Christian Stricker

Statistical analysis of amplitude fluctuations in EPSCs evoked in rat CA1 pyramidal neurones in vitro.

1. EPSCs were evoked in CA1 pyramidal neurones of young rats in vitro by extracellular stimulation of axons in a restricted stratum radiatum field, and were recorded using the whole‐cell technique. 2. Quantal fluctuations in EPSC amplitude could be demonstrated for nineteen of fifty EPSCs analysed. Quantal currents (at the soma) ranged from 2.6 to 9.5 pA (after correction for the access resistance) with a mean of 4.0 +/‐ 2.0 pA. 3. Quantal variance was negligible for the majority (13/19) of the EPSCs. However, a large quantal variance (with a coefficient of variation > 0.4) is one possible reason why a large number of the EPSCs (29/50) could not be shown to have quantal fluctuations. 4. The statistical pattern of fluctuations in the amplitude of the majority of the quantal EPSCs (18/19) could not be described by conventional models of transmitter release. 5. The time course of the EPSC and a compartmental model of CA1 pyramidal neurones were used to calculate synaptic location. The quantal current (at the soma) was independent of the electrotonic location of the synapse at which it was evoked. The peak quantal conductance generating each quantal current ranged from 0.5 to 6.8 nS (mean 1.3 +/‐ 1.4 nS), its magnitude increasing with distance from the soma. The mean peak conductance is likely to be generated by the opening of at least 60‐160 AMPA channels.

Animal navigation: the difficulty of moving in a straight line

In principle, there are two strategies for navigating a straight course. One is to use an external directional reference and continually reorienting with reference to it, while the other is to infer body rotations from internal sensory information only. We show here that, while the first strategy will enable an animal or mobile agent to move arbitrarily far away from its starting point, the second strategy will not do so, even after an infinite number of steps. Thus, an external directional reference—some form of compass—is indispensable for ensuring progress away from home. This limitation must place significant constraints on the evolution of biological navigation systems. Some specific examples are discussed. An important corollary arising from the analysis of compassless navigation is that the maximum expected displacement represents a robust measure of the straightness of a path.

CHANGES IN QUANTAL PARAMETERS OF EPSCS IN RAT CA1 NEURONES IN VITRO AFTER THE INDUCTION OF LONG-TERM POTENTIATION

1. Long‐term potentiation (LTP) was induced in EPSCs evoked in CA1 pyramidal neurones of young rats in vitro by extracellular stimulation of stratum radiatum. Low frequency stimulation was paired with postsynaptic depolarization to induce LTP, using whole‐cell recording techniques. 2. Sufficient control and potentiated records were obtained under stable recording conditions to allow a quantal analysis of eleven EPSCs. The fluctuations in amplitude of all eleven EPSCs were quantized before conditioning stimulation, and they remained quantized after LTP induction, usually with an increased quantal variance. 3. Quantal current was increased by conditioning for nine out of eleven EPSCs. The increase in quantal current was correlated with the percentage increase in the EPSC. For only two EPSCs could the entire potentiation be attributed to an increase in quantal current. 4. The amplitude fluctuations of five control EPSCs could be described by binomial statistics, but after conditioning the binomial description held for only one of these EPSCs. For this EPSC, conditioning caused the release probability to increase from 0.39 +/‐ 0.05 to 0.47 +/‐ 0.02. 5. Quantal content was increased by conditioning stimulation for ten out of eleven EPSCs. The increase in quantal content was correlated with the percentage increase in the EPSC. However, for only four EPSCs could the entire potentiation be attributed to an increase in quantal content. 6. Most EPSCs were evoked with a high proportion of response failures. The probability of response failures decreased in eight out of eleven EPSCs following the induction of LTP. There was a negative correlation between the change in the probability of response failures and the amount of LTP. 7. The minimal number of sites at which transmission occurred increased for ten out of eleven EPSCs following LTP induction. Increases in the minimal number of active sites following conditioning were associated with decreases in the probability of response failures for seven out of eleven EPSCs. 8. The induction of LTP usually resulted in changes in the time course of the EPSCs. Cable analysis using a passive compartmental model of a CA1 pyramidal cell suggested that these time course changes were associated with shifts in the average electrotonic location of the active sites following LTP induction, rather than being caused by an increased duration of synaptic current. 9. LTP expression involves postsynaptic modifications to enhance the synaptic current at active sites. New sites are recruited, and our data cannot be used to determine if this is a result of a pre‐ or a postsynaptic change. Evidence for an increase in release probability was found for one EPSC.

Multiple mechanisms govern the dynamics of depression at neocortical synapses of young rats.

Synaptic transmission between pairs of excitatory neurones in layers V (N= 38) or IV (N= 6) of somatosensory cortex was examined in a parasagittal slice preparation obtained from young Wistar rats (14–18 days old). A combined experimental and theoretical approach reveals two characteristics of short‐term synaptic depression. Firstly, as well as a release‐dependent depression, there is a release‐independent component that is evident in smaller postsynaptic responses even following failure to release transmitter. Secondly, recovery from depression is activity dependent and is faster at higher input frequencies. Frequency‐dependent recovery is a Ca2+‐dependent process and does not reflect an underlying augmentation. Frequency‐dependent recovery and release‐independent depression are correlated, such that at those connections with a large amount of release‐independent depression, recovery from depression is faster. In addition, both are more pronounced in experiments performed at physiological temperatures. Simulations demonstrate that these homeostatic properties allow the transfer of rate information at all frequencies, essentially linearizing synaptic responses at high input frequencies.

Statistical analysis of synaptic transmission: model discrimination and confidence limits

Procedures for discriminating between competing statistical models of synaptic transmission, and for providing confidence limits on the parameters of these models, have been developed. These procedures were tested against simulated data and were used to analyze the fluctuations in synaptic currents evoked in hippocampal neurones. All models were fitted to data using the Expectation-Maximization algorithm and a maximum likelihood criterion. Competing models were evaluated using the log-likelihood ratio (Wilks statistic). When the competing models were not nested, Monte Carlo sampling of the model used as the null hypothesis (H0) provided density functions against which H0 and the alternate model (H1) were tested. The statistic for the log-likelihood ratio was determined from the fit of H0 and H1 to these probability densities. This statistic was used to determine the significance level at which H0 could be rejected for the original data. When the competing models were nested, log-likelihood ratios and the chi 2 statistic were used to determine the confidence level for rejection. Once the model that provided the best statistical fit to the data was identified, many estimates for the model parameters were calculated by resampling the original data. Bootstrap techniques were then used to obtain the confidence limits of these parameters.

Statistical models of synaptic transmission evaluated using the expectation-maximization algorithm

Amplitude fluctuations of evoked synaptic responses can be used to extract information on the probabilities of release at the active sites, and on the amplitudes of the synaptic responses generated by transmission at each active site. The parameters that describe this process must be obtained from an incomplete data set represented by the probability density of the evoked synaptic response. In this paper, the equations required to calculate these parameters using the Expectation-Maximization algorithm and the maximum likelihood criterion have been derived for a variety of statistical models of synaptic transmission. These models are ones where the probabilities associated with the different discrete amplitudes in the evoked responses are a) unconstrained, b) binomial, and c) compound binomial. The discrete amplitudes may be separated by equal (quantal) or unequal amounts, with or without quantal variance. Alternative models have been considered where the variance associated with the discrete amplitudes is sufficiently large such that no quantal amplitudes can be detected. These models involve the sum of a normal distribution (to represent failures) and a unimodal distribution (to represent the evoked responses). The implementation of the algorithm is described in each case, and its accuracy and convergence have been demonstrated.

Arbitrary multisite two-photon excitation in four dimensions

We demonstrate dynamic and arbitrary multisite two-photon excitation in three dimensions using the holographic projection method. Rapid response (fourth dimension) is achieved through high-speed noniterative calculation of the hologram using a video graphics accelerator board. We verify that the projected asymmetric spot configurations have sufficient spatiotemporal photon density for localized two-photon excitation. This system is a significant advance and can be applied to time-resolved photolysis of caged compounds in biological cells and complex neuronal networks, nonlinear microfabrication and volume holographic optical storage.

Animal navigation: general properties of directed walks

The ability to locomote is a defining characteristic of all animals. Yet, all but the most trivial forms of navigation are poorly understood. Here we report and discuss the analytical results of an in-depth study of a simple navigation problem. In principle, there are two strategies for navigating a straight course. One is to use an external directional reference and to continually reorient with reference to it. The other is to monitor body rotations from internal sensory information only. We showed previously that, at least for simple representations of locomotion, the first strategy will enable an animal or mobile agent to move arbitrarily far away from its starting point, but the second strategy will not do so, even after an infinite number of steps. This paper extends and generalizes the earlier results by demonstrating that these findings are true even when a very general model of locomotion is used. In this general model, error components within individual steps are not independent, and directional errors may be biased. In the absence of a compass, the expected path of a directed walk in general approximates a logarithmic spiral. Some examples are given to illustrate potential applications of the quantitative results derived here. Motivated by the analytical results developed in this work, a nomenclature for directed walks is proposed and discussed. Issues related to path integration in mammals and robots, and measuring the curvature of a noisy path are also addressed using directed walk theory.

Simultaneous multi-site two-photon photostimulation in three dimensions.

We demonstrate simultaneous multi-site two-photon photolysis of caged neurotransmitters with close to diffraction-limited resolution in all three dimensions (3D). We use holographic projection of multiple focal spots, which allows full control over the 3D positions of uncaging sites with a high degree of localized excitation. Our system incorporates a two-photon imaging setup to visualize the 3D morphology of the neurons in order to accurately determine the photostimulation sites. We show its application to studies of synaptic integration by performing simultaneous and controlled glutamate delivery at multiple locations on dendritic trees.

Four-dimensional multi-site photolysis of caged neurotransmitters

Neurons receive thousands of synaptic inputs that are distributed in space and time. The systematic study of how neurons process these inputs requires a technique to stimulate multiple yet highly targeted points of interest along the neurons dendritic tree. Three-dimensional multi-focal patterns produced via holographic projection combined with two-photon photolysis of caged compounds can provide for highly localized release of neurotransmitters within each diffraction-limited focus, and in this way emulate simultaneous synaptic inputs to the neuron. However, this technique so far cannot achieve time-dependent stimulation patterns due to fundamental limitations of the hologram-encoding device and other factors that affect the consistency of controlled synaptic stimulation. Here, we report an advanced technique that enables the design and application of arbitrary spatio-temporal photostimulation patterns that resemble physiological synaptic inputs. By combining holographic projection with a programmable high-speed light-switching array, we have overcome temporal limitations with holographic projection, allowing us to mimic distributed activation of synaptic inputs leading to action potential generation. Our experiments uniquely demonstrate multi-site two-photon glutamate uncaging in three dimensions with submillisecond temporal resolution. Implementing this approach opens up new prospects for studying neuronal synaptic integration in four dimensions.