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Visualization of a multi-turnover Cas9 after product release
No full textWhile the most widely used CRISPR-Cas enzyme is the Cas9 endonuclease from Streptococcus pyogenes (Cas9), it exhibits single-turnover enzyme kinetics which leads to long residence times on product DNA. This blocks access to DNA repair machinery and acts as a major bottleneck during CRISPR-Cas9 gene editing. Cas9 can eventually be removed from the product by extrinsic factors, such as translocating polymerases, but the mechanisms contributing to Cas9 dissociation following cleavage remain poorly understood. Here, we employ truncated guide RNAs as a strategy to weaken PAM-distal nucleic acid interactions and promote faster enzyme turnover. Using kinetics-guided cryo-EM, we examine the conformational landscape of a multi-turnover Cas9, including the first detailed snapshots of Cas9 dissociating from product DNA. We discovered that while the PAM-distal product dissociates from Cas9 following cleavage, tight binding of the PAM-proximal product directly inhibits re-binding of new targets. Our work provides direct evidence as to why Cas9 acts as a single-turnover enzyme and will guide future Cas9 engineering efforts
Wasserstein distances, neuronal entanglement, and sparsity
No full textDisentangling polysemantic neurons is at the core of many current approaches to interpretability of large language models. Here we attempt to study how disentanglement can be used to understand performance, particularly under weight sparsity, a leading post-training optimization technique. We suggest a novel measure for estimating neuronal entanglement: the Wasserstein distance of a neuron's output distribution to a Gaussian. Moreover, we show the existence of a small number of highly entangled "Wasserstein Neurons" in each linear layer of an LLM, characterized by their highly non-Gaussian output distributions, their role in mapping similar inputs to dissimilar outputs, and their significant impact on model accuracy. To study these phenomena, we propose a new experimental framework for disentangling polysemantic neurons. Our framework separates each layer's inputs to create a mixture of experts where each neuron's output is computed by a mixture of neurons of lower Wasserstein distance, each better at maintaining accuracy when sparsified without retraining. We provide strong evidence that this is because the mixture of sparse experts is effectively disentangling the input-output relationship of individual neurons, in particular the difficult Wasserstein neurons
Near-optimal leader election in population protocols on graphs
No full textIn the stochastic population protocol model, we are given a connected graph with n nodes, and in every time step, a scheduler samples an edge of the graph uniformly at random and the nodes connected by this edge interact. A fundamental task in this model is stable leader election, in which all nodes start in an identical state and the aim is to reach a configuration in which (1)
exactly one node is elected as leader and (2) this node remains as the unique leader no matter what sequence of interactions follows. On cliques, the complexity of this problem has recently been settled: time-optimal protocols stabilize in (n log n) expected steps using (log log n) states, whereas protocols that use O(1) states require (n2) expected steps. In this work, we investigate the complexity of stable leader election on graphs. We provide the first non-trivial time lower bounds on general graphs, showing that, when moving beyond cliques, the complexity of stable leader election can range from O(1) to (n3) expected steps. We describe a protocol that is time-optimal on many graph families, but uses polynomially-many states. In contrast, we give a near-time-optimal protocol that uses only O(log2 n) states that is at most a factor O(log n) slower. Finally, we observe that for many graphs the constant-state protocol of Beauquier et al. [OPODIS 2013] is at most a factor O(n log n) slower than the fast polynomial-state protocol, and among constant-state protocols, this protocol has near-optimal average case complexity on dense random graphs
PSME3 regulates migration and differentiation of myoblasts
No full textThe acquisition of cellular identity requires large-scale alterations in cellular state. The noncanonical proteasome activator PSME3 is known to regulate diverse cellular processes, but its importance for differentiation remains unclear. Here, we demonstrate that PSME3 binds dynamically to highly active promoters over the course of differentiation. However, loss of PSME3 does not globally affect mRNA transcription. We find instead that PSME3 influences the levels of several adhesion-related proteins and acts upstream of the HSP90 co-chaperone NUDC to regulate cell motility and myoblast differentiation in a proteasome-independent manner. Our findings reveal several new facets of PSME3 functionality and highlight its importance for the differentiation of myogenic cells
An extremely metal-poor Lyα emitter candidate at z = 6 revealed through absorption spectroscopy
No full textWe report the discovery of a Lyα emitter (LAE) candidate in the immediate foreground of the quasar PSO J158-14 at zQSO = 6.0685 at a projected distance ∼29 pkpc that is associated with an extremely metal-poor absorption system. This system was found in archival observations of the quasar field with the Very Large Telescope (VLT)/Multi-Unit Spectroscopic Explorer (MUSE) and was previously missed in searches of absorption systems using quasar absorption line spectroscopy, as it imparts no detectable metal absorption lines on the background quasar spectrum. The detected Lyα emission line at a redshift of zLAE = 6.0323 is well aligned with the outer edge of the quasar’s proximity zone and can plausibly cause its observed damping wing if it is associated with a proximate subdamped Lyα absorption system with a column density of log Nhi/cm^-2 19.7. A >10 hr medium-resolution spectrum of the quasar observed with the Magellan/Folded-port InfraRed Echellette (FIRE) and VLT/X-Shooter spectrographs reveals a metallicity constraint of [Z/H] < −3. Such low metallicity makes this system an extremely metal-poor galaxy candidate and provides an exciting site to study possible signatures of Population III stars
Stability estimate for the Lane–Emden inequality
No full textThe Lane–Emden inequality controls (math. formular) in terms of the L^1 and L^p norms of p. We provide a remainder estimate for this inequality in terms of a suitable distance of p to the manifold of optimizers
Latent Ewald summation for machine learning of long-range interactions
No full textMachine learning interatomic potentials (MLIPs) often neglect long-range interactions, such as electrostatic and dispersion forces. In this work, we introduce a straightforward and efficient method to account for long-range interactions by learning a hidden variable from local atomic descriptors and applying an Ewald summation to this variable. We demonstrate that in systems including charged and polar molecular dimers, bulk water, and water-vapor interface, standard short-ranged MLIPs can lead to unphysical predictions even when employing message passing. The long-range models effectively eliminate these artifacts, with only about twice the computational cost of short-range MLIPs
Virtual bound states of the Pauli operator with an Aharonov–Bohm potential
No full textA maximal realization of the two-dimensional Pauli operator, subject to Aharonov–Bohm magnetic field, is investigated. Contrary to the case of the Pauli operator with regular magnetic potentials, it is shown that both components of the Pauli operator are critical. Asymptotics of the weakly coupled eigenvalues, generated by electric (not necessarily self-adjoint) perturbations, are derived
Hybrid decentralized optimization: Leveraging both first- and zeroth-order optimizers for faster convergence
No full textDistributed optimization is the standard way of speeding up machine learning training, and most of the research in the area focuses on distributed first-order, gradient-based methods. Yet, there are settings where some computationally-bounded nodes may not be able to implement first-order, gradient-based optimization, while they could still contribute to joint optimization tasks. In this paper, we initiate the study of hybrid decentralized optimization, studying settings where nodes with zeroth-order and first-order optimization capabilities co-exist in a distributed system, and attempt to jointly solve an optimization task over some data distribution. We essentially show that, under reasonable parameter settings, such a system can not only withstand noisier zeroth-order agents but can even benefit from integrating such agents into the optimization process, rather than ignoring their information. At the core of our approach is a new analysis of distributed optimization with noisy and possibly-biased gradient estimators, which may be of independent interest. Our results hold for both convex and non-convex objectives. Experimental results on standard optimization tasks confirm our analysis, showing that hybrid first-zeroth order optimization can be practical, even when training deep neural networks
Foraging for water by MIZ1-mediated antagonism between root gravitropism and hydrotropism
No full textRoot system integrates multiple environmental cues, chiefly gravity and soil humidity, to anchor plants in soil and forage for water. While the mechanism of auxin-mediated root gravitropism is comparably well-understood, the root’s capability to grow toward moist soil for water uptake and drought avoidance, termed root hydrotropism, remains largely mysterious. Here, we provide key insights into the mechanism of hydrotropic growth and assign a role to the master regulator of hydrotropism, MIZU-KUSSEI 1 (MIZ1). We show that efficient hydrotropism requires the attenuation of antagonistically acting gravitropism, which is inhibited under drought conditions. Drought stress interferes with subcellular trafficking and the lateral mobility of PIN auxin transporters, which are polarly localized at the root cell plasma membranes. This leads to defects in PIN2 polarity and gravity-induced polarization of PIN3, ultimately inhibiting gravity-induced auxin redistribution and root bending. The miz1 mutant is defective in all these regulations, and in support of MIZ1’s action on PINs, pin mutations rescue the hydrotropic defects in the miz1 mutant. These observations identify a mechanism for how drought via MIZ1 attenuates gravitropism to promote root hydrotropism for efficient water foraging under drought conditions