Wavelet transform-based de-noising for two-photon imaging of synaptic Ca2+ transients.

Postsynaptic Ca(2+) transients triggered by neurotransmission at excitatory synapses are a key signaling step for the induction of synaptic plasticity and are typically recorded in tissue slices using two-photon fluorescence imaging with Ca(2+)-sensitive dyes. The signals generated are small with very low peak signal/noise ratios (pSNRs) that make detailed analysis problematic. Here, we implement a wavelet-based de-noising algorithm (PURE-LET) to enhance signal/noise ratio for Ca(2+) fluorescence transients evoked by single synaptic events under physiological conditions. Using simulated Ca(2+) transients with defined noise levels, we analyzed the ability of the PURE-LET algorithm to retrieve the underlying signal. Fitting single Ca(2+) transients with an exponential rise and decay model revealed a distortion of τ(rise) but improved accuracy and reliability of τ(decay) and peak amplitude after PURE-LET de-noising compared to raw signals. The PURE-LET de-noising algorithm also provided a ∼30-dB gain in pSNR compared to ∼16-dB pSNR gain after an optimized binomial filter. The higher pSNR provided by PURE-LET de-noising increased discrimination accuracy between successes and failures of synaptic transmission as measured by the occurrence of synaptic Ca(2+) transients by ∼20% relative to an optimized binomial filter. Furthermore, in comparison to binomial filter, no optimization of PURE-LET de-noising was required for reducing arbitrary bias. In conclusion, the de-noising of fluorescent Ca(2+) transients using PURE-LET enhances detection and characterization of Ca(2+) responses at central excitatory synapses.

[1]  T. Oertner,et al.  Functional Imaging of Single Synapses in Brain Slices , 2002, Experimental physiology.

[2]  P. Besbeas,et al.  A Comparative Simulation Study of Wavelet Shrinkage Estimators for Poisson Counts , 2004 .

[3]  David L. Donoho,et al.  Nonlinear Wavelet Methods for Recovery of Signals, Densities, and Spectra from Indirect and Noisy Da , 1993 .

[4]  Jelena Kovacevic,et al.  Wavelets and Subband Coding , 2013, Prentice Hall Signal Processing Series.

[5]  Thierry Blu,et al.  The SURE-LET Approach to Image Denoising , 2007, IEEE Transactions on Image Processing.

[6]  Roberto Malinow,et al.  Synaptic calcium transients in single spines indicate that NMDA receptors are not saturated , 1999, Nature.

[7]  R. Yuste,et al.  Mechanisms of Calcium Decay Kinetics in Hippocampal Spines: Role of Spine Calcium Pumps and Calcium Diffusion through the Spine Neck in Biochemical Compartmentalization , 2000, The Journal of Neuroscience.

[8]  Thierry Blu,et al.  Image Denoising in Mixed Poisson–Gaussian Noise , 2011, IEEE Transactions on Image Processing.

[9]  K. Svoboda,et al.  The Life Cycle of Ca2+ Ions in Dendritic Spines , 2002, Neuron.

[10]  T. Bliss,et al.  Single Synaptic Events Evoke NMDA Receptor–Mediated Release of Calcium from Internal Stores in Hippocampal Dendritic Spines , 1999, Neuron.

[11]  Bernardo L. Sabatini,et al.  Competitive regulation of synaptic Ca influx by D2 dopamine and A2A adenosine receptors , 2010, Nature Neuroscience.

[12]  B. Sakmann,et al.  Spine Ca2+ Signaling in Spike-Timing-Dependent Plasticity , 2006, The Journal of Neuroscience.

[13]  W. Wright Electron multiplier pulse-height distributions. , 1968 .

[14]  K. Svoboda,et al.  Imaging Calcium Concentration Dynamics in Small Neuronal Compartments , 2004, Science's STKE.

[15]  S. Wang,et al.  Alignment and calibration of a focal neurotransmitter uncaging system , 2006, Nature Protocols.

[16]  K. Svoboda,et al.  Estimating intracellular calcium concentrations and buffering without wavelength ratioing. , 2000, Biophysical journal.

[17]  Stephan Saalfeld,et al.  Globally optimal stitching of tiled 3D microscopic image acquisitions , 2009, Bioinform..

[18]  F v Wegner,et al.  Automated detection of elementary calcium release events using the á trous wavelet transform. , 2006, Biophysical journal.

[19]  Nigel Emptage,et al.  Ca2+ and synaptic plasticity. , 2005, Cell calcium.

[20]  B. Sabatini,et al.  Nonlinear Regulation of Unitary Synaptic Signals by CaV2.3 Voltage-Sensitive Calcium Channels Located in Dendritic Spines , 2007, Neuron.

[21]  T. Bliss,et al.  State-Dependent Mechanisms of LTP Expression Revealed by Optical Quantal Analysis , 2006, Neuron.

[22]  Pierre Baldi,et al.  Assessing the accuracy of prediction algorithms for classification: an overview , 2000, Bioinform..

[23]  A T Young,et al.  Use of photomultiplier tubes for photon counting. , 1971, Applied optics.

[24]  P. Marchand,et al.  Binomial smoothing filter: A way to avoid some pitfalls of least‐squares polynomial smoothing , 1983 .

[25]  B. Sabatini,et al.  M1 Muscarinic Receptors Boost Synaptic Potentials and Calcium Influx in Dendritic Spines by Inhibiting Postsynaptic SK Channels , 2010, Neuron.

[26]  T. Oertner,et al.  Depolarization gates spine calcium transients and spike-timing-dependent potentiation , 2012, Current Opinion in Neurobiology.

[27]  Dirk P. Kroese,et al.  Kernel density estimation via diffusion , 2010, 1011.2602.

[28]  James B. Pawley,et al.  Fundamental Limits in Confocal Microscopy , 2006 .

[29]  Bernardo L. Sabatini,et al.  Biphasic Synaptic Ca Influx Arising from Compartmentalized Electrical Signals in Dendritic Spines , 2009, PLoS biology.

[30]  Nathalie L Rochefort,et al.  Functional mapping of single spines in cortical neurons in vivo , 2011, Nature.

[31]  R. Yuste,et al.  Two-photon calcium imaging of spines and dendrites. , 2009, Cold Spring Harbor protocols.

[32]  A. G. Wright The statistics of multi-photoelectron pulse-height distributions , 2007 .

[33]  J. Lisman,et al.  A mechanism for the Hebb and the anti-Hebb processes underlying learning and memory. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[34]  Rafael Yuste,et al.  From form to function: calcium compartmentalization in dendritic spines , 2000, Nature Neuroscience.

[35]  Patrick Bouthemy,et al.  Patch-Based Nonlocal Functional for Denoising Fluorescence Microscopy Image Sequences , 2010, IEEE Transactions on Medical Imaging.

[36]  S. Mallat A wavelet tour of signal processing , 1998 .

[37]  Bernardo L. Sabatini,et al.  Analysis of calcium channels in single spines using optical fluctuation analysis , 2000, Nature.

[38]  Karel Svoboda,et al.  Plasticity of calcium channels in dendritic spines , 2003, Nature Neuroscience.

[39]  Yasunori Hayashi,et al.  Dendritic Spine Geometry: Functional Implication and Regulation , 2005, Neuron.

[40]  Alan Fine,et al.  Expression of Long-Term Plasticity at Individual Synapses in Hippocampus Is Graded, Bidirectional, and Mainly Presynaptic: Optical Quantal Analysis , 2009, Neuron.

[41]  I. Johnstone,et al.  Adapting to Unknown Smoothness via Wavelet Shrinkage , 1995 .

[42]  D W Tank,et al.  Direct Measurement of Coupling Between Dendritic Spines and Shafts , 1996, Science.

[43]  S. Siegelbaum,et al.  A Role for Synaptic Inputs at Distal Dendrites: Instructive Signals for Hippocampal Long-Term Plasticity , 2007, Neuron.

[44]  B. Sabatini,et al.  Calcium Signaling in Dendrites and Spines: Practical and Functional Considerations , 2008, Neuron.

[45]  J. J. Art,et al.  Photon Detectors for Confocal Microscopy , 2006 .

[46]  Benjamin F. Grewe,et al.  High-speed in vivo calcium imaging reveals neuronal network activity with near-millisecond precision , 2010, Nature Methods.

[47]  R. Yuste,et al.  High Speed Two-Photon Imaging of Calcium Dynamics in Dendritic Spines: Consequences for Spine Calcium Kinetics and Buffer Capacity , 2007, PLoS ONE.

[48]  W. Denk,et al.  Two-photon scanning photochemical microscopy: mapping ligand-gated ion channel distributions. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[49]  J. R. Prescott,et al.  A statistical model for photomultiplier single-electron statistics , 1966 .

[50]  A. Christopoulos,et al.  Fitting Models to Biological Data Using Linear and Nonlinear Regression: A Practical Guide to Curve Fitting , 2004 .

[51]  S. Wang,et al.  Confocal imaging and local photolysis of caged compounds: Dual probes of synaptic function , 1995, Neuron.

[52]  D. Fried Noise in Photoemission Current , 1965 .

[53]  Carl Taswell,et al.  The what, how, and why of wavelet shrinkage denoising , 2000, Comput. Sci. Eng..