexer 248, the output multiplexer 224 and the output buffer 240. The multiplexed and buffered output signals are then supplied from the output buffer 240 to data-out lines 360 connected to output ports on the integrated circuit device 100. The number of data-out lines 360 on the integrated circuit device 100 can vary from embodiment to embodiment. For example, the integrated circuit device 100 may include a total of four data-out lines. Alternatively, the number of data-out lines may be different from four.

[0047] FIG. 4 illustrates a block diagram of an example multiplexer configuration that can be used for the sensor array 205. In the illustrated example, each of the data-out lines of the integrated circuit device 100 are connected to the output of a corresponding two stage multiplexer, one of which is shown in FIG. 4. Alternatively, other multiplexer configurations and arrangements of the data-out lines may be used. [0048] The first-stage multiplexer includes two column multiplexers 410 and 420 that operate at, for example, 26 MHz. Each of multiplexers 410 and 420 have multiple selectable channels, with each channel coupled to a particular column line on the sensor array. The outputs 431, 432 of multiplexers 410 and 420 feed into a faster, output multiplexer 430 that selects between which outputs of multiplexers 410 and 420 to data-out line 436. Thus, second-stage multiplexer 430 has two selectable channels 431 and 432, channel 431 for the output of multiplexer 410 and channel 432 for the output of multiplexer 420. Multiplexer 430 can operate at, for example, 53 MHz.

[0049] In this particular configuration, each of column multiplexers 410 and 420 is assigned to handle one -eighth of the columns in the sensor array. Thus, in this particular embodiment, each of the multiple channels in multiplexer 410 are coupled to one of columns 1, 9, 17, etc. of the sensor array; whereas the channels of multiplexer 420 are coupled to columns 5, 13, 21, etc. of the sensor array. Thus, through this configuration, each of the columns 1, 9, 17, etc. are coupled to separate channels of multiplexer 410; and each of columns 5, 13, etc. are coupled to a separate channels of multiplexer 420. In this configuration, multiplexers 410 and 420 combined handle one-fourth of the columns of the sensor array. Similar two-stage multiplexer

configurations are coupled to the other column lines of the sensor array, and each group of multiplexers may similarly handle one -fourth of the columns.

[0050] In operation, reagents are flowed over the sensor array to initiate simultaneous, individual chemical reactions within each of the microwells in the microwell array coupled to the sensor array, for example as described above. Examples of how the sensor array can be used to detect chemical reactions are described in U.S. Patent Application Publication No.

2010/0300559, No. 2010/0197507, No. 2010/0301398, No. 2010/0300895, No. 2010/0137143, and No. 2009/0026082, and U.S. Patent No. 7,575,865, which are incorporated by reference herein. As a result of the simultaneous and distinct chemical reactions detected by separate sensors, the sensors in the array generate output signals that can be read upon being selected. For example, every fourth column of the sensor array may be selected (i.e., columns 1, 5, 9, 13, etc. for the multiplexer configuration shown in FIG. 4) for output through one of the data-out lines of the integrated circuit device 100.

[0051] Upon selection of the channel coupled to column 1 in response to signals provided by the array controller 124, column multiplexer 410 feeds the output signal from column 1 as the input to channel 431 of output multiplexer 430. Upon selection of channel 431 , the multiplexer 430 then directs the output signal from column 1 to the data-out line 436. While the output signal from column 1 is being fed to output line 436, the channel of multiplexer 420 assigned to column 5 of the sensor array is selected. This causes the output signal from column 5 to be fed as input to channel 432 of multiplexer 430. Upon selection of channel 432, multiplexer 430 then directs the column 5 output signal to the data-out line 436.

[0052] Next, the channel of multiplexer 410 assigned to column 1 is de-selected and the channel of multiplexer 410 that is assigned to column 9 of the sensor array is selected, which feeds the output signal from column 9 as input to channel 431 of multiplexer 430. Upon selection of channel 431, multiplexer 430 then directs the column 9 signal to the data-out line 436. In similar fashion, the output signals from other column lines are fed to data-out line 436 through the alternating use of multiplexers 410 and 420 via multiplexer 430 until all the output signals for all the columns in the sensor array assigned to multiplexers 410 and 420 are read out. And in similar fashion, other multiplexer groups may be used to read out the other columns in the sensor array assigned to such other multiplexers.

[0053] The output signals from the sensor array may be coupled from the data-out lines of the integrated circuit device 100 to a data processing system, which may process the output signals and perform the calculations as described herein. The data processing system may include various components of a computer system, including processors and memory.

[0054] FIG. 5 illustrates a block diagram of example of a data processing system for processing output signals from sensors in the sensor array as described herein. The data processing system 500 includes a mother board 502, a display 508, and a reader board 510 which is coupled to the output ports of the integrated circuit device 100. The mother board 502 may include processors 504 and memory 506. The reader board 510 may include various components used in signal processing, including analog-to-digital converters.

[0055] As discussed above, after a channel of a multiplexer has been used to receive an output signal from a column line, that channel is switched off and the next channel is switched on. However, even though the prior channel is switched off, there may still be a charge retained in the multiplexer (e.g. due to internal capacitance coupled to the channel). This retained charge can couple to the output of the multiplexer, resulting in cross-talk between the channels.

[0056] Thus, referring back to FIG. 4, after multiplexer 410 receives input from column 1 of the sensor array, that particular channel is turned off and the next channel is turned on when column 9 is read. However, the signal charge remaining from the channel for column 1 may couple with the channel for column 9 when that channel is turned on and read. Moreover, there may be similar cross-talk between the channels of multiplexer 430, resulting in cross-talk between signals from column 9 (from multiplexer 410) and column 5 (from multiplexer 420). Thus, when the signal for column 49 is read from data-out line 436, the measured signal may include components of the cross-talk from prior-selected channels of column multiplexer 410 and/or column multiplexer 420 (through output multiplexer 430).

[0057] This effect is demonstrated in FIG. 6, which shows the magnitude of cross-talk between two channels that read columns that are 8 sensors apart (e.g. between a sensor in column 1 of the array, and a sensor in column 9 of the array). The x-axis represents the frame number and the y-axis represents the signal counts. An output signal was transmitted as input through one of the channels of the multiplexer (see line 640). This signal caused a cross-talk signal in an adjacent channel that reads a column that is 8 pixels apart (see line 642). For example, the amplitude of this cross-talk signal in the adjacent channel was observed to be 14% of the amplitude of the "aggressor" signal. Thus, the cross-talk introduces an error in the output signal that is being read out for the column corresponding to a selected sensor. A similar effect was also observed for the fast 2-to-l output multiplexer 430 shown in FIG. 4.

[0058] As described in more detail below, the processing of the collected output signals by the data processing system corrects or compensates for the cross-talk occurring between channels of the multiplexer such as described above. Since the collected output signal may include cross-talk signals from other channels of the multiplexer, the processing involves calculating an adjusted signal based on the relationship between the collected signal and the actual signal that was generated in the absence of cross-talk. This relationship between the collected output signal and the actual signal can be derived from empirical observations and/or mathematical modeling, and can be described by some mathematical relationships (such as one or more mathematical equations). In doing so, an accurate output signal can be obtained.

[0059] The calculations may for example be based on the relationship that the collected signal received through a channel of a multiplexer is the actual signal plus any cross-talk contribution from one or more other channels of the multiplexer (e.g. those used in prior reads). In some cases, the adjusted signal may be calculated using a coefficient that relates to the amount of cross-talk that is contributed by one or more other channels of the multiplexer from prior reads of the sensor array, which may be related to the amount of charge retained in these other channels from prior reads.

[0060] For example, the calculation may comprise multiplying the collected signal by the correction coefficient. In some cases, the calculation may involve the use of multiple coefficients, each relating to the amount of cross-talk contributed by a particular channel of the multiplexer. For example, the calculation may comprise the sum of the collected signals from multiple readings in different channels of the multiplexer, each multiplied by a correction coefficient.

[0061] In an embodiment, the calculation takes the following form:

^Vj =

.,-8, Σ "k - ^Vmj-k

£=.. -4,0,4,8,... where:

Vm,_j-_k = collected value of the output signal for the selected sensor in column j-k;

V_j = adjusted value for the output signal for the selected sensor in column j (i.e. actual signal value) to compensate for cross-talk;

d_k = correction coefficient for the collected value Vm_j._k

[0062] In this embodiment, the index k involves the collected values from several channels of the same multiplexer preceding and following the channel whose adjusted value is being calculated. The ¾ correction coefficients may be obtained from either modeling and/or from empirical observations.

[0063] In some cases, the ¾ correction coefficients are calculated by inverting a correlation or cross-talk kernel. This calculation may be based on the relationship between the collected signal and the actual signal expressed as follows:

N

where:

Vni_j = collected value of the output signal for the selected sensor in column j;

V_j-_k = adjusted value of the output signal for the selected sensor in column j-k;

N = span of non-zero convolution terms;

at = amount of cross talk that column j-k contributes to column j

Thus, for example (assuming the signal read starts at column 1),

for column 1 (j = 1): Vmi = a₀Vi

for column 5 (j = 5): Vms = a₀Vs + a₄Vi

for column 9 (j = 9): Vm₉ = aoVg + a₄V₅ + a₈Vi

for column 13 (j = 13): Vmi₃ = a₀Vi₃ + a₄Vg + a₈Vs + ai₂Vi

[0064] Each correction coefficient <¾ can be derived in any suitable way. In some cases, each correction coefficient <¾ can be derived by extrapolating the behavior of the multiplexer. For example, the multiplexer may be modeled as a circuit whose output voltage approaches the input voltage over time such that the collected signal Vm for any channel can be written in terms of the actual signal for the same channel and the previous measurements taken from the multiplexer. Thus, for example:

for column 13: Vmn = f_mVi3 + (l-f_m)Vmci;

for column 9: Vm₉ = f_mV₉ + (l-f_m)Vm₅;

for column 5: Vms = f_mVs + (l-f_m)Vmi;

where f_m is the fraction to which the multiplexer settles. If the multiplexer were operated at a very slow speed, f_m would be equal to 1.0, and no correction would be necessary.

[0065] To derive the a_t correction coefficients, the equations for each individual measured signal can be substituted into one another. For example, for column 13: Vmi₃ = f_mVi3 + (1- fm)(fmV9+(l-f_m)(f_mV5+(l-f_m)Vmi)), in which the Vm terms have been substituted for to put Vmi₃ in terms of actual signal. Thus, in this example, ao= f_m, ¾ = (l-f_m)f_m, as = (l-f_m)²f_m, and so on. Since f_m is a small number in most real systems, each successive term is smaller and the extrapolation may be carried out only until the a_t terms are near zero.

[0066] The set of terms that express the above relationship can be represented in matrix form as follows: Vm = A · V, where A is a matrix containing the coefficients <¾; V is a matrix containing the actual sensor values; and Vm is a matrix containing the collected values of the output signals. By rearranging the terms and inverting the A matrix to make a vector matrix A^"2 containing the correction coefficients ¾, V (the actual sensor values) can be solved as follows: V = A^'1 · Vm. Since matrix A was formed of a repeating structure, the solution is also repetitive, and can be reduced to a single vector that is convolved with the data.

[0067] In another embodiment, the a_k correction coefficients are derived from an empirical measurement of the multiplexer's behavior. In some cases, a calibration step may be taken to characterize the behavior of the multiplexers. This calibration step may be performed at any suitable time point in the operation of the apparatus, such as prior to beginning the chemical analysis steps (e.g. before flowing reagents onto the sensor array). In some cases, the calibration step involves taking readings from the sensor array through a set of channels of the multiplexer (all or less than all the channels) while operating the multiplexer at two (or more) different operating rates. For example, a first set of measurements can be taken through each channel of the multiplexer while operating at a relatively fast operating rate (e.g. at the normal operating rate of the multiplexer, such as 53 Mhz). A second set of measurements can be taken from each channel while the multiplexer is operating at a relatively slow operating rate, for example, at 5 Mhz. This slower operating rate may be slower than the normal operating rate of the multiplexer and may be selected to allow sufficient time for substantial settling of the multiplexer such that the measured signal is close to the actual signal. The first measurement taken at the faster operating rate thus contains the value Vm that would be measured in normal operation of the multiplexer. The second measurement contains the actual value V and can be referred to as the reference measurement. This embodiment takes advantage of fixed-pattern offsets in the array to provide stimulus for the measurement (i.e., no reagent flow or incorporation signal is necessary to detect signals Vm and V). This calibration step may be performed in one or more of the multiplexers of the sensor array.

[0068] Once V and Vm are obtained, they may be used to build a matrix equation that can be solved for the correction coefficients ¾. Each row of the matrix equation is of the form:

where V _j corresponds to one particular sensors reference signal, and Vni_j._k is therefore the measured values for all of the channels surrounding and including channel j. The equation for each channel j's reference signal is combined into a matrix equation: Vm · A = V. This matrix equation can be inverted and solved for the correction coefficients ¾ in the column vector A.

[0069] Not all the reads of the sensor array may need signal correction. For example, in operation, column 1 or other initially read columns may be allowed sufficient settling time that signal correction is not required. The techniques described herein can be used with any multiplexer configuration for a sensor array. For example, the techniques can be used with a one- stage multiplexer configuration or a multistage multiplexer configuration (such as the two-stage configuration described above). In another example, the techniques can be used with a single multiplexer or multiple multiplexers (such as alternating between two multiplexers via a third multiplexer, as described above). The output signals from the sensors may be read from any suitable signal array line on the sensor array, such as column lines and/or row lines.

[0070] The actual values of the output signals can then be analyzed by the data processing system to identify or determine characteristics or properties of an analyte of interest. For example, in an exemplary embodiment, the data processing system may be process the adjusted values of the output signals using the techniques disclosed in Rearick et al., U.S. Pat. Appl. No.

13/339,846, filed December 29, 2011, based on U.S. Prov. Pat. Appl. Nos. 61/428,743, filed December 30, 2010, and 61/429,328, filed January 3, 2011 , and in Hubbell, U.S. Pat. Appl. No. 13/339,753, filed December 29, 2011, based on U.S. Prov. Pat. Appl. No 61/428,097, filed December 29, 2010, which are all incorporated by reference herein in their entirety.

[0071] The techniques described herein may be used with various nucleic acid sequencing techniques and apparatuses, including those described in U.S. Patent Application Publication No. 2010/0300559, No. 2010/0197507, No. 2010/0301398, No. 2010/0300895, No. 2010/0137143, and No. 2009/0026082, and U.S. Patent No. 7,575,865. Such sequencing platforms may involve sequencing-by-synthesis techniques that operate by the detection of inorganic pyrophosphate or hydrogen ions produced by nucleotide incorporation reactions. In some cases, the sensor array is a chemFET sensor array. In some cases, the chemFET sensors of the sensor array detect hydrogen ions. In some cases, flowing of the reagent(s) onto the sensor array causes chemical reactions that release hydrogen ions. In some cases, the amplitude of the signals from the chemFET sensors is related to the amount of hydrogen ions detected. In some cases, the sensor array is a light-sensing array. In some cases, flowing of the reagent(s) onto the sensor array causes chemical reactions that release inorganic pyrophosphate, which causes the emission of light via an enzyme cascade initiated by the inorganic pyrophosphate.

[0072] FIG. 7 is a flow chart of an example process for processing output signals from a sensor array to compensate for multiplexer cross-talk. Other embodiments may perform the steps in different orders and/or perform different or additional steps than the ones illustrated in FIG. 7. For convenience, FIG. 7 will be described with reference to a system of one or more computers that performs the process. The system can be, for example, the data processing system 500 described above with reference to FIG. 5.

[0073] At step 750, one or more chemical reactions are initiated in proximity to sensors in the sensor array. As shown in step 752, a first output signal is received from a first sensor of the sensor array via a first channel of the multiplexer. As shown in step 754, a second output signal is received from a second sensor of the sensor array via a second channel of the multiplexer. As shown in step 756, an adjusted second output signal is calculated to account for cross-talk from one or more other channels in the multiplexer, wherein the calculation uses a correction coefficient that has a mathematical relationship to the amount of cross-talk contributed by the first channel of the multiplexer from the receipt of the first output signal from the first sensor.

[0074] The value of the adjusted second signal can then be analyzed by the data processing system to identify or determine characteristics or properties of the chemical reaction occurring proximate to the second sensor. [0075] Various embodiments may be implemented using hardware elements, software elements, or a combination of both. Examples of hardware elements may include processors, microprocessors, circuits, circuit elements (e.g., transistors, resistors, capacitors, inductors, and so forth), integrated circuits, application specific integrated circuits (ASIC), programmable logic devices (PLD), digital signal processors (DSP), field programmable gate array (FPGA), logic gates, registers, semiconductor device, chips, microchips, chip sets, and so forth. Examples of software may include software components, programs, applications, computer programs, application programs, system programs, machine programs, operating system software, middleware, firmware, software modules, routines, subroutines, functions, methods, procedures, software interfaces, application program interfaces (API), instruction sets, computing code, computer code, code segments, computer code segments, words, values, symbols, or any combination thereof. Determining whether an embodiment is implemented using hardware elements and/or software elements may vary in accordance with any number of factors, such as desired computational rate, power levels, heat tolerances, processing cycle budget, input data rates, output data rates, memory resources, data bus speeds and other design or performance constraints.

[0076] Some embodiments may be implemented, for example, using a computer-readable medium or article which may store an instruction or a set of instructions that, if executed by a machine, may cause the machine to perform a method and/or operations in accordance with the embodiments. Such a machine may include, for example, any suitable processing platform, computing platform, computing device, processing device, computing system, processing system, computer, processor, or the like, and may be implemented using any suitable combination of hardware and/or software. The computer-readable medium or article may include, for example, any suitable type of memory unit, memory device, memory article, memory medium, storage device, storage article, storage medium and/or storage unit, for example, memory, removable or non-removable media, erasable or non-erasable media, writeable or re-writeable media, digital or analog media, hard disk, floppy disk, read-only memory compact disc (CD-ROM), recordable compact disc (CD-R), rewriteable compact disc (CD-RW), optical disk, magnetic media, magneto-optical media, removable memory cards or disks, various types of Digital Versatile Disc (DVD), a tape, a cassette, or the like. The instructions may include any suitable type of code, such as source code, compiled code, interpreted code, executable code, static code, dynamic code, encrypted code, and the like, implemented using any suitable high-level, low-level, object-oriented, visual, compiled and/or interpreted programming language. [0077] Those skilled in the art may appreciate from the foregoing description that the present teachings may be implemented in a variety of forms, and that the various embodiments may be implemented alone or in combination. Therefore, while the embodiments of the present teachings have been described in connection with particular examples thereof, the true scope of the embodiments and/or methods of the present teachings should not be so limited since other modifications will become apparent to the skilled practitioner upon a study of the drawings, specification, and following claims.

Claims

CLAIMS What is claimed is:

1. A method of processing signals from an integrated circuit device comprising a sensor array and a multiplexer that receives output signals from sensors of the sensor array, the method comprising:

initiating one or more chemical reactions in proximity to sensors in the sensor array; receiving a first output signal from a first sensor of the sensor array via a first channel of the multiplexer;

receiving a second output signal from a second sensor of the sensor array via a second channel of the multiplexer; and

calculating an adjusted second output signal to compensate for cross-talk from the first channel of the multiplexer due to the received first output signal from the first sensor.

2. The method of claim 1, wherein the calculating comprises multiplying the second output signal by a correction coefficient based on an amount of cross-talk contributed by the first channel of the multiplexer due to the received first output signal.

3. The method of claim 1, wherein the calculating comprises multiplying the second output signal by multiple correction coefficients, each correction coefficient based on an amount of cross-talk contributed by output signals received via corresponding channels of the multiplexer.

4. The method of claim 1, further comprising:

between receiving the first output signal and the second output signal, receiving a third output signal from a third sensor of the sensor array via a second multiplexer.

5. The method of claim 4, wherein the integrated circuit device further includes a third multiplexer that receives outputs of the first multiplexer and the second multiplexer, wherein the third multiplexer has a first channel for the output of the first multiplexer and a second channel for the output of the second multiplexer;

wherein the calculation further compensates for cross-talk contributed by the second channel of the third multiplexer from the receipt of the output from the second multiplexer.

6. The method of claim 1, wherein the first output signal is received from a first array line that is connected to the first sensor of the sensor array, and the second output signal is received from a second array line that is connected to the second sensor of the sensor array.

7. The method of claim 6, wherein the array lines are column lines on the sensor array.

8. The method of claim 1, wherein the sensor array is a chemFET sensor array.

9. The method of claim 8, wherein the chemFET sensors of the sensor array detect hydrogen ions, and wherein the chemical reactions release hydrogen ions.

10. The method of claim 1, further comprising performing a calibration step that characterizes the behavior of the multiplexer.

11. An apparatus for detecting chemical reactions, comprising:

an integrated circuit device comprising a sensor array, and a multiplexer that receives output signals from sensors of the sensor array due to chemical reactions occurring proximate to the sensors; and

a controller system including memory and one or more processors operable to execute instructions, stored in memory, comprising instructions to:

receive a first output signal from a first sensor of the sensor array via a first channel of the multiplexer;

receive a second output signal from a second sensor of the sensor array via a second channel of the multiplexer; and

calculate an adjusted second output signal to compensate for cross-talk from the first channel of the multiplexer due to the received first output signal from the first sensor.

12. The apparatus of claim 11, wherein the calculation comprises multiplying the second output signal by a correction coefficient based on an amount of cross-talk contributed by the first channel of the multiplexer due to the received first output signal.

13. The apparatus of claim 11, wherein the calculation comprises multiplying the second output signal by multiple correction coefficients, each correction coefficient based on an amount of cross-talk contributed by output signals received via corresponding channels of the multiplexer.

14. The apparatus of claim 11, wherein:

the integrated circuit device further comprises a second multiplexer; and

the controller system further comprises instructions to receive a third output signal from a third sensor of the sensor array via a second multiplexer, between receiving the first output signal and the second output signal.

15. The apparatus of claim 14, wherein:

the integrated circuit device includes a third multiplexer that receives outputs of the first multiplexer and the second multiplexer, wherein the third multiplexer has a first channel for the output of the first multiplexer and a second channel for the output of the second multiplexer; and the instructions to calculate includes instructions to compensate for cross-talk contributed by the second channel of the third multiplexer from the receipt of the output from the second multiplexer.

16. The apparatus of claim 11, wherein the first output signal is received from a first array line that is connected to the first sensor of the sensor array, and the second output signal is received from a second array line that is connected to the second sensor of the sensor array.

17. The apparatus of claim 16, wherein the array lines are column lines in the sensor array.

18. The apparatus of claim 11, wherein the sensor array is a chemFET sensor array.

19. A non-transitory computer-readable storage medium storing instructions for operating an apparatus that comprises an integrated circuit device comprising a sensor array, and a multiplexer that receives output signals from sensors of the sensor array due to chemical reactions occurring proximate to the sensors, the instructions executable by a processor to: initiate one or more chemical reactions in proximity to sensors in the sensor array;

receive a second output signal from a second sensor of the sensor array via a second channel of the multiplexer; and calculate an adjusted second output signal to compensate for cross-talk from the first channel of the multiplexer due to the received first output signal from the first sensor.