Predicting Reactive Astrogliosis Propagation by Bayesian Computational Modeling: the Repeater Stations Model.

Reactive astrogliosis occurs upon focal brain injury and in neurodegenerative diseases. The mechanisms that propagate reactive astrogliosis to distal parts of the brain, in a rapid wave that activates astrocytes and other cell types along the way, are not completely understood. It is proposed that damage-associated molecular patterns (DAMP) released by necrotic cells from the injury core have a major role in the reactive astrogliosis initiation but whether they also participate in reactive astrogliosis propagation remains to be determined. We here developed a Bayesian computational model to define the most probable model for reactive astrogliosis propagation. Starting with experimental data from GFAP-immunostained reactive astrocytes, we defined five types of astrocytes based on morphometrical cues and registered the position of each reactive astrocyte cell type in the hemisphere ipsilateral to the injured site after 3 and 7 days post-ischemia. We developed equations for the changes in DAMP concentration (due to diffusion, binding to receptors or degradation), soluble mediators secretion, and for the evolution reactive astrogliosis. We tested four predefined models based on abovementioned previous hypothesis and modifications to it. Our results showed that DAMP diffusion alone has not justified the reactive astrogliosis propagation as previously assumed. Only two models succeeded in accurately reproducing the experimentally measured data and they highlighted the role of microglia and the glial secretion of soluble mediators to sustain the reactive signal and activating neighboring astrocytes. Thus, our in silico analysis proposes that glial cells behave as repeater stations of the injury signal in order to propagate reactive astrogliosis.

The Dynamic Behavior of the P2X4 Ion Channel in the Closed Conformation.

We present the results of a detailed molecular dynamics study of the closed form of the P2X4 receptor. The fluctuations observed in the simulations were compared with the changes that occur in the transition from the closed to the open structure. To get further insight on the opening mechanism, the actual displacements were decomposed into interchain motions and intrachain deformations. This analysis revealed that the iris-like expansion of the transmembrane helices mainly results from interchain motions that already take place in the closed conformation. However, these movements cannot reach the amplitude required for the opening of the channel because they are impeded by interactions occurring around the ATP binding pocket. This suggests that the union of ATP produces distortions in the chains that eliminate the restrictions on the interchain displacements, leading to the opening of the pore.

Dynamics of T-Junction Solution Switching Aimed at Patch Clamp Experiments.

Solutions exchange systems are responsible for the timing of drug application on patch clamp experiments. There are two basic strategies for generating a solution exchange. When slow exchanges are bearable, it is easier to perform the exchange inside the tubing system upstream of the exit port. On the other hand, fast, reproducible, exchanges are usually performed downstream of the exit port. As both strategies are combinable, increasing the performance of upstream exchanges is desirable. We designed a simple method for manufacturing T-junctions (300 µm I.D.) and we measured the time profile of exchange of two saline solutions using a patch pipette with an open tip. Three factors were found to determine the timing of the solution switching: pressure, travelled distance and off-center distance. A linear relationship between the time delay and the travelled distance was found for each tested pressure, showing its dependence to the fluid velocity, which increased with pressure. The exchange time was found to increase quadratically with the delay, although a sizeable variability remains unexplained by this relationship. The delay and exchange times increased as the recording pipette moved away from the center of the stream. Those increases became dramatic as the pipette was moved close to the stream borders. Mass transport along the travelled distance between the slow fluid at the border and the fast fluid at the center seems to contribute to the time course of the solution exchange. This effect would be present in all tubing based devices. Present results might be of fundamental importance for the adequate design of serial compound exchangers which would be instrumental in the discovery of drugs that modulate the action of the physiological agonists of ion channels with the purpose of fine tuning their physiology.

Bayesian approach to model CD137 signaling in human M. tuberculosis in vitro responses.

Immune responses are qualitatively and quantitatively influenced by a complex network of receptor-ligand interactions. Among them, the CD137:CD137L pathway is known to modulate innate and adaptive human responses against Mycobacterium tuberculosis. However, the underlying mechanisms of this regulation remain unclear. In this work, we developed a Bayesian Computational Model (BCM) of in vitro CD137 signaling, devised to fit previously gathered experimental data. The BCM is fed with the data and the prior distribution of the model parameters and it returns their posterior distribution and the model evidence, which allows comparing alternative signaling mechanisms. The BCM uses a coupled system of non-linear differential equations to describe the dynamics of Antigen Presenting Cells, Natural Killer and T Cells together with the interpheron (IFN)-γ and tumor necrosis factor (TNF)-α levels in the media culture. Fast and complete mixing of the media is assumed. The prior distribution of the parameters that describe the dynamics of the immunological response was obtained from the literature and theoretical considerations Our BCM applies successively the Levenberg-Marquardt algorithm to find the maximum a posteriori likelihood (MAP); the Metropolis Markov Chain Monte Carlo method to approximate the posterior distribution of the parameters and Thermodynamic Integration to calculate the evidence of alternative hypothesis. Bayes factors provided decisive evidence favoring direct CD137 signaling on T cells. Moreover, the posterior distribution of the parameters that describe the CD137 signaling showed that the regulation of IFN-γ levels is based more on T cells survival than on direct induction. Furthermore, the mechanisms that account for the effect of CD137 signaling on TNF-α production were based on a decrease of TNF-α production by APC and, perhaps, on the increase in APC apoptosis. BCM proved to be a useful tool to gain insight on the mechanisms of CD137 signaling during human response against Mycobacterium tuberculosis.

Achieving maximal speed of solution exchange for patch clamp experiments.

BACKGROUND: Resolving the kinetics of agonist binding events separately from the subsequent channel gating processes requires the ability of applying and removing the agonist before channel gating occurs. No reported system has yet achieved pulses shorter than 100 µs, necessary to study nicotinic ACh receptor or AMPA receptor activation. METHODOLOGY/PRINCIPAL FINDINGS: Solution exchange systems deliver short agonist pulses by moving a sharp interface between a control and an experimental solution across a channel preparation. We achieved shorter pulses by means of an exchange system that combines a faster flow velocity, narrower partition between the two streams, and increased velocity and bandwidth of the movement of the interface. The measured response of the entire system was fed back to optimize the voltage signal applied to the piezoelectric actuator overcoming the spurious oscillations arising from the mechanical resonances when a high bandwidth driving function was applied. Optimization was accomplished by analyzing the transfer function of the solution exchange system. When driven by optimized command pulses the enhanced system provided pulses lasting 26 ± 1 µs and exchanging 93 ± 1% of the solution, as measured in the open tip of a patch pipette. CONCLUSIONS/SIGNIFICANCE: Pulses of this duration open the experimental study of the molecular events that occur between the agonist binding and the opening of the channel.

Increasing the reliability of solution exchanges by monitoring solenoid valve actuation.

Solenoid valves are a core component of most solution perfusion systems used in neuroscience research. As they open and close, they control the flow of solution through each perfusion line, thereby modulating the timing and sequence of chemical stimulation. The valves feature a ferromagnetic plunger that moves due to the magnetization of the solenoid and returns to its initial position with the aid of a spring. The delays between the time of voltage application or removal and the actual opening or closing of the valve are difficult to predict beforehand and have to be measured experimentally. Here we propose a simple method for monitoring whether and when the solenoid valve opens and closes. The proposed method detects the movement of the plunger as it generates a measurable signal on the solenoid that surrounds it. Using this plunger signal, we detected the opening and closing of diaphragm and pinch solenoid valves with a systematic error of less than 2ms. After this systematic error is subtracted, the trial-to-trial error was below 0.2ms.

Responses of rat P2X2 receptors to ultrashort pulses of ATP provide insights into ATP binding and channel gating.

To gain insight into the way that P2X(2) receptors localized at synapses might function, we explored the properties of outside-out patches containing many of these channels as ATP was very rapidly applied and removed. Using a new method to calibrate the speed of exchange of solution over intact patches, we were able to reliably produce applications of ATP lasting <200 micros. For all concentrations of ATP, there was a delay of at least 80 micros between the time when ATP arrived at the receptor and the first detectable flow of inward current. In response to 200-micros pulses of ATP, the time constant of the rising phase of the current was approximately 600 micros. Thus, most channel openings occurred when no free ATP was present. The current deactivated with a time constant of approximately 60 ms. The amplitude of the peak response to a brief pulse of a saturating concentration of ATP was approximately 70% of that obtained during a long application of the same concentration of ATP. Thus, ATP leaves fully liganded channels without producing an opening at least 30% of the time. Extensive kinetic modeling revealed three different schemes that fit the data well, a sequential model and two allosteric models. To account for the delay in opening at saturating ATP, it was necessary to incorporate an intermediate closed state into all three schemes. These kinetic properties indicate that responses to ATP at synapses that use homomeric P2X(2) receptors would be expected to greatly outlast the duration of the synaptic ATP transient produced by a single presynaptic spike. Like NMDA receptors, P2X(2) receptors provide the potential for complex patterns of synaptic integration over a time scale of hundreds of milliseconds.

Estimation of ion channel kinetics from fluctuations of macroscopic currents.

For single channel recordings, the maximum likelihood estimation (MLE) of kinetic rates and conductance is well established. A direct extrapolation of this method to macroscopic currents is computationally prohibitive: it scales as a power of the number of channels. An approximated MLE that ignored the local time correlation of the data has been shown to provide estimates of the kinetic parameters. In this article, an improved approximated MLE that takes into account the local time correlation is proposed. This method estimates the channel kinetics using both the time course and the random fluctuations of the macroscopic current generated by a homogeneous population of ion channels under white noise. It allows arbitrary kinetic models and stimulation protocols. The application of the proposed algorithm to simulated data from a simple three-state model on nonstationary conditions showed reliable estimates of all the kinetic constants, the conductance and the number of channels, and reliable values for the standard error of those estimates. Compared to the previous approximated MLE, it reduces by a factor of 10 the amount of data needed to secure a given accuracy and it can even determine the kinetic rates in macroscopic stationary conditions.