Floer Cohomology and Higher Mutations

We extend the construction of higher mutation as introduced in Pascaleff-Tonkonog to local higher mutation, which is applicable to a larger class of monotone Lagrangians. In two-dimensional Lagrangians, local higher mutation is the same as performing a Lagrangian anti-surgery in the sense of Haug followed by a Lagrangian surgery. We prove that up to a change of local systems, the Lagrangian intersection Floer cohomology of a pair of Lagrangians is invariant under local mutation. This result generalizes the wall-crossing formula in Pascaleff-Tonkonog. For two-dimensional Lagrangians, this result agrees with the invariance result in Palmer-Woodward.Comment: v3: Minor revisions, changed numbering scheme. Fixed an error in exponential convergence (Theorem 3.5 in the current version

Infinitely many monotone Lagrangian tori in higher projective spaces

Vianna constructed infinitely many exotic Lagrangian tori in the complex projective plane. We lift these tori to higher-dimensional projective spaces and show that they remain non-symplectomorphic. Our proof is elementary except for an application of the wall-crossing formula by Pascaleff-Tonkonog.Comment: 11 pages, 1 figure. Comments welcome

Augmentation varieties and disk potentials III

This is the third in a series of papers in which we construct Chekanov-Eliashberg algebras for Legendrians in circle-fibered contact manifolds and study the associated augmentation varieties. In this part, we prove that for connected Legendrian covers of monotone Lagrangian tori, the augmentation variety is equal to the image of the zero level set of the disk potential, as suggested by Dimitroglou-Rizell-Golovko. In particular, we show that Legendrian lifts of Vianna's exotic tori are not Legendrian isotopic. Using related ideas, we show that the Legendrian lift of the Clifford torus admits no exact fillings, extending results of Dimitroglou-Rizell and Treumann-Zaslow in dimension two. We consider certain disconnected Legendrians, and show, similar to another suggestion of Aganagic-Ekholm-Ng-Vafa that the components of the augmentation variety correspond to certain partitions and each component is defined by a (not necessarily exact) Lagrangian filling.Comment: 42 pages; The original manuscript arXiv:2310.17821v1 was split into three parts: this being part II

Augmentation varieties and disk potentials

We elaborate on a suggestion of Aganagic-Ekholm-Ng-Vafa, that in order for Lagrangian fillings such as the Harvey-Lawson filling to define augmentations of Chekanov-Eliashberg differential graded algebras, one should count configurations of holomorphic disks connected by gradient trajectories. We propose a definition of the Chekanov-Eliashberg dga in higher dimensions which includes as generators both Reeb chords and the space of chains on the Legendrian, similar to the definition of immersed Lagrangian Floer theory whose generators are chains on the Lagrangian as well as self-intersection points. We prove that for connected Legendrian covers of monotone Lagrangian tori, the augmentation variety in this model is equal to the image of the zero level set of the disk potential, as suggested by Dimitroglou-Rizell-Golovko. In particular, we show that Legendrian lifts of Vianna's exotic tori are not Legendrian isotopic, as conjectured in Dimitroglou-Rizell-Golovko. Using related ideas, we show that the Legendrian lift of the Clifford torus admits no exact fillings, extending the results of Dimitroglou-Rizell and Treumann-Zaslow in dimension two. We consider certain disconnected Legendrians, and show, similar to another suggestion of Aganagic-Ekholm-Ng-Vafa, that the components of the augmentation variety correspond to certain partitions and each component is defined by a (not necessarily exact) Lagrangian filling. An adaptation of the theory of holomorphic quilts shows that the cobordism maps associated to bounding chains are independent of all choices up to chain homotopy.Comment: 157 page

Augmentation varieties and disk potentials II

This is the second in a sequence of papers in which we construct Chekanov-Eliashberg algebras for Legendrians in circle-fibered contact manifolds and study the associated augmentation varieties. In this part, we first define the Chekanov-Eliashberg algebra and its Legendrian contact homology. For a tame Lagrangian cobordism between Legendrians, we define a chain map between their Chekanov-Eliashberg algebras.Comment: 52 pages; The original manuscript arXiv:2310.17821v1 was split into three parts: this being part I

Rapid Single-Step Induction of Functional Neurons from Human Pluripotent Stem Cells

SummaryAvailable methods for differentiating human embryonic stem cells (ESCs) and induced pluripotent cells (iPSCs) into neurons are often cumbersome, slow, and variable. Alternatively, human fibroblasts can be directly converted into induced neuronal (iN) cells. However, with present techniques conversion is inefficient, synapse formation is limited, and only small amounts of neurons can be generated. Here, we show that human ESCs and iPSCs can be converted into functional iN cells with nearly 100% yield and purity in less than 2 weeks by forced expression of a single transcription factor. The resulting ES-iN or iPS-iN cells exhibit quantitatively reproducible properties independent of the cell line of origin, form mature pre- and postsynaptic specializations, and integrate into existing synaptic networks when transplanted into mouse brain. As illustrated by selected examples, our approach enables large-scale studies of human neurons for questions such as analyses of human diseases, examination of human-specific genes, and drug screening

Myt1l safeguards neuronal identity by actively repressing many non-neuronal fates

Normal differentiation and induced reprogramming require the activation of target cell programs and silencing of donor cell programs(1,2). In reprogramming, the same factors are often used to reprogram many different donor cell types3. As most developmental repressors, such as RE1-silencing transcription factor (REST) and Groucho (also known as TLE), are considered lineage-specific repressors(4,5), it remains unclear how identical combinations of transcription factors can silence so many different donor programs. Distinct lineage repressors would have to be induced in different donor cell types. Here, by studying the reprogramming of mouse fibroblasts to neurons, we found that the pan neuron-specific transcription factor Myt1-like (Myt1l)(6) exerts its pro-neuronal function by direct repression of many different somatic lineage programs except the neuronal program. The repressive function of Myt1l is mediated via recruitment of a complex containing Sin3b by binding to a previously uncharacterized N-terminal domain. In agreement with its repressive function, the genomic binding sites of Myt1l are similar in neurons and fibroblasts and are preferentially in an open chromatin configuration. The Notch signalling pathway is repressed by Myt1l through silencing of several members, including Hes1. Acute knockdown of Myt1l in the developing mouse brain mimicked a Notch gain-of-function phenotype, suggesting that Myt1l allows newborn neurons to escape Notch activation during normal development. Depletion of Myt1l in primary postmitotic neurons de-repressed non-neuronal programs and impaired neuronal gene expression and function, indicating that many somatic lineage programs are actively and persistently repressed by Myt1l to maintain neuronal identity. It is now tempting to speculate that similar 'many-but-one' lineage repressors exist for other cell fates; such repressors, in combination with lineage-specific activators, would be prime candidates for use in reprogramming additional cell types.Non peer reviewe

Neuromodulation by GABA Converts a Relay Into a Coincidence Detector

Modulation of synaptic strength by γ-aminobutyric acid receptors (GABARs) is a common feature in sensory pathways that contain relay cell types. However, the functional impact of these receptors on information processing is not clear. We considered this issue at bushy cells (BCs) in the cochlear nucleus, which relay auditory nerve (AN) activity to higher centers. BCs express GABAARs, and synaptic inputs to BCs express GABABRs. We tested the effects of GABAR activation on the relaying of AN activity using patch-clamp recordings in mature mouse brain slices at 34°C. GABA affected BC firing in response to trains of AN activity at concentrations as low as 10 μM. GABAARs reduced firing primarily late in high-frequency trains, whereas GABABRs reduced firing early and in low-frequency trains. BC firing was significantly restored when two converging AN inputs were activated simultaneously, with maximal effect over a window of <0.5 ms. Thus GABA could adjust the function of BCs, to suppress the relaying of individual inputs and require coincident activity of multiple inputs

Characterization of a Human Neuronal Culture System for the Study of Cofilin–Actin Rod Pathology

Cofilactin rod pathology, which can initiate synapse loss, has been extensively studied in rodent neurons, hippocampal slices, and in vivo mouse models of human neurodegenerative diseases such as Alzheimer’s disease (AD). In these systems, rod formation induced by disease-associated factors, such as soluble oligomers of Amyloid-β (Aβ) in AD, utilizes a pathway requiring cellular prion protein (PrPC), NADPH oxidase (NOX), and cytokine/chemokine receptors (CCR5 and/or CXCR4). However, rod pathways have not been systematically assessed in a human neuronal model. Here, we characterize glutamatergic neurons differentiated from human-induced pluripotent stem cells (iPSCs) for the formation of rods in response to activators of the PrPC-dependent pathway. Optimization of substratum, cell density, and use of glial-conditioned medium yielded a robust system for studying the development of Aβ-induced rods in the absence of glia, suggesting a cell-autonomous pathway. Rod induction in younger neurons requires ectopic expression of PrPC, but this dependency disappears by Day 55. The quantification of proteins within the rod-inducing pathway suggests that increased PrPC and CXCR4 expression may be factors in the doubling of the rod response to Aβ between Days 35 and 55. FDA-approved antagonists to CXCR4 and CCR5 inhibit the rod response. Rods were predominantly observed in dendrites, although severe cytoskeletal disruptions prevented the assignment of over 40% of the rods to either an axon or dendrite. In the absence of glia, a condition in which rods are more readily observed, neurons mature and fire action potentials but do not form functional synapses. However, PSD95-containing dendritic spines associate with axonal regions of pre-synaptic vesicles containing the glutamate transporter, VGLUT1. Thus, our results identified stem cell-derived neurons as a robust model for studying cofilactin rod formation in a human cellular environment and for developing effective therapeutic strategies for the treatment of dementias arising from multiple proteinopathies with different rod initiators