# Spaghetti Tracer: A Framework for Tracing Semiregular Filamentous Densities in 3D Tomograms

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. Noise Calibration and Simulation of Tomograms

#### 2.2. Density Map Preprocessing: Accumulation of Forward and Backward Path Densities

#### 2.2.1. Pyramidal Search Window and Maximum Path Density Selection

#### 2.2.2. Accumulation and Reverse Pyramid Influence Zone

#### 2.3. Combining Forward and Backward Path Densities for Filament Pattern Enhancement

#### 2.4. Candidate Seed Point Selection

#### 2.5. Tracing of Candidate Filament Segments

#### 2.6. Grouping and Selection of Candidate Filament Segments

#### 2.7. Fusion of Filaments

## 3. Results

#### 3.1. Visualization

#### 3.2. Statistical Performance Evaluation

#### 3.3. Algorithm Run Times

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The filament-tracing framework originally developed in [19]. The enhancement step filters the tomogram by utilizing a cumulative path-based density-contrast enhancement algorithm. This relatively slow preprocessing step raises the intensity values of filaments to make them stand out better from the noise. Subsequently, the filaments can be quickly generated in a bottom-up manner from candidate seed points (CSPs), which is followed by tracing short candidate filament segments (CFSs) from the CSPs. The large number of short CFSs are then refined and fused to generate the detected output filaments.

**Figure 2.**Manually traced filaments in the stereocilia taper region. The manual “spaghetti” model is consistent with the experimentally observed density of the actin filaments [18] in cryo-ET. The true position of actin filaments in the experimental map is not known with complete certainty, but manual tracing can serve as a ground truth for testing our algorithms when using simulated tomograms modeled after the shown filament traces. All molecular graphics figures in the present paper have been prepared with UCSF Chimera [23] and oriented with the $+Y$ direction to the right.

**Figure 3.**Illustration of the simulated density maps at various noise levels relative to noise in the experimental map [18] (see text). (

**A**) noise level 0.40; (

**B**) noise level 0.60; (

**C**) noise level 0.80; (

**D**) noise level 1.00. For the illustration, we used a 10-voxel-thick slab (corresponding to Z-indices 120–129, using experimental map voxel spacing 0.947 nm [18]), with an isocontour density threshold of mean plus two times the standard deviation.

**Figure 4.**Two path density accumulation schemes were employed in the filament pattern enhancement and CFS tracing steps (Figure 1). (

**A**) illustrates how the forward path density ($FPD$) of length $l=5$ voxels accumulated from the voxel ($i,j,k$) (green) using the original DP approach [19] in Equation (1). The accumulation zone (red) is shown for a random target voxel (${i}^{\prime},j+l,{k}^{\prime}$) (blue), but the final $FPD$ has been taken as the maximum among all potential targets (black) at the base of the search pyramid ($i-l\le {i}^{\prime}\le i+l,k-l\le {k}^{\prime}\le k+l$, Equation (1)). (

**B**) shows how the $FPD$ accumulated with the alternative straight-line approach (also $l=5$ voxels) in the CFS tracing (Figure 1).

**Figure 5.**Comparison of the unfiltered and various $CPD$-filtered maps using $l=5$ voxels. The same 10-voxel-wide slab of Figure 3C) is shown, except that it is rendered at the mean + standard deviation isolevel to emphasize the noise. (

**A**) Original unfiltered map with a noise level of 0.8 (as in Figure 3C). (

**B**) The map filtered by multiplication of $FPD$ and $BPD$ (Equation (5)). (

**C**) The map filtered by addition/arithmetic mean (Equation (6)). (

**D**) The map filtered by the geometric mean (Equation (7)). (

**E**) The map filtered by the minimum (Equation (8)).

**Figure 6.**Automatically detected FSs (solid blue; this work) superimposed by the ground truth manually traced filaments (transparent yellow, [18]). (

**A**) The green areas in this full-view rendering indicate good agreement because of the subtractive color mixing. (

**B**) A slab consisting of 10 Z-slices, which is taken from the center portion of (

**A**), provides a detailed view of the individual filaments. The FSs (blue) have been obtained from the 0.60 noise level simulated map (Figure 3B), which is closest to the automatically matched noise (see the Methods section), here by using DP-based enhancement with multiplication (Equation (5)), DP-based CFS tracing, and $l=5$.

**Table 1.**A performance comparison of the proposed DP-based framework with the line-based approach for tracing actin filaments without density enhancement preprocessing at various levels of noise. UND = undefined because the FP and TP values are both zero.

Noise | DP-Tracing | Line-Tracing | DP-Tracing | ||||||
---|---|---|---|---|---|---|---|---|---|

w/DP-Enhancement | w/DP-Enhancement | w/o Enhancement | |||||||

Pre. | Rec. | F1 | Pre. | Rec. | F1 | Pre. | Rec. | F1 | |

0.4 | 0.945 | 0.994 | 0.969 | 0.591 | 0.988 | 0.740 | 0.963 | 0.909 | 0.935 |

0.6 | 0.923 | 0.978 | 0.950 | 0.603 | 0.962 | 0.742 | 0.952 | 0.878 | 0.913 |

0.8 | 0.848 | 0.965 | 0.903 | 0.568 | 0.940 | 0.709 | UND | 0 | UND |

1.0 | 0.828 | 0.898 | 0.861 | 0.575 | 0.813 | 0.674 | UND | 0 | UND |

**Table 2.**Performance achieved with both DP enhancement and DP tracing using addition/arithmetic mean (Equation (6)), geometric mean (Equation (7)), and minimum (Equation (8)) blending functions.

Noise | Addition | Square-Root | Minimum | ||||||
---|---|---|---|---|---|---|---|---|---|

Pre. | Rec. | F1 | Pre. | Rec. | F1 | Pre. | Rec. | F1 | |

0.4 | 0.945 | 0.994 | 0.969 | 0.950 | 0.982 | 0.966 | 0.946 | 0.99 | 0.968 |

0.6 | 0.948 | 0.806 | 0.806 | 0.967 | 0.250 | 0.397 | 0.95 | 0.35 | 0.514 |

0.8 | 0.926 | 0.686 | 0.788 | 0.936 | 0.176 | 0.296 | 0.938 | 0.444 | 0.602 |

1.0 | 0.939 | 0.879 | 0.907 | 0.874 | 0.138 | 0.239 | 0.904 | 0.139 | 0.241 |

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**MDPI and ACS Style**

Sazzed, S.; Scheible, P.; He, J.; Wriggers, W.
*Spaghetti Tracer*: A Framework for Tracing Semiregular Filamentous Densities in 3D Tomograms. *Biomolecules* **2022**, *12*, 1022.
https://doi.org/10.3390/biom12081022

**AMA Style**

Sazzed S, Scheible P, He J, Wriggers W.
*Spaghetti Tracer*: A Framework for Tracing Semiregular Filamentous Densities in 3D Tomograms. *Biomolecules*. 2022; 12(8):1022.
https://doi.org/10.3390/biom12081022

**Chicago/Turabian Style**

Sazzed, Salim, Peter Scheible, Jing He, and Willy Wriggers.
2022. "*Spaghetti Tracer*: A Framework for Tracing Semiregular Filamentous Densities in 3D Tomograms" *Biomolecules* 12, no. 8: 1022.
https://doi.org/10.3390/biom12081022