Beyond spike timing: the role of nonlinear plasticity and unreliable synapses

 Spike-timing-dependent plasticity (STDP) strengthens synapses that are activated immediately before a postsynaptic spike, and weakens those that are activated after a spike. To prevent an uncontrolled growth of the synaptic strengths, weakening must dominate strengthening for uncorrelated spike times. However, this weight-normalization property would preclude Hebbian potentiation when the pre- and postsynaptic neurons are strongly active without specific spike-time correlations. We show that nonlinear STDP as inherent in the data of Markram et al. [(1997) Science 275:213–215] can preserve the benefits of both weight normalization and Hebbian plasticity, and hence can account for learning based on spike-time correlations and on mean firing rates. As examples we consider the moving-threshold property of the Bienenstock–Cooper–Munro rule, the development of direction-selective simple cells by changing short-term synaptic depression, and the joint adaptation of axonal and dendritic delays. Without threshold nonlinearity at low frequencies, the development of direction selectivity does not stabilize in a natural stimulation environment. Without synaptic unreliability there is no causal development of axonal and dendritic delays. Received: 22 April 2002 / Accepted: 23 May 2002 Acknowledgements. This study was supported by the Swiss National Science Foundation (grant 3152-065234.01) and the Silva-Casa foundation. The author thanks Stefano Fusi, Henry Markram, and Misha Tsodyks for helpful discussions, Nissim Buchs and Martin Schneider for their simulations, and Jan Reutimann for proof reading. Correspondence to: e-mail: wsenn@cns.unibe.ch, Tel.: +41-31-6318721, Fax: 41-31-6314611     

Fractal and nonfractal analysis of cell images: comparison and application to neuronal dendritic arborization

 Neurons of the rat spinal cord were stained using the Golgi impregnation method. Successfully impregnated neurons from laminae II, III, and VI were subjected to fractal and nonfractal analyses. Fractal analysis was performed using length-related techniques. Since an application of fractal methods to the analysis of dendrite arbor structures requires caution, we adopted as appropriate a nonfractal method proposing a generalized power-law model with two main nonfractal parameters: (i) the anfractuosity, characterizing the degree of dendritic deviation from straight lines; and (ii) an estimate of the total length of arbor dendrites. The anfractuosity can distinguish between two sets of drawings where the fractal methods failed. We also redefine some basic concepts of fractal geometry, present the ruler-counting method, and propose a new definition of fractal dimension. Received: 5 February 2002 / Accepted: 25 June 2002 Acknowledgement. We thank Ing. Dejan Ristanović for preparing the computer program used in this study. Correspondence to: D. Ristanović (e-mail: dusan@ristanovic.com, Tel.: +381-11-3615767)     

Use of `relative-phase' analysis to assess correlation between neuronal spike trains

 We propose a new method of studying the correlation between neuronal spike trains. This technique is based on the analysis of relative phase between two point processes. Relative phase here is defined as the relative timing difference between two spike trains normalized by the associated interspike interval of one cell. This phase measurement is intended to reveal the relative timing relationship between spike trains atdifferent firing rates. We apply this method to a numerical example and an example from two cerebellar neuronal spike trains of a behaving rat. The results are compared with classical cross-correlation analysis. We show that the technique can avoid some of the limitations of cross-correlation methods, reveal certain statistical dependencies that cannot be shown by cross correlation, and provide information as to the direction of influence between two spike trains. Received: 8 November 2001 / Accepted: 30 September 2002 / Published online: 24 January 2003 Correspondence to: Y. Chen (e-mail: chen@nsi.edu, Fax: + 1-858-626-2099) Acknowledgements. Research for this paper was supported by the Alafi Family Foundation and the Neurosciences Research Foundation.     

Dynamical synaptic plasticity: a model and connection to some experiments

 Using a modified version of a phenomenological model for the dynamics of synaptic plasticity, we examine some recent experiments of Wu et al. [(2001) J Physiol 533:745–755]. We show that the model is quantitatively consistent with their experimental protocols producing long-term potentiation (LTP) and long-term depression (LTD) in slice preparations of rat hippocampus. We also predict the outcome of similar experiments using different frequencies and depolarization levels than reported in their results. Received: 3 September 2002 / Accepted in revised form: 22 October 2002 / Published online: 24 February 2003 Correspondence to: H.D.I. Abarbanel (e-mail: hdia@jacobi.ucsd.edu) Acknowledgements. We are very grateful to A. Selverston and D. Feldman for conversations about this work. This work was partially supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Engineering and Geosciences, under grants No. DE-FG03-90ER14138 and No. DE-FG03-96ER14592, by a grant from the National Science Foundation, NSF PHY0097134, by a grant from the Army Research Office, DAAD19-01-1-0026, by a grant from the Office of Naval Research, N00014-00-1-0181, and by a grant from the National Institutes of Health, NIH R01 NS40110-01A2. This work was also partially supported by M. Ciencia y Tecnologa BFI2000-0157 (R.H.).     

Analysis of higher-order neuronal interactions based on conditional inference

 Higher-order neural interactions, i.e., interactions that cannot be reduced to interactions between pairs of cells, have received increasing attention in the context of recent attempts to understand the cooperative dynamics in cortical neural networks. Typically, likelihood-ratio tests of log-linear models are being employed for statistical inference. The parameter estimation of these models for simultaneously recorded single-neuron spiking activities is a crucial ingredient of this approach. Extending a previous investigation of a two-neuron system, we present here the general formulation of an exact test suited for the detection of positive higher-order interactions between m neurons. This procedure does not require the estimation of any interaction parameters and additionally optimizes the test power of the statistical inference. We apply the approach to a three-neuron system and show how second-order and third-order interactions can be reliably distinguished. We study the performance of the method as a function of the interaction strength. Received: 18 January 2002 / Accepted in revised form: 26 November 2002 / Published online: 13 March 2003 RID="*" ID="*" Present address: Institute for Theoretical Biology, Humboldt University, 10115 Berlin, Germany Correspondence to: R. Gütig (e-mail: r.guetig@biologie.hu-berlin.de, Tel.: +49 30 2093 9112, Fax: +49 30 2093 8801) Acknowledgements. We thank Shun-ichi Amari and Hiro Nakahara for valuable discussions on the information geometry of the exponential family of probability distributions underlying the present approach. Supported in part by the Studienstiftung des deutschen Volkes, the German-Israeli Foundation for Scientific Research and Development (GIF), the Deutsche Forschungsgemeinschaft (DFG), and the Institut für Grenzgebiete der Psychologie, Freiburg.     

Independently Outgrowing Neurons and Geometry-Based Synapse Formation Produce Networks with Realistic Synaptic Connectivity

Neuronal signal integration and information processing in cortical networks critically depend on the organization of synaptic connectivity. During development, neurons can form synaptic connections when their axonal and dendritic arborizations come within close proximity of each other. Although many signaling cues are thought to be involved in guiding neuronal extensions, the extent to which accidental appositions between axons and dendrites can already account for synaptic connectivity remains unclear. To investigate this, we generated a local network of cortical L2/3 neurons that grew out independently of each other and that were not guided by any extracellular cues. Synapses were formed when axonal and dendritic branches came by chance within a threshold distance of each other. Despite the absence of guidance cues, we found that the emerging synaptic connectivity showed a good agreement with available experimental data on spatial locations of synapses on dendrites and axons, number of synapses by which neurons are connected, connection probability between neurons, distance between connected neurons, and pattern of synaptic connectivity. The connectivity pattern had a small-world topology but was not scale free. Together, our results suggest that baseline synaptic connectivity in local cortical circuits may largely result from accidentally overlapping axonal and dendritic branches of independently outgrowing neurons.     

Stimulus-dependent onset latency of inhibitory recurrent activity

 This paper gives an explanation for the experimentally observed onset latencies of the inhibitory responses that vary from a few milliseconds to hundreds of milliseconds in systems where the conduction delays are only several milliseconds in the feedback pathways. To do this we use a simple mathematical model. The model consists of two delay differential equations (DDE) where the nonlinear relation between the postsynaptic potential and the firing frequency of the neuron population arises from the stoichiometry of the transmitter-receptor kinetics. The parameters of the model refer to the hippocampal feedback system, and the modeling results are compared with corresponding experiments. Received: 31 May 2002 / Accepted: 5 February 2003 / Published online: 20 May 2003 Correspondence to: C. Hauptmann (e-mail: chauptma@cnd.mcgill.ca) Acknowledgements. We thank Prof. Krnjevic and Prof. Glavinovic for helpful and extensive discussions about this problem. This work was supported by MITACS (Canada), the Natural Sciences and Engineering Research Council (NSERC grant OGP-0036920, Canada), the Alexander von Humboldt Stiftung, Le Fonds pour la Formation de Chercheurs et l'Aide à la Recherche (FCAR grant 98ER1057, Québec), and the Leverhulme Trust (U.K.).     

Effect of trehalose on the spawn storage in some edible mushroom fungi (2): Effect on preservation in the freezer

 We describe the effects of trehalose on spawn storage in a home freezer (average temperature, −16°C) where edible fungi usually do not survive. When the mycelia of Lentinula edodes were stored in a freezer for 3 days, the survival rate of mycelia cultivated on 2% glucose medium was 30%, whereas those on media containing 2% and 5% trehalose were 50% and 60%, respectively. Addition of trehalose to the culture was more effective in Pleurotus ostreatus. These results suggest that trehalose played the role of a stress protectant against freezing, because the mycelia cultured on a trehalose medium grew more rapidly and produced more fruiting bodies compared to those cultured on glucose. Received: February 6, 2002 / Accepted: October 1, 2002 Acknowledgments This work was partially supported by a Grant in Aid for Scientific Research (c) (2) No. 12660156 from the Japan Society for the Promotion of Science. We also gratefully acknowledge a grant from Hokuto Foundation for the Promotion of Biological Science. Correspondence to:T. Terashita     

Spike propagation synchronized by temporally asymmetric Hebbian learning

 Synchronously spiking neurons have been observed in the cerebral cortex and the hippocampus. In computer models, synchronous spike volleys may be propagated across appropriately connected neuron populations. However, it is unclear how the appropriate synaptic connectivity is set up during development and maintained during adult learning. We performed computer simulations to investigate the influence of temporally asymmetric Hebbian synaptic plasticity on the propagation of spike volleys. In addition to feedforward connections, recurrent connections were included between and within neuron populations and spike transmission delays varied due to axonal, synaptic and dendritic transmission. We found that repeated presentations of input volleys decreased the synaptic conductances of intragroup and feedback connections while synaptic conductances of feedforward connections with short delays became stronger than those of connections with longer delays. These adaptations led to the synchronization of spike volleys as they propagated across neuron populations. The findings suggests that temporally asymmetric Hebbian learning may enhance synchronized spiking within small populations of neurons in cortical and hippocampal areas and familiar stimuli may produce synchronized spike volleys that are rapidly propagated across neural tissue. Received: 28 May 2002 / Accepted: 3 June 2002 RID="*" ID="*" Correspondence to: R. E. Suri Intelligent Optical Systems (IOS), 2520 W 237th St, Torrance, CA 90505-5217, USA (e-mail: rsuri@intopsys.com, Tel.: +1-310-5307130 ext. 108, Fax: +1-210-5307417)     

Computer-integrated finite element modeling of human middle ear

 The objective of this study was to produce an improved finite element (FE) model of the human middle ear and to compare the model with human data. We began with a systematic and accurate geometric modeling technique for reconstructing the middle ear from serial sections of a freshly frozen temporal bone. A geometric model of a human middle ear was constructed in a computer-aided design (CAD) environment with particular attention to geometry and microanatomy. Using the geometric model, a working FE model of the human middle ear was created using previously published material properties of middle ear components. This working FE model was finalized by a cross-calibration technique, comparing its predicted stapes footplate displacements with laser Doppler interferometry measurements from fresh temporal bones. The final FE model was shown to be reasonable in predicting the ossicular mechanics of the human middle ear. Received: 18 February 2002 / Accepted: 6 June 2002 The preparation of temporal bone histological sections of Robert K. Dyer, Jr., MD is gratefully recognized. The Whitaker Foundation supported this work (Research Grant RG-98-0305).     

Elimination of response latency variability in neuronal spike trains

 Neuronal activity in the mammalian cortex exhibits a considerable amount of trial-by-trial variability. This may be reflected by the magnitude of the activity as well as by the response latency with respect to an external event, such as the onset of a sensory stimulus, or a behavioral event. Here we present a novel nonparametric method for estimating trial-by-trial differences in response latency from neuronal spike trains. The method makes use of the dynamic rate profile for each single trial and maximizes their total pairwise correlation by appropriately shifting all trials in time. The result is a new alignment of trials that largely eliminates the variability in response latency and provides a new internal trigger that is independent of experiment time. To calibrate the method, we simulated spike trains based on stochastic point processes using a parametric model for phasic response profiles. We illustrate the method by an application to simultaneous recordings from a pair of neurons in the motor cortex of a behaving monkey. It is demonstrated how the method can be used to study the temporal relation of the neuronal response to the experiment, to investigate whether neurons share the same dynamics, and to improve spike correlation analysis. Differences between this and other previously published methods are discussed. Received: 8 April 2002 / Accepted: 26 November 2002 / Published online: 7 April 2003 Correspondence to: Stefan Rotter (e-mail: rotter@biologie.uni-freiburg.de), Tel.: +49-761-2032862, Fax: +49-761-2032860 Acknowledgements. We are grateful to Alexa Riehle for providing us with the monkey data and for valuable discussions. We also thank Felix Kümmell, Hiroyuki Nakahara, and Shun-ichi Amari for helpful discussions. Partial funding was received by the Deutsche Forschungsgemeinschaft (DFG, SFB 505) and the German-Israeli Foundation (GIF). Additional support was provided by the RIKEN Brain Science Institute.     

Mathematical formulations of Hebbian learning

 Several formulations of correlation-based Hebbian learning are reviewed. On the presynaptic side, activity is described either by a firing rate or by presynaptic spike arrival. The state of the postsynaptic neuron can be described by its membrane potential, its firing rate, or the timing of backpropagating action potentials (BPAPs). It is shown that all of the above formulations can be derived from the point of view of an expansion. In the absence of BPAPs, it is natural to correlate presynaptic spikes with the postsynaptic membrane potential. Time windows of spike-time-dependent plasticity arise naturally if the timing of postsynaptic spikes is available at the site of the synapse, as is the case in the presence of BPAPs. With an appropriate choice of parameters, Hebbian synaptic plasticity has intrinsic normalization properties that stabilizes postsynaptic firing rates and leads to subtractive weight normalization. Received: 1 February 2002 / Accepted: 28 March 2002 Correspondence to: W. Gerstner (e-mail: wulfram.gerstner@epfl.ch, Tel.: +41-21-6936713, Fax: +41-21-6935263)     

Time representing cortical activities: two models inspired by prefrontal persistent activity

 Timing information in the range of seconds is significantly correlated with our behavior. There is growing interest in the cognitive behaviors that rely on perception, comparison, or generation of timing. However, little is known about the neural mechanisms underlying such behaviors. Here we model two different neural mechanisms to represent timing information in the range of seconds. In one model, a recurrent network of bistable spiking neurons shows a quasistable state that is initiated by a brief input and typically lasts for a few to several seconds. The duration of this quasistable activity may be regarded as the neural representation of internal time obeying a psychophysical law of time recognition. Another model uses synfire chains to provide the timing information necessary for predicting the times of anticipated events. In this model, the neurons projected to by multiple synfire chains are conditioned to fire synchronously at the times when an external event (GO signal) is expected. The conditioning is accomplished by spike-timing-dependent plasticity. The two models are inspired by the prefrontal activities of the monkeys engaging in different timing-information-related tasks. Thus, this cortical region may provide the timing information required for organizing various behaviors. Received: 12 March 2002 / Accepted in revised form: 26 November 2002 / Published online: 28 March 2003 Correspondence to: T. Fukai (e-mail: tfukai@eng.tamagawa.ac.jp, Tel.: +81-42-7398434, Fax: +81-42-7397135) Acknowledgements. K. Kitano was supported by Japan Society for the Promotion of Science.     

Ornstein-Uhlenbeck model neuron revisited

 The temporal patterns of action potentials fired by a two-point stochastic neuron model were investigated. In this model the membrane potential of the dendritic compartment follows the Orstein-Uhlenbeck process and is not affected by the spiking activity. The axonal compartment, corresponding to the spike initiation site, is described by a simplified RC circuit. Estimators of the mean and variance of the input, based on a sampling of the axonal membrane potential, were derived and applied to simulated data. The dependencies of the mean firing frequency and of the coefficient of variation and serial correlation of interspike intervals on the mean and variance of the input were also studied by computer simulation in both 1- and 2-point models. The main property distinguishing the 2-point model from the classical 1-point model is its ability to produce clusters of short (or long) intervals between spikes under conditions of constant stimulation, as often observed in real neurons. It is shown that the nearly linear frequency response of the neuron, starting with subthreshold values of the input, is accounted for by the variability of the input (noise), which indicates that noise can play a positive role in nervous systems. The linear response frequency with respect to noise of the models suggests that the neuron can function as a noise encoder. Received: 2 April 1993/Accepted in revised form: 15 September 1994     

Neuronal network modelling of the effects of anaesthetic agents on somatosensory pathways

 The whole question of consciousness, awareness and depth of anaesthesia is both timely, little understood and deeply challenging. Models of the underlying neural pathway mechanisms/dynamics are necessary for understanding the interactions involved and their structure and function. A neuronal network of the somatosensory pathways is proposed in this paper based on experimental information and physiological investigation into anaesthesia. Existing mathematical neuronal models from the literature have been modified and then employed to describe the dynamics of the proposed pathway network. Effects of anaesthetic agents on the cortex were simulated in the model which describes the evoked cortical responses. By comparison with responses from anaesthetised rats, the model's responses are able to describe the dynamics of typical responses. Thus, the proposed model promises to be valuable for investigating the mechanisms of anaesthesia on the cortex and the effects of brain lesions. Received: 4 March 2002 / Accepted in revised form: 8 July 2002 Correspondence to: D. A. Linkens (e-mail: d.linkens@sheffield.ac.uk, Tel.: +44-114-2225133, Fax: +44-114-2731729) Acknowledgements. C.H. Ting was supported by a postgraduate scholarship from the University of Sheffield.     

Computational model of the cockroach escape behavior: winner and losers in a population code

 I present a comprehensive biologically oriented computational model to account for the escape response of the cockroach on the ground. This model is an expansion of previous work that accounted only for discriminating left from right wind directions [Ezrachi et al. (1999) Biol Cybern 81: 89–99]. The model is composed of computational elements describing the biological processes taking place in the various neurons and includes input which emulates empirical data. With this model it is possible to obtain escape behavior that resembles natural behavior. The model is used to address an ongoing debate as to whether the cockroach's turn direction is determined by computations carried out by the entire neuronal population (PC) or rather by a “winner-take-all” (WTA) mechanism. I suggest that the computation mechanism that underlies the cockroach escape response is composed of both PC and WTA principles. Based on the properties of the suggested new mechanism I denote it a “Darwinian population code.” Received: 26 March 2002 / Accepted in revised form: 24 June 2002 Acknowledgements. I thank H. Parnas for her advice and assistance, J. M. Camhi for helpful comments, and D. Lipson for developing the simulation tools. Correspondence to: E. A. Ezrachi (e-mail: erez@piano.ls.huji.ac.il, Tel.: +972-2-6585818, Fax: +972-2-6585569)     

A new species of <Emphasis Type="Italic">Ophiodothella</Emphasis> on <Emphasis Type="Italic">Casearia</Emphasis> from Venezuela

 Ophiodothella caseariae sp. nov. from leaves of Casearia tremula in Venezuela is described and illustrated. Received: February 19, 2002 / Accepted: April 30, 2002     

A numerical method for renal models that represent tubules with abrupt changes in membrane properties

 The urine concentrating mechanism of mammals and birds depends on a counterflow configuration of thousands of nearly parallel tubules in the medulla of the kidney. Along the course of a renal tubule, cell type may change abruptly, resulting in abrupt changes in the physical characteristics and transmural transport properties of the tubule. A mathematical model that faithfully represents these abrupt changes will have jump discontinuities in model parameters. Without proper treatment, such discontinuities may cause unrealistic transmural fluxes and introduce suboptimal spatial convergence in the numerical solution to the model equations. In this study, we show how to treat discontinuous parameters in the context of a previously developed numerical method that is based on the semi-Lagrangian semi-implicit method and Newton's method. The numerical solutions have physically plausible fluxes at the discontinuities and the solutions converge at second order, as is appropriate for the method. Received: 13 November 2001 / Revised version: 28 June 2002 / Published online: 26 September 2002 This work was supported in part by the National Institutes of Health (National Institute of Diabetes and Digestive and Kidney Diseases, grant DK-42091.) Mathematics Subject Classification (2000): 65-04, 65M12, 65M25, 92-04, 92C35, 35-04, 35L45 Keywords or phrases: Mathematical models – Differential equations – Mathematical biology – Kidney – Renal medulla – Semi-Lagrangian semi-implicit     

Spike timing dependent synaptic plasticity in biological systems

 Association of a presynaptic spike with a postsynaptic spike can lead to changes in synaptic efficacy that are highly dependent on the relative timing of the pre- and postsynaptic spikes. Different synapses show varying forms of such spike-timing dependent learning rules. This review describes these different rules, the cellular mechanisms that may be responsible for them, and the computational consequences of these rules for information processing and storage in the nervous system. Received: 16 January 2002 / Accepted: 3 June 2002 Acknowledgements. This research is supported in part by a National Science Foundation grant IBN 98-08887 (awarded to PDR), and by National Institutes of Health grants R01-MH49792 (awarded to CCB), R01-MH60996 (awarded to CCB), and R01-MH60996 (awarded to PDR). Correspondence to: P. D. Roberts (e-mail: robertpa@ohsu.edu)