All-in-One Dual CRISPR-Cas12a (AIOD-CRISPR) Assay: A Case for Rapid, Ultrasensitive and Visual Detection of Novel Coronavirus SARS-CoV-2 and HIV virus at the Point of Care

The recent outbreak of novel Coronavirus (SARS-CoV-2), the causative agent of COVID-19 disease, has spread rapidly all over the world. Human immunodeciency virus (HIV) is another deadly virus and causes acquired immunodeciency syndrome (AIDS). Rapid and early detection of these viruses will facilitate early intervention and prevent disease spread. Here, we present an All-In-One Dual CRISPR-Cas12a (termed "AIOD-CRISPR") assay method for simple, rapid, ultrasensitive, specic, one-pot, and visual detection of coronavirus SARS-CoV- 2 and HIV-1 virus. In our AIOD-CRISPR assay, a pair of crRNAs was introduced to initiate dual CRISPR-Cas12a-based detection and improve both detection sensitivity and uorescence signals. The AIOD-CRISPR assay method was utilized to detect nucleic acids (DNA and RNA) of the SARS-CoV-2 and HIV-1 with a sensitivity of few copies. We validated our AIOD-CRISPR method by using COVID-19 swab samples and obtained consistent results with that of RT-PCR method. More importantly, we successfully demonstrated to use a low- cost hand warmer (~$ 0.3) as an incubator of our AIOD-CRISPR assay and detect COVID-19 patient samples within 20 minutes, enabling an instrument-free, visual detection of COVID-19 at the point of care. Thus, our method has signicant potential for developing next-generation point-of-care molecular diagnostics.

there are ~37.9 million people living with HIV. 3 Rapid and early detection of these deadly viruses plays a critical role in facilitating early intervention and treatment, which, in turn, may reduce disease transmission risk.
Polymerase chain reaction (PCR) method is the most commonly used technology for pathogen nucleic acid detection and has been considered as a "gold standard" for infectious disease diagnostics due to its high sensitivity and speci city. 4,5,6 However, it typically relies on expensive equipment and well-trained personnel, all of which is not suitable for simple, rapid point of care (POC) diagnostic applications. In recent decades, several isothermal ampli cation methods, such as recombinase polymerase ampli cation (RPA) 7 and loop-mediated isothermal ampli cation (LAMP) 8 , have been developed as attractive alternatives to conventional PCR method because of their simplicity, rapidity and low cost. However, there is still a challenge to apply them to develop accurate and reliable POC testing for clinical diagnostics due to undesired non-speci c ampli cation signals (e.g., false-positive). 9,10 Recently, RNA-guided CRISPR/Cas nuclease-based nucleic acid detection has shown great promise for the development of next-generation point of care molecular diagnostics technology due to its high sensitivity, speci city and reliability. 11,12 For example, several Cas nucleases, such as Cas12a, Cas12b and Cas13a, perform strong collateral cleavage activities in which the Cas nucleases activated by crRNAtarget duplex can indiscriminately cleave surrounding non-target single-stranded nucleic acids. 13,14,15,16,17 By combining with RPA pre-ampli cation, Cas13 and Cas12a nucleases have, respectively, been used to develop SHERLOCK (Speci c High-sensitivity Enzymatic Reporter UnLOCKing) system 18 and DETECTR (DNA Endonuclease-Targeted CRISPR Trans Reporter) system 14 for highly sensitive and speci c nucleic acid detection. Apart from the RPA pre-ampli cation method, some CRISPR-Cas-based nucleic acid detection utilized LAMP and PCR pre-ampli cation, such as CRISPR-Cas12b-assisted HOLMESv2 platform and SARS-CoV-2 DNA Endonuclease-Targeted CRISPR Trans Reporter (DETECTR). 16,19 However, these CRISPR-Cas-based nucleic acid detection methods typically require separate nucleic acid pre-ampli cation and multiple manual operations, which undoubtedly complicates the testing procedures and potentially increases the risk of carry-over contaminations due to ampli cation products transferring.
In this study, we report an All-In-One Dual CRISPR-Cas12a (termed "AIOD-CRISPR") assay for simple, rapid, ultrasensitive, speci c, one-pot and visual detection of nucleic acids (DNA and RNA). Dual crRNAs are introduced to initiate highly sensitive dual CRISPR-based nucleic acid detection. In our AIOD-CRISPR assay, all components for nucleic acid ampli cation and CRISPR-based detection are thoroughly mixed in a single, one-pot reaction system and incubated at a single temperature (e.g., 37 °C), eliminating the need for separate pre-ampli cation and transfer of ampli ed product. As application examples, the AIOD-CRISPR assay was used to detect SARS-CoV-2 20 and HIV-1 virus. 21 Since the SARS-CoV-2 and HIV-1 are retroviruses, we evaluated the performance of our AIOD-CRISPR assay by detecting both of their DNA and RNA. The AIOD-CRISPR method was clinically validated using COVID-19 patient samples and a lowcost hand warmer was directly used to as its incubator for instrument-free point of care diagnostics of COVID-19.

Results
AIOD-CRISPR assay system. As shown in Figure 1A, the AIOD-CRISPR assay system uses a pair of Cas12a-crRNA complexes generated by two individual crRNAs to bind two different sites which are close to the recognition sites of primers in the target sequence. The Cas12a-crRNA complexes are rst prepared prior to being adding into the reaction solution containing RPA primers, ssDNA-FQ reporters, recombinase, single-stranded DNA binding protein (SSB), strand-displacement DNA polymerase, and target sequences. When incubating the AIOD-CRISPR reaction system in one pot at ~37°C, the RPA ampli cation is initiated and exposes the binding sites of the Cas12a-crRNA complexes due to the strand displacement. On one hand, when the Cas12a-crRNA complexes bind the target sites, the Cas12a endonuclease is activated and cleaves the ssDNA-FQ reporters, generating strong uorescence signals.
On the other hand, the ampli ed products generated during the RPA continuously trigger CRISPR-Cas12abased collateral cleavage activity. Previous studies 14,17 have demonstrated that the collateral cleavage activity of the CRISPR-Cas12a system is independent of target strand cleavage. Therefore, target sequences for our AIOD-CRISPR assay are not limited by the Cas12a's protospacer adjacent motif (PAM) 22 .
To systematically evaluate our AIOD-CRISPR assay system, we prepared and tested eight reaction systems (reactions # 1-8) with various components ( Figure 1B (i)).. The ssDNA-FQ reporter was a 5 nt oligonucleotide (5'-TTATT-3') labelled by 5' 6-FAM (Fluorescein) uorophore and 3' Iowa Black ® FQ quencher. After incubation at 37°C for 40 min, only reaction # 5 containing target nucleic acid sequence, dual crRNAs, Cas12a, and RPA reaction mixture produced super-bright uorescence signal ( Figure 1B (i)),, which could be directly visualized under a blue LED or UV light illuminator. Surprisingly, even under ambient light conditions without excitation, a color change from orange-yellow to green was directly observed in the reaction tube # 5 by naked eyes. To further verify the speci city of the generated uorescence signal, the assay products (self-probed uorescence reporters) were subjected to denaturing polyacrylamide gel electrophoresis (PAGE). As shown in Figure 1B(ii), a strong band with shorter DNA size was observed only in the lane of reaction # 5, which resulted from the cleaved ssDNA-FQ reporters with strong uorescence signal. In comparison, for other reaction systems, only weak bands with relatively longer DNA sizes were observed in their corresponding lanes, which may be attributed to uorescence quench of the intact uncut ssDNA-FQ reporters. In addition, in real-time uorescence curves, only reaction # 5 showed a signi cantly increased uorescence signal that saturated at 13 min ( Figure 1B(iii)).. Thus, these results show that our AIOD-CRISPR assay provides a simple, rapid, one-pot approach for targetspeci c nucleic acid detection.
Since a previous study reported that RPA ampli cation reaction is initiated after adding MgOAc, 23 we are interested in knowing if nucleic acid ampli cation is e ciently initiated at room temperature during sample preparation in our AIOD-CRISPR assay system. We prepared two AIOD-CRISPR solutions (one positive and one negative) and allowed them to remain at room temperature for 10 min. As shown in Figure S1, no signi cant uorescence change between positive and negative samples was observed in the AIOD-CRISPR systems at room temperature. In comparison, there was an obvious uorescence increase after just one-minute incubation at 37 °C ( Figure S1).. Eventually, the uorescence signal was saturated after 15-min incubation at 37 °C. Therefore, our AIOD-CRISPR assay system is mainly triggered after reaction temperature is elevated to ~37°C.
Optimization of AIOD-CRISPR assay. Collateral cleavage of the ssDNA-FQ reporters by the Cas12a nuclease is triggered by the binding of crRNA to target sites. 13,14 Here, we hypothesize that more binding opportunities can increase the collateral cleavage activity and eventually improve the detection sensitivity. To test our hypothesis, we designed a pair of crRNAs to respectively recognize two different target sites in our AIOD-CRISPR assay. A pUCIDT-AMP plasmid containing 300 bp HIV-1 p24 gene cDNA (p24 plasmid) was used as the target and three different design strategies for primers and crRNAs were investigated (Figure 2A).. As shown in Figure 2B, the AIOD-CRISPR with dual crRNAs (crRNA1+crRNA2) showed slightly higher uorescence signals compared to that with single crRNA2, but much better than that with single crRNA1. In addition, doubling the amount of either crRNA1 or crRNA2 did not bene t the detection e ciency. Furthermore, we evaluated and compared the detection sensitivity of the AIOD-CRISPR system with dual crRNAs and single crRNA. As shown in Figure 2C and D, the AIOD-CRISPR with dual crRNAs was able to consistently detect as low as 1.2 copies of the p24 plasmid templates with improved uorescence, while the AIOD-CRISPR assay with single crRNA2 did not. Thus, by introducing dual crRNAs into the AIOD-CRISPR assay, it does not only increase uorescence signals, but also improve the detection sensitivity.
We further optimized ssDNA-FQ reporters in our AIOD-CRISPR assay because the reporter concentration plays a crucial role in uorescence readout. As shown in Figure S2A, the higher the concentration of the ssDNA-FQ reporters, the stronger the uorescence signal and the shorter the threshold time. As to threshold time and visual detection, the minimal concentration for saturated values was 4 μM ( Figure  S2B-S2D).. Collateral cleavage e ciency of the activated Cas12a nuclease represents an ability to cut ssDNA-FQ reporters around it. 13,14 Thus, increasing the ssDNA-FQ reporter concentration can improve the uorescence signals. In addition, we also investigated the effect of the primer concentration on the AIOD-CRISPR assay. As shown in Figure S3, the optimal concentration of the primers was 0.32 μM. Together, introducing dual crRNAs with an increased ssDNA-FQ reporter concentration enables highly e cient AIOD-CRISPR assay.
HIV-1 detection by AIOD-CRISPR assay. To investigate the sensitivity of the AIOD-CRISPR assay for HIV-1 DNA detection, we rst applied the optimized AIOD-CRISPR assay to detect various copies of HIV-1 p24 plasmid templates (from 1.2× 10 0 to 1.2× 10 5 copies). As shown in Figure 3A, the AIOD-CRISPR could consistently detect as low as 1.2 copies HIV-1 p24 plasmid DNA in both real-time and endpoint visual detection, which was further veri ed by the denaturing PAGE. Although incubated for 40 min, the AIOD-CRISPR assay could detect and identify 1.2 copies of HIV-1 DNA in just 1-min incubation based on the endpoint uorescence intensity ( Figure S4),, which shows that our AIOD-CRISPR assay provides a superfast (few minutes) and ultrasensitive (several copies) detection of nucleic acids.
In addition to detecting arti cial HIV-1 gag RNA, we also evaluated the RT-AIOD-CRISPR's performance using HIV-1 RNA extracted from human plasma samples. As shown in Figure 3C, real-time RT-AIOD-CRISPR assay was able to detect 500 copies of HIV viral RNA within less than 20 min. However, visual RT-AIOD-CRISPR detection took relatively long incubation time (up to 90 min) to achieve the similar sensitivity ( Figure S6A).. The reduced sensitivity of the RT-AIOD-CRISPR for extracted HIV RNA detection may be attributed to either potential inhibitors in the extracts or RNA degradation during extraction. Despite this, the real-time AIOD-CRISPR assay showed a comparable sensitivity compared to real-time RT-PCR assay ( Figure S6B).. SARS-CoV-2 detection by AIOD-CRISPR assay. As shown in Figure 4A, a pUCIDT-AMP plasmid containing 316 nt SARS-CoV-2 N gene cDNA (N plasmid) was rst prepared as the target to develop our AIOD-CRISPR assay. Figure 4B shows that our AIOD-CRISPR assay could detect 1.3 copies of SARS-CoV-2 N plasmids in both real-time and visual detections, offering a rapid and nearly single-molecule level sensitive detection. To evaluate the detection speci city, we tested our AIOD-CRISPR assay using  Figure 4C shows that only the reaction with SARS-CoV-2_PC had the positive signal in both real-time and visual detections, demonstrating that our developed AIOD-CRISPR assay possesses high speci city without cross reactions for non-SARS-CoV-2 targets.
Next, we used T7 promotor-tagged PCR and T7 RNA polymerase to prepare SARS-CoV-2 N gene RNA sequences to develop the RT-AIOD-CRISPR assay ( Figure S7A).. The detection region of the RT-AIOD-CRISPR was veri ed by Sanger sequencing (Figure 7B).. As shown in Figure 4D, the RT-AIOD-CRISPR assay could consistently detect down to 4.6 copies of SARS-CoV-2 N RNA targets in both real-time and visual detections. In addition, Figure 4E shows that the endpoint uorescence intensity after 1 min RT-AIOD-CRISPR reaction was able to identify 4.6 copies of SARS-CoV-2 N RNA. Therefore, our AIOD-CRISPR assay provides an ultrarapid, highly sensitive and speci c method for SARS-CoV-2 detection.
To further demonstrate its point of care diagnostic application, we used a low-cost hand warmer (~$ 0.3 per bag) as the incubator of our AIOD-CRISPR assay and detect COVID-19 patient samples. As shown in Figure 6A, the AIOD-CRISPR assay tubes were directly placed on an air-activated hand warmer without need for any electric incubator. The endpoint uorescence result can be observed by the naked eye under LED light. Figure 6B shows that two SARS-CoV-2-positive samples incubated in the hand warmer bag were visually detected and identi ed within as short as 20 min. The longer the incubation time, the stronger the uoscence signal of the positive samples. Additionally, a similar result was achieved through analyzing the green value of the uorescence images using the ImageJ software ( Figure 6C).. Therefore, our AIOD-CRISPR method provides a simple, rapid and visual approach for SARS-CoV-2 detection and has the potential to develop an instrument-free point of care diagnostics of the COVID-19.

Discussion
The emergence of the new coronavirus SARS-CoV-2, and its rapid spread through many countries, has been labeled as a global health emergency by the WHO. 24 HIV is another deadly retrovirus that has caused deaths of 32 million people since the beginning of the epidemic. 3 Early diagnosis of these severe infections is crucial to prevent the rapid spread of these deadly viruses globally. Nucleic acid ampli cation testing (e.g., PCR/RT-PCR) represents the most sensitive and speci c method for the early detection of the pathogens, 25, 26 but current PCR technology is not suitable for rapid point of care diagnostic application due to the need for specialized laboratory equipment and trained technicians. The limitations of current detection technology represent serious barriers for the real-time monitoring and detection of these highly contagious pathogens to prevent them spreading from person-to-person. Thus, there is an urgent need for a simple, easy-to-use, and inexpensive diagnostic approach.
In this study, we described a simple, rapid, ultrasensitive and highly speci c AIOD-CRISPR assay for the detection of the SARS-CoV-2 and HIV-1 virus. This AIOD-CRISPR assay method is, to the best of our knowledge, the rst system that allows all components to be incubated in one pot for CRISPR-based nucleic acid detection, enabling simple, all-in-one molecular diagnostics without need for separate and complex manual operations. The AIOD-CRISPR assay takes advantage of dual CRISPR-Cas12a-based detection strategy to improve the detection sensitivity and uorescence signals. Importantly, the detection results of the AIOD-CRISPR assay can be directly visualized by the naked eye, signi cantly simplifying the detection process and eliminating the need for separate lateral ow-based detection 19 .
Compared to previously reported CRISPR-based nucleic acid detection methods, 14,16,18,19, 27, 28, 29 our versatile and robust AIOD-CRISPR assay has some distinctive advantages and provides a true single reaction system. In our AIOD-CRISPR assay, the components for both isothermal ampli cation and CRISPR-based detection are prepared in one-pot, completely circumventing the separate pre-ampli cation of target nucleic acids, 14 or physical separation of Cas enzyme. 29 The AIOD-CRISPR assay enables superfast (few minutes), ultrasensitive (few copies), and highly speci c nucleic acid detection. With our AIOD-CRISPR assay, we were able to detect as low as 1.3 copies of DNA targets and 4.6 copies of RNA targets in SARS-CoV-2 detection. Although we incubated our assay system at 37°C for 40 min in our experiment, we demonstrated that the AIOD-CRISPR assay could detect and identify 1.2 copies of HIV-1 DNA and 4.6 copies of SARS-CoV-2 N RNA after just 1-minute incubation ( Figure S4A and 4E).. We attribute the superfast testing speed and ultra-high detection sensitivity of our AIOD-CRISPR assay to: i) the introduction of unique dual CRISPR-Cas12a detection methodology, ii) the increased concentration of ssDNA-FQ reporters, and iii) the combination of RPA ampli cation and CRISPR-Cas12a-based detection. Also, the AIOD-CRISPR assay showed a high speci city in the SARS-CoV-2 detection without any crossinteraction (false positives) with other sequences (e.g., SARS-CoV, MERS-CoV) ( Figure 4C),, which may be due to the nature of the CRIPSR-Cas12a's single-base speci city 30, 31 . Although in this manuscript, we demonstrated only qualitative detection of nucleic acids, we anticipate that our method is able to achieve semi-quantitative detection by reducing its incubation time and quantifying endpoint uorescence intensities. Indeed, as shown in Figure S4A, we demonstrated the feasibility of the semi-quantitative detection of the HIV DNA by incubating the AIOD-CRISPR reaction system for 1 minute. In addition, by adding AMV reverse transcriptase, the AIOD-CRISPR assay can be easily developed as one-step RT-AIOD-CRISPR assay to detect RNA targets such as HIV-1 and SARS-CoV-2 RNAs, which facilitates the CRISPR-Cas12a-based RNA detection without need for the separate preparation of cDNA. To evaluate the validity and clinical applications of our AIOD-CRISPR assay, we adapted it to detect HIV-1 virus in human plasma samples and SARS-CoV-2 virus in nasal swab samples, achieving consistent detection results with that of RT-PCR method. Most importantly, we successfully demonstrated an instrument-free AIOD-CRISPR assay for SARS-CoV-2 detection in clinical samples by using a simple hand warmer.
Further improvement and development are to integrate our AIOD-CRISPR assay into a disposable micro uidics chip platform, 32,33,34,35 enabling fully-integrated, "sample to result", multiplexed detection. On one hand, all reagents of the AIOD-CRISPR assay can be lyophilized and pre-stored in a disposable micro uidic chamber, 36 which eliminates need for cold chains and enables rapid detection outside of a laboratory setting. On the other hand, multiplexing detection can be developed by combining multiplexed micro uidics technology. 37, 38, 39 Symptom of COVID-19 is non-speci c and similar to other respiratory illnesses. 40 Therefore, to enable effective disease treatment and management, it is critical to simultaneously detect and differentiate SARS-CoV-2 and other viral infections (e.g., SARS-CoV, MERS-CoV) by micro uidic-based multiplexed detection with single sample.
Since our AIOD-CRISPR assay generates strong uorescence signals at the endpoint, it is possible to record, analyze and report the detection results by taking advantage of ubiquitous smartphone technology. 41,42,43 The smartphone can be programmed to take uorescence photos, convert the images into uorescence intensity, analyze the data, and report the qualitative/semi-quantitative test results.
Further, the test results can be wirelessly transmitted to a website or remote server 42 and made available together with GPS coordinates to the patient's doctor and public health o cials. This is critical to allow simple, rapid, smart, connected disease diagnostics and tracking.
In summary, the AIOD-CRISPR assay has been demonstrated to be a rapid, all-in-one, isothermal approach for nucleic acid (DNA and RNA) detection with nearly single-molecule level sensitive and single-base speci city. In turn, such simple and robust method has great potential in the future development of a next-generation point of care molecular diagnostics technology for the rapid detection of infectious diseases (e.g., COVID-19) at home or in small clinics. OneStep RT-PCR Enzyme Mix, and 1.0 μL of the viral RNA extracted from HIV-1 plasma control was conducted to amplify the 1057 nt gag sequence. The thermal cycling protocol included 30 min at 50°C for reverse transcription, 15 min at 95°C for initial PCR activation, 35 cycles of the 3-step cycling (1 min at 94°C for denaturation, 1 min at 55°C for annealing, and 1 min at 72°C for extension), and 10 min at 50°C for nal extension. For SARS-CoV-2 N RNA, the PCR system contained 1× SsoAdvanced™ Universal SYBR ® Green PCR Supermix, 0.4 μM of each primer, and 1.0 μL of 1.2× 10 5 copies/μL HIV-1 p24 plasmid solution was used to amplify the 316 nt N sequence. The thermal cycling was 2.5 min at 98°C for initial denaturation, 35 cycles of 15 s at 95°C for denaturation and 30 s at 60°C for annealing and extension. The products of PCR/RT-PCR were all con rmed by agarose gel electrophoresis and Sanger sequencing. Afterwards, the products with the accurate sizes were extracted and puri ed using the Gel Extraction Kit.
In vitro transcription was achieved through incubating the reaction system containing 8 μL of 5× T7 Transcription Buffer, 3 μL each of 100 mM rNTPs, 4 μL of the Enzyme Mix with T7 RNA polymerase, 16 μL of the gel-extracted PCR/RT-PCR products at 37°C for 4 h. Then, the transcription products were treated by DNase (from the TURBO DNA-free TM Kit) to degrading the DNA and the RNA was extracted and puri ed using the RNeasy @ MinElute TM Cleanup Kit. The purity and concentration of the collected RNA were determined using NanoDrop™ One/One C Microvolume UV-Vis Spectrophotometry (Thermo Fisher Scienti c).
OneStep RT-PCR assay. QIAGEN ® OneStep RT-PCR Kit was used for the RT-PCR assay. The primers (FP: 5'-ATTATCAGAAGGAGCCACC-3'; RP: 5'-CATCCTATTTGTTCCTGAAGG-3') for HIV-1 RNA detection were obtained from the reported literature. 44 According to the instruction manual, the OneStep RT-PCR assay (50 μL) contained 1× QIAGEN OneStep RT-PCR Buffer, 400 µM of each dNTP, 600 nM each of primers (FP and RP), 2.0 μL of QIAGEN OneStep RT-PCR Enzyme Mix, 0.8× EvaGreen ® dye, and 5.0 μL of the RNA template solution. The thermal cycling protocol included 30 min at 50°C for reverse transcription, 15 min at 95°C for initial PCR activation step, 35 cycles of the 3-step cycling (30 s at 94°C for denaturation, 30 s at 55°C for annealing, and 1 min at 72 °C for extension), and 10 min at 72°C for nal extension, followed by the melt-curve analysis (from 65 °C to 95 °C with 0.5 °C increment). Real-time OneStep RT-PCR assay was conducted in the CFX96 Touch™ Real-Time PCR Detection System and the plate read was set at the annealing in the 3-step cycling.  Comparison of the all-in-one CRISPR-Cas12a assay using dual crRNAs or single crRNA. (A) The pUCIDT-AMP plasmid containing 300 bp HIV-1 p24 gene cDNA (p24 plasmid) and the sequences of its primers and crRNAs. (B) Real-time uorescence detection of the all-in-one CRISPR-Cas12a assay using dual crRNAs (crRNA1+crRNA2) or single crRNA (crRNA1/crRNA2). Either 2*crRNA1 or 2*crRNA2 means doubling its amount. P, the positive control with 1.2× 103 copies of HIV-1 p24 plasmids. Three replicates were run for each reaction with the plasmid. (C) Sensitivities of the all-in-one CRISPR-Cas12a assays with dual crRNAs (crRNA1+crRNA2) or crRNA2 for the detection of various copies of HIV-1 p24 plasmids. (D) Endpoint uorescence intensity comparisons of the all-in-one CRISPR-Cas12a assays with dual crRNAs (crRNA1+crRNA2) or crRNA2 in three independent experiments. The dashed line indicates the cutoff uorescence intensity which was the average of the NTC plus two standard deviations. NTC, non-template control reaction. Each reaction contained 2 μM ssDNA-FQ. Endpoint uorescence analysis was conducted after 40 min incubation.    NC, the SARS-CoV-2-negative sample. Each measuring was run with three replicates.

Supplementary Files
This is a list of supplementary les associated with this preprint. Click to download.