Developmental switching inPhysarum polycephalum: Petri net analysis of single cell trajectories of gene expression indicates responsiveness and genetic plasticity of the Waddington quasipotential landscape

Abstract

The developmental switch to sporulation in Physarum polycephalum is a phytochrome-mediated far-red light-induced cell fate decision that synchronously encompasses the entire multinucleate plasmodial cell and is associated with extensive reprogramming of the transcriptome. By repeatedly taking samples of single cells after delivery of a light stimulus pulse, we analysed differential gene expression in two mutant strains and in a heterokaryon of the two strains all of which display a different propensity for making the cell fate decision. Multidimensional scaling of the gene expression data revealed individually different single cell trajectories eventually leading to sporulation. Characterization of the trajectories as walks through states of gene expression discretized by hierarchical clustering allowed the reconstruction of Petri nets that model and predict the observed behavior. Structural analyses of the Petri nets indicated stimulus-and genotypedependence of both, single cell trajectories and of the quasipotential landscape through which these trajectories are taken. The Petri net-based approach to the analysis and decomposition of complex cellular responses and of complex mutant phenotypes may provide a scaffold for the data-driven reconstruction of causal molecular mechanisms that shape the topology of the quasipotential landscape.

Regulatory Dynamics of Cell Differentiation Revealed by True Time Series From Multinucleate Single Cells

“…In previous studies we have shown that the gene expression pattern in samples taken at the same time from different sites of a plasmodium covering a standard Petri dish (9 cm Ø) did not change within the limits of accuracy of the measurements. Accordingly, repeated sampling of the same plasmodial cell yields true time series ( Rätzel, 2015 ; Werthmann and Marwan, 2017 ). To allow more samples to be taken without consuming too much of the plasmodial mass, we now prepared plasmodia on 14 cm Ø Petri dishes, increasing the surface area covered by the plasmodial mass by 2.4-fold, and took smaller samples by punching agar plugs of 1.13 cm 2 per sample, to harvest a small portion of the initial total plasmodial mass.…”

“…The temporal sequences of gene expression patterns classified as Simprof significant clusters defined a trajectory for each individual cell and revealed significant differences between cell trajectories ( Table 2 ). To relate gene expression states and trajectories we constructed a Petri net (bipartite graph) as previously described ( Werthmann and Marwan, 2017 ; Rätzel et al, 2020 ), by representing each gene expression state by a place and the temporal transit between two states by a transition ( Figure 5 ). A single token marking one place of the Petri net indicates the current gene expression state of a cell.…”

“…Because cell cycle, cell fate choice, and development are synchronous throughout the plasmodium ( Rusch et al, 1966 ; Starostzik and Marwan, 1995a ; Hoffmann et al, 2012 ; Walter et al, 2013 ; Rätzel and Marwan, 2015 ), single-cell gene expression trajectories can indeed be constructed from time series. By assembling finite state machines made from trajectories we have constructed Petri net models for the state transitions that predict Markov chains as variable developmental routes to differentiation ( Werthmann and Marwan, 2017 ; Rätzel et al, 2020 ) which may be considered as trajectories through the Waddington landscape ( Waddington, 1957 ; Huang et al, 2009 ). These Petri nets also predict reversible and irreversible steps, commitment points, and meta-stable states in cells responding to a differentiation stimulus.…”

Extended robust boolean network of budding yeast cell cycle

“…[ 36 ] PN is very appropriate for the quantitative and qualitative modeling of concurrent, asynchronous and distributed systems and widely used for modeling of biological networks. [ 39 40 41 42 43 44 ] Steggles et al introduced a method for automatic translation of BN into PN model. [ 45 ] Zhang et al created a stochastic model of BYCC and defined 2048 cell states whose transition probabilities between these states are affected by noise parameter.…”

Active poroelastic two-phase model for the motion of physarum microplasmodia

“…The true slime mold Physarum polycephalum is a well known model organism [8] that exhibits mechano-chemical spatio-temporal patterns. Previous research in Physarum has addressed many different topics in biophysics, such as genetic activity [9], habituation [10], decision making [11] and cell locomotion [12, 13]. Physarum is an unicellular organism, which builds large networks that exhibit self-organized synchronized contraction patterns [8, 14, 15].…”