A Method to Present and Analyze Ensembles of Information Sources.

Information theory is a powerful tool for analyzing complex systems. In many areas of neuroscience, it is now possible to gather data from large ensembles of neural variables (e.g., data from many neurons, genes, or voxels). The individual variables can be analyzed with information theory to provide estimates of information shared between variables (forming a network between variables), or between neural variables and other variables (e.g., behavior or sensory stimuli). However, it can be difficult to (1) evaluate if the ensemble is significantly different from what would be expected in a purely noisy system and (2) determine if two ensembles are different. Herein, we introduce relatively simple methods to address these problems by analyzing ensembles of information sources. We demonstrate how an ensemble built of mutual information connections can be compared to null surrogate data to determine if the ensemble is significantly different from noise. Next, we show how two ensembles can be compared using a randomization process to determine if the sources in one contain more information than the other. All code necessary to carry out these analyses and demonstrations are provided.

NMR structure of the HIV-1 reverse transcriptase thumb subdomain.

The solution NMR structure of the isolated thumb subdomain of HIV-1 reverse transcriptase (RT) has been determined. A detailed comparison of the current structure with dozens of the highest resolution crystal structures of this domain in the context of the full-length enzyme reveals that the overall structures are very similar, with only two regions exhibiting local conformational differences. The C-terminal capping pattern of the αH helix is subtly different, and the loop connecting the αI and αJ helices in the p51 chain of the full-length p51/p66 heterodimeric RT differs from our NMR structure due to unique packing interactions in mature RT. Overall, our data show that the thumb subdomain folds independently and essentially the same in isolation as in its natural structural context.

Protein ensemble modeling and analysis with MMMx.

Proteins, especially of eukaryotes, often have disordered domains and may contain multiple folded domains whose relative spatial arrangement is distributed. The MMMx ensemble modeling and analysis toolbox (https://github.com/gjeschke/MMMx) can support the design of experiments to characterize the distributed structure of such proteins, starting from AlphaFold2 predictions or folded domain structures. Weak order can be analyzed with reference to a random coil model or to peptide chains that match the residue-specific Ramachandran angle distribution of the loop regions and are otherwise unrestrained. The deviation of the mean square end-to-end distance of chain sections from their average over sections of the same sequence length reveals localized compaction or expansion of the chain. The shape sampled by disordered chains is visualized by superposition in the principal axes frame of their inertia tensor. Ensembles of different sizes and with weighted conformers can be compared based on a similarity parameter that abstracts from the ensemble width.

De Novo Design of a ß-Helix Tau Protein Scaffold: An Oligomer-Selective Vaccine Immunogen Candidate for Alzheimer's Disease.

Tau pathology is associated with many neurodegenerative disorders, including Alzheimer's disease (AD), where the spatio-temporal pattern of tau neurofibrillary tangles strongly correlates with disease progression, which motivates therapeutics selective for misfolded tau. Here, we introduce a new avidity-enhanced, multi-epitope approach for protein-misfolding immunogen design, which is predicted to mimic the conformational state of an exposed epitope in toxic tau oligomers. A predicted oligomer-selective tau epitope 343KLDFK347 was scaffolded by designing a ß-helix structure that incorporated multiple instances of the 16-residue tau fragment 339VKSEKLDFKDRVQSKI354. Large-scale conformational ensemble analyses involving Jensen-Shannon Divergence and the embedding depth D showed that the multi-epitope scaffolding approach, employed in designing the ß-helix scaffold, was predicted to better discriminate toxic tau oligomers than other "monovalent" strategies utilizing a single instance of an epitope for vaccine immunogen design. Using Rosetta, 10,000 sequences were designed and screened for the linker portions of the ß-helix scaffold, along with a C-terminal stabilizing α-helix that interacts with the linkers, to optimize the folded structure and stability of the scaffold. Structures were ranked by energy, and the lowest 1% (82 unique sequences) were verified using AlphaFold. Several selection criteria involving AlphaFold are implemented to obtain a lead-designed sequence. The structure was further predicted to have free energetic stability by using Hamiltonian replica exchange molecular dynamics (MD) simulations. The synthesized ß-helix scaffold showed direct binding in surface plasmon resonance (SPR) experiments to several antibodies that were raised to the structured epitope using a designed cyclic peptide. Moreover, the strength of binding of these antibodies to in vitro tau oligomers correlated with the strength of binding to the ß-helix construct, suggesting that the construct presents an oligomer-like conformation and may thus constitute an effective oligomer-selective immunogen.

NETWORK-ENSEMBLE COMPARISONS WITH STOCHASTIC REWIRING AND VON NEUMANN ENTROPY.

Assessing whether a given network is typical or atypical for a random-network ensemble (i.e., network-ensemble comparison) has widespread applications ranging from null-model selection and hypothesis testing to clustering and classifying networks. We develop a framework for network-ensemble comparison by subjecting the network to stochastic rewiring. We study two rewiring processes-uniform and degree-preserved rewiring-which yield random-network ensembles that converge to the Erdos-Rényi and configuration-model ensembles, respectively. We study convergence through von Neumann entropy (VNE)-a network summary statistic measuring information content based on the spectra of a Laplacian matrix-and develop a perturbation analysis for the expected effect of rewiring on VNE. Our analysis yields an estimate for how many rewires are required for a given network to resemble a typical network from an ensemble, offering a computationally efficient quantity for network-ensemble comparison that does not require simulation of the corresponding rewiring process.