Dynamic spherical harmonics approach for shape classification of migrating cells

Anna Medyukhina,Nora Ruef,Marco Blickensdorf,Marc Thilo Figge,Jens V Stein,Zoltán Cseresnyés

doi:10.1038/s41598-020-62997-7

Abstract

Cell migration involves dynamic changes in cell shape. Intricate patterns of cell shape can be analyzed and classified using advanced shape descriptors, including spherical harmonics (SPHARM). Though SPHARM have been used to analyze and classify migrating cells, such classification did not exploit SPHARM spectra in their dynamics. Here, we examine whether additional information from dynamic SPHARM improves classification of cell migration patterns. We combine the static and dynamic SPHARM approach with a support-vector-machine classifier and compare their classification accuracies. We demonstrate that the dynamic SPHARM analysis classifies cell migration patterns more accurately than the static one for both synthetic and experimental data. Furthermore, by comparing the computed accuracies with that of a naive classifier, we can identify the experimental conditions and model parameters that significantly affect cell shape. This capability should – in the future – help to pinpoint factors that play an essential role in cell migration.

Highlights

Cell migration involves dynamic changes in cell shape
In cell migration simulator (CMS), each cell consists of a set of grid-based spatial units (SU), and the cell migration in 3D is simulated by iteratively moving SU from the rear of the cell to the front (Fig. 2a). mreliagTtrihavteeiosSniUmdpuiroleasctiittoiioonnnsP tv→aaDrst(stFhwiegit.dh2oata)p.srEpoahdceuhrciSctUableoctfewltelhewenicttehhlletrhneecoercimevneastleavrepocoftsomirtsiaos nv→sPvaetacnptdoors iv t→Div→oP:n,Pwp=ihniitc ahv→nDids⋅uas v→rePadnt∈dooc[m−oml1yp, cu1ht].oeTstehhnee value of P defines whether the corresponding SU belongs to the cell’s rear or front: for all front SU, P must be greater than a pre-defined front-rear threshold FR, whereas all SU with P ≤ FR belong to the cell’s rear
We tested the neighbor-weight parameter neighbor weight (NW), which determines the cell surface roughness, the parameter for position weight PW, which affects the cell elongation, the distance weight parameter DW, which governs the size of cell protrusions, and the front-rear threshold FR, which is associated with the cell volume fraction considered as the front

Summary

Introduction

Cell migration involves dynamic changes in cell shape. Intricate patterns of cell shape can be analyzed and classified using advanced shape descriptors, including spherical harmonics (SPHARM). Even averaging cell shape descriptors over time[7] may not always be sufficient to distinguish some migration patterns, for example when all cells evolve through similar phases of cell shape but different cells do this with different frequencies (Fig. S1)[8] To distinguish such details of migration behavior we need dynamic shape analysis that takes into account relative changes in cell shape between consecutive time points. SPHARM is a 3D extension of a Fourier analysis, where an arbitrary shape function is expanded on a sphere using a set of orthogonal spherical functions as a basis This approach was shown to be effective for characterizing the shape of proteins[20,21], red blood cells[22,23], brain structures[19,24,25], as well as migrating cells[7,26,27,28]. SPHARM descriptors represent an ideal first candidate to be extended for dynamic 3D shape analysis

Methods

Results

Conclusion