1
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Song Y, Gao Y, Fang H. Unexpected large charge transfer rate mediated by adenine in twisted DNA structure. Phys Rev E 2024; 109:064412. [PMID: 39020924 DOI: 10.1103/physreve.109.064412] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2023] [Accepted: 04/15/2024] [Indexed: 07/20/2024]
Abstract
DNA exhibits remarkable charge transfer ability, which is crucial for its biological functions and potential electronic applications. The charge transfer process in DNA is widely recognized as primarily mediated by guanine, while the contribution of other nucleobases is negligible. Using the tight-binding models in conjunction with first-principles calculations, we investigated the charge transfer behavior of homogeneous GC and AT pairs. We found that the charge transfer rate of adenine significantly changes. With overstretching, the charge transfer rate of adenine can even surpass that of guanine, by as much as five orders of magnitude at a twist angle of around 26°. Further analysis reveals that it is attributed to the turnover of the relative coupling strength between homogeneous GC and AT base pairs, which is caused by the symmetry exchange between the two highest occupied molecular orbitals of base pairs occurring at different twist angles. Given the high degree of flexibility of DNA in vivo and in vitro conditions, these findings prompt us to reconsider the mechanism of biological functions concerning the charge transfer in DNA molecules and further open the potential of DNA as a biomaterial for electronic applications.
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2
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Demir B, Mohammad H, Anantram MP, Oren EE. DNA-Au (111) interactions and transverse charge transport properties for DNA-based electronic devices. Phys Chem Chem Phys 2023. [PMID: 37309195 DOI: 10.1039/d2cp05009a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
DNA's charge transfer and self-assembly characteristics have made it a hallmark of molecular electronics for the past two decades. A fast and efficient charge transfer mechanism with programmable properties using DNA nanostructures is required for DNA-based nanoelectronic applications and devices. The ability to integrate DNA with inorganic substrates becomes critical in this process. Such integrations may affect the conformation of DNA, altering its charge transport properties. Thus, using molecular dynamics simulations and first-principles calculations in conjunction with Green's function approach, we explore the impact of the Au (111) substrate on the conformation of DNA and analyze its effect on the charge transport. Our results indicate that DNA sequence, leading to its molecular conformation on the Au substrate, is critical to engineer charge transport properties. We demonstrate that DNA fluctuates on a gold substrate, sampling various distinct conformations over time. The energy levels, spatial locations of molecular orbitals and the DNA/Au contact atoms can differ between these distinct conformations. Depending on the sequence, at the HOMO, the charge transmission differs up to 60 times between the top ten conformations. We demonstrate that the relative positions of the nucleobases are critical in determining the conformations and the coupling between orbitals. We anticipate that these results can be extended to other inorganic surfaces and pave the way for understanding DNA-inorganic interface interactions for future DNA-based electronic device applications.
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Affiliation(s)
- Busra Demir
- Department of Materials Science & Nanotechnology Engineering, TOBB University of Economics and Technology, Ankara, Turkey.
- Bionanodesign Laboratory, Department of Biomedical Engineering, TOBB University of Economics and Technology, Ankara, Turkey
- Department of Electrical and Computer Engineering, University of Washington, 98195 Seattle, WA, USA
| | - Hashem Mohammad
- Department of Electrical Engineering, Kuwait University, P. O. Box 5969, Safat 13060, Kuwait
| | - M P Anantram
- Department of Electrical and Computer Engineering, University of Washington, 98195 Seattle, WA, USA
| | - Ersin Emre Oren
- Department of Materials Science & Nanotechnology Engineering, TOBB University of Economics and Technology, Ankara, Turkey.
- Bionanodesign Laboratory, Department of Biomedical Engineering, TOBB University of Economics and Technology, Ankara, Turkey
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3
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Aggarwal A, Sahoo AK, Bag S, Kaliginedi V, Jain M, Maiti PK. Fine-tuning the DNA conductance by intercalation of drug molecules. Phys Rev E 2021; 103:032411. [PMID: 33862831 DOI: 10.1103/physreve.103.032411] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2020] [Accepted: 03/08/2021] [Indexed: 11/07/2022]
Abstract
In this work we study the structure-transport property relationships of small ligand intercalated DNA molecules using a multiscale modeling approach where extensive ab initio calculations are performed on numerous MD-simulated configurations of dsDNA and dsDNA intercalated with two different intercalators, ethidium and daunomycin. DNA conductance is found to increase by one order of magnitude upon drug intercalation due to the local unwinding of the DNA base pairs adjacent to the intercalated sites, which leads to modifications of the density of states in the near-Fermi-energy region of the ligand-DNA complex. Our study suggests that the intercalators can be used to enhance or tune the DNA conductance, which opens new possibilities for their potential applications in nanoelectronics.
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Affiliation(s)
- Abhishek Aggarwal
- Center for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - Anil Kumar Sahoo
- Center for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - Saientan Bag
- Center for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - Veerabhadrarao Kaliginedi
- Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560012, India
| | - Manish Jain
- Center for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - Prabal K Maiti
- Center for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
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4
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Aggarwal A, Vinayak V, Bag S, Bhattacharyya C, Waghmare UV, Maiti PK. Predicting the DNA Conductance Using a Deep Feedforward Neural Network Model. J Chem Inf Model 2020; 61:106-114. [PMID: 33320660 DOI: 10.1021/acs.jcim.0c01072] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
Double-stranded DNA (dsDNA) has been established as an efficient medium for charge migration, bringing it to the forefront of the field of molecular electronics and biological research. The charge migration rate is controlled by the electronic couplings between the two nucleobases of DNA/RNA. These electronic couplings strongly depend on the intermolecular geometry and orientation. Estimating these electronic couplings for all the possible relative geometries of molecules using the computationally demanding first-principles calculations requires a lot of time and computational resources. In this article, we present a machine learning (ML)-based model to calculate the electronic coupling between any two bases of dsDNA/dsRNA and bypass the computationally expensive first-principles calculations. Using the Coulomb matrix representation which encodes the atomic identities and coordinates of the DNA base pairs to prepare the input dataset, we train a feedforward neural network model. Our neural network (NN) model can predict the electronic couplings between dsDNA base pairs with any structural orientation with a mean absolute error (MAE) of less than 0.014 eV. We further use the NN-predicted electronic coupling values to compute the dsDNA/dsRNA conductance.
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Affiliation(s)
- Abhishek Aggarwal
- Center for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - Vinayak Vinayak
- Undergraduate Program, Indian Institute of Science, Bangalore 560012, India
| | - Saientan Bag
- Center for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - Chiranjib Bhattacharyya
- Department of Computer Science and Automation, Indian Institute of Science, Bangalore 560012, India
| | - Umesh V Waghmare
- Theoretical Sciences Unit, Jawaharlal Nehru Center for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
| | - Prabal K Maiti
- Center for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
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5
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What do we know about DNA mechanics so far? Curr Opin Struct Biol 2020; 64:42-50. [DOI: 10.1016/j.sbi.2020.05.010] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2020] [Accepted: 05/17/2020] [Indexed: 12/14/2022]
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6
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Aggarwal A, Bag S, Venkatramani R, Jain M, Maiti PK. Multiscale modelling reveals higher charge transport efficiencies of DNA relative to RNA independent of mechanism. NANOSCALE 2020; 12:18750-18760. [PMID: 32970051 DOI: 10.1039/d0nr02382e] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
In this study, we compare the charge transport properties of multiple double-stranded (ds)RNA sequences with corresponding dsDNA sequences. Recent studies have presented a contradictory picture of relative charge transport efficiencies in A-form DNA : RNA hybrids and dsDNA. Using a multiscale modelling framework, we compute conductance of dsDNA and dsRNA using Landauer formalism in the coherent limit and Marcus-Hush theory in the incoherent limit. We find that dsDNA conducts better than dsRNA in both the charge transport regimes. Our analysis shows that the structural differences in the twist angle and slide of dsDNA and dsRNA are the main reasons behind the higher conductance of dsDNA in the incoherent hopping regime. In the coherent limit however, for the same base pair length, the conductance of dsRNA is higher than that of dsDNA for the morphologies where dsRNA has a smaller end-to-end length relative to that of dsDNA.
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Affiliation(s)
- Abhishek Aggarwal
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India.
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7
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Bag S, Aggarwal A, Maiti PK. Machine Learning Prediction of Electronic Coupling between the Guanine Bases of DNA. J Phys Chem A 2020; 124:7658-7664. [DOI: 10.1021/acs.jpca.0c04368] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Affiliation(s)
- Saientan Bag
- Center for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - Abhishek Aggarwal
- Center for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - Prabal K. Maiti
- Center for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
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Shepherd JW, Greenall RJ, Probert M, Noy A, Leake M. The emergence of sequence-dependent structural motifs in stretched, torsionally constrained DNA. Nucleic Acids Res 2020; 48:1748-1763. [PMID: 31930331 PMCID: PMC7038985 DOI: 10.1093/nar/gkz1227] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2019] [Revised: 12/16/2019] [Accepted: 12/20/2019] [Indexed: 11/26/2022] Open
Abstract
The double-helical structure of DNA results from canonical base pairing and stacking interactions. However, variations from steady-state conformations resulting from mechanical perturbations in cells have physiological relevance but their dependence on sequence remains unclear. Here, we use molecular dynamics simulations showing sequence differences result in markedly different structural motifs upon physiological twisting and stretching. We simulate overextension on different sequences of DNA ((AA)12, (AT)12, (CC)12 and (CG)12) with supercoiling densities at 200 and 50 mM salt concentrations. We find that DNA denatures in the majority of stretching simulations, surprisingly including those with over-twisted DNA. GC-rich sequences are observed to be more stable than AT-rich ones, with the specific response dependent on the base pair order. Furthermore, we find that (AT)12 forms stable periodic structures with non-canonical hydrogen bonds in some regions and non-canonical stacking in others, whereas (CG)12 forms a stacking motif of four base pairs independent of supercoiling density. Our results demonstrate that 20-30% DNA extension is sufficient for breaking B-DNA around and significantly above cellular supercoiling, and that the DNA sequence is crucial for understanding structural changes under mechanical stress. Our findings have important implications for the activities of protein machinery interacting with DNA in all cells.
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Affiliation(s)
- Jack W Shepherd
- Department of Physics, University of York, York YO10 5DD, UK
| | | | | | - Agnes Noy
- Department of Physics, University of York, York YO10 5DD, UK
| | - Mark C Leake
- Department of Physics, University of York, York YO10 5DD, UK
- Department of Biology, University of York, York,YO10 5NG, UK
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Liu Y, Ren X, He L. A DFT study of energetic and structural properties of a full turn of A-form DNA under relaxed and stretching conditions. J Chem Phys 2019; 151:215102. [DOI: 10.1063/1.5129716] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Affiliation(s)
- Yue Liu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, Anhui, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, Anhui, China
| | - Xinguo Ren
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, Anhui, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, Anhui, China
| | - Lixin He
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, Anhui, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, Anhui, China
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Sahoo AK, Bagchi B, Maiti PK. Understanding enhanced mechanical stability of DNA in the presence of intercalated anticancer drug: Implications for DNA associated processes. J Chem Phys 2019; 151:164902. [PMID: 31675856 DOI: 10.1063/1.5117163] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
Most of the anticancer drugs bind to double-stranded DNA (dsDNA) by intercalative-binding mode. Although experimental studies have become available recently, a molecular-level understanding of the interactions between the drug and dsDNA that lead to the stability of the intercalated drug is lacking. Of particular interest are the modifications of the mechanical properties of dsDNA observed in experiments. The latter could affect many biological functions, such as DNA transcription and replication. Here, we probe, via all-atom molecular dynamics (MD) simulations, the change in the mechanical properties of intercalated drug-DNA complexes for two intercalators, daunomycin and ethidium. We find that, upon drug intercalation, the stretch modulus of DNA increases significantly, whereas its persistence length and bending modulus decrease. Steered MD simulations reveal that it requires higher forces to stretch the intercalated dsDNA complexes than the normal dsDNA. Adopting various pulling protocols to study force-induced DNA melting, we find that the dissociation of dsDNA becomes difficult in the presence of intercalators. The results obtained here provide a plausible mechanism of function of the anticancer drugs, i.e., via altering the mechanical properties of DNA. We also discuss long-time consequences of using these drugs, which require further in vivo investigations.
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Affiliation(s)
- Anil Kumar Sahoo
- Center for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - Biman Bagchi
- Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, India
| | - Prabal K Maiti
- Center for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
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Bag S, Maiti PK. Tuning molecular fluctuation to boost the conductance in DNA based molecular wires. Phys Chem Chem Phys 2019; 21:23514-23520. [PMID: 31617554 DOI: 10.1039/c9cp03589c] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
Inherent molecular fluctuations are known to have a significant influence on the charge transport properties of biomolecules like DNA, PNA and proteins. In this work, we show ways to control these fluctuations and further demonstrate their use to enhance the conductance of two widely studied molecular wires, namely dsDNA (DNA) and G4 Quadruplex (G4-Quad). We quantify the molecular fluctuation in terms of the root mean square deviation (RMSD) of the molecule. In the case of DNA, we use temperature to control the fluctuations, while in the case of G4-Quad the fluctuations are tuned by the ions inside the pore. The electronic coupling between the bases of dsDNA and G4-Quad, which measures the conductance of these molecular wires, shows a non-monotonic behaviour with the increase in fluctuation. We find values of fluctuation which give rise to maximum electronic coupling and hence high conductivity for both the cases. In the case of DNA, these optimal fluctuations (∼2.5 Å) are achieved at a temperature of 210 K, which gives rise to an electronic coupling of 0.135 eV between the DNA bases. The optimal fluctuations in G4-Quad are achieved (∼7 Å) in a 4 base pair long system with 2 Na+ ions inside the pore, giving rise to an electronic coupling of 0.09 eV.
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Affiliation(s)
- Saientan Bag
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bengaluru, Karnataka, India.
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12
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DNA partitions into triplets under tension in the presence of organic cations, with sequence evolutionary age predicting the stability of the triplet phase. Q Rev Biophys 2018; 50:e15. [PMID: 29233227 DOI: 10.1017/s0033583517000130] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
Using atomistic simulations, we show the formation of stable triplet structure when particular GC-rich DNA duplexes are extended in solution over a timescale of hundreds of nanoseconds, in the presence of organic salt. We present planar-stacked triplet disproportionated DNA (Σ DNA) as a possible solution phase of the double helix under tension, subject to sequence and the presence of stabilising co-factors. Considering the partitioning of the duplexes into triplets of base pairs as the first step of operation of recombinase enzymes like RecA, we emphasise the structure-function relationship in Σ DNA. We supplement atomistic calculations with thermodynamic arguments to show that codons for 'phase 1' amino acids (those appearing early in evolution) are more likely than a lower entropy GC-rich sequence to form triplets under tension. We further observe that the four amino acids supposed (in the 'GADV world' hypothesis) to constitute the minimal set to produce functional globular proteins have the strongest triplet-forming propensity within the phase 1 set, showing a series of decreasing triplet propensity with evolutionary newness. The weak form of our observation provides a physical mechanism to minimise read frame and recombination alignment errors in the early evolution of the genetic code.
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Aggarwal A, Bag S, Maiti PK. Remarkable similarity of force induced dsRNA conformational changes to stretched dsDNA and their detection using electrical measurements. Phys Chem Chem Phys 2018; 20:28920-28928. [DOI: 10.1039/c8cp03574a] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
We show the emergence of S-RNA under stretching in analogy to S-DNA and propose a method for its detection using electrical measurement.
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14
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Garai A, Mogurampelly S, Bag S, Maiti PK. Overstretching of B-DNA with various pulling protocols: Appearance of structural polymorphism and S-DNA. J Chem Phys 2017; 147:225102. [DOI: 10.1063/1.4991862] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Affiliation(s)
- Ashok Garai
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
- Department of Physics, The LNM Institute of Information Technology, Jamdoli, Jaipur 302031, India
| | - Santosh Mogurampelly
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - Saientan Bag
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - Prabal K. Maiti
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
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Zhang S, Qu LJ, Suo T, Liu Z, Yan D. Multiple transitions between various ordered and disordered states of a helical polymer under stretching. J Chem Phys 2017; 146:174904. [DOI: 10.1063/1.4982757] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
Affiliation(s)
| | - Li-Jian Qu
- Institute of Disaster Prevention, Sanhe, Hebei 101601, China
| | - Tongchuan Suo
- College of Pharmaceutical Engineering of Traditional Chinese Medicine, Tianjin University of Traditional Chinese Medicine, Tianjin 300193, China
| | - Zhenxing Liu
- Department of Physics, Beijing Normal University, Beijing 100875, China
| | - Dadong Yan
- Department of Physics, Beijing Normal University, Beijing 100875, China
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Beall E, Ulku S, Liu C, Wierzbinski E, Zhang Y, Bae Y, Zhang P, Achim C, Beratan DN, Waldeck DH. Effects of the Backbone and Chemical Linker on the Molecular Conductance of Nucleic Acid Duplexes. J Am Chem Soc 2017; 139:6726-6735. [PMID: 28434220 DOI: 10.1021/jacs.7b02260] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
Scanning tunneling microscope break junction measurements are used to examine how the molecular conductance of nucleic acids depends on the composition of their backbone and the linker group to the electrodes. Molecular conductances of 10 base pair long homoduplexes of DNA, aeg-PNA, γ-PNA, and a heteroduplex of DNA/aeg-PNA with identical nucleobase sequence were measured. The molecular conductance was found to vary by 12 to 13 times with the change in backbone. Computational studies show that the molecular conductance differences between nucleic acids of different backbones correlate with differences in backbone structural flexibility. The molecular conductance was also measured for duplexes connected to the electrode through two different linkers, one directly to the backbone and one directly to the nucleobase stack. While the linker causes an order-of-magnitude increase in the overall conductance for a particular duplex, the differences in the electrical conductance with backbone composition are preserved. The highest molecular conductance value, 0.06G0, was measured for aeg-PNA duplexes with a base stack linker. These findings reveal an important new strategy for creating longer and more complex electroactive, nucleic acid assemblies.
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Affiliation(s)
- Edward Beall
- Chemistry Department, University of Pittsburgh , Pittsburgh, Pennsylvania 15260, United States
| | - Selma Ulku
- Chemistry Department, Carnegie Mellon University , Pittsburgh, Pennsylvania 15213, United States
| | - Chaoren Liu
- Chemistry Department, Duke University , Durham, North Carolina 27708, United States
| | - Emil Wierzbinski
- Chemistry Department, University of Pittsburgh , Pittsburgh, Pennsylvania 15260, United States
| | - Yuqi Zhang
- Chemistry Department, Duke University , Durham, North Carolina 27708, United States
| | - Yookyung Bae
- Chemistry Department, Carnegie Mellon University , Pittsburgh, Pennsylvania 15213, United States
| | - Peng Zhang
- Chemistry Department, Duke University , Durham, North Carolina 27708, United States
| | - Catalina Achim
- Chemistry Department, Carnegie Mellon University , Pittsburgh, Pennsylvania 15213, United States
| | - David N Beratan
- Chemistry Department, Duke University , Durham, North Carolina 27708, United States
| | - David H Waldeck
- Chemistry Department, University of Pittsburgh , Pittsburgh, Pennsylvania 15260, United States
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