Monte-Carlo simulation of confocal spot detection data

In the fluorescence fluctuation spectroscopy (FFS) experiments described by Jordan (2000), a standard confocal microscope was used to focus a laser spot onto single hip-pocampal synapses. Vesicles in the presynapse were labelled with fluorescent styryl dye and their movement led to fluctuations in the detected fluorescence signal. The following section will explain what information was already available from those exper-iments and which information was missing to simulate the complete FFS experexper-iments.

The aim was to specify the type of vesicle mobility that describes the experimental data measured in the FFS experiments. The results from these simulations, together with additional experimental data, are given in section 4.1.1.

3.1.1 What does one need to know to simulate FFS experiments?

1. The geometry of the detection volume: In the confocal microscope (Zeiss Confocor 1, Oberkochen, Germany) used by Jordan (2000), the detection vol-ume was best described by a three dimensional Gaussian profile. The geometry of this volume was determined from calibration measurements and was found to extend considerably along the optical axes out of the small hippocampal synapse if centered on the synapse (average bouton diameter ∅ = 1 µm, for details see Jordan (2000)). It was shown that in such systems fluorescence fluc-tuations of particle movement along the optical axes can be neglected and that such a detection volume can be approximated to have the form of a cylinder (Gennerich and Schild, 2000), thus the illumination profile along the optical axis (in z-direction) is roughly constant, while in the xy-plane the illumination

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24 3 Computational methods and simulations

profile is best described by a 2D Gaussian. As a consequence only movements of vesicles in x- or y-direction cause fluctuations in the detected fluorescence intensity. It was thus legitimate to simplify the problem from a 3D geometry to a 2D geometry. This corresponds to a projection of the approximately three dimensional spherical synapse (∅ ∼ 1 µm) onto a two-dimensional circle with an area of 3.14µm² (∅∼1µm). The same holds true for the detection volume, which is projected to the detection area (2D Gaussian disk).

2. The number of stained vesicles in the synapse: This number was not determined by Jordan (2000). In section 4.1.1 this number will be determined to be 24 vesicles in average per synapse using fluorescent imaging techniques of single dye stained vesicles and strong stained synapses (application of the two-step one-color protocol, see methods section 2.5 for details).

3. The brightness of each individual vesicle: Jordan (2000) estimated directly the brightness of a single vesicle from the FFS experiments. This approach was however, not very reliable. Thus this value was again estimated using a combination of imaging and fluorescence correlation spectroscopy techniques.

This is explained in detail in section 4.1.1.

4. The type of movement of the objects of interest: To determine the parameters of movement was the aim of the simulation. Different types of motion were simulated and compared with the experimental data (see section 4.1.1).

3.1.2 Monte-Carlo simulation of FFS experiments

Small vesicles were simulated as fluorescent point sources with a brightness deter-mined from experiments in section 4.1.1.

24 vesicles were placed at random positions in the 2D projection of the synapse.

The particles were allowed to undergo a random walk in a 2D grid, with h = 1 nm the grid space constant, p= ^D·τ_h2 being the probability to jump to the next grid point, D being the 2D diffusion coefficient, andτ = 0.01msthe time step of the simulation.

Since vesicle movement in hippocampal synapses is believed to be restricted, the random walk was further confined within a small cage of radius r (this parameter was varied betweenr= 12.5−200nmand for simplicity a square cage was simulated with

3.1 Monte-Carlo simulation of confocal spot detection data 25

x y

z

r_x = 170 nm

a = 500 nm Figure 3.1: Schematic of a confocal

laser volume centered on a synapse.

Vesicles were allowed to undergo a random walk within a cage in a 2D disk. The relative dimensions of the confocal volume and the synapses ap-proximate the true values as given in the text and described by Jordan (2000). Dashed ellipsoids indicate the cage and red lines the random walk of the vesicles (black dots).

edge length r), and the object was reflected only if it reached the cage border.Please note that the type of movement simulated was an assumption, which was only legit-imized when the simulation could indeed explain the experimental data (see results section 4.1).

Since only vesicles within the detection area contribute to the fluorescence signal (please note that the e⁻² radius of the detection profile in the experiments by Jordan (2000) was ∼ 0.17 µm) and only confined movement of vesicles was simulated, this properties could be used to enhance computation time of the simulation. Instead of simulating 24 vesicles in the projection of the synapse, only 8 vesicles where simulated in a three times smaller region (a square with edge length a= 0.5 µm) that was cen-tered on the detection area. Since vesicles at the edge of this region do not contribute anymore to the fluorescence signal, they could also cross the edge of the square when this happened during the random walk simulation. Figure 3.1 shows a schematic of the simulation.

Since the illumination profile was known, the intensity of each object was deter-mined according to its spatial position in the 2D Gaussian disk relative to the center

26 3 Computational methods and simulations

of the focal point. Intensities of all objects were integrated to yield the final fluo-rescence signal at each time point of the simulation. To simulate shot-noise (that is present in every experimental fluorescence signal), random numbers were drawn from a Poisson probability distribution with an expectation value given by the actual simulated fluorescence at each time point. Each simulation was performed to give a fluorescence trace of 120 s sampled at 10 Hz to match the experimental data (see Jordan (2000)). The data was analyzed similarly as described by Jordan (2000). In brief the fluorescence signal was high pass filtered with 0.05 Hz to remove slow fre-quency components. Jordan (2000) found this step necessary to obtain reproducible measurements. From the filtered data, the power spectra (PS) or the autocorrelation function (ACF) were calculated as well as mean and variance of the fluorescence sig-nal. Approximately 6-10 simulations of 120 s length were averaged. Error bars will be given as s.e.m..