Determining Sequence-Dependent DNA Oligonucleotide Hybridization and Dehybridization Mechanisms Using Coarse-Grained Molecular Simulation, Markov State Models, and Infrared Spectroscopy

Thermodynamics and Kinetics-Directed Regulation of Nucleic Acid-Based Molecular Recognition

Nucleic acid-based molecular recognition plays crucial roles in various fields like biosensing and disease diagnostics. To achieve optimal detection and analysis, it is essential to regulate the response performance of nucleic acid probes or switches to match specific application requirements by regulating thermodynamics and kinetics properties. However, the impacts of thermodynamics and kinetics theories on recognition performance are sometimes obscure and the relative conclusions are not intuitive. To promote the thorough understanding and rational utilization of thermodynamics and kinetics theories, this review focuses on the landmarks and recent advances of nucleic acid thermodynamics and kinetics and summarizes the nucleic acid thermodynamics and kinetics-based strategies for regulation of nucleic acid-based molecular recognition. This work hopes such a review can provide reference and guidance for the development and optimization of nucleic acid probes and switches in the future, as well as for advancements in other nucleic acid-related fields.

Simulation-Guided Rational Design of DNA Walker-Based Theranostic Platform

Biomolecule-functionalized nanoparticles represent a type of promising biomaterials in biomedical applications owing to their excellent biocompatibility and versatility. DNA-based reactions on nanoparticles have enabled emerging applications including intelligent biosensors, drug delivery, and biomimetic devices. Among the reactions, strand hybridization is the critical step to control the sensitivity and specificity of biosensing, and the efficiency of drug delivery. However, a comprehensive understanding of DNA hybridization on nanoparticles is still lacking, which may differ from the process in homogeneous solutions. To address this limitation, coarse-grained model-based molecular dynamic simulation is harnessed to disclose the critical factors involved in intermolecular hybridization. Based on simulation guidance, DNA walker-based smart theranostic platform (DWTP) based on "on-particle" hybridization is developed, showing excellent consistency with simulation. DWTP is successfully applied for highly sensitive miRNA 21 detection and tumor-specific miRNA 21 imaging, driven by tumor-endogenous APE 1 enzyme. It enables the precise release of antisense oligonucleotide triggered by tumor-endogenous dual-switch miRNA 21 and APE 1, facilitating effective gene silencing therapy with high biosafety. The simulation of "on-particle" DNA hybridization has improved the corresponding biosensing performance and the release efficiency of therapeutic agents, representing a conceptually new approach for DNA-based device design.

Atomistic simulations of RNA duplex thermal denaturation: Sequence- and forcefield-dependence

Double-stranded RNA is the end-product of template-based replication, and is also the functional state of some biological RNAs. Similarly to proteins and DNA, they can be denatured by temperature, with important physiological and technological implications. Here, we use an in silico strategy to probe the thermal denaturation of RNA duplexes. Following previous results that were obtained on a few different duplexes, and which nuanced the canonical 2-state picture of nucleic acid denaturation, we here specifically address three different aspects that greatly improve our description of the temperature-induced dsRNA separation. First, we investigate the effect of the spatial distribution of weak and strong base-pairs among the duplex sequence. We show that the deviations from the two-state dehybridization mechanism are more pronounced when a strong core is flanked with weak extremities, while duplexes with a weak core but strong extremities exhibit a two-state behavior, which can be explained by the key role played by base fraying. This was later verified by generating artificial hairpin or circular states containing one or two locked duplex extremities, which results in an important reinforcement of the entire HB structure of the duplex and higher melting temperatures. Finally, we demonstrate that our results are little sensitive to the employed combination of RNA and water forcefields. The trends in thermal stability among the different sequences as well as the observed unfolding mechanisms (and the deviations from a two-state scenario) remain the same regardless of the employed atomistic models. However, our study points to possible limitations of recent reparametrizations of the Amber RNA forcefield, which sometimes results in duplexes that readily denature under ambient conditions, in contradiction with available experimental results.

Transient states during the annealing of mismatched and bulged oligonucleotides

Oligonucleotide hybridization is crucial in various biological, prebiotic and nanotechnological processes, including gene regulation, non-enzymatic primer extension and DNA nanodevice assembly. Although extensive research has focused on the thermodynamics and kinetics of nucleic acid hybridization, the behavior of complex mixtures and the outcome of competition for target binding remain less well understood. In this study, we investigate the impact of mismatches and bulges in a 12 bp DNA or RNA duplex on its association (kon) and dissociation (koff) kinetics. We find that such defects have relatively small effects on the association kinetics, while the dissociation kinetics vary in a position-dependent manner by up to 6 orders of magnitude. Building upon this observation, we explored a competition scenario involving multiple oligonucleotides, and observed a transient low specificity of probe hybridization to fully versus partially complementary targets in solution. We characterize these long-lived metastable states and their evolution toward equilibrium, and show that sufficiently long-lived mis-paired duplexes can serve as substrates for prebiotically relevant chemical copying reactions. Our results suggest that transient low accuracy states may spontaneously emerge within all complex nucleic acid systems comprising a large enough number of competing strands, with potential repercussions for gene regulation in the realm of modern biology and the prebiotic preservation of genetic information.

Site specifically probing the unfolding process of human telomere i-motif DNA using vibrationally enhanced alkynyl stretch

The microscopic unfolding process of a cytosine-rich DNA forming i-motif by hemi-protonated base pairs is related to gene regulation. However, the detailed thermal unfolding mechanism and the protonation/deprotonation status of site-specific cytosine in DNA in a physiological environment are still obscure. To address this issue, a vibration-enhanced CC probe tagged on 5'E terminal cytosine of human telomere i-motif DNA was examined using linear and nonlinear infrared (IR) spectroscopies and quantum-chemistry calculations. The CC probe extended into the major groove of the i-motif was found using nonlinear IR results only to introduce a minor steric effect on both steady-state structure and local structure dynamics; however, its IR absorption profile effectively reports the cleavage of the hemi-protonated base pair of C1-C13 upon the unfolding with C1 remaining protonated. The temperature mid-point (Tm) of the local transition reported using the CC tag was slightly lower than the Tm of global transition, and the enthalpy of the former exceeds 60% of the global transition. It is shown that the base-pair unraveling is noncooperative, with outer base pairs breaking first and being likely the rate limiting step. Our results offered an in-depth understanding of the macroscopic unfolding characteristics of the i-motif DNA and provided a nonlinear IR approach to monitoring the local structural transition and dynamics of DNA and its complexes.

Molecular insight into how the position of an abasic site modifies DNA duplex stability and dynamics

Local perturbations to DNA base-pairing stability from lesions and chemical modifications can alter the stability and dynamics of an entire oligonucleotide. End effects may cause the position of a disruption within a short duplex to influence duplex stability and structural dynamics, yet this aspect of nucleic acid modifications is often overlooked. We investigate how the position of an abasic site (AP site) impacts the stability and dynamics of short DNA duplexes. Using a combination of steady-state and time-resolved spectroscopy and molecular dynamics simulations, we unravel an interplay between AP-site position and nucleobase sequence that controls energetic and dynamic disruption to the duplex. The duplex is disrupted into two segments by an entropic barrier for base-pairing on each side of the AP site. The barrier induces fraying of the short segment when an AP site is near the termini. Shifting the AP site inward promotes a transition from short-segment fraying to fully encompassing the barrier into the thermodynamics of hybridization, leading to further destabilization of the duplex. Nucleobase sequence determines the length scale for this transition by tuning the barrier height and base-pair stability of the short segment, and certain sequences enable out-of-register base-pairing to minimize the barrier height.

Biomolecular infrared spectroscopy: making time for dynamics

Time resolved infrared spectroscopy of biological molecules has provided a wealth of information relating to structural dynamics, conformational changes, solvation and intermolecular interactions. Challenges still exist however arising from the wide range of timescales over which biological processes occur, stretching from picoseconds to minutes or hours. Experimental methods are often limited by vibrational lifetimes of probe groups, which are typically on the order of picoseconds, while measuring an evolving system continuously over some 18 orders of magnitude in time presents a raft of technological hurdles. In this Perspective, a series of recent advances which allow biological molecules and processes to be studied over an increasing range of timescales, while maintaining ultrafast time resolution, will be reviewed, showing that the potential for real-time observation of biomolecular function draws ever closer, while offering a new set of challenges to be overcome.

Thermodynamics and kinetics of DNA and RNA dinucleotide hybridization to gaps and overhangs

Hybridization of short nucleic acid segments (<4 nt) to single-strand templates occurs as a critical intermediate in processes such as nonenzymatic nucleic acid replication and toehold-mediated strand displacement. These templates often contain adjacent duplex segments that stabilize base pairing with single-strand gaps or overhangs, but the thermodynamics and kinetics of hybridization in such contexts are poorly understood because of the experimental challenges of probing weak binding and rapid structural dynamics. Here we develop an approach to directly measure the thermodynamics and kinetics of DNA and RNA dinucleotide dehybridization using steady-state and temperature-jump infrared spectroscopy. Our results suggest that dinucleotide binding is stabilized through coaxial stacking interactions with the adjacent duplex segments as well as from potential noncanonical base-pairing configurations and structural dynamics of gap and overhang templates revealed using molecular dynamics simulations. We measure timescales for dissociation ranging from 0.2-40 μs depending on the template and temperature. Dinucleotide hybridization and dehybridization involve a significant free energy barrier with characteristics resembling that of canonical oligonucleotides. Together, our work provides an initial step for predicting the stability and kinetics of hybridization between short nucleic acid segments and various templates.

Molecular insight into how the position of an abasic site and its sequence environment influence DNA duplex stability and dynamics

Local perturbations to DNA base-pairing stability from lesions and chemical modifications can alter the stability and dynamics of an entire oligonucleotide. End effects may cause the position of a disruption within a short duplex to influence duplex stability and structural dynamics, yet this aspect of nucleic acid modifications is often overlooked. We investigate how the position of an abasic site (AP site) impacts the stability and dynamics of short DNA duplexes. Using a combination of steady-state and time-resolved spectroscopy and molecular dynamics simulations, we unravel an interplay between AP-site position and nucleobase sequence that controls energetic and dynamic disruption to the duplex. The duplex is disrupted into two segments by an entropic barrier for base pairing on each side of the AP site. The barrier induces fraying of the short segment when an AP site is near the termini. Shifting the AP site inward promotes a transition from short-segment fraying to fully encompassing the barrier into the thermodynamics of hybridization, leading to further destabilization the duplex. Nucleobase sequence determines the length scale for this transition by tuning the barrier height and base-pair stability of the short segment, and certain sequences enable out-of-register base pairing to minimize the barrier height.

Toward a Molecular Mechanism of Complementary RNA Duplexes Denaturation

RNA duplexes are relatively rare but play very important biological roles. As an end-product of template-based RNA replication, they also have key implications for hypothetical primitive forms of life. Unless they are specifically separated by enzymes, these duplexes denature upon a temperature increase. However, mechanistic and kinetic aspects of RNA (and DNA) duplex thermal denaturation remain unclear at the microscopic level. We propose an in silico strategy that probes the thermal denaturation of RNA duplexes and allows for an extensive conformational space exploration along a wide temperature range with atomistic precision. We show that this approach first accounts for the strong sequence and length dependence of the duplexes melting temperature, reproducing the trends seen in the experiments and predicted by nearest-neighbor models. The simulations are then instrumental at providing a molecular picture of the temperature-induced strand separation. The textbook canonical "all-or-nothing" two-state model, very much inspired by the protein folding mechanism, can be nuanced. We demonstrate that a temperature increase leads to significantly distorted but stable structures with extensive base-fraying at the extremities, and that the fully formed duplexes typically do not form around melting. The duplex separation therefore appears as much more gradual than commonly thought.

Computational Modeling of DNA 3D Structures: From Dynamics and Mechanics to Folding

DNA carries the genetic information required for the synthesis of RNA and proteins and plays an important role in many processes of biological development. Understanding the three-dimensional (3D) structures and dynamics of DNA is crucial for understanding their biological functions and guiding the development of novel materials. In this review, we discuss the recent advancements in computer methods for studying DNA 3D structures. This includes molecular dynamics simulations to analyze DNA dynamics, flexibility, and ion binding. We also explore various coarse-grained models used for DNA structure prediction or folding, along with fragment assembly methods for constructing DNA 3D structures. Furthermore, we also discuss the advantages and disadvantages of these methods and highlight their differences.

Direct monitoring of the thermodynamics and kinetics of DNA and RNA dinucleotide dehybridization from gaps and overhangs

Hybridization of short nucleic acid segments (<4 nucleotides) to single-strand templates occurs as a critical intermediate in processes such as non-enzymatic nucleic acid replication and toehold-mediated strand displacement. These templates often contain adjacent duplex segments that stabilize base pairing with single-strand gaps or overhangs, but the thermodynamics and kinetics of hybridization in such contexts are poorly understood due to experimental challenges of probing weak binding and rapid structural dynamics. Here we develop an approach to directly measure the thermodynamics and kinetics of DNA and RNA dinucleotide dehybridization using steady-state and temperature-jump infrared spectroscopy. Our results suggest that dinucleotide binding is stabilized through coaxial stacking interactions with the adjacent duplex segments as well as from potential non-canonical base pairing configurations and structural dynamics of gap and overhang templates revealed using molecular dynamics simulations. We measure timescales for dissociation ranging from 0.2 to 40 µs depending on the template and temperature. Dinucleotide hybridization and dehybridization involves a significant free energy barrier with characteristics resembling that of canonical oligonucleotides. Together, our work provides an initial step for predicting the stability and kinetics of hybridization between short nucleic acid segments and various templates.

Girsanov Reweighting Enhanced Sampling Technique (GREST): On-the-Fly Data-Driven Discovery of and Enhanced Sampling in Slow Collective Variables

Molecular dynamics simulations of microscopic phenomena are limited by the short integration time steps which are required for numerical stability but which limit the practically achievable simulation time scales. Collective variable (CV) enhanced sampling techniques apply biases to predefined collective coordinates to promote barrier crossing, phase space exploration, and sampling of rare events. The efficacy of these techniques is contingent on the selection of good CVs correlated with the molecular motions governing the long-time dynamical evolution of the system. In this work, we introduce Girsanov Reweighting Enhanced Sampling Technique (GREST) as an adaptive sampling scheme that interleaves rounds of data-driven slow CV discovery and enhanced sampling along these coordinates. Since slow CVs are inherently dynamical quantities, a key ingredient in our approach is the use of both thermodynamic and dynamical Girsanov reweighting corrections for rigorous estimation of slow CVs from biased simulation data. We demonstrate our approach on a toy 1D 4-well potential, a simple biomolecular system alanine dipeptide, and the Trp-Leu-Ala-Leu-Leu (WLALL) pentapeptide. In each case GREST learns appropriate slow CVs and drives sampling of all thermally accessible metastable states starting from zero prior knowledge of the system. We make GREST accessible to the community via a publicly available open source Python package.

Disruption of energetic and dynamic base pairing cooperativity in DNA duplexes by an abasic site

DNA duplex stability arises from cooperative interactions between multiple adjacent nucleotides that favor base pairing and stacking when formed as a continuous stretch rather than individually. Lesions and nucleobase modifications alter this stability in complex manners that remain challenging to understand despite their centrality to biology. Here, we investigate how an abasic site destabilizes small DNA duplexes and reshapes base pairing dynamics and hybridization pathways using temperature-jump infrared spectroscopy and coarse-grained molecular dynamics simulations. We show how an abasic site splits the cooperativity in a short duplex into two segments, which destabilizes small duplexes as a whole and enables metastable half-dissociated configurations. Dynamically, it introduces an additional barrier to hybridization by constraining the hybridization mechanism to a step-wise process of nucleating and zipping a stretch on one side of the abasic site and then the other.

Modeling the Infrared Spectroscopy of Oligonucleotides with 13C Isotope Labels

The carbonyl stretching modes have been widely used in linear and two-dimensional infrared (IR) spectroscopy to probe the conformation, interaction, and biological functions of nucleic acids. However, due to their universal appearance in nucleobases, the IR absorption bands of nucleic acids are often highly congested in the 1600-1800 cm^-1 region. Following the fruitful applications in proteins, ¹³C isotope labels have been introduced to the IR measurements of oligonucleotides to reveal their site-specific structural fluctuations and hydrogen bonding conditions. In this work, we combine recently developed frequency and coupling maps to develop a theoretical strategy that models the IR spectra of oligonucleotides with ¹³C labels directly from molecular dynamics simulations. We apply the theoretical method to nucleoside 5'-monophosphates and DNA double helices and demonstrate how elements of the vibrational Hamiltonian determine the spectral features and their changes upon isotope labeling. Using the double helices as examples, we show that the calculated IR spectra are in good agreement with experiments and the ¹³C isotope labeling technique can potentially be applied to characterize the stacking configurations and secondary structures of nucleic acids.

Chasing collective variables using temporal data-driven strategies

The convergence of free-energy calculations based on importance sampling depends heavily on the choice of collective variables (CVs), which in principle, should include the slow degrees of freedom of the biological processes to be investigated. Autoencoders (AEs), as emerging data-driven dimension reduction tools, have been utilised for discovering CVs. AEs, however, are often treated as black boxes, and what AEs actually encode during training, and whether the latent variables from encoders are suitable as CVs for further free-energy calculations remains unknown. In this contribution, we review AEs and their time-series-based variants, including time-lagged AEs (TAEs) and modified TAEs, as well as the closely related model variational approach for Markov processes networks (VAMPnets). We then show through numerical examples that AEs learn the high-variance modes instead of the slow modes. In stark contrast, time series-based models are able to capture the slow modes. Moreover, both modified TAEs with extensions from slow feature analysis and the state-free reversible VAMPnets (SRVs) can yield orthogonal multidimensional CVs. As an illustration, we employ SRVs to discover the CVs of the isomerizations of N-acetyl-N'-methylalanylamide and trialanine by iterative learning with trajectories from biased simulations. Last, through numerical experiments with anisotropic diffusion, we investigate the potential relationship of time-series-based models and committor probabilities.

Computer Aided Development of Nucleic Acid Applications in Nanotechnologies

Utilization of nucleic acids (NAs) in nanotechnologies and nanotechnology-related applications is a growing field with broad application potential, ranging from biosensing up to targeted cell delivery. Computer simulations are useful techniques that can aid design and speed up development in this field. This review focuses on computer simulations of hybrid nanomaterials composed of NAs and other components. Current state-of-the-art molecular dynamics simulations, empirical force fields (FFs), and coarse-grained approaches for the description of deoxyribonucleic acid and ribonucleic acid are critically discussed. Challenges in combining biomacromolecular and nanomaterial FFs are emphasized. Recent applications of simulations for modeling NAs and their interactions with nano- and biomaterials are overviewed in the fields of sensing applications, targeted delivery, and NA templated materials. Future perspectives of development are also highlighted.

Simulation-Assisted Localized DNA Logical Circuits for Cancer Biomarkers Detection and Imaging

DNA-based nanodevices equipped with localized modules have been promising probes for biomarker detection. Such devices heavily rely on the intramolecular hybridization reaction. However, there is a lack of mechanistic insights into this reaction that limits the sensing speed and sensitivity. A coarse-grained model is utilized to simulate the intramolecular hybridization of localized DNA circuits (LDCs) not only optimizing the performance, but also providing mechanistic insights into the hybridization reaction. The simulation guided-LDCs enable the detection of multiple biomarkers with high sensitivity and rapid speed showing good consistency with the simulation. Fluorescence assays demonstrate that the simulation-guided LDC shows an enhanced sensitivity up to 9.3 times higher than that of the same probes without localization. The detection limits of ATP, miRNA, and APE1 reach 0.14 mM, 0.68 pM, and 0.0074 U mL^-1 , respectively. The selected LDC is operated in live cells with good success in simultaneously detecting the biomarkers and discriminating between cancer cells and normal cells. LDC is successfully applied to detect the biomarkers in cancer tissues from patients, allowing the discrimination of cancer/adjacent/normal tissues. This work herein presents a design workflow for DNA nanodevices holding great potential for expanding the applications of DNA nanotechnology in diagnostics and therapeutics.

Displacement and dissociation of oligonucleotides during DNA hairpin closure under strain

The hybridization kinetic of an oligonucleotide to its template is a fundamental step in many biological processes such as replication arrest, CRISPR recognition, DNA sequencing, DNA origami, etc. Although single kinetic descriptions exist for special cases of this problem, there are no simple general prediction schemes. In this work, we have measured experimentally, with no fluorescent labelling, the displacement of an oligonucleotide from its substrate in two situations: one corresponding to oligonucleotide binding/unbinding on ssDNA and one in which the oligonucleotide is displaced by the refolding of a dsDNA fork. In this second situation, the fork is expelling the oligonucleotide thus significantly reducing its residence time. To account for our data in these two situations, we have constructed a mathematical model, based on the known nearest neighbour dinucleotide free energies, and provided a good estimate of the residence times of different oligonucleotides (DNA, RNA, LNA) of various lengths in different experimental conditions (force, temperature, buffer conditions, presence of mismatches, etc.). This study provides a foundation for the dynamics of oligonucleotide displacement, a process of importance in numerous biological and bioengineering contexts.

Ab initio predictions for 3D structure and stability of single- and double-stranded DNAs in ion solutions

The three-dimensional (3D) structure and stability of DNA are essential to understand/control their biological functions and aid the development of novel materials. In this work, we present a coarse-grained (CG) model for DNA based on the RNA CG model proposed by us, to predict 3D structures and stability for both dsDNA and ssDNA from the sequence. Combined with a Monte Carlo simulated annealing algorithm and CG force fields involving the sequence-dependent base-pairing/stacking interactions and an implicit electrostatic potential, the present model successfully folds 20 dsDNAs (≤52nt) and 20 ssDNAs (≤74nt) into the corresponding native-like structures just from their sequences, with an overall mean RMSD of 3.4Å from the experimental structures. For DNAs with various lengths and sequences, the present model can make reliable predictions on stability, e.g., for 27 dsDNAs with/without bulge/internal loops and 24 ssDNAs including pseudoknot, the mean deviation of predicted melting temperatures from the corresponding experimental data is only ~2.0°C. Furthermore, the model also quantificationally predicts the effects of monovalent or divalent ions on the structure stability of ssDNAs/dsDNAs.

To determine 3D structures and quantify stability of single- (ss) and double-stranded (ds) DNAs is essential to unveil the mechanisms of their functions and to further guide the production and development of novel materials. Although many DNA models have been proposed to reproduce the basic structural, mechanical, or thermodynamic properties of dsDNAs based on the secondary structure information or preset constraints, there are very few models can be used to investigate the ssDNA folding or dsDNA assembly from the sequence. Furthermore, due to the polyanionic nature of DNAs, metal ions (e.g., Na⁺ and Mg²⁺) in solutions can play an essential role in DNA folding and dynamics. Nevertheless, ab initio predictions for DNA folding in ion solutions are still an unresolved problem. In this work, we developed a novel coarse-grained model to predict 3D structures and thermodynamic stabilities for both ssDNAs and dsDNAs in monovalent/divalent ion solutions from their sequences. As compared with the extensive experimental data and available existing models, we showed that the present model can successfully fold simple DNAs into their native-like structures, and can also accurately reproduce the effects of sequence and monovalent/divalent ions on structure stability for ssDNAs including pseudoknot and dsDNAs with/without bulge/internal loops.

Hybridization kinetics of out-of-equilibrium mixtures of short RNA oligonucleotides

Hybridization and strand displacement kinetics determine the evolution of the base paired configurations of mixtures of oligonucleotides over time. Although much attention has been focused on the thermodynamics of DNA and RNA base pairing in the scientific literature, much less work has been done on the time dependence of interactions involving multiple strands, especially in RNA. Here we provide a study of oligoribonucleotide interaction kinetics and show that it is possible to calculate the association, dissociation and strand displacement rates displayed by short oligonucleotides (5nt–12nt) that exhibit no expected secondary structure as simple functions of oligonucleotide length, CG content, ΔG of hybridization and ΔG of toehold binding. We then show that the resultant calculated kinetic parameters are consistent with the experimentally observed time dependent changes in concentrations of the different species present in mixtures of multiple competing RNA strands. We show that by changing the mixture composition, it is possible to create and tune kinetic traps that extend by orders of magnitude the typical sub-second hybridization timescale of two complementary oligonucleotides. We suggest that the slow equilibration of complex oligonucleotide mixtures may have facilitated the nonenzymatic replication of RNA during the origin of life.

Lattice model on the rate of DNA hybridization

We develop a lattice model on the rate of hybridization of the complementary single-stranded DNAs (c-ssDNAs). Upon translational diffusion mediated collisions, c-ssDNAs interpenetrate each other to form correct (cc), incorrect (icc), and trap correct contacts (tcc) inside the reaction volume. Correct contacts are those with exact registry matches, which leads to nucleation and zipping. Incorrect contacts are the mismatch contacts which are less stable compared to tcc, which can occur in the repetitive c-ssDNAs. Although tcc possess registry match within the repeating sequences, they are incorrect contacts in the view of the whole c-ssDNAs. The nucleation rate (k_{N}) is directly proportional to the collision rate and the average number of correct contacts (〈n_{cc}〉) formed when both c-ssDNAs interpenetrate each other. Detailed lattice model simulations suggest that 〈n_{cc}〉∝L/V where L is the length of c-ssDNAs and V is the reaction volume. Further numerical analysis revealed the scaling for the average radius of gyration of c-ssDNAs (R_{g}) with their length as R_{g}∝sqrt[L]. Since the reaction space will be approximately a sphere with radius equals to 2R_{g} and V∝L^{3/2}, one obtains k_{N}∝1/sqrt[L]. When c-ssDNAs are nonrepetitive, the overall renaturation rate becomes as k_{R}∝k_{N}L, and one finally obtains k_{R}∝sqrt[L] in line with the experimental observations. When c-ssDNAs are repetitive with a complexity of c, earlier models suggested the scaling k_{R}∝sqrt[L]/c, which breaks down at c=L. This clearly suggests the existence of at least two different pathways of renaturation in the case of repetitive c-ssDNAs, viz., via incorrect contacts and trap correct contacts. The trap correct contacts can lead to the formation of partial duplexes which can keep the complementary strands in the close proximity for a prolonged timescale. This is essential for the extended 1D slithering, inchworm movements, and internal displacement mechanisms which can accelerate the searching for the correct contacts. Clearly, the extent of slithering dynamics will be inversely proportional to the complexity. When the complexity is close to the length of c-ssDNAs, the pathway via incorrect contacts will dominate. When the complexity is much less than the length of c-ssDNA, pathway via trap correct contacts would be the dominating one.