Fast spatiotemporal smoothing of calcium measurements in dendritic trees

We discuss methods for fast spatiotemporal smoothing of calcium signals in dendritic trees, given single-trial, spatially localized imaging data obtained via multi-photon microscopy. By analyzing the dynamics of calcium binding to probe molecules and the effects of the imaging procedure, we show that calcium concentration can be estimated up to an affine transformation, i.e., an additive and multiplicative constant. To obtain a full spatiotemporal estimate, we model calcium dynamics within the cell using a functional approach. The evolution of calcium concentration is represented through a smaller set of hidden variables that incorporate fast transients due to backpropagating action potentials (bAPs), or other forms of stimulation. Because of the resulting state space structure, inference can be done in linear time using forward-backward maximum-a-posteriori methods. Non-negativity constraints on the calcium concentration can also be incorporated using a log-barrier method that does not affect the computational scaling. Moreover, by exploiting the neuronal tree structure we show that the cost of the algorithm is also linear in the size of the dendritic tree, making the approach applicable to arbitrarily large trees. We apply this algorithm to data obtained from hippocampal CA1 pyramidal cells with experimentally evoked bAPs, some of which were paired with excitatory postsynaptic potentials (EPSPs). The algorithm recovers the timing of the bAPs and provides an estimate of the induced calcium transient throughout the tree. The proposed methods could be used to further understand the interplay between bAPs and EPSPs in synaptic strength modification. More generally, this approach allows us to infer the concentration on intracellular calcium across the dendritic tree from noisy observations at a discrete set of points in space.     

Learning by structural remodeling in a class of single cell models

Changes in neural connectivity are thought to underlie the most permanent forms of memory in the brain. We consider two models, derived from the clusteron (Mel, Adv Neural Inf Process Syst 4:35-42, 1992), to study this method of learning. The models show a direct relationship between the speed of memory acquisition and the probability of forming appropriate synaptic connections. Moreover, the strength of learned associations grows with the number of fibers that have taken part in the learning process. We provide simple and intuitive explanations of these two results by analyzing the distribution of synaptic activations. The obtained insights are then used to extend the model to perform novel tasks: feature detection, and learning spatio-temporal patterns. We also provide an analytically tractable approximation to the model to put these observations on a firm basis. The behavior of both the numerical and analytical models correlate well with experimental results of learning tasks which are thought to require a reorganization of neuronal networks.     

Semi-preparative chromatographic purification of the enantiomers S-(−)-amlodipine and R-(+)-amlodipine

Pharmacokinetic studies of optically pure compounds after single enantiomer administration are becoming increasingly important. The process of racemization in vivo can diminish all expected advantages of single enantiomer treatment. Amlodipine, one of the calcium channel blockers, currently used in therapy as a racemate, is one of such drugs under study. In order to administer single enantiomers of amlodipine to healthy volunteers both were chromatographically purified and characterised. The two optical isomers of amlodipine, active S-(−)- and non-active R-(+)-amlodipine, were purified using chromatographic procedure adopted from the analytical separation. Enantiomers were successfully converted to benzenesulphonic salt without any racemization. All semi-preparative purifications were monitored with complementary analytical methods, HPLC and CE, along with the determination of optical activity so that the final product was sufficiently defined for further in vivo studies. The analytical method developed for the determination of plasma concentrations of each enantiomer of amlodipine in these studies is also briefly described.     

A finite volume method for stochastic integrate-and-fire models

The stochastic integrate and fire neuron is one of the most commonly used stochastic models in neuroscience. Although some cases are analytically tractable, a full analysis typically calls for numerical simulations. We present a fast and accurate finite volume method to approximate the solution of the associated Fokker-Planck equation. The discretization of the boundary conditions offers a particular challenge, as standard operator splitting approaches cannot be applied without modification. We demonstrate the method using stationary and time dependent inputs, and compare them with Monte Carlo simulations. Such simulations are relatively easy to implement, but can suffer from convergence difficulties and long run times. In comparison, our method offers improved accuracy, and decreases computation times by several orders of magnitude. The method can easily be extended to two and three dimensional Fokker-Planck equations.

Issues in the development of medical products based on human plasma

Product development and process validation are shown in the case of several products obtained from human plasma. These are virus-inactivated plasma, intravenous immunoglobulins and the clotting factors VIII and IX. Different analytical methods are presented, which are used for product control and in-process control. For the production of virus-inactivated human plasma a down-scale protocol is presented, allowing a simulation of the production on a laboratory scale. Virus validation has shown that the reduction of transfusion-relevant viruses in the process was higher than six log steps. Determination of leachables from the RP-column, which was used in this production, proved that they appear in the final product in quantities below the detection limits only. It was also shown that the chemicals used for virus inactivation could be quantitatively removed from the product. For the isolation of other products, here intravenous gamma globulins and the clotting factors VIII and IX, similar validation steps had to be taken. In the case of clotting factor VIII the following data were determined, the reduction of viruses, the amount of leachables from the column, the residues of chemicals from the solvent/detergent treatment for virus inactivation. Virus reduction was successfully performed as well as the removal of chemicals used for virus inactivation. The amount of leachables from the columns used for chromatographic purification was found to be far below the permissible levels.     

Improved Estimation and Interpretation of Correlations in Neural Circuits

Ambitious projects aim to record the activity of ever larger and denser neuronal populations in vivo. Correlations in neural activity measured in such recordings can reveal important aspects of neural circuit organization. However, estimating and interpreting large correlation matrices is statistically challenging. Estimation can be improved by regularization, i.e. by imposing a structure on the estimate. The amount of improvement depends on how closely the assumed structure represents dependencies in the data. Therefore, the selection of the most efficient correlation matrix estimator for a given neural circuit must be determined empirically. Importantly, the identity and structure of the most efficient estimator informs about the types of dominant dependencies governing the system. We sought statistically efficient estimators of neural correlation matrices in recordings from large, dense groups of cortical neurons. Using fast 3D random-access laser scanning microscopy of calcium signals, we recorded the activity of nearly every neuron in volumes 200 μm wide and 100 μm deep (150–350 cells) in mouse visual cortex. We hypothesized that in these densely sampled recordings, the correlation matrix should be best modeled as the combination of a sparse graph of pairwise partial correlations representing local interactions and a low-rank component representing common fluctuations and external inputs. Indeed, in cross-validation tests, the covariance matrix estimator with this structure consistently outperformed other regularized estimators. The sparse component of the estimate defined a graph of interactions. These interactions reflected the physical distances and orientation tuning properties of cells: The density of positive ‘excitatory’ interactions decreased rapidly with geometric distances and with differences in orientation preference whereas negative ‘inhibitory’ interactions were less selective. Because of its superior performance, this ‘sparse+latent’ estimator likely provides a more physiologically relevant representation of the functional connectivity in densely sampled recordings than the sample correlation matrix.     

Application of monoliths as supports for affinity chromatography and fast enzymatic conversion.

Monoliths are useful chromatographic supports, as their structure allows improved mass transport. This results in fast separation. Once the ligand of interest has been immobilized, chromatographic separation can also be accomplished in affinity mode. Ligands with low molecular mass have been shown to be the easiest to immobilize. Nowadays, ligands with low molecular mass are often designed by combinatorial chemical techniques. In addition, many applications have been described where ligands with high molecular mass, such as Proteins A and G, antibodies, lectins and receptors are used. The immobilization of an enzyme on the monolithic support creates a flow-through reactor. Small proteins, such as carbonic anhydrase, can be directly immobilized on the support. However, in the case of large molecules, the active center of the enzyme is no longer accessible at all or only to a limited degree. An improvement can be achieved by introducing a spacer, which allows maximum enzymatic conversion. Fast conversion of substrates with high molecular mass has been investigated with immobilized trypsin. It was shown that in case of high-molecular-mass substrates, the conversion rate depends very much on the flow-rate. Most applications described have been performed on an analytical or semi-preparative scale. However, the technical problems of up-scaling are close to being definitely solved, enabling enzymatic conversion on a preparative scale in the future.     

Zebrafish enpp1 mutants exhibit pathological mineralization,mimicking features of generalized arterial calcification of infancy (GACI) and pseudoxanthoma elasticum (PXE)

In recent years it has become clear that, mechanistically, biomineralization is a process that has to be actively inhibited as a default state. This inhibition must be released in a rigidly controlled manner in order for mineralization to occur in skeletal elements and teeth. A central aspect of this concept is the tightly controlled balance between phosphate, a constituent of the biomineral hydroxyapatite, and pyrophosphate, a physiochemical inhibitor of mineralization. Here, we provide a detailed analysis of a zebrafish mutant, dragonfish (dgf), which is mutant for ectonucleoside pyrophosphatase/phosphodiesterase 1 (Enpp1), a protein that is crucial for supplying extracellular pyrophosphate. Generalized arterial calcification of infancy (GACI) is a fatal human disease, and the majority of cases are thought to be caused by mutations in ENPP1. Furthermore, some cases of pseudoxanthoma elasticum (PXE) have recently been linked to ENPP1. Similar to humans, we show here that zebrafish enpp1 mutants can develop ectopic calcifications in a variety of soft tissues – most notably in the skin, cartilage elements, the heart, intracranial space and the notochord sheet. Using transgenic reporter lines, we demonstrate that ectopic mineralizations in these tissues occur independently of the expression of typical osteoblast or cartilage markers. Intriguingly, we detect cells expressing the osteoclast markers Trap and CathepsinK at sites of ectopic calcification at time points when osteoclasts are not yet present in wild-type siblings. Treatment with the bisphosphonate etidronate rescues aspects of the dgf phenotype, and we detected deregulated expression of genes that are involved in phosphate homeostasis and mineralization, such as fgf23, npt2a, entpd5 and spp1 (also known as osteopontin). Employing a UAS-GalFF approach, we show that forced expression of enpp1 in blood vessels or the floorplate of mutant embryos is sufficient to rescue the notochord mineralization phenotype. This indicates that enpp1 can exert its function in tissues that are remote from its site of expression.KEY WORDS: Zebrafish, Ectopic mineralization, Generalized arterial calcification of infancy, GACI, Pseudoxanthoma elasticum, PXE, Pyrophosphate     

Branching dendrites with resonant membrane: a “sum-over-trips” approach

Dendrites form the major components of neurons. They are complex branching structures that receive and process thousands of synaptic inputs from other neurons. It is well known that dendritic morphology plays an important role in the function of dendrites. Another important contribution to the response characteristics of a single neuron comes from the intrinsic resonant properties of dendritic membrane. In this paper we combine the effects of dendritic branching and resonant membrane dynamics by generalising the “sum-over-trips” approach (Abbott et al. in Biol Cybernetics 66, 49–60 1991). To illustrate how this formalism can shed light on the role of architecture and resonances in determining neuronal output we consider dual recording and reconstruction data from a rat CA1 hippocampal pyramidal cell. Specifically we explore the way in which an I _h current contributes to a voltage overshoot at the soma.