Publications

We introduce an efficient numerical method for second-order linear ODEs whose solution may vary between highly oscillatory and slowly changing over the solution interval. In oscillatory regions the solution is generated via a nonoscillatory phase function that obeys the nonlinear Riccati equation. We propose a defect correction iteration that gives an asymptotic series for such a phase function; this is numerically approximated on a Chebyshev grid with a small number of nodes. For analytic coefficients we prove that each iteration, up to a certain maximum number, reduces the residual by a factor of order of the local frequency. The algorithm adapts both the stepsize and the choice of method, switching to a conventional spectral collocation method away from oscillatory regions. In numerical experiments we find that our proposal outperforms other state-of-the-art oscillatory solvers, most significantly at low to intermediate frequencies and at low tolerances, where it may use up to \(10^6\) times fewer function evaluations. Even in high-frequency regimes, our implementation is on average 10 times faster than other specialized solvers.

High throughput gene expression profiling measures individual gene expression across conditions. However, genes are regulated in complex networks, not as individual entities, limiting the interpretability of gene expression data. Machine learning models that incorporate prior biological knowledge are a powerful tool to extract meaningful biology from gene expression data. Pathway-level information extractor (PLIER) is an unsupervised machine learning method that defines biological pathways by leveraging the vast amount of published transcriptomic data. PLIER converts gene expression data into known pathway gene sets, termed latent variables (LVs), to substantially reduce data dimensionality and improve interpretability. In the current study, we trained the first mouse PLIER model on 190,111 mouse brain RNA-sequencing samples, the greatest amount of training data ever used by PLIER. We then validated the mousiPLIER approach in a study of microglia and astrocyte gene expression across mouse brain aging. mousiPLIER identified biological pathways that are significantly associated with aging, including one latent variable (LV41) corresponding to striatal signal. To gain further insight into the genes contained in LV41, we performed k-means clustering on the training data to identify studies that respond strongly to LV41. We found that the variable was relevant to striatum and aging across the scientific literature. Finally, we built a web server (http://mousiplier.greenelab.com/) for users to easily explore the learned latent variables. Taken together this study defines mousiPLIER as a method to uncover meaningful biological processes in mouse brain transcriptomic studies.

We study the dynamics of proliferating cell collectives whose microscopic constituents' growth is inhibited by macroscopic growth-induced stress. Discrete particle simulations of a growing collective show the emergence of concentric-ring patterns in cell size whose spatio-temporal structure is closely tied to the individual cell's stress response. Motivated by these observations, we derive a multiscale continuum theory whose parameters map directly to the discrete model. Analytical solutions of this theory show the concentric patterns arise from anisotropically accumulated resistance to growth over many cell cycles. This work shows how purely mechanical processes can affect the internal patterning and morphology of cell collectives, and provides a concise theoretical framework for connecting the micro- to macroscopic dynamics of proliferating matter.

Nearly all circadian clocks maintain a period that is insensitive to temperature changes, a phenomenon known as temperature compensation (TC). Yet, it is unclear whether there is any common feature among different systems that exhibit TC. From a general timescale invariance, we show that TC relies on the existence of certain period-lengthening reactions wherein the period of the system increases strongly with the rates in these reactions. By studying several generic oscillator models, we show that this counterintuitive dependence is nonetheless a common feature of oscillators in the nonlinear (far-from-onset) regime where the oscillation can be separated into fast and slow phases. The increase of the period with the period-lengthening reaction rates occurs when the amplitude of the slow phase in the oscillation increases with these rates while the progression speed in the slow phase is controlled by other rates of the system. The positive dependence of the period on the period-lengthening rates balances its inverse dependence on other kinetic rates in the system, which gives rise to robust TC in a wide range of parameters. We demonstrate the existence of such period-lengthening reactions and their relevance for TC in all four model systems we considered. Theoretical results for a model of the Kai system are supported by experimental data. A study of the energy dissipation also shows that better TC performance requires higher energy consumption. Our study unveils a general mechanism by which a biochemical oscillator achieves TC by operating in parameter regimes far from the onset where period-lengthening reactions exist.

Error correction is central to many biological systems and is critical for protein function and cell health. During mitosis, error correction is required for the faithful inheritance of genetic material. When functioning properly, the mitotic spindle segregates an equal number of chromosomes to daughter cells with high fidelity. Over the course of spindle assembly, many initially erroneous attachments between kinetochores and microtubules are fixed through the process of error correction. Despite the importance of chromosome segregation errors in cancer and other diseases, there is a lack of methods to characterize the dynamics of error correction and how it can go wrong. Here, we present an experimental method and analysis framework to quantify chromosome segregation error correction in human tissue culture cells with live cell confocal imaging, timed premature anaphase, and automated counting of kinetochores after cell division. We find that errors decrease exponentially over time during spindle assembly. A coarse-grained model, in which errors are corrected in a chromosome autonomous manner at a constant rate, can quantitatively explain both the measured error correction dynamics and the distribution of anaphase onset times. We further validated our model using perturbations that destabilized microtubules and changed the initial configuration of chromosomal attachments. Taken together, this work provides a quantitative framework for understanding the dynamics of mitotic error correction.

Learning in living organisms is typically associated with networks of neurons. The use of large numbers of adjustable units has also been a crucial factor in the continued success of artificial neural networks. In light of the complexity of both living and artificial neural networks, it is surprising to see that very simple organisms -- even unicellular organisms that do not possess a nervous system -- are capable of certain forms of learning. Since in these cases learning may be implemented with much simpler structures than neural networks, it is natural to ask how simple the building blocks required for basic forms of learning may be. The purpose of this study is to discuss the simplest dynamical systems that model a fundamental form of non-associative learning, habituation, and to elucidate technical implementations of such systems, which may be used to implement non-associative learning in neuromorphic computing and related applications.

Huntington’s disease (HD) is a fatal neurodegenerative disorder resulting from an abnormal expansion of polyglutamine (polyQ) repeats in the N terminus of the Huntingtin protein. When the polyQ tract surpasses 35 repeats, the mutated protein undergoes misfolding, culminating in the formation of intracellular aggregates. Research in mouse models suggests that HD pathogenesis involves the aggregation of N-terminal fragments of the Huntingtin protein (htt). These early oligomeric assemblies of htt, exhibiting diverse characteristics during aggregation, are implicated as potential toxic entities in HD. However, a consensus on their specific structures remains elusive.

Understanding the heterogeneous nature of htt oligomers provides crucial insights into disease mechanisms, emphasizing the need to identify various oligomeric conformations as potential therapeutic targets. Employing coarse-grained molecular dynamics, our study aims to elucidate the mechanisms governing the aggregation process and resultant aggregate architectures of htt. The polyQ tract within htt is flanked by two regions: an N-terminal domain (N17) and a short C-terminal proline-rich segment.

We conducted self-assembly simulations involving five distinct N17 + polyQ systems with polyQ lengths ranging from 7 to 45, utilizing the ProMPT force field. Prolongation of the polyQ domain correlates with an increase in β-sheet-rich structures. Longer polyQ lengths favor intra-molecular β-sheets over inter-molecular interactions due to the folding of the elongated polyQ domain into hairpin-rich conformations. Importantly, variations in polyQ length significantly influence resulting oligomeric structures. Shorter polyQ domains lead to N17 domain aggregation, forming a hydrophobic core, while longer polyQ lengths introduce a competition between N17 hydrophobic interactions and polyQ polar interactions, resulting in densely packed polyQ cores with outwardly distributed N17 domains. Additionally, at extended polyQ lengths, we observe distinct oligomeric conformations with varying degrees of N17 bundling. These findings can help explain the toxic gain-of function that htt with expanded polyQ acquires.

Regular exercise has many physical and brain health benefits, yet the molecular mechanisms mediating exercise effects across tissues remain poorly understood. Here we analyzed 400 high-quality DNA methylation, ATAC-seq, and RNA-seq datasets from eight tissues from control and endurance exercise-trained (EET) rats. Integration of baseline datasets mapped the gene location dependence of epigenetic control features and identified differing regulatory landscapes in each tissue. The transcriptional responses to 8 weeks of EET showed little overlap across tissues and predominantly comprised tissue-type enriched genes. We identified sex differences in the transcriptomic and epigenomic changes induced by EET. However, the sex-biased gene responses were linked to shared signaling pathways. We found that many G protein-coupled receptor-encoding genes are regulated by EET, suggesting a role for these receptors in mediating the molecular adaptations to training across tissues. Our findings provide new insights into the mechanisms underlying EET-induced health benefits across organs.

A primary cilium, made of nine microtubule doublets enclosed in a cilium membrane, is a mechanosensing organelle that bends under an external mechanical load and sends an intracellular signal through transmembrane proteins activated by cilium bending. The nine microtubule doublets are the main load-bearing structural component, while the transmembrane proteins on the cilium membrane are the main sensing component. No distinction was made between these two components in all existing models, where the stress calculated from the structural component (nine microtubule doublets) was used to explain the sensing location, which may be totally misleading. For the first time, we developed a microstructure-based primary cilium model by considering these two components separately. First, we refined the analytical solution of bending an orthotropic cylindrical shell for individual microtubule, and obtained excellent agreement between finite element simulations and the theoretical predictions of a microtubule bending as a validation of the structural component in the model. Second, by integrating the cilium membrane with nine microtubule doublets and simulating the tip-anchored optical tweezer experiment on our computational model, we found that the microtubule doublets may twist significantly as the whole cilium bends. Third, besides being cilium-length-dependent, we found the mechanical properties of the cilium are also highly deformation-dependent. More important, we found that the cilium membrane near the base is not under pure in-plane tension or compression as previously thought, but has significant local bending stress. This challenges the traditional model of cilium mechanosensing, indicating that transmembrane proteins may be activated more by membrane curvature than membrane stretching. Finally, we incorporated imaging data of primary cilia into our microstructure-based cilium model, and found that comparing to the ideal model with uniform microtubule length, the imaging-informed model shows the nine microtubule doublets interact more evenly with the cilium membrane, and their contact locations can cause even higher bending curvature in the cilium membrane than near the base.

Biomolecular recruitment by phase separated condensates has emerged as a key organising principle of biological processes. One such process is the RNA silencing pathway, which regulates gene expression and genomic defense against foreign nucleic acids. In C. elegans, this pathway involves siRNA amplification at perinuclear germ granules named Mutator foci. The formation of Mutator foci depends on the phase separation of MUT-16, acting as a scaffolding protein to recruit other components of the Mutator complex. Earlier studies have indicated a crucial role for an exoribonuclease, MUT-7, in RNA silencing. The recruitment of MUT-7 to Mutator foci is facilitated by a bridging protein, MUT-8. However, how MUT-8 binds to MUT-16 remains elusive. We resolved the molecular drivers of MUT-16 phase separation and the recruitment of MUT-8 using multi-scale molecular dynamics simulations and in vitro experiments. Residue-level coarse-grained simulations predicted the relative phase separation propensities of MUT-16 disordered regions, which we validated by experiments.

Coarse-grained simulations at residue-level and near atomic-resolution also indicated the essential role of aromatic amino acids (Tyr and Phe) in MUT-16 phase separation. Furthermore, coarse-grained and atomistic simulations of MUT-8 N-terminal prion-like domain with phase separated MUT-16 condensate revealed the importance of cation-π interaction between Tyr residues of MUT-8 and Arg/Lys residues of MUT-16. By re-introducing atomistic detail to condensates from coarse-grained and 350 µs all-atom simulations in explicit solvent on Folding@Home, we demonstrate Arg-Tyr interaction surpasses the strength of Lys-Tyr interactions in the recruitment of MUT-8. The atomistic simulations show that the planar guanidinium group of Arg also engages in sp2-π interaction, and hydrogen bonds with the Tyr residues and these additional favorable contacts are missing in the Lys-Tyr interactions. In agreement with simulations, the mutation of seven Arg residues in MUT-16 to Lys and Ala weakens MUT-8 binding in vitro.