Self-avoiding wormlike chain model for double-stranded-DNA loop formation

Deep Learning and Single-Molecule Localization Microscopy Reveal Nanoscopic Dynamics of DNA Entanglement Loci

Understanding molecular dynamics at the nanoscale remains challenging due to limitations in the temporal resolution of current imaging techniques. Deep learning integrated with Single-Molecule Localization Microscopy (SMLM) offers opportunities to probe these dynamics. Here, we leverage this integration to reveal entangled polymer dynamics at a fast time scale, which is relatively poorly understood at the single-molecule level. We used Lambda DNA as a model system and modeled their entanglement using the self-avoiding wormlike chain model, generated simulated localizations along the contours, and trained the deep learning algorithm on these simulated images to predict chain contours from sparse localization data. We found that the localizations are heterogeneously distributed along the contours. Our assessments indicated that chain entanglement creates local diffusion barriers for switching buffer molecules, affecting the photoswitching kinetics of fluorescent dyes conjugated to the DNA molecules at discrete DNA segments. Tracking these segments demonstrated stochastic and subdiffusive migration of the entanglement loci. Our approach provides direct visualization of nanoscale polymer dynamics and local molecular environments previously inaccessible to conventional imaging techniques. In addition, our results suggest that the switching kinetics of the fluorophores in SMLM can be used to characterize nanoscopic local environments.

Simulating the Cellular Context in Synthetic Datasets for Cryo-Electron Tomography

Cryo-electron tomography (cryo-ET) allows to visualize the cellular context at macromolecular level. To date, the impossibility of obtaining a reliable ground truth is limiting the application of deep learning-based image processing algorithms in this field. As a consequence, there is a growing demand of realistic synthetic datasets for training deep learning algorithms. In addition, besides assisting the acquisition and interpretation of experimental data, synthetic tomograms are used as reference models for cellular organization analysis from cellular tomograms. Current simulators in cryo-ET focus on reproducing distortions from image acquisition and tomogram reconstruction, however, they can not generate many of the low order features present in cellular tomograms. Here we propose several geometric and organization models to simulate low order cellular structures imaged by cryo-ET. Specifically, clusters of any known cytosolic or membrane-bound macromolecules, membranes with different geometries as well as different filamentous structures such as microtubules or actin-like networks. Moreover, we use parametrizable stochastic models to generate a high diversity of geometries and organizations to simulate representative and generalized datasets, including very crowded environments like those observed in native cells. These models have been implemented in a multiplatform open-source Python package, including scripts to generate cryo-tomograms with adjustable sizes and resolutions. In addition, these scripts provide also distortion-free density maps besides the ground truth in different file formats for efficient access and advanced visualization. We show that such a realistic synthetic dataset can be readily used to train generalizable deep learning algorithms.

Investigation of the dynamical structures of double-chain deoxyribonucleic acid model in biological sciences

The present research investigates the double-chain deoxyribonucleic acid model, which is important for the transfer and retention of genetic material in biological domains. This model is composed of two lengthy uniformly elastic filaments, that stand in for a pair of polynucleotide chains of the deoxyribonucleic acid molecule joined by hydrogen bonds among the bottom combination, demonstrating the hydrogen bonds formed within the chain's base pairs. The modified extended Fan sub equation method effectively used to explain the exact travelling wave solutions for the double-chain deoxyribonucleic acid model. Compared to the earlier, now in use methods, the previously described modified extended Fan sub equation method provide more innovative, comprehensive solutions and are relatively straightforward to implement. This method transforms a non-linear partial differential equation into an ODE by using a travelling wave transformation. Additionally, the study yields both single and mixed non-degenerate Jacobi elliptic function type solutions. The complexiton, kink wave, dark or anti-bell, V, anti-Z and singular wave shapes soliton solutions are a few of the creative solutions that have been constructed utilizing modified extended Fan sub equation method that can offer details on the transversal and longitudinal moves inside the DNA helix by freely chosen parameters. Solitons propagate at a consistent rate and retain their original shape. They are widely used in nonlinear models and can be found everywhere in nature. To help in understanding the physical significance of the double-chain deoxyribonucleic acid model, several solutions are shown with graphics in the form of contour, 2D and 3D graphs using computer software Mathematica 13.2. All of the requisite constraint factors that are required for the completed solutions to exist appear to be met. Therefore, our method of strengthening symbolic computations offers a powerful and effective mathematical tool for resolving various moderate nonlinear wave problems. The findings demonstrate the system's potentially very rich precise wave forms with biological significance. The fundamentals of double-chain deoxyribonucleic acid model diffusion and processing are demonstrated by this work, which marks a substantial development in our knowledge of double-chain deoxyribonucleic acid model movements.

Strongly Bent Double-Stranded DNA: Reconciling Theory and Experiment

The strong bending of polymers is poorly understood. We propose a general quantitative framework of polymer bending that includes both the weak and strong bending regimes on the same footing, based on a single general physical principle. As the bending deformation increases beyond a certain (polymer-specific) point, the change in the convexity properties of the effective bending energy of the polymer makes the harmonic deformation energetically unfavorable: in this strong bending regime the energy of the polymer varies linearly with the average bending angle as the system follows the convex hull of the deformation energy function. For double-stranded DNA, the effective bending deformation energy becomes non-convex for bends greater than ~ 2° per base-pair, equivalent to the curvature of a closed circular loop of ~ 160 base pairs. A simple equation is derived for the polymer loop energy that covers both the weak and strong bending regimes. The theory shows quantitative agreement with recent DNA cyclization experiments on short DNA fragments, while maintaining the expected agreement with experiment in the weak bending regime. Counter-intuitively, cyclization probability (j-factor) of very short DNA loops is predicted to increase with decreasing loop length; the j-factor reaches its minimum for loops of ≃ 45 base pairs. Atomistic simulations reveal that the attractive component of the short-range Lennard-Jones interaction between the backbone atoms can explain the underlying non-convexity of the DNA effective bending energy, leading to the linear bending regime. Applicability of the theory to protein-DNA complexes, including the nucleosome, is discussed.

Identifying Physical Causes of Apparent Enhanced Cyclization of Short DNA Molecules with a Coarse-Grained Model

DNA cyclization is a powerful technique to gain insight into the nature of DNA bending. While the wormlike chain model provides a good description of small to moderate bending fluctuations, it is expected to break down for large bending. Recent cyclization experiments on strongly bent shorter molecules indeed suggest enhanced flexibility over and above that expected from the wormlike chain. Here, we use a coarse-grained model of DNA to investigate the subtle thermodynamics of DNA cyclization for molecules ranging from 30 to 210 base pairs. As the molecules get shorter, we find increasing deviations between our computed equilibrium j-factor and the classic wormlike chain predictions of Shimada and Yamakawa for a torsionally aligned looped molecule. These deviations are due to sharp kinking, first at nicks, and only subsequently in the body of the duplex. At the shortest lengths, substantial fraying at the ends of duplex domains is the dominant method of relaxation. We also estimate the dynamic j-factor measured in recent FRET experiments. We find that the dynamic j-factor is systematically larger than its equilibrium counterpart—with the deviation larger for shorter molecules—because not all the stress present in the fully cyclized state is present in the transition state. These observations are important for the interpretation of recent cyclization experiments, suggesting that measured anomalously high j-factors may not necessarily indicate non-WLC behavior in the body of duplexes.

Self-Avoiding Wormlike Chain Confined in a Cylindrical Tube: Scaling Behavior

Within a confining tube section, the multithreads of a strongly confined, backfolding polymer exert the excluded-volume repulsions on each other and produce physical properties that are very different from those of a confined ideal chain. The conformational properties of a such confined wormlike chain are of fundamental interest and are also practically useful in understanding the DNA confinement problems. Here, the excluded-volume effects are added to the standard wormlike-chain model by a self-consistent field theory. The numerical solutions are examined in light of their scaling properties.

A Looping-Based Model for Quenching Repression

We model the regulatory role of proteins bound to looped DNA using a simulation in which dsDNA is represented as a self-avoiding chain, and proteins as spherical protrusions. We simulate long self-avoiding chains using a sequential importance sampling Monte-Carlo algorithm, and compute the probabilities for chain looping with and without a protrusion. We find that a protrusion near one of the chain’s termini reduces the probability of looping, even for chains much longer than the protrusion–chain-terminus distance. This effect increases with protrusion size, and decreases with protrusion-terminus distance. The reduced probability of looping can be explained via an eclipse-like model, which provides a novel inhibitory mechanism. We test the eclipse model on two possible transcription-factor occupancy states of the D. melanogastereve 3/7 enhancer, and show that it provides a possible explanation for the experimentally-observed eve stripe 3 and 7 expression patterns.

Biological regulation-at-a-distance, whereby a transcription factor (TF) is able to generate susbstantial regulatory effects on gene expression even though it may be bound a large distance away from its target (500 bp–1 Mbp), is only partially understood. Using a biophysical model and a computer simulation that take dsDNA and TF volumes into account, we identify a downregulatory mechanism which functions at large distances, whereby a TF bound within ∼ 150 bp from an activator decreases the probability of looping-based interaction between the activator and the distant core promoter. This “eclipse” mechanism provides insight into the question of how enhancer architecture dictates gene expression.

Using synthetic bacterial enhancers to reveal a looping-based mechanism for quenching-like repression

We explore a model for 'quenching-like' repression by studying synthetic bacterial enhancers, each characterized by a different binding site architecture. To do so, we take a three-pronged approach: first, we compute the probability that a protein-bound dsDNA molecule will loop. Second, we use hundreds of synthetic enhancers to test the model's predictions in bacteria. Finally, we verify the mechanism bioinformatically in native genomes. Here we show that excluded volume effects generated by DNA-bound proteins can generate substantial quenching. Moreover, the type and extent of the regulatory effect depend strongly on the relative arrangement of the binding sites. The implications of these results are that enhancers should be insensitive to 10-11 bp insertions or deletions (INDELs) and sensitive to 5-6 bp INDELs. We test this prediction on 61 σ(54)-regulated qrr genes from the Vibrio genus and confirm the tolerance of these enhancers' sequences to the DNA's helical repeat.