Provably correct, asymptotically efficient, higher-order reverse-mode automatic differentiation

In this paper, we give a simple and efficient implementation of reverse-mode automatic differentiation, which both extends easily to higher-order functions, and has run time and memory consumption linear in the run time of the original program. In addition to a formal description of the translation, we also describe an implementation of this algorithm, and prove its correctness by means of a logical relations argument.

Na+/Ca2+ exchanger isoform 1 takes part to the Ca2+-related prosurvival pathway of SOD1 in primary motor neurons exposed to beta-methylamino-l-alanine

Background The cycad neurotoxin beta-methylamino-l-alanine (L-BMAA), one of the environmental trigger factor for amyotrophic lateral sclerosis/Parkinson-dementia complex (ALS/PDC), may cause neurodegeneration by disrupting organellar Ca2+ homeostasis. Through the activation of Akt/ERK1/2 pathway, the Cu,Zn-superoxide dismutase (SOD1) and its non-metallated form, ApoSOD1, prevent endoplasmic reticulum (ER) stress-induced cell death in motor neurons exposed to L-BMAA. This occurs through the rapid increase of intracellular Ca2+ concentration ([Ca2+]i) in part flowing from the extracellular compartment and in part released from ER. However, the molecular components of this mechanism remain uncharacterized. Methods By an integrated approach consisting on the use of siRNA strategy, Western blotting, confocal double- labeling immunofluorescence, patch-clamp electrophysiology, and Fura 2-/SBFI-single-cell imaging, we explored in rat motor neuron-enriched cultures the involvement of the plasma membrane proteins Na+/Ca2+ exchanger (NCX) and purinergic P2X7 receptor as well as that of the intracellular cADP-ribose (cADPR) pathway, in the neuroprotective mechanism of SOD1. Results We showed that SOD1-induced [Ca2+]i rise was prevented neither by A430879, a P2X7 receptor specific antagonist or 8-bromo-cADPR, a cell permeant antagonist of cADP-ribose, but only by the pan inhibitor of NCX, CB-DMB. The same occurred for the ApoSOD1. Confocal double labeling immunofluorescence showed a huge expression of plasmalemmal NCX1 and intracellular NCX3 isoforms. Furthermore, we identified NCX1 reverse mode as the main mechanism responsible for the neuroprotective ER Ca2+ refilling elicited by SOD1 and ApoSOD1 through which they promoted translocation of active Akt in the nuclei of a subset of primary motor neurons. Finally, the activation of NCX1 by the specific agonist CN-PYB2 protected motor neurons from L-BMAA-induced cell death, mimicking the effect of SOD1. Conclusion Collectively, our data indicate that SOD1 and ApoSOD1 exert their neuroprotective effect by modulating ER Ca2+ content through the activation of NCX1 reverse mode and Akt nuclear translocation in a subset of primary motor neurons.

Discrete adjoint methodology for general multiphysics problems

This article presents a methodology whereby adjoint solutions for partitioned multiphysics problems can be computed efficiently, in a way that is completely independent of the underlying physical sub-problems, the associated numerical solution methods, and the number and type of couplings between them. By applying the reverse mode of algorithmic differentiation to each discipline, and by using a specialized recording strategy, diagonal and cross terms can be evaluated individually, thereby allowing different solution methods for the generic coupled problem (for example block-Jacobi or block-Gauss-Seidel). Based on an implementation in the open-source multiphysics simulation and design software SU2, we demonstrate how the same algorithm can be applied for shape sensitivity analysis on a heat exchanger (conjugate heat transfer), a deforming wing (fluid–structure interaction), and a cooled turbine blade where both effects are simultaneously taken into account.

Arrhythmogenesis in heart cells involves reverse E–C coupling and reverse electrotonic conduction along T-tubules

Early afterdepolarization (EAD) is an aberrant cardiac afterpotential that underlies the development of life-threatening ventricular arrhythmias. It is believed that the development of EAD is caused by the reactivation of L-type Ca2+ current during the period of the action potential plateau; however, the cellular mechanisms that underlie the development of EAD is still controversial. One favorable alternative is the depolarizing reverse-mode operation of the Na+/Ca2+ exchanger, which is activated by aberrant Ca2+ release from the sarcoplasmic reticulum in the process of reverse E–C coupling. Since EADs develop preferentially in damaged heart cells with abnormal Ca2+-signaling, here I studied the causal link between the development of EADs and aberrant intracellular Ca2+ level ([Ca2+]i) dynamics in mouse heart cells using the whole-cell clamp technique. My results show (1) the generation of EADs was preceded by the development of depolarizing membrane potential (Vm) fluctuation, (2) the depolarizing Vm fluctuation is associated with [Ca2+]i elevation, suggesting an involvement of reverse E–C coupling via the Na+/Ca2+ exchanger, and (3) that extending the T-tubules’ length constant by decreasing the extracellular K+ level facilitated the development of the Vm fluctuation and EADs. Taken together, I conclude that EADs are caused by the depolarizing Vm fluctuation, which is induced locally in the T-tubule membrane by aberrant [Ca2+]i elevation and is conducted back electrotonically along the T-tubules.

Assessing Enzyme Immobilization on Reverse Asymmetric Membranes and Biocatalytic Reactor Performance

Integration of membrane filtration and biocatalysis has appealing benefits in terms of simultaneous substrate conversion and product separation in one reactor. Nevertheless, the interaction between enzymes and membrane is complex and the mechanism of enzyme docking on membrane is similar to membrane fouling. In this study, focus is given on the assessment of enzyme immobilization mechanism on reverse asymmetric polymer membrane based on the permeate flux data during the procedure. Evaluation of membrane performance in terms of its permeability, fouling mechanisms, enzyme loading, enzyme reusability and biocatalytic productivity were also conducted. Alcohol Dehydrogenase (EC 1.1.1.1), able to catalyze formaldehyde to methanol with subsequent oxidation of NADH to NAD was selected as the model enzyme. Two commercial, asymmetric, flat sheet polymer membranes (PES and PVDF) were immobilized with the enzyme in the reverse mode. Combination of concentration polarization phenomenon and pressure driven filtration successfully immobilized almost 100% of the enzymes in the feed solutions. The biocatalytic membrane reactor recorded more than 90% conversion, stable permeate flux with no enzyme leaching even after 5 cycles. The technique showing promising results to be expanded to continuous membrane separation setup for repeated use of enzymes.

AutoMat: automatic differentiation for generalized standard materials on GPUs

We propose a universal method for the evaluation of generalized standard materials that greatly simplifies the material law implementation process. By means of automatic differentiation and a numerical integration scheme, AutoMat reduces the implementation effort to two potential functions. By moving AutoMat to the GPU, we close the performance gap to conventional evaluation routines and demonstrate in detail that the expression level reverse mode of automatic differentiation as well as its extension to second order derivatives can be applied inside CUDA kernels. We underline the effectiveness and the applicability of AutoMat by integrating it into the FFT-based homogenization scheme of Moulinec and Suquet and discuss the benefits of using AutoMat with respect to runtime and solution accuracy for an elasto-viscoplastic example.

Ebola: Destroys Na+/K+ Ion Exchange to Accelerate Electrolyte Imbalance by Scorpion Venom-like System

Ebola sickness is a hemorrhagic fever caused by the Ebola virus that has an extremely high fatality rate. Electrolyte imbalance is a typical sign in Ebola patients who have already contracted the virus. The use of bioinformatics calculation tools to research Ebola's electrolyte imbalance mechanism is critical for halting the development of the epidemic and saving lives. The computational method of conserved domain search was employed to investigate the protein function of EBOV in this work. This study demonstrates that L, N, S, VP24, and VP35 have LCN type CS-α/β domains. It is a peptide neurotoxin found in scorpions, sea anemone, and snake venom. It can activate Na+ channels and gradually deactivate them, and deactivate voltage- and Ca+2-activated K+ channels. S LCN type CS-α/β is a neurotoxin with a lengthy chain that can activate Na+ channels. VP24, VP35, and N LCN type CS-α/β are short-chain toxins that inhibit voltage-dependent or Ca+2-activated K+ channels and partially inactivate sodium channels. L contains both long- and short-chain LCN type CS-α/β toxins that can activate Na+ channels and inhibit K+ channels. These LCN type CS-α/β can activate Na+ channels and Na+/K+ pumps while simultaneously inactivating K+ channels. It may result in many Na+ entering the cell and a large amount of K+ accumulating within the cell. Simultaneously, the Na+/Ca+ exchange pump outputs Na+ and inputs Ca+2 in “the reverse” mode. The results in an electrolytic environment outside the cell with hyponatremia, hypocalcemia and hypokalemia.

Seismic Wave Propagation and Inversion with Neural Operators

Seismic wave propagation forms the basis for most aspects of seismological research, yet solving the wave equation is a major computational burden that inhibits the progress of research. This is exacerbated by the fact that new simulations must be performed whenever the velocity structure or source location is perturbed. Here, we explore a prototype framework for learning general solutions using a recently developed machine learning paradigm called neural operator. A trained neural operator can compute a solution in negligible time for any velocity structure or source location. We develop a scheme to train neural operators on an ensemble of simulations performed with random velocity models and source locations. As neural operators are grid free, it is possible to evaluate solutions on higher resolution velocity models than trained on, providing additional computational efficiency. We illustrate the method with the 2D acoustic wave equation and demonstrate the method’s applicability to seismic tomography, using reverse-mode automatic differentiation to compute gradients of the wavefield with respect to the velocity structure. The developed procedure is nearly an order of magnitude faster than using conventional numerical methods for full waveform inversion.

Astrocytic extracellular vesicles modulate neuronal calcium homeostasis via transglutaminase-2

We have uncovered a novel role for astrocytes-derived extracellular vesicles (EVs) in controlling intraneuronal Ca2+ concentration ([Ca2+]i) and identified transglutaminase-2 (TG2) as a surface-cargo of astrocytes-derived EVs. Incubation of hippocampal neurons with primed astrocyte-derived EVs have led to an increase in [Ca2+]i, unlike EVs from TG2-knockout astrocytes. Exposure of neurons or brain slices to extracellular TG2 promoted a [Ca2+]i rise, which was reversible upon TG2 removal and was dependent on Ca2+ influx through the plasma membrane. Patch-clamp and calcium imaging recordings revealed TG2-dependent neuronal membrane depolarisation and activation of inward currents, due to the opening of L-type-VOCCs and to Na+/Ca2+-exchanger (NCX) operation in the reverse mode, as indicated by VOCCs/NCX pharmacological inhibitors. A subunit of Na+/K+-ATPase was selected by comparative proteomics and identified as being functionally inhibited by extracellular TG2, implicating Na+/K+-ATPase inhibition in NCX reverse mode-switching leading to Ca2+ influx and higher basal [Ca2+]i. These data suggest that reactive astrocytes control intraneuronal [Ca2+]i through release of EVs with TG2 as responsible cargo, which could have a significant impact on synaptic activity in brain inflammation.