Probe-based bacterial single-cell RNA sequencing predicts toxin regulation.

Clonal bacterial populations rely on transcriptional variation across individual cells to produce specialized states that increase fitness. Understanding all cell states requires studying isogenic bacterial populations at the single-cell level. Here we developed probe-based bacterial sequencing (ProBac-seq), a method that uses libraries of DNA probes and an existing commercial microfluidic platform to conduct bacterial single-cell RNA sequencing. We sequenced the transcriptome of thousands of individual bacterial cells per experiment, detecting several hundred transcripts per cell on average. Applied to Bacillus subtilis and Escherichia coli, ProBac-seq correctly identifies known cell states and uncovers previously unreported transcriptional heterogeneity. In the context of bacterial pathogenesis, application of the approach to Clostridium perfringens reveals heterogeneous expression of toxin by a subpopulation that can be controlled by acetate, a short-chain fatty acid highly prevalent in the gut. Overall, ProBac-seq can be used to uncover heterogeneity in isogenic microbial populations and identify perturbations that affect pathogenicity.

Computing the Riemannian curvature of image patch and single-cell RNA sequencing data manifolds using extrinsic differential geometry.

Most high-dimensional datasets are thought to be inherently low-dimensional-that is, data points are constrained to lie on a low-dimensional manifold embedded in a high-dimensional ambient space. Here, we study the viability of two approaches from differential geometry to estimate the Riemannian curvature of these low-dimensional manifolds. The intrinsic approach relates curvature to the Laplace-Beltrami operator using the heat-trace expansion and is agnostic to how a manifold is embedded in a high-dimensional space. The extrinsic approach relates the ambient coordinates of a manifold's embedding to its curvature using the Second Fundamental Form and the Gauss-Codazzi equation. We found that the intrinsic approach fails to accurately estimate the curvature of even a two-dimensional constant-curvature manifold, whereas the extrinsic approach was able to handle more complex toy models, even when confounded by practical constraints like small sample sizes and measurement noise. To test the applicability of the extrinsic approach to real-world data, we computed the curvature of a well-studied manifold of image patches and recapitulated its topological classification as a Klein bottle. Lastly, we applied the extrinsic approach to study single-cell transcriptomic sequencing (scRNAseq) datasets of blood, gastrulation, and brain cells to quantify the Riemannian curvature of scRNAseq manifolds.

An Engineered CRISPR-Cas9 Mouse Line for Simultaneous Readout of Lineage Histories and Gene Expression Profiles in Single Cells.

Tracing the lineage history of cells is key to answering diverse and fundamental questions in biology. Coupling of cell ancestry information with other molecular readouts represents an important goal in the field. Here, we describe the CRISPR array repair lineage tracing (CARLIN) mouse line and corresponding analysis tools that can be used to simultaneously interrogate the lineage and transcriptomic information of single cells in vivo. This model exploits CRISPR technology to generate up to 44,000 transcribed barcodes in an inducible fashion at any point during development or adulthood, is compatible with sequential barcoding, and is fully genetically defined. We have used CARLIN to identify intrinsic biases in the activity of fetal liver hematopoietic stem cell (HSC) clones and to uncover a previously unappreciated clonal bottleneck in the response of HSCs to injury. CARLIN also allows the unbiased identification of transcriptional signatures associated with HSC activity without cell sorting.

Atomic-level characterization of protein-protein association.

Despite the biological importance of protein-protein complexes, determining their structures and association mechanisms remains an outstanding challenge. Here, we report the results of atomic-level simulations in which we observed five protein-protein pairs repeatedly associate to, and dissociate from, their experimentally determined native complexes using a molecular dynamics (MD)-based sampling approach that does not make use of any prior structural information about the complexes. To study association mechanisms, we performed additional, conventional MD simulations, in which we observed numerous spontaneous association events. A shared feature of native association for these five structurally and functionally diverse protein systems was that if the proteins made contact far from the native interface, the native state was reached by dissociation and eventual reassociation near the native interface, rather than by extensive interfacial exploration while the proteins remained in contact. At the transition state (the conformational ensemble from which association to the native complex and dissociation are equally likely), the protein-protein interfaces were still highly hydrated, and no more than 20% of native contacts had formed.

Closed-loop control of a fragile network: application to seizure-like dynamics of an epilepsy model.

It has recently been proposed that the epileptic cortex is fragile in the sense that seizures manifest through small perturbations in the synaptic connections that render the entire cortical network unstable. Closed-loop therapy could therefore entail detecting when the network goes unstable, and then stimulating with an exogenous current to stabilize the network. In this study, a non-linear stochastic model of a neuronal network was used to simulate both seizure and non-seizure activity. In particular, synaptic weights between neurons were chosen such that the network's fixed point is stable during non-seizure periods, and a subset of these connections (the most fragile) were perturbed to make the same fixed point unstable to model seizure events; and, the model randomly transitions between these two modes. The goal of this study was to measure spike train observations from this epileptic network and then apply a feedback controller that (i) detects when the network goes unstable, and then (ii) applies a state-feedback gain control input to the network to stabilize it. The stability detector is based on a 2-state (stable, unstable) hidden Markov model (HMM) of the network, and detects the transition from the stable mode to the unstable mode from using the firing rate of the most fragile node in the network (which is the output of the HMM). When the unstable mode is detected, a state-feedback gain is applied to generate a control input to the fragile node bringing the network back to the stable mode. Finally, when the network is detected as stable again, the feedback control input is switched off. High performance was achieved for the stability detector, and feedback control suppressed seizures within 2 s after onset.

Fragility in dynamic networks: application to neural networks in the epileptic cortex.

Epilepsy is a network phenomenon characterized by atypical activity at the neuronal and population levels during seizures, including tonic spiking, increased heterogeneity in spiking rates, and synchronization. The etiology of epilepsy is unclear, but a common theme among proposed mechanisms is that structural connectivity between neurons is altered. It is hypothesized that epilepsy arises not from random changes in connectivity, but from specific structural changes to the most fragile nodes or neurons in the network. In this letter, the minimum energy perturbation on functional connectivity required to destabilize linear networks is derived. Perturbation results are then applied to a probabilistic nonlinear neural network model that operates at a stable fixed point. That is, if a small stimulus is applied to the network, the activation probabilities of each neuron respond transiently but eventually recover to their baseline values. When the perturbed network is destabilized, the activation probabilities shift to larger or smaller values or oscillate when a small stimulus is applied. Finally, the structural modifications to the neural network that achieve the functional perturbation are derived. Simulations of the unperturbed and perturbed networks qualitatively reflect neuronal activity observed in epilepsy patients, suggesting that the changes in network dynamics due to destabilizing perturbations, including the emergence of an unstable manifold or a stable limit cycle, may be indicative of neuronal or population dynamics during seizure. That is, the epileptic cortex is always on the brink of instability and minute changes in the synaptic weights associated with the most fragile node can suddenly destabilize the network to cause seizures. Finally, the theory developed here and its interpretation of epileptic networks enables the design of a straightforward feedback controller that first detects when the network has destabilized and then applies linear state feedback control to steer the network back to its stable state.

Instability detector of a fragile neural network: application to seizure detection in epilepsy.

It has recently been proposed that the epileptic cortex is fragile in the sense that seizures manifest through small perturbations in the synaptic connections that render the entire cortical network unstable. Therefore, one method for detecting seizures is to detect when the neuronal network has gone unstable. This is important for implementing a closed-loop therapy to suppress seizures. In this paper, we consider a widely used nonlinear stochastic model of a neuronal network, and assume that spiking dynamics during non-seizure periods correspond to certain synaptic connections that render its fixed point stable. We then apply a minimum energy perturbation theory we recently developed for networks to determine the changes in the most fragile node's synaptic connections that make the same fixed point unstable (our model during seizure). Then a detector is designed as follows. First a 2-state HMM is constructed (stable=state 1 and unstable=state 2) with fixed state transition probabilities, where the output observation is the firing rate of the most fragile node in the network. The output density functions are assumed to be Gaussian with parameters computed using maximum likelihood estimation on data generated from the nonlinear network model in each state. Then, to detect a transition from stable to unstable, spiking activity is simulated in all nodes from the nonlinear model. The detector first measures the firing rate of the fragile node, and computes the derivative of the cumulative likelihood ratio of the observed firing rate from the HMM's output distributions. When the derivative exceeds a certain threshold, a transition to the unstable state is detected. Various thresholds were tested when firing rate was computed by averaging over a different number of windows of different lengths. High performance was achieved and a tradeoff was found between the accuracy of the detector and the detection delay.

Fluctuating inhibitory inputs promote reliable spiking at theta frequencies in hippocampal interneurons.

Theta-frequency (4-12 Hz) rhythms in the hippocampus play important roles in learning and memory. CA1 interneurons located at the stratum lacunosum-moleculare and radiatum junction (LM/RAD) are thought to contribute to hippocampal theta population activities by rhythmically pacing pyramidal cells with inhibitory postsynaptic potentials. This implies that LM/RAD cells need to fire reliably at theta frequencies in vivo. To determine whether this could occur, we use biophysically based LM/RAD model cells and apply different cholinergic and synaptic inputs to simulate in vivo-like network environments. We assess spike reliabilities and spiking frequencies, identifying biophysical properties and network conditions that best promote reliable theta spiking. We find that synaptic background activities that feature large inhibitory, but not excitatory, fluctuations are essential. This suggests that strong inhibitory input to these cells is vital for them to be able to contribute to population theta activities. Furthermore, we find that Type I-like oscillator models produced by augmented persistent sodium currents (I(NaP)) or diminished A-type potassium currents (I(A)) enhance reliable spiking at lower theta frequencies. These Type I-like models are also the most responsive to large inhibitory fluctuations and can fire more reliably under such conditions. In previous work, we showed that I(NaP) and I(A) are largely responsible for establishing LM/RAD cells' subthreshold activities. Taken together with this study, we see that while both these currents are important for subthreshold theta fluctuations and reliable theta spiking, they contribute in different ways - I(NaP) to reliable theta spiking and subthreshold activity generation, and I(A) to subthreshold activities at theta frequencies. This suggests that linking subthreshold and suprathreshold activities should be done with consideration of both in vivo contexts and biophysical specifics.

A network analysis of the dynamics of seizure.

Seizures are events that spread through the brain's network of connections and create pathological activity. To understand what is occurring in the brain during seizure we investigated the time progression of the brain's state from seizure onset to seizure suppression. Knowledge of a seizure's dynamics and the associated spatial structure is important for localizing the seizure foci and determining the optimal location and timing of electrical stimulation to mitigate seizure development. In this study, we analyzed intracranial EEG data recorded in 2 human patients with drug-resistant epilepsy prior to undergoing resection surgery using network analyses. Specifically, we computed a time sequence of connectivity matrices from iEEG (intracranial electroencephalography) recordings that represent network structure over time. For each patient, connectivity between electrodes was measured using the coherence in the band of frequencies with the strongest modulation during seizure. The connectivity matrices' structure was analyzed using an eigen-decomposition. The leading eigenvector was used to estimate each electrode's time dependent centrality (importance to the network's connectivity). The electrode centralities were clustered over the course of each seizure and the cluster centroids were compared across seizures. We found, for each patient, there was a consistent set of centroids that occurred during each seizure. Further, the brain reliably evolved through the same progression of states across multiple seizures including characteristic onset and suppression states.