Understanding Thermodynamic Competitivity between Biopolymer Folding and Misfolding under Large-Scale Intermolecular Interactions

Cooperativity is a hallmark of spontaneous biopolymer folding. The presence of intermolecular interactions could create off-pathway misfolding structures and suppress folding cooperativity. This raises the hypothesis that thermodynamic competitivity between off-pathway misfolding and on-pathway folding may intervene with cooperativity and govern biopolymer folding dynamics under conditions permitting large-scale intermolecular interactions. Here we report direct imaging and theoretical modeling of thermodynamic competitivity between biopolymer folding and misfolding under such conditions, using a two-dimensional array of proton-fueled DNA molecular motors packed at the maximal density as a model system. Time-resolved liquid-phase atomic force microscopy with enhanced phase contrast revealed that the misfolding and folding intermediates transiently self-organize into spatiotemporal patterns on the nanoscale in thermodynamic states far away from equilibrium as a result of thermodynamic competitivity. Computer simulations using a novel cellular-automaton network model provide quantitative insights into how large-scale intermolecular interactions correlate the structural dynamics of individual biomolecules together at the systems level

Understanding Thermodynamic Competitivity between Biopolymer Folding and Misfolding under Large-Scale Intermolecular Interactions

Cooperativity is a hallmark of spontaneous biopolymer folding. The presence of intermolecular interactions could create off-pathway misfolding structures and suppress folding cooperativity. This raises the hypothesis that thermodynamic competitivity between off-pathway misfolding and on-pathway folding may intervene with cooperativity and govern biopolymer folding dynamics under conditions permitting large-scale intermolecular interactions. Here we report direct imaging and theoretical modeling of thermodynamic competitivity between biopolymer folding and misfolding under such conditions, using a two-dimensional array of proton-fueled DNA molecular motors packed at the maximal density as a model system. Time-resolved liquid-phase atomic force microscopy with enhanced phase contrast revealed that the misfolding and folding intermediates transiently self-organize into spatiotemporal patterns on the nanoscale in thermodynamic states far away from equilibrium as a result of thermodynamic competitivity. Computer simulations using a novel cellular-automaton network model provide quantitative insights into how large-scale intermolecular interactions correlate the structural dynamics of individual biomolecules together at the systems level

Additional file 1: Figure S1. of A deep convolutional neural network approach to single-particle recognition in cryo-electron microscopy

The feature maps of the convolutional and subsampling layers from a typical particle image of KLH learned by our CNN. Figure S2. (a) and (b) show a comparison of the results obtained before and after additional selection using standard deviation of the KLH dataset, respectively. (c) and (d) show a comparison of the results obtained before and after additional selection using standard deviation of the 19S, respectively. Figure S3. (a) and (b) show a comparison of the results obtained before and after optimization of the training dataset, respectively. Figure S4. Comparison of DeepEM with TMACS and RELION using the KLH dataset as benchmark. The curves of TMACS [16] and RELION [36] were directly obtained from published data. Figure S5. Reference-free 2D classification of 19S proteasomes recognized by DeepEM. Figure S6. Results of the recognition of the side view of the 26S proteasome by DeepEM. Figure S7. A comparison of the results of different activation functions tested on the KLH dataset (PDF 477 kb

Unsupervised Cryo-EM Data Clustering through Adaptively Constrained K-Means Algorithm - Fig 3

<p><b>2D class averages of GroEL using the traditional K-means (a), EQK-means (b) and ACK-means (c) in MRA approach from SPARX</b>. Class size is shown at the left bottom of each class average. ACK-means (b) is the best by having the most number of clear classes.</p

Convergence of K-means, EQK-means and ACK-means in MRA.

<p>The three algorithms behave similarly as iteration increases, converging very fast at the first several iterations.</p

Unsupervised Cryo-EM Data Clustering through Adaptively Constrained K-Means Algorithm - Fig 10

<p><b>2D class averages of RP using the traditional K-means (a) and ACK-means (b) in MRA/MSA from EMAN2.</b> Class size is shown at the left bottom of each class average. Classes generated by ACK-means (a) are clearer than those by the traditional K-means (a).</p

Comparison of classification results of simulated data with SNR = 1/10.

<p>The First column (panels a, c and e) is the normalized histogram of angular distances. More accurate classification produces curve with higher peak concentrated at lower angular distance. The second column (panels b, d and f) shows the class sizes arranged in an ascend order. The most balanced classification has a horizontal line in this plot. (a) and (b) are from experiments using different clustering algorithms in MRA approach under SPARX. (c) and (d) are from experiments using different clustering algorithms in MRA/MSA approach under EMAN2. (e) and (f) are from experiments using different clustering algorithms in RFA approach under SPIDER. In all graphs, red curves present the results from the ACK-means algorithm.</p

The running time of different algorithms in different approaches.

<p>The running time of different algorithms in different approaches.</p

AFM topographic images for the different states of the device on Au(111) surface

<p><b>Copyright information:</b></p><p>Taken from "Alternating-electric-field-enhanced reversible switching of DNA nanocontainers with pH"</p><p></p><p>Nucleic Acids Research 2007;35(5):e33-e33.</p><p>Published online 31 Jan 2007</p><p>PMCID:PMC1865044.</p><p>© 2007 The Author(s).</p> () Initial closed state at pH 4.5 after self-assembly shows 1.5 ± 0.5 nm surface roughness. () Open state at pH 8.0 shows 6.0 ± 1.0 nm surface roughness. () Repeated closed state at pH 4.5 restores the surface roughness to 1.5 ± 0.5 nm. Height scales for all images are adjusted to a uniform range of 15 nm. The color mapping to height is indicated by the height scale bar. The poly-dA spacer length of DNA motif is 10 bp. () The height analysis of the horizontal cross sections along the middle dashed white lines shown in (). (D) corresponds to (A), (E) to (B), and (F) to (C), respectively

Initial 3D reconstruction from the reference-free class averages of ROME and EMAN2.

<p><b>(A)</b> The initial reconstruction calculated by the ROME-generated class averages is superimposed with the atomic model of free RP shown in a ribbon representation, suggesting that they are highly compatible with each other. <b>(B)</b> The initial reconstruction calculated by the EMAN2-generated class averages is superimposed over the atomic model of free RP shown in a ribbon representation. A substantial part of the atomic model is outside of the density of the initial reconstruction, suggesting poor map quality and a large reconstruction error. <b>(C)</b> FSC curves between the RP atomic model and the initial reconstructions generated by ROME- and EMAN2-based class averages.</p