Mitochondrial variability as a source of extrinsic cellular noise

Abstract

We present a study investigating the role of mitochondrial variability in generating noise in eukaryotic cells. Noise in cellular physiology plays an important role in many fundamental cellular processes, including transcription, translation, stem cell differentiation and response to medication, but the specific random influences that affect these processes have yet to be clearly elucidated. Here we present a mechanism by which variability in mitochondrial volume and functionality, along with cell cycle dynamics, is linked to variability in transcription rate and hence has a profound effect on downstream cellular processes. Our model mechanism is supported by an appreciable volume of recent experimental evidence, and we present the results of several new experiments with which our model is also consistent. We find that noise due to mitochondrial variability can sometimes dominate over other extrinsic noise sources (such as cell cycle asynchronicity) and can significantly affect large-scale observable properties such as cell cycle length and gene expression levels. We also explore two recent regulatory network-based models for stem cell differentiation, and find that extrinsic noise in transcription rate causes appreciable variability in the behaviour of these model systems. These results suggest that mitochondrial and transcriptional variability may be an important mechanism influencing a large variety of cellular processes and properties.

Figure 1. An illustration of the model we employ for mitochondrial variability.

This illustration qualitatively shows the key components of our model. Cell growth progresses deterministically according to the variables that characterise a cell: volume, mitochondrial mass (illustrated here by copy number) and functionality (illustrated here by shading). At mitosis, stochastic partitioning occurs and daughter cells inherit a random volume, mitochondrial mass and functionality level from a parent cell. This stochastic inheritance leads to a heterogeneous population. Cells with high mitochondrial density and functionality have higher ATP levels, are able to grow faster, and have higher transcription rates than cells with lower mitochondrial mass and functionality. The variances associated with stochastic partitioning, the dependence of ATP concentration on cellular properties, and the dependence of growth and transcription rates on ATP are all parameters of the model.

Figure 2. The set of data used to parameterise our model.

Experimental data shown in blue, fitted simulated data shown in red. A. Ratio of larger cell volume to smaller cell volume between sisters at birth. B. Ratio of larger mitochondrial mass to smaller mitochondrial mass between sisters at birth. C. Mean and standard deviation of the cell cycle length in a population of cells. D. Noise levels in transcription rate in (C)ontrol, (A)ntioxidant-treated and (P)ro-oxidant-treated populations, and between (S)ister cells. Two other experimental values, not pictured, that were used to parameterise our model are a maximum cell volume of (for consistency with Ref. [53]) and a mean ATP concentration of (from Ref. [70]).

Figure 3. Our simple model is consistent with experimental probes of mitochondrial and cellular variability.

Comparison between our model (red) and experimental data (blue), following discussion in the Main Text. Experimental data from das Neves et al. . A. Distribution of mitochondrial mass in an unsynchronised population of cells. B. Distribution of cell volume in an unsynchronised population of cells. C. Comparison of the lengths of cell cycles between generations: Gen 1 is the parent cell, Gen 2 the daughter. Cell cycle lengths are only weakly correlated. D. Relationship between the ratio of mitochondrial masses at birth against ratio of cell cycle lengths for sister pairs. E. Relationship between the ratio of cellular volumes at birth and the ratio of cell cycle lengths for sister pairs, showing a weaker correlation than D. F. Transcription rate noise in subsets of the population in , , and phases (see Main Text). G. Mitochondrial mass and cell volume are strongly correlated in our model. Some experimental evidence is contradictory (see Main Text). H. Distribution of transcription rate per unit volume . New experimental data (see Methods ). I. Distribution of total mitochondrial functionality ( in our model, CMXRos readings from experiments). J. Mean and standard deviation of cell cycle lengths in (A)nti-oxidant-treated, (C)ontrol, and (P)ro-oxidant-treated populations. Experimental histograms, originally presented in arbitrary units, have been scaled to match the mean value of the simulated data.

Figure 4. Illustration of the dynamics of our model.

Example time series of (transcription rate), (mitochondrial functionality), (mitochondrial mass) and (cell volume), as a cell grows and divides repeatedly in our model.

Figure 5. Variability in mitochondrial mass and functionality can both contribute to noise in transcription rate.

Effects of changing variability in mitochondrial mass inheritance () and functionality () on overall transcription rate noise . This contour plot shows the value of for a given combination of . More stochasticity associated with inheritance of mitochondrial properties leads to higher transcription rate noise, and stochasticity in both mass and functional inheritance plays an important role in transcription rate noise. Contour lines on the bottom surface mark different values of . The ‘X’ mark denotes the default parameterisation of our model. Other contour lines show that this relationship remains essentially identical when variability due to cell cycle stage and volume inheritance is removed, suggesting that and are the key sources of transcription rate noise.

Figure 6. Mitochondrial variability contributes strongly to noise in mRNA levels.

Analytic and modified Gillespie simulation results for time evolution of mRNA levels with and without mitochondrial and volume variability. Bars show the mean and standard deviation of the corresponding distribution at a given time. Red () give simulated results without inherited variability. Black () give analytic results without inherited variability. Blue () give simulated results with mitochondrial and volume variability, displaying much greater variance in mRNA expression. Bars are slightly offset in the x-direction for clarity. The inset shows two example time series for both simulated cases.

Figure 7. Effects of mitochondrial variability dominate protein expression variability in our model.

Dual reporter simulation with different sources of noise in our protein expression simulations. All plots except (E) are normalised so that the highest protein expression level in the cell population is 1. Red (diamonds) show results from Raj et al.'s default parameterisation used to model transcription, translation and degradation (see Methods). Blue (triangles) show results from this parameter set with degradation rates increased 100-fold. Protein levels are shown from population of (A) unsynchronised cells with mitochondrial and volume variability, (B) synchronised cells with mitochondrial and volume variability, (C) unsynchronised cells with no mitochondrial or volume variability, and (D) synchronised cells with no mitochondrial or volume variability. (E) Mean protein expression levels in the default parameterisation of Raj et al. with the product of mitochondrial mass and function , in the system corresponding to (A). (F) The equivalent plot of (A) with translation rates independent of .

Figure 8. Transcription rate affects the stability of model stem cell systems.

In both diagrams, curves delineate the boundary of the attractor basin corresponding to the undifferentiated cell state. Red (solid) to black (dotted) lines show the basin structure as transcription rate increases through the given values. (A) The structure of the undifferentiated attractor basin in the Huang model given different transcription parameters, showing the widening of the stable undifferentiated region at high transcription rate. (B) The structure of the undifferentiated attractor basin in the Chickarmane model, showing a decrease in undifferentiated basin size as transcription rate increases. The activation-repression structure of both models is illustrated – in (B), external terms representing the activation of GATA1 and X exist but are set to zero in our analysis to allow PU.1 to be expressed under some conditions.