Capillary Electrophoresis Sensitivity Enhancement Based on Adaptive

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Capillary Electrophoresis Sensitivity Enhancement Based on Adaptive Moving Average Method Tomas Drevinskas, Laimutis Telksnys, Audrius Maruska, Jelena Gorbatsova, and Mihkel Kaljurand Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.8b00664 • Publication Date (Web): 30 Apr 2018 Downloaded from http://pubs.acs.org on May 3, 2018

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Analytical Chemistry

Capillary Electrophoresis Sensitivity Enhancement Based on Adaptive Moving Average Method

Tomas Drevinskas1,2, Laimutis Telksnys2,3, Audrius Maruška1*, Jelena Gorbatsova4, Mihkel Kaljurand4,1

1

Instrumental Analysis Open Access Centre, Faculty of Natural Sciences, Vytautas Magnus University, Vileikos 8, LT44404 Kaunas, Lithuania 2

Department of Systems’ Analysis, Faculty of Informatics, Vytautas Magnus University, Vileikos 8, LT44404 Kaunas, Lithuania 3

Recognition Processes Department, Institute of Mathematics and Informatics, Goštauto 12, LT01108 Vilnius, Lithuania 4

Department of Chemistry, Faculty of Sciences, Tallinn University of Technology, Akadeemia tee 15, 12618 Tallinn, Estonia

Keywords: Capillary electrophoresis, Noise filtering, Contactless conductivity detection, Instrumentation, Software, Migration velocity

Correspondence to: Prof. Audrius Maruška [email protected]

Abstract: In the present work we demonstrate the novel approach to improve the sensitivity of the “out of lab” portable capillary electrophoretic measurements. Nowadays, many enhancement methods are: (i) underused (non-optimal), (ii) overused (distorts the data), or (iii) inapplicable in field-portable instrumentation due to lack of computational power. Described innovative migration velocity-adaptive moving average method uses optimal averaging window size and can be easily implemented with microcontroller. The contactless conductivity detection was used as a model for the development of a signal processing method and the demonstration of its impact on the sensitivity. The frequency characteristics of the recorded electropherograms and peaks were clarified. Higher electrophoretic mobility analytes exhibit higher frequency peaks, while lower electrophoretic mobility analytes exhibit lower frequency peaks. Based on obtained data, a migration velocity-adaptive moving average algorithm was created, adapted and programmed into capillary electrophoresis data processing software. Employing the developed algorithm, each data point is processed depending on a certain migration time of the analyte. Because of the implemented migration velocityadaptive moving average method the signal-to-noise ratio improved up to 11 times for sampling frequency of 4.6 Hz and up to 22 times for sampling frequency of 25 Hz. This paper could potentially be used as a methodological guideline for the development of new smoothing algorithms that require adaptive conditions in capillary electrophoresis, and other separation methods.

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Introduction In the era of high speed and high-resolution data acquisition, there is a need for novel yet simple and efficient computational algorithms.1,2 The good example of such modernization is the last generation of analog-to-digital converters3,4. Affordable price, quality and size ratio allows to integrate such models (including field programmable gate array-based converters) as the main data acquisition modules5 not only into the expensive commercial laboratory equipment, but into the portable analytical systems as well. This is important for rapid microseparation methods, where little to none of the peak in the chromatogram/electropherogram should be lost in the filter. Whereas filtering of chromatographic, or electrophoretic data, in real-time requires significant computational power.6 Unfortunately, the microprocessors that are responsible for the computation in autonomous and portable instruments are not capable of handling high amount of data with computationally intensive algorithms. Therefore, current in situ data analysis systems are restricted only to low-speed data acquisition.7,8 The current trends in analytical method and instrumentation development includes miniaturization and performance.9 Miniaturization of the instrument could decrease the sensitivity.10 However, miniaturized techniques offer numerous advantages: miniaturized instruments (i) can be easily integrated into other hardware, (ii) can be coupled with other methods, so that in-line and on-line techniques can be realized, (iii) and can be used for in situ analysis in portable and autonomous instrumentation.7,11 The design of such instrumentation is not a trivial task due to the requirements for operation in a harsh and changing environment.12 The capillary electrophoresis (CE) separation method can be used for field-portable analytical investigations.13 Electrophoretic techniques offer several advantages over chromatographic techniques: they are (i) compact14, (ii) require fewer moving parts,15,16 (iii) are less susceptible to column/ capillary clogging17 and (iv) do not require complex sample preparation.18,19 Nevertheless, electrophoretic techniques are considered less sensitive (up to 2 orders of magnitude) compared to the chromatographic techniques, which pose problems detecting low amounts of chemicals.20,21 This is due to a minute dimension of a detection cell, which is mostly determined by an inner diameter of the separation capillary (25-75µm). There are three main strategies of increasing the sensitivity of the miniaturized and conventional separation instrumentation: (i) hardware improvement (such as Z or bubble cells for UV/VIS detection, higher excitation voltage used for contactless conductivity detection), (ii) software improvement and (iii) analysis condition adjustment.22,23 Signal conditioning using special software with previously developed algorithms is not a new approach; it has already been used in the field of analytical chemistry for several decades20,24,25. Software improvements mainly deal with signal compensation and signal filtering techniques26. There are several signal conditioning methods used with separation techniques: (i) low pass filtering (that includes hardware analog operational amplifier filtering, switched capacitor filtering, digital filtering, fast Fourier transform filtering), (ii) moving average and its variations (simple moving average filtering, weighted average filtering) and (iii) more complex mathematical algorithms such as Savitzky-Golay, or a finite impulse response method that requires more computer processing power for signal recording and processing than simple moving average method.24,26,27 In conventional separation systems, the detector signals are oversampled: the data is acquired at the higher rate than is required to record the peaks; therefore, noise is visible in the electropherograms. Random process theory implies that the information of peaks in the electropherograms is contained in the low-frequency region of the frequency spectrum, and the noise is encoded in the high-frequency region. This work clarifies the optimal smoothing


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parameters for each peak in the electropherogram, and the development of a smoothing algorithm that reduces the noise at each peak, depending on the optimal smoothing parameters. In this work, contactless conductivity detection (C4D), was selected to test the model due to its ease of use and modification possibilities.28,29 This technique is modifiable opposed to instrumentation supplied by official suppliers, which is closed-source and, unmodifiable since the algorithms are pre-programmed and restricted to a certain platform.30 The method described in this paper utilizes a posteriori information: (i) electrophoretic velocity and (i) frequency characteristics of the electropherograms. The method is simple, easily implemented, computationally efficient, and applicable to portable and stand-alone instrumentation in real-time and post-processing applications. The aim of this work was to design and test a migration velocity-adaptive moving average method that improves the sensitivity of acquired data in capillary electrophoresis.

Experimental Section Chemicals Acetic acid (99.8%) was purchased from Reachem (Slovakia). Sodium chloride (99.5%), potassium chloride (>99%) and 2-amino-2-methyl-1-propanol (AMP) (90%) were from Sigma-Aldrich (Germany). Tris(hydroxymethyl)aminomethane (TRIS) (99.8%) was from Merck (Germany). Bidistilled water was produced in the laboratory using Fistreem Cyclon bidistillator (UK).

Instrumentation The capillary electrophoresis system was donated by Agilent Technologies (Germany). Detection: previously optimized wireless, capacitance-to-digital technology based on differential measurement capability and, contactless conductivity detection system was used.31,32 Detection was performed using 32 kHz square wave signal with an amplitude of 3.3 V. Each electrode width was 24 mm, and the detection gap was 0.3 mm. The detector was completely shielded from the outer environment. The detector was connected to an Arduino Nano R3 microcontroller board, and data was sent using two-wire interface (TWI). The microcontroller board pre-processed the data so that values corresponding to picofarads (pF), or femtofarads (fF) were obtained and sent to the computer via transceiver module at the sampling frequencies of 4.6 Hz, 13 Hz, and 25 Hz. The function, named as “CAPCHOP”, which increases the sensitivity of the detector and in the specification of integrated circuit, was switched on during the operation.33 UV detection was used for comparative reasons.

Workflow of the research The research work was comprised of 4 stages (supporting information Figure S1): (i) capillary electrophoresis separations, (ii) signal analysis, (iii) design of migration velocity adaptive moving average method (algorithm) and (iv) ACS Paragon Plus Environment


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testing. First, the capillary electrophoresis procedure was performed and electropherogram recorded. The frequency characteristics of the peaks were determined, the cutoff frequency was found and the relationship between peak migration time and cutoff frequency was clarified by fitting the logarithmic equation. The migration velocity adaptive moving average algorithm was designed as follows: (a) the averaging window was calculated for each data-point of the electropherogram according to the logarithmic equation obtained, (b) the moving average was calculated for each point in the electropherogram and (c) the data processing software was upgraded with the new algorithm. Last, the developed algorithm was tested and processed, and unprocessed data was compared, showing significant improvement of signal-to-noise ratio (S/N ratio) and limits of quantification.

Sample preparation For the preparation of the stock solution, an adequate amount of chemical compound was dissolved in bidistilled water and frozen at -20 °C. For further use, solutions were defrosted and mixed together in adequate ratios. The obtained mixture was diluted, and 8 levels of different concentrations were obtained in the range of 0.23 – 417 μM, which were used for calibration and determination of detection and quantification limits.

Capillary electrophoresis procedure The procedure for the capillary electrophoretic analysis of cation was optimized and indirect mode was applied to detect negative peaks19. Analyses were performed in 0.5 M acetic acid background electrolyte (BGE), where 13 kV voltage potential was applied in 40 °C. The separation capillary was 59 cm total length (Ltot), 47 cm effective length (Leff), 50 μm inner diameter (I.D.) and 365 μm outer diameter (O.D.). Prior to each analysis, the capillary was flushed with background electrolyte for 3 min and electro-conditioned with 13 kV for 5 min. Samples were injected hydrodynamically at 50 mbar for 30 s. Calibration was performed in accordance with method validation guidelines (ICHQ2R1). 8 levels of different concentrations were used for calibration. At least 3 repetitions were performed for determination of concentration. Precision was expressed providing a percentage of relative standard deviation (RSD (%)). For each calibration curve, (y = a * b; y – peak area, a – slope of the calibration curve, b - concentration) the coefficient of determination (R2) was calculated. The quantification limit (LOQ) was calculated in accordance with the equation indicated in supporting information (equation S1).

Electrophoresis signal analysis Electrophoresis signal is observed (Figure 1A): x(j)=xr(j) (j=1,…,J;r=1,…,R); sampling period Δ = 0.216 s; r = 1,..,R – the number of the local peak of electrophoresis signal; xr(j)(j=rb, rb+1,…,re); rb is the starting point of xr(j). re – the end point of the xr(j).


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Figure 1. Representation of signal analysis using STADIA3 software (A) imported electropherogram signal into STADIA3 software: x(j) = xr(j) (j=1,…,J; r=1,…,R). Sampling period Δ = 0.216 s34. r – the number of the local peak of electrophoresis signal. xr(j) (j=rb, rb+1,…,re); rb is the starting point of xr(j). re – the end point of the xr(j). (B) Calculated estimation of spectral density function Sr(f) of the rth peak and Frcutoff – cutoff frequency of the rth peak

The beginning (rb) and the end (re) of the peaks in the electropherogram were manually selected according to chromatographic peak determination procedure fixing starting and ending points. Since the peak selection stage was considered critical; therefore, each peak was inspected manually. Each peak in the electropherogram has its own frequency characteristics; therefore, the optimal averaging window size for each peak in the electropherogram is different. In order to clarify frequency characteristics of the peaks, spectral density functions were calculated for each selected peak using STADIA3 software following the equation indicated in supporting information (equation S2 and S3).34 Estimation of covariance function was calculated using equation indicated in supporting information (equation S4). It must be mentioned that such calculations can be performed using conventional software such as Matlab, or Rstudio if equations S2, S3 and S4 are followed.

Model of smoothing method Calculated spectral density functions help to determine the cutoff frequency of the peak, which is a threshold value (Hz) between information-carrying and noise frequencies in STADIA3 software. The cutoff frequency for each analyzed peak (Frcutoff) was manually determined at the peak and baseline breakpoint (Figure 1B). The Frcutoff is required for calculation of optimal averaging window size for a particular peak in the electropherogram following equation (1): =

(1) 2

Where Wr – the averaging window size of the rth peak, Fs – sampling frequency (Hz) and Frcutoff – the cutoff frequency (Hz) of the rth peak. If averaging window size is calculated for each peak, it leads to the development of adaptive ACS Paragon Plus Environment


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averaging algorithm, where the migration velocity-adaptive moving average algorithm is defined by following statements: (i) during electrophoresis process, the C4D detector provides an array of values, where analysis time – t (t = Δ * j, Δ – sampling period (0.216 s), j – point number) and amplitude x(j) is measured; (ii) depending on the data point number j, averaging window size Wr(j) is calculated at each data point following equation (2): () = − 3.12 ln + 16.8 (2) Where Wr(j) – averaging window size, Fs – sampling frequency, ln – natural logarithm, Leff – effective length of the separation capillary (m), j – point number (j = t / Δ, t – analysis time and Δ – sampling period (0.216 s)); (iii) at each point – j estimation of smoothed signal zr(j) is calculated from original electropherogram (amplitude values) – x(j) following equation (3) (Supporting information Figure S2): () 1 − = 2 ()

#$(%)&(

! ')*

"()#$(%)&' ; , = 1, 2 … , (); () = − (3.12 ln

+ 16.8) (3)

Where zr(j-Wr(j)/2) (r = 1, 2,…, R) – calculated estimation of smoothed signal, Wr(j) – averaging window size, x(j) – original signal (amplitude values), i – step, Fs – sampling frequency (Hz), ln – natural logarithm, Leff – effective length of the separation capillary (m), j – point number (j = t / Δ, t – analysis time and Δ – sampling period (0.216 s)). The result of this procedure is an array of values providing migration velocity adaptively averaged electropherogram.

Results and discussion Frequency characteristics of the peaks The electro-migration velocity of the analytes depend on the charge, ionic volume and viscosity of the background electrolyte.35 Analyses of the mixture of the model analytes and real samples were performed. It was observed that during steady-state CE analysis, each later peak is wider than the former, providing a higher peak width value (supporting information Figure S3). These observations comply with the theoretical background stating that analyte migration velocity is a vector sum of the electrophoretic velocity of the substance and electroosmotic velocity of the BGE.35,36 The same concentration zones of various analytes do not migrate at equal speed, resulting in the difference of time required to pass the detection gap and result in uneven peak widths.36 A similar observation of analyte elution profiles is observed in isocratic chromatographic separations due to chromatographic zone broadening. For the electrophoretic and chromatographic signal smoothing finite response filtering method, which is classified as a weighted averaging method, can be used.27 Literature states that finite response filtering outperforms moving average filtering technique, or Savitzky-Golay method, because the recorded signals are transported to frequency domain, analyzed and transported back to time domain filtered.27,37 Finite response filtering is appropriate for chromatographic techniques, if gradient elution programs are used, due to the fact that (i) the peak shape and frequency characteristics that need signal analysis are hardly predictable, and (ii) chromatography systems are connected to computers that can analyze acquired data and readily process it. In electrophoretic techniques, the peak shape and frequency characteristics depend on the migration velocity and can be predicted (as stated below), which makes the signal filtering algorithm simpler and computationally efficient


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without the signal analysis process. As electrophoretic separation results show (Supporting information Figure S-3), the lowest peak widths were found for potassium ions (15.4 s and 20.1 s), which have highest electrophoretic mobility in BGE of 0.5 M acetic acid. Peak widths of other inorganic cations ranged between 18.2 s and 20.1 s, and organic cations provided a higher peak (AMP – 40.0 s and TRIS – 46.2 s). The highest peak width was observed for the unidentified compound in a real sample (ion-exchanger bleeding products) (69.7 s). Strong relationship between peak width and migration time was observed providing correlation of 0.86 (R2 0.74). Oversampled signals provide electropherograms with noise. In order to clarify if the signal is oversampled, the frequency characteristics must be determined.38 The main parameter is the cutoff frequency, which is the threshold in the frequency spectrum between noise and electropherogram peak information. The spectral density function is a measure that is used to determine the cutoff frequency of the peaks. Spectral density functions were calculated for each peak and the cutoff frequency was determined (Supporting information Figure S-4). All the calculated spectral density functions were found to have a single peak in the lowfrequency region (Supporting information Figure S-4 B). The peak in the low-frequency region of the spectral density function was considered as significant frequency carrying the peak information. The estimates in spectral density function of the high-frequency region that were at the level of the baseline were considered as a noise carrying frequency. It was observed that each later peak provides lower cutoff frequency. The same procedure was repeated for other electropherograms investigated in this work. The maximum frequency that was significant in recording the peak was determined, as depicted in Figure 1B (and supporting information Figure S-4 B). It was noticed that a single dataset from a single analysis, where concentrations of the analytes are similar, providing a comparable peak area, results in a strong relationship between frequency and analyte migration parameters (Supporting information Figure S-5 A). For a single dataset of the real sample (ion exchanger bleeding products), the highest relationship between migration velocity (m/s) and cutoff frequency (Hz) that is significant in recording the information of the peak, was found fitting linear curve where R2 was 0.99. According to Nyquist–Shannon sampling theorem, in order to not lose the information, the sampling frequency must be at least 2 times higher than the cutoff frequency of the signal.39,40 If the cutoff frequency of the peak is known, then the minimum sampling frequency is calculated by multiplying the cutoff frequency by 2. From the minimum sampling frequency, the period can be calculated when multiplied by the sampling frequency of the data acquisition system, provides a value that corresponds to maximum averaging window size (the equation (1) in Model of smoothing method). The relationship in the same dataset (ion exchanger bleeding product peaks) between peak migration velocity (Leff / mt (m/s); Leff – effective length of the capillary, mt – migration time of the peak) and averaging window size was clarified. Strong correlation (Supporting information Figure S-5) was observed providing R2 0.99 of the fitted logarithmic curve.



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Figure 2. Determination of cutoff frequency (A) and averaging window size (B) for peaks

Scatterplots were created for multiple datasets of 27 data points, containing real and modeled samples, separated and unseparated, symmetric and asymmetric peaks of high, medium and low concentrations covering more cases and profiles of electrophoretic separations (Figure 2 A and B). In this case, a more scattered relationship was determined providing R2 0.88 of linear trend-line fitting for a scatterplot in Figure 2 A (cutoff frequency versus against migration velocity). The logarithmic fitting represented in Figure 2 B (averaging window size plotted against migration velocity (m/s)) provided a high negative correlation (-0.92 (R2 0.92)) of multiple electrophoretic profiles and analytical cases. Findings indicated that all investigated peaks provided similar tendency, which was the following: lower electrophoretic mobility analytes provided lower cutoff frequency.

Migration velocity-adaptive moving average algorithm Using the techniques represented in Figure 2 B, the empirical equation was obtained that was used for calculation of optimal averaging window size (supporting information, equation (S-5)), which was modified to equation (2) (Model of smoothing method section). The equation (2) instructs that a peak, depending on its migration time, can be averaged using moving average function when certain sampling frequency is used in data acquisition system and the effective length of the capillary is known. The obtained trivial equation serves as a constraint in a migration velocity– adaptive moving average function and can be explained by equation (3) (Electrophoresis signal analysis section). Considering the obtained migration velocity-adaptive moving average equation, the function was programmed in the software and further analyses were performed with an upgraded version of the software. The algorithm (Supporting information Figure S-6) performs specific sequence of the functions. At each point in the electropherogram the optimal averaging window is calculated and moving average function, according to the optimal averaging window, is calculated for each point of the electropherogram. At the beginning the averaging window size is 1, meaning that no averaging is performed at the start. Later, after a defined amount of time has passed, the averaging window size is incremented and kept unchanged until further incrementing. Average values are calculated from the original signal data-points, according to the averaging window size. This technique does not change the discreteness level, or information density of the recorded data, and no points in the electropherogram are lost. The result of this procedure


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is a smoothing of the noise in the electropherograms with no alterations to the shape of the peak. The code of the algorithm is represented in supporting information Annex S-5. The algorithm was tested with simulated repetitive (at different moments of simulated analysis time) step unit functions (Figure 3 A, B, and C) and simulated repetitive Gaussian peaks (Figure 3 D, E and F) following the methodology described in the literature41. Additionally, simulated white noise filtering was investigated (Figure 3 G), Gaussian noise (Figure 3 H) and filtering of simulated electrophoretic spikes (mainly caused by air bubbles) (Figure 3 I).

Figure 3. Smoothing of simulated signals. A, B and C – repetitive step unit functions (baseline at 0 and step at 1.0), window size 10 s, sampling frequency 4.6 Hz. Step position at (A) 30 s, (B) 220.5 s, (C) 602.5 s. D, E and F – Gaussian functions (baseline at 0) a = 1.0, c = 1. Step position at (D) 30 s, (E) 220.5 s, (F) 602.5 s. (G) White noise smoothing (sampling frequency 4.6 Hz), (H) Gaussian noise (sampling frequency 4.6 Hz) smoothing, (I) smoothing of simulated spikes in the electropherogram

Each later step or Gaussian peak is smoothed using bigger averaging window size.

Improvement of sensitivity



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The algorithm that uses original electropherogram and processes it into a smoothed signal was employed in three different ways: (i) real-time processing in Arduino nano microcontroller, (ii) real-time processing in data acquisition software Universal Acquisition and (iii) post-processing in data visualization software Viewer. All alternatives provided identical analytical results stating that this method can be used: (i) in real-time data acquisition in the case of data storage restrictions and (ii) as a post-processing method for later analysis if there are no data storage restrictions. The first alternative is beneficial for the in situ autonomous analytical systems, such as on rovers.7,12,42 The second alternative is beneficial in clinical/ pre-clinical studies, process and quality control and other analytical applications, where data storage is not a concern. When used, the algorithm significantly improves the signal to noise (S/N) ratio of the electropherograms (Figure 4). The improvement of the S/N ratio of peaks, which have higher electrophoretic mobility, was found to be smaller than for those peaks, which migrate slower. This is due to the logarithmic equation used for the determination of averaging window size. Since the peaks of higher electrophoretic migration velocity are narrower and encoded by higher frequency information than low electrophoretic mobility analytes, the optimal averaging window size is lower. This means, that just after the start of the electrophoretic separation, the moving average function must not be used; after some time has passed, it should be used with utmost care so that peak shape would not be altered. After the defined amount of time has passed, the averaging window size is incremented. For K+ ions, which are fundamentally one of the fastest electro-migrating cations (migrate at 283 s) at the current conditions (Fs 4.6 Hz, 13 kV Ltot 59 cm, Leff 47 cm, temperature 40 °C, BGE – 0.5 M acetic acid solution) used, the averaging window size is 16 and TRIS peak, which migrates at mt of 948 s has the averaging window size of 31 points. For varying sampling frequency, capillary length, voltage, or temperature and electroosmotic instability the averaging window sizes are different and they only depend on the apparent analyte velocity. As observed in Figure 4 A, B and C, baseline drift is visible in original and processed electropherograms; therefore, it must be stressed that developed algorithm has no effect on baseline drift. For the compensation of the baseline drift due to temperature fluctuations, a different algorithm has been developed.43 If a uniform averaging window size is used for the whole electropherogram, non-optimal signal filtering is obtained if: (i) the averaging window size is too small, then the noise is still visible in the electropherograms (as demonstrated for moving average, FFT and Savitzky-Golay filters (Figure 4 G, H and I)) and (ii) if the averaging window size is too high, moving average algorithm distorts peaks and corrupts the information (as demonstrated for moving average, FFT and Savitzky-Golay filters (Figure 4 D, E and F)). It was observed that the proposed algorithm filters the noise of the electropherograms well if a higher Fs is used (Figure 4 A, B, and C). The sampling frequency should be selected with care since signal performance degrades at a higher Fs. Particularly for the experimental setup described in this paper, the effective dynamic range (effective resolution) of the detector operated at Fs of 4.6 Hz is 20.9 bits (the range is encoded by 220.9 (1956712) steps, detector operated at Fs of 13 Hz provides effective resolution of 20.7 bit and a detector operated at Fs of 25 Hz provides effective resolution of 20.1 bits.33 The tradeoff between the signal-to-noise ratio over the sampling frequency and averaging should be considered and carefully calculated.


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Figure 4. Visual comparison of original and differently smoothed signals. Electropherograms: (A) collected at a sampling frequency of 4.6 Hz; (B) at 13 Hz; (C) at 25 Hz. Peaks: 1 – K+, 2 – Ca2+, 3 – Na+, 4 – AMP and 5 – TRIS. CE Conditions: 13 kV, 40 °C, Ltot 59 cm, Leff 47 cm, I.D. 50 μm, O.D. 365 μm. Detection: contactless conductivity at 3.3 V square wave of 32 kHz. K+ peak smoothing (D, E, and F) compared to different filters: proposed adaptive averaging, conventional averaging with a window size of 7 and 31, FFT filter with 7 and 31 points and Savitzky-Golay filter with 7 (4 + 3) and 31 (16 + 15) points

Different signal smoothing methods (moving average with the window size of 7 and 31, FFT filter with the window size of 7 and 31 and Savitzky-Golay smoothing method with the window size of 7 and 31) were compared by calculating main peak parameters, including a UV absorbance peak. The electropherograms were smoothed and the parameters (peak height, width and baseline noise) of each peak were measured. The increase of S/N ratio, height change, and width change was calculated, comparing them to original unsmoothed peaks; this is represented in Table 1 (full details represented in supporting information Table S-1). The methods with higher averaging window sizes (W = 31) provided higher S/N gain; however, those methods also distorted the peaks, which are of higher migration velocity. The methods with an averaging window of 7 provided insignificant peak distortions; however, the S/N gain was relatively low. The adaptive moving average method provided insignificant peak distortions and optimal S/N ratio.

Table 1. Comparison of main peak parameters after data processing using different methods



Smoothing method

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Height Width S/N change change increase (%) (%)

Analyte: K+ Original Adaptive averaging Averaging, W=7 Averaging, W=31 FFT, W=7 FFT, W=31 Savitzky-Golay, (4+3) Savitzky-Golay, (16+15) Analyte: TRIS Original Adaptive averaging Averaging, W=7 Averaging, W=31 FFT, W=7 FFT, W=31 Savitzky-Golay, (4+3) Savitzky-Golay, (16+15)

100.0 98.0 97.8 72.0 94.3 54.4 100.0 95.3

100.0 103.0 102.9 128.3 113.4 165.7 107.4 108.9

1.0 4.6 3.0 8.3 3.9 6.9 1.8 5.3

100.0 101.8 112.8 99.0 104.0 90.1 97.3 95.4

100.0 102.9 97.4 110.4 98.8 117.9 100.4 100.8

1.0 11.1 3.4 11.4 4.3 11.4 1.8 5.3

Calibration parameters for each model analyte were calculated (Table 2). The comparison of calibration data using different filtering methods is represented in supporting information Table S-2. The precision of the method used did not exceed 3 % of relative standard deviation. An Insignificant difference in the calibration data between the processed and unprocessed electropherograms was observed. For calibration curves of (i) K+ cations, it was found that the difference was < 0.6 %, (ii) Na+ cations the difference was < 0.1 %, (iii) AMP < 0.2 % and (iv) TRIS < 0.2 %. The difference of R2 for (i) K+ was 0.02 %, (ii) Na+ was 0.17 %, (iii) AMP was 0.014 % and for (iv) TRIS the difference was 0.02 %. These differences can be considered as insignificant and related only to peak integration repeatability. It must be stressed that in the analytical process (sampling, sample preparation, pipetting, sample injection and measurement) errors that are introduced are usually up to two orders higher than calibration curve differences obtained in this work44.

Table 2. Comparison of calibration parameters for different analytes of processed and unprocessed data

Data Analyte K+ Na+ AMP

Unprocessed Equation

R2

y = 0.000185x y = 0.000398x y = 0.001176x

0.9961 0.9948 0.9970

Processed

LOQ (μM) 0.223 0.140 0.107

Equation y = 0.000184x y = 0.000398x y = 0.001174x

LOQ (μM) 0.9964 0.013 0.9965 0.008 0.9969 0.003 R2


S/N increase (times) Fs 4.6 Hz

Fs 13 Hz

Fs 25 Hz

4.6 7.6 7.2

8.3 8.5 13.6

9.8 11.8 16.4

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TRIS


y = 0.001327x

0.9988

0.094

y = 0.001329x

0.9986 0.002

11.1

14.4

22.3

The integrated area of the peaks in the electropherograms are two-dimensional values, while the S/N ratio is a onedimensional value, therefore the increase of LOQ is higher than the increase of the S/N ratio. Such tendency is observed and represented in Table 2. The literature states that the increase of S/N ratio is a square root of averaging window size26. Empirical determination of the increase of the S/N ratio was found slightly higher than the theoretical calculations. This observation can be explained by the fact that electropherograms contain less spectral components than white noise signal, which is typically used in theoretical calculations. For peaks: K+, Na+, AMP, and TRIS, the S/N ratio increased. 4.6, 7.6, 7.2 and 11.1 times at Fs of 4.6 Hz and LOQ decreased 16.8, 16.9, 35.6 and 47.0 times at Fs of 4.6 Hz. The significant decrease of LOQ can be explained by the fact that the peaks, which electro-migrate at slower velocity have more data-points and, are therefore averaged using a higher number of averaging points. Although concentrations at improved LOQ were not investigated, concentration close to the LOQ of TRIS (5 nM) was analyzed using capillary electrophoresis and is represented in supporting information Figure S-7. Although the adaptive smoothing approach has been used in the past for several applications, it has not been applied for capillary electrophoresis or similar separation method since the allowable size of the averaging window for different segments in electrophoretic data is unknown. This research work provides an answer to the main question raised: what is the allowable averaging window for a peak (actual and theoretical) in the electrophoretic data series? Knowing the allowable averaging window for different peaks in the electropherograms’ adaptive (or segmented) smoothing can be applied, resulting in significant sensitivity improvement. In many separations situations exist, when peaks are unseparated indicating overlapping. The averaging method is not directly targeted for resolution of overlapping peaks. However, if overlapped peaks are of a different cutoff frequency, they will be averaged using a different averaging window size, depending on their migration velocity. If overlapped peaks of a similar migration velocity fall into the same averaging window, they will be averaged using the same averaging window size. The developed algorithm is intended for use with portable and autonomous instrumentation, which normally have limited computational capabilities and cannot handle high speed and high-resolution data. In addition to this, the proposed algorithm is suitable not only for C4D detector data, but also for UV (supporting information table S-1 and Figure S-8) and other type detector data or separation methods. As represented in the figure, minor deviations from the original data was observed (peak no. 3 - phospholipase A2 glycosylated forms). This can be explained by the fact that the method, optimized for C4D detector and original UV detector, has a different detection window size. Moreover, the proposed methodology should not be restricted to adaptive FFT low pass, or Savitzky-Golay filtering methods. This paper can be used as a methodological guideline for the development of new smoothing algorithms that require adaptive conditions in capillary electrophoresis, or similar peak migration tendency providing separation methods.

Conclusions The migration velocity adaptive moving average algorithm, which significantly improves the sensitivity of detectors and the electropherograms, was developed. The algorithm improves the signal-to-noise ratio from 4.6 to 11.1 times, and the limit of quantification from 16 to 47 times, a sampling frequency is 4.6 Hz. The algorithm improves signal-toACS Paragon Plus Environment


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noise ratio from 9.8 to 22.3 times, when the sampling frequency is 25 Hz. The algorithm is intended for use of the detector data processing in a portable or autonomous capillary electrophoresis systems.

Acknowledgement This research was funded by a grant (Nr. 09.3.3-LMT-K-712-02-0202) from the Research Council of Lithuania. The authors also want to express the appreciation to: (i) Agilent Technologies (Dr. Gerard Rozing) for donating capillary electrophoresis system HP3DCE. We would like to express our gratitude to Shadeh Ferris-Francis and Nathan Kovarik (CalTech, NASA, JPL, Microdevices and Sensor Systems, Advanced optical and electro-mechanical microsystems). The authors dedicate this work to the Centennial of the restored Baltic States: Estonia, Latvia and Lithuania.


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Figure 1. Representation of signal analysis using STADIA3 software (A) imported electropherogram signal into STADIA3 software: x(j) = xr(j) (j=1,…,J; r=1,…,R). Sampling period ∆ = 0.216 s34. r – the number of the local peak of electrophoresis signal. xr(j) (j=rb, rb+1,…,re); rb is the starting point of xr(j). re – the end point of the xr(j). (B) Calculated estimation of spectral density function Sr(f) of the rth peak and Frcutoff – cutoff frequency of the rth peak 70x28mm (300 x 300 DPI)



Figure 2. Determination of cutoff frequency (A) and averaging window size (B) for peaks 59x21mm (300 x 300 DPI)


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Figure 3. Smoothing of simulated signals. A, B and C – repetitive step unit functions (baseline at 0 and step at 1.0), window size 10 s, sampling frequency 4.6 Hz. Step position at (A) 30 s, (B) 220.5 s, (C) 602.5 s. D, E and F – Gaussian functions (baseline at 0) a = 1.0, c = 1. Step position at (D) 30 s, (E) 220.5 s, (F) 602.5 s. (G) White noise smoothing (sampling frequency 4.6 Hz), (H) Gaussian noise (sampling frequency 4.6 Hz) smoothing, (I) smoothing of simulated spikes in the electropherogram 108x69mm (300 x 300 DPI)



Figure 4. Visual comparison of original and differently smoothed signals. Electropherograms: (A) collected at a sampling frequency of 4.6 Hz; (B) at 13 Hz; (C) at 25 Hz. Peaks: 1 – K+, 2 – Ca2+, 3 – Na+, 4 – AMP and 5 – TRIS. CE Conditions: 13 kV, 40 °C, Ltot 59 cm, Leff 47 cm, I.D. 50 µm, O.D. 365 µm. Detection: contactless conductivity at 3.3 V square wave of 32 kHz. K+ peak smoothing (D, E, and F) compared to different filters: proposed adaptive averaging, conventional averaging with a window size of 7 and 31, FFT filter with 7 and 31 points and Savitzky-Golay filter with 7 (4 + 3) and 31 (16 + 15) points 101x59mm (300 x 300 DPI)


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TOC 42x22mm (600 x 600 DPI)


Capillary Electrophoresis Sensitivity Enhancement Based on Adaptive

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