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Edited by: Dirk Feldmeyer, Julich Research Centre, Germany

Reviewed by: Christian Stricker, Australian National University, Australia; Stefan Hallermann, Leipzig University, Germany

^{†}Co-senior authors

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Previous studies based on the ‘Quantal Model’ for synaptic transmission suggest that neurotransmitter release is mediated by a single release site at individual synaptic contacts in the neocortex. However, recent studies seem to contradict this hypothesis and indicate that multi-vesicular release (MVR) could better explain the synaptic response variability observed _{RRP}), from paired whole-cell recordings of connections between layer 5 thick tufted pyramidal cell (L5_TTPC) in the juvenile rat somatosensory cortex. Our approach extends the work of _{RRP} to be between two to three for synaptic connections between L5_TTPCs. To constrain N_{RRP} values for other connections in the microcircuit, we developed and validated a generalization approach using published data on the coefficient of variation (CV) of the amplitudes of post-synaptic potentials (PSPs) from literature and comparing them against

Synaptic transmission is the basis for neuronal communication and information processing in the brain. Synaptic communication between neurons is mediated by neurotransmitters contained in presynaptic vesicles that are stochastically released from axonal boutons by incoming action potentials (APs) and diffuse across the synaptic cleft to bind receptors. Synaptic receptors are a class of ion channels which open as a result of transmitter binding, and the resulting transmembrane currents either depolarize or hyperpolarize the postsynaptic membrane, depending on the ion to which the channel is permeable (

In 1954, del Castillo and Katz described the ‘Quantal model’ of synaptic transmission (

Recent studies in the rodent neocortex support the idea of MVR between pyramidal cells (

Theoretical and computational models have enabled a mechanistic understanding of MVR through investigating synaptic processes such as short-term synaptic plasticity (_{RRP}) with more than one vesicle for synaptic plasticity (

In this study, we leveraged a rigorously validated data-driven model of neocortical tissue at the cellular and synaptic levels of detail to estimate the average size of the N_{RRP} for individual synaptic contacts between cell-type-specific connections (_{RRP}, we sampled synaptically connected pairs of neurons within the virtual neocortical tissue model and simulated paired whole-cell recordings _{RRP}, extending the work of Loebel and colleges (_{RRP}, to reproduce response variability as observed in experiments, which is typically assessed by the coefficient of variation (CV; standard deviation/mean) of PSPs. We further developed an approach to estimate N_{RRP} for both excitatory and inhibitory connection types using published literature that reported the CV of PSPs for synaptic connections in the neocortex. Our study combining _{RRP} values than previously reported (

Fourteen- to eighteen-day-old Wistar rats were decapitated according to the guidelines of the Swiss Animal Welfare Act, and the Swiss National Institutional and Veterinary office guidelines in the Canton of Vaud on Animal Experimentation for the ethical use of animals. Multiple, simultaneous somatic whole cell patch-clamp recordings from clusters of 6–12 cells were carried out with Multiclamp 700B amplifiers in current clamp mode. Brain sagittal slices of 300 μM width were cut on an HR2 vibratome (Sigmann Elektronik). Temperature was maintained at 34 ± 1°C in all experiments. The extracellular solution contained 125 mM NaCl, 2.5 mM KCl, 25 mM D-glucose, 25 mM NaHCO_{3}, 1.25 mM NaH2PO4, 2 mM CaCl2, and 1 mM MgCl2 bubbled with 95% O2 and 5% CO2. The intracellular pipette solution contained 110 mM potassium gluconate, 10 mM KCl, 4 mM ATP-Mg, 10 mM phosphocreatine, 0.3 mM GTP, 10 Hepes, and 13 mM biocytin adjusted to pH 7.3–7.4 with 5 M KOH.

Data was acquired through an ITC-1600 board (Instrutech) connected to a PC running a custom-written routine (PulseQ) under IGOR Pro (WaveMetrics, Lake Oswego, OR, United States). L5_TTPCs were selected according to their large soma size (15–25 μm) and their apparent large trunk of the apical dendrite. Cells were visualized by infrared differential interference contrast video microscopy using a VX55 camera (Till Photonics) mounted on an upright BX51WI microscope (Olympus). Sampling rates were 5–10 kHz, and the voltage signal was filtered with a 2-kHz Bessel filter. The resting membrane potential was −65.3 ± 4.3 mV, the input resistance was 59.7 ± 17.1 MΩ and the access resistance was 15.2 ± 3.7 MΩ. The stimulation protocol consisted of pre-synaptic stimulation with eight electric pulses at 20 Hz followed by a single pulse 500 ms later (recovery test), at the sufficient current intensity to generate APs in the presynaptic neuron while the postsynaptic neuron responses were recorded. The protocol was repeated between 20 to 60 times with a time between repetitions of 12 s (

With the UVR hypothesis it was not possible to reproduce the variability observed

Our model describes the short-term synaptic dynamics defined by a stochastic generalization of the Tsodyks-Markram model (TM-model) (_{RRP} that could be in ready or recovery state. In this study we followed the synaptic dynamics described previously that is able to predict the sequence of PSP amplitudes produced by any spike train (

In short, when the _{n}. Accordingly, the product _{n}_{n} models the fraction of synaptic efficacy used by the _{n} assuming that the synaptic efficacy has an exponential recovery with time constant _{n+1}) is used when (_{n+1} which increases for each subsequent spike from _{n} to _{n}) + _{n} and goes back to

Thus, if a vesicle is successfully released, these receptors get activated with a conductance g_{max}/N_{RRP} with g_{max} as the maximal conductance.

We constrained our synaptic model by extracting the parameters _{mem}, so we could extract the peaks from the EPSPs (

To express this process mathematically we used the next equation:

The right-hand part of the expression is the voltage deconvolution, while the left hand contains the unfiltered synaptic current. The requirement here is to compute τ_{mem} for each

Once the EPSP peaks were extracted from the deconvolved and normalized trace, we introduced them as an input into a genetic algorithm (GA) (

For the ^{3} giving rise to 8 million synaptic connections mediated by 37 million synaptic contacts. All the neuronal and synaptic models can be freely obtained through the open-access Neocortical Microcircuit Collaboration (NMC) portal (

Having computed the mean and the standard deviation of the synaptic parameters from fitting the _{max} value for a simulated connection. Next, we performed patch-clamp _{RRP} values. These values were defined based on the mean of a Poisson distribution shifted one unit to the right, because at least one vesicle had to be released per synaptic site. The range of means of the Poisson distributions varied from 0 to 13 (1 ≤ N_{RRP} ≥ 14) in the case of studying MVR and 0 (N_{RRP} = 1) while studying UVR. We decided to set the maximum value to 14 vesicles on average per release site because is already the double of what Loebel and colleges predicted on their research (

As the next step, we simulated 100 L5_TTPC connections

After simulating _{RRP} values and selecting a subset where the 1st EPSP amplitude was within the experimentally observed range, we artificially applied voltage fluctuations to

Mathematically the expression used in this work for this process was:

Where τ is the membrane time constant, σ is the standard deviation of the voltage and W_{t} is a random term coming from the Wiener process. In the case of σ = 0 the equation will have the solution _{0}^{−(t−t0)/τ} so X(t) relaxes exponentially toward 0. In general, X(t) fluctuates randomly, the third term pushes it away from zero, while the second term pulls it back to zero (

In our specific case, we defined σ and τ using the voltage values between the 8th and the 9th EPSPs, 400 ms in total, for each repetition (sweep) in a connection and then we averaged the resulting values (

In order to compute the CV for the EPSP amplitudes for

This method consists in excluding one observation at a time from a group of observations. In our specific case, from a set of single traces we computed the average of all but one off the traces each time, obtaining a set of averaged-JKK traces in the end. From each of these averaged-JKK traces we computed the amplitudes for all nine EPSPs in a train of synaptic responses. Through this computation, we were able to compute the EPSP amplitudes more precisely considering that we removed the noise by averaging. Thereafter, we computed the CV profiles for the

Where n denotes the EPSP index (

Having two sets of simulations, to study UVR and MVR, we computed the CV profile of EPSP amplitudes using the JKK approach in both cases and compared them with the CV profile measured in the _{RRP} that correspond with the smallest error.

Mean values for the EPSP amplitudes, the CVs and the synaptic parameters were expressed as their respective mean ± their standard deviation. Differences between distributions were measured using the Kruskal-Wallis test which shows a significant difference when

To reproduce the synaptic release variability observed

Next, we compared the distribution profiles of the first EPSP amplitude for the entire ^{–9}). The distributions (

This striking difference motivated us to implement the MVR hypothesis, which is known to provide enhance the dynamic range of synapses through higher variability (

Before applying our method to an _{RRP} value by using our procedure. For this purpose, we built 3 _{RRP}_{s} with mean values around 1, 4 and 10, each of them composed of 30 L5TTPC connections, similarly to the number of connections that is possible to obtain from _{RRP} values ranging from 1 to 14 (see section “

Validating the method. _{RRP} against error for the different _{RRP} (dots, N_{RRP} = 1; squares, N_{RRP} = 4; triangles, N_{RRP} = 10).

In this manner, we obtained N_{RRP}_{s} that characterized each of the three different _{RRP}_{s} were 1.01 ± 0.10, 4.07 ± 0.30 and 9.85 ± 0.45, obtaining as results N_{RRP} = 1.10 ± 0.31 (dots), N_{RRP} = 4.11 ± 1.75 (squares) and N_{RRP} = 10.71 ± 3.21 (triangles), respectively (

To enable comparison between the _{max} for connections. We simulated _{ma}_{x} value until the first EPSP amplitude matched experimental measurements. The resulting g_{max} was 1.54 ± 1.20 nS, which is consistent with previous estimates (_{max} parameters, and adding a synthetic membrane voltage noise to each simulated

Fitting

Noise calibration.

Having defined the core synaptic parameter set, we next simulated _{JKK} computed from the _{RRP} and the CV for L5_TTPC connections (_{RRP} was smaller. Therefore, for UVR-like connections the variability between individual sweeps is larger than for MVR-like connections. This result is in agreement with previous studies (_{RRP} = 1 (_{RRP} = 20 (

NRRP computation. _{RRP} over the CV. _{RRP} values. _{RRP} against error, showed a clear minimum around the value obtained for this specific connection.

In order to determine N_{RRP}, we next computed the CV profiles of the _{RRP}_{s} and measured their mean square distance (_{RRP} = 3.78 ± 1.65 (

We next sought to test if our hypothesis of MVR between L5_TTPCs could better explain variability in experimental as against UVR (

Releasing multiple vesicles improved the variability of the model. _{RRP} value that produces the minimum error. In the distributions and the CV profile, dots represent the mean and vertical and horizontal bars represent the standard deviation of all the experiments.

Further results, shown in the distributions for the first EPSP amplitude (

We extended this method to other cell-type-specific connections predicted in the neocortical tissue model (

Before computing the CV for different cell-type-specific synaptic connections obtained from the literature, we had to take into account that they were not necessarily computed using the JKK bootstrapping approach. Our previous analyses demonstrate that the CV of the first EPSP computed through the JKK method has a slightly larger value than the CV computed analytically. In the case of L5_TTPC connections the CV_{JKK} was 0.38 ± 0.21 as against the analytical CV of 0.31 ± 0.14 for the _{RRP}_{s} computed after 50 iterations in both cases were mostly similar (N_{RRP} without JKK = 2.41 ± 1.08 and N_{RRP} with JKK = 2.73 ± 1.22; _{RRP} obtained by comparing the _{RRP} obtained by comparing the CV for all the EPSPs, but as revealed in the previous analysis we did not match the exact CV value for the 1st pulse, although there were no significant difference.

Extension of the method for connections reported in literature. Transformation from CV to CV_{JKK} using L5_TTPC connection as example _{RRP}. Solid black line represents the CV computed for the _{JKK} computed for different N_{RRP}. Solid black line represents the CV_{JKK} obtained from the lineal fitting on _{JKK.} Short dotted black line represents the original CV found in literature. _{JKK} transformation. Solid black line represents the mean of the 50 iterations and dotted black line represent the linear fitting which equation is at the top of the plot. In _{RRP} as the one corresponding with the closest CV.

Knowing that the JKK bootstrapping method provided a more accurate method to compute EPSP amplitudes, we applied a transformation from CV to CV_{JKK} (_{RRP} values and we performed a linear fit to the mean of 50 repetitions (_{JKK} = 0.39 ± 0.15 with a correspondent N_{RRP} = 2.84 ± 1.34. We did that for every connection for which we could find data in the literature and our simulation matched the variability (

Results for connections reported in literature.

_{RRP} |
|||

0.40 ± 0.09 ( |
0.38 ± 0.21 | 1.96 ± 0.98 | |

0.33 ± 0.18 ( |
0.48 ± 0.23 | 2.60 ± 1.28 | |

0.27 ± 0.13 ( |
0.37 ± 0.09 | 1.81 ± 0.37 | |

0.33 ± 0.20 ( |
0.46 ± 0.15 | 1.26 ± 0.50 | |

0.32 ± 0.08 ( |
0.34 ± 0.16 | 1.82 ± 0.90 | |

0.31 ± 0.14 (Measured in this study) | 0.39 ± 0.15 | 2.84 ± 1.34 |

_{JKK}computed for other five cell connections through the collection of data from literature and applying the JKK conversion explained in

The generalized results to five different cell-type-specific connections are summarized in _{RRP} = 1.26 ± 0.50), while for the remainder of connections the predicted N_{RRP} is between 2 to 3 (see _{RRP} = 2.60 ± 1.28 for L23_PC-L23_PC; N_{RRP} = 1.96 ± 0.98 for L23_NBC_LBC-L23_PC; N_{RRP} = 1.81 ± 0.37 for L4_SSC-L23_PC and N_{RRP} = 1.82 ± 0.90 for L5_TTPC-L5_SBC).

Our results predict that synaptic release at most connections in the neocortex are more likely mediated by MVR rather than UVR, supporting the idea that the release of multiple vesicles enhances the response variability of neocortical synapses and augments information transmission.

In this work we computed the N_{RRP} building on the previous work of _{RRP} values within the framework of a large-scale, data driven tissue level model of juvenile rat neocortical microcircuitry (

Our analysis demonstrates that the UVR hypothesis cannot reproduce the variability observed on the

Before obtaining evidence, which supports the MVR hypothesis, we extracted a core set of synaptic important parameters from an _{RRP} was set to 1, 4 and 10, respectively. Although the mean values obtained using the method were slightly larger, no significant differences were found, and therefore, we used the validated method with experimental data sets.

Increasing the N_{RRP} improved the variability of our model, resulting in synapses that more faithfully reproduced the experimentally observed physiology. Consequently, for synaptic connections between L5_TTPCs the predicted N_{RRP} was 3.78 ± 1.65 within a range of 1 to 9 vesicles. Synaptic connections between L5_TTPCs are mediated by about 4 to 8 contacts on average (

We extended our method to predict the N_{RRP} for L5_TTPC synapses to other cell-type-specific connections in the neocortex reported in the literature. For five different cell-type-specific connections, we predict that the average N_{RRP} is between 2 and 3 (see

Due to lack of specific data, we extrapolated synaptic parameters measured in the superficial layers (_{RRP}. Our data-driven framework is designed in to integrate specific data sets as and when they become available to enable predictions on the N_{RRP} of cortical synapses.

Despite the occurrence of weak _{RRP}. It should be noted that other parameters relevant to predict the N_{RRP}, such as g_{max} were determined indirectly in our study, which could impact our results. For instance, if g_{max} was underestimated, we would have had obtained a larger N_{RRP} by increasing its value considering the same CV. It is also known that other synaptic mechanisms such as the membrane fusion, receptor saturation, and vesicle recycling directly influence vesicle release (_{RRP} for cortical connections.

In summary, we described an approach built upon previous work (_{RRP} per active synaptic contact for neocortical connections. By systematically comparing _{RRP}. Our preliminary results suggest that MVR could serve as a fundamental mechanism in the brain to increase the dynamic range of synapses and their variability.

The raw data supporting the conclusions of this manuscript will be made available by the authors, without undue reservation, to any qualified researcher.

All experiments were performed according to the Swiss national and institutional guidelines.

NB-Z developed and performed the data analysis and the

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The authors thank Dr. Michael Reimann and the Blue Brain Project team for insightful discussions.