Mitochondrial Variability as a Source of Extrinsic Cellular Noise

Introduction

• Cellular noise has many biological effects, but the quantitative contribution of mitochondrial mass and functionality to transcriptional noise remains unclear.Prior observations connect mitochondrial properties, ATP, and transcription, motivating a model that formalizes these links.Source: Introduction · pp. 1–2

Model

• The model treats cell volume, mitochondrial mass, and mitochondrial functionality as variable properties that shape ATP levels and, in turn, transcription rates.It links mitochondrial variability to downstream expression variability and is designed to reproduce experimental observations while permitting analytic treatment.Source: Model · p. 2

Stochastic Partitioning at Mitosis

• At mitosis, mitochondrial mass and cell volume are randomly partitioned; functionality is modeled as stable within a cycle and changing stochastically at division.Mass and volume partitioning are uncorrelated in the model, while both daughters inherit the same functionality value.Source: Stochastic Partitioning at Mitosis · pp. 2–3

[ATP] and Transcription Rate

• ATP depends on mitochondrial mass and functionality relative to cell volume, and transcription rate follows a sigmoidal relationship with ATP concentration.The model uses an experimentally determined ATP response that can also capture transcriptional effects associated with chromatin remodeling.Source: Model · p. 2, [ATP] and Transcription Rate · p. 4

Cellular Dynamics

• Cell volume grows exponentially, while mitochondrial density is modeled with mean reversion toward β/α; ATP is proposed to support cell growth and mitochondrial growth.The model does not distinguish growth rates at different cell-cycle stages.Source: Cellular Dynamics · p. 4

Model Parameterisation

• Model parameters were selected using a subset of experimental data, including sister-cell partition ratios, cell-cycle length statistics, and transcription-noise measurements.Figure 2 contrasts experimental data with fitted simulations across these measurements.Source: Figure 2 · p. 4, Model Parameterisation · p. 4

Results

• Model predictions broadly agree with experimental data, and the model estimates substantial mitochondrial contributions to noise in mRNA and protein levels and architecture-dependent effects on differentiation.The reported differentiation effects depend on the symmetry of regulatory interactions.Source: Results · p. 5
• The model produces a low-skewed mitochondrial-mass distribution and a quadratic-decay cell-volume distribution; transcription per unit nuclear volume is similarly peaked to experimental data.The nuclear-volume measure is modeled as proportional to cell volume.Source: Results · p. 5
• Successive cell-cycle lengths are weakly related, while transcription-rate noise remains around 0.4 across cell-cycle stages, matching reported experimental patterns.Stages are assigned using cell volume thresholds.Source: Results · p. 5
• Birth mitochondrial mass predicts cell-cycle length more strongly than birth volume (R2 = 0.69 versus experimental 0.78; volume R2 = 0.22 versus experimental 0.22).The model’s correlation patterns match the corresponding experimental comparisons.Source: Results · p. 5
• The model predicts strong correlation between mitochondrial mass and cell volume, unlike one flow-cytometry study; the authors note that this method may not provide absolute volume measurements.The prediction also contrasts with historical findings of low variability in mitochondrial density.Source: Results · p. 5

and model predictions

• Mitochondrial inheritance at birth predicts cell-cycle length better than volume inheritance, alongside pronounced cell-to-cell variability in mitochondrial mass and functionality.The comparison depends on mitochondrial variability and its influence on cellular growth.Source: Figure 3 · p. 6, and model predictions · p. 7

model

• Anti-oxidant treatment shortens cell cycles, whereas pro-oxidant treatment lengthens them, consistent with functionality-linked ATP affecting volume-growth rate.The model represents oxidative treatments by changing mean mitochondrial functionality.Source: Figure 3 · p. 6, model · p. 6
• Predicted and measured total mitochondrial functionality distributions share a skewed shape and similar variances; experiments quantify function with whole-cell CMXRos signal.The experimental signal integrates membrane potential across the cell and combines information about mitochondrial mass and functionality.Source: model · pp. 5–6, Figure 3 · p. 6
• Experimental mitochondrial mass and membrane potential correlate linearly, qualitatively supporting the model's representation of total functionality as mass times functionality.The model represents total functionality as nf, where n is mitochondrial mass and f is a functional measure.Source: model · p. 6

and model predictions

• The model is a phenomenological, coarse-grained account with simple functional forms, intended to summarize data and motivate further experiments.The authors note that refinements and other functional forms are possible.Source: and model predictions · p. 7
• Mitochondrial segregation and functionality both significantly contribute to transcription-rate noise; removing volume-partition variability or cell-cycle-position differences has little impact.The simulations therefore identify mitochondrial sources as a strong contribution to cell-to-cell transcription-rate variability.Source: and model predictions · p. 7

• Both mitochondrial mass inheritance and functionality contribute to transcription-rate noise, with their effects essentially unchanged after removing cell-cycle-stage and volume-inheritance variability.Source: Figure 5 · p. 8
• At t = 8.3 hours, mRNA noise ηm was ≃0.04 without extrinsic factors and ≃0.40 with mitochondrial, functionality, and cell-volume variability.Source: and protein expression · p. 8, Figure 6 · p. 8
• Mitochondrial and volume variability dominate protein-expression noise in the model, producing a wider spread than the two-fold range from cell-cycle variability alone.Higher mitochondrial mass and functionality generally correspond to higher protein expression, although inheritance noise weakens this correlation.Source: and protein expression · p. 8, Figure 7 · p. 9
• The model omits many factors affecting mRNA and protein process rates, and including them rapidly makes an analytic description impossible.Stochastic simulations could explore more complex models given estimates of how process rates depend on extrinsic variables.Source: and protein expression · pp. 8–9

can affect stem cell differentiation

• High protein-production rates stabilize the undifferentiated basin in the Huang model, whereas increasing transcription rate shrinks that basin in the Chickarmane model.Source: can affect stem cell differentiation · p. 10
• The contrasting outcomes reflect network architecture: the Chickarmane model’s intermediate species and asymmetric interactions shift the basin toward GATA1 at high transcription rates.Source: can affect stem cell differentiation · p. 10

Discussion

• The model formalizes mitochondrial segregation and functional variability as extrinsic-noise sources, and adequate fit to the data required variability in both mitochondrial mass and function.Source: Discussion · p. 10

can affect stem cell differentiation

• Mitochondrial variability may affect bipotent-cell stability through transcription-rate variability, with the direction of the effect depending on regulatory-network architecture.Source: Discussion · p. 10, can affect stem cell differentiation · p. 10

Discussion

• The model treats transcription rate as a function of ATP rather than explicitly representing mRNA processes, and it does not capture protein-expression noise at protein-specific detail.Source: Discussion · p. 11

Conclusions

• Mitochondrial inheritance and functional variability may be important sources of transcription noise and may contribute to downstream protein-expression noise.The authors propose multimodal single-cell measurements through cell division to clarify links among energy status, cell volume, mitochondrial mass, and expression rates.Source: Conclusions · p. 11

Methods

• Cells grow deterministically until reaching a volume cutoff, then divide with stochastic partitioning of mitochondrial mass and volume.The model treats volume and mitochondrial partitioning as uncorrelated.Source: Methods · p. 12
• Mitochondrial functionality changes stochastically at division, is shared by both daughters, and remains constant during each cell cycle.A cutoff of 0.01 prevents functionality values at or below that level; continuously varying functionality is considered as an alternative model.Source: Methods · p. 12
• Expression simulations combine cell-dynamics simulations with stochastic mRNA and protein production, then partition these molecules among daughter cells at division.The simpler mRNA-only simulations compare intrinsic noise in identical cells with extrinsic noise in a heterogeneous simulated population.Source: Methods · p. 12
• The study also varies parameters in two stem-cell differentiation models to examine how transcription and translation rates relate to differentiation-system behavior.The Huang model varies activation and repression parameters; the Chickarmane model varies parameters proportional to transcription rate.Source: Methods · p. 13

Parameterisation of λ(t)

• The transcription-rate response to ATP concentration is modeled with an inverse-tangent function fitted to measurements with and without chromatin decondensation.The authors choose this form for mathematical simplicity and note that other forms, including Hill functions, are possible.Source: Parameterisation of λ(t) · p. 14
• ATP and transcription rate vary slowly over the cell cycle in the model, allowing a linear approximation of λ(t) around t′.The authors take t′ to be half the mean cell-cycle length.Source: Parameterisation of λ(t) · p. 14
• The slope of the linearized transcription-rate trajectory depends on initial conditions and whether mitochondrial density is over- or under-populated at mitosis.Over-population leads mean reversion to decrease transcription rate with time, and under-population has the opposite effect.Source: Parameterisation of λ(t) · p. 14

Fitting Other Parameters

• Parameter fitting optimizes σf, α, β, and γ against seven experimental observables, while functionality parameters are set for mean control functionality of 1.The model then adjusts functionality parameters to match experimentally observed transcription-noise levels under corresponding oxidative conditions.Source: Fitting Other Parameters · p. 15

Mitochondrial Membrane Potential

• Both simulations and new experiments show a linear correlation between total membrane potential and mitochondrial mass.In the model, total membrane potential is represented by the product of mitochondrial mass n and functionality f.Source: Mitochondrial Membrane Potential · p. 15

Estimating Noise Contributions

• The modeled functionality distribution closely matches the steady-state AR(1) distribution, while cellular-age variability contributes negligibly to transcription-rate variability.The authors approximate the default cellular-age distribution with mean 16 hours and standard deviation 14 hours.Source: Estimating Noise Contributions · pp. 16–17
• The weighted contributions from functionality and initial mitochondrial mass exceed those from initial volume, while cell age contributes zero within working precision.For default parameters, the weights are wf = 8.5 × 10^5, wn0 = wv0 = 4.2 × 10^5, and wt is zero; simulated noise levels are ηf = 0.34, ηn0 = 0.13, and ηv0 = 0.07.Source: Estimating Noise Contributions · p. 17

Continuous f

• The alternative lets functionality f follow a constrained random walk, with step size δf measuring its variability.The model avoids unphysical values by constraining f to 0.1 ≤ f < 1.9.Source: Continuous f · pp. 17–18
• The continuously varying functionality model captures most experimental results to a similar extent as the default model.The comparison is shown in Figs. 13 and 14.Source: Continuous f · p. 18, Figure 14 · p. 18, Figure 13 · p. 18
• The model’s agreement with experiments is robust to the fine details of functionality’s within-cycle evolution and inheritance.The authors infer that variability magnitude, rather than the specific dynamics, drives the important physiological effects.Source: Continuous f · p. 18

ATP and Alternatives

• The model omits an ATP sink, assuming any ATP deficit is immediately compensated for.The authors motivate this simplification by the presumed homeostasis of cellular ATP.Source: ATP and Alternatives · p. 19
• An ATP-use model treats ATP level a as supporting cell-volume and mitochondrial-mass growth, and produces results similar to the simpler model.When a = γn, the original model equations are recovered.Source: ATP and Alternatives · p. 19
• The authors also describe a homeostatic ATP model in which mitochondria produce ATP and cellular growth consumes it.The representation could be extended to track the ATP:ADP ratio.Source: ATP and Alternatives · p. 19
• Potential ROS effects on transcription and growth are excluded for lack of experimental justification and to preserve analytic tractability.The authors leave these factors for possible future work.Source: ATP and Alternatives · p. 19

Other Deterministic Dynamic Forms

• Alternative mean-reverting models admit analytic solutions for mitochondrial mass and cell volume, though their mean-reversion rates differ.The trajectories for the alternatives are illustrated in Fig. 15.Source: Other Deterministic Dynamic Forms · p. 19, Figure 15 · p. 20
• The authors favor a phenomenological model that matches experiments and remains analytically tractable; more complex alternatives can impede deeper analysis.The alternatives can become analytically intractable.Source: Other Deterministic Dynamic Forms · p. 19
• Replacing ATP with a transcription- or translation-rate term could capture nonlinear growth responses, but the response curve is difficult to estimate.The simpler ATP term acts as a linear approximation, which the authors report gives similar numerical behavior to the nonlinear case.Source: Other Deterministic Dynamic Forms · p. 20
• Without mean reversion, mitochondrial-density variance generally grows without bound; density cutoffs can instead produce a stationary population distribution.This alternative was considered because flow-cytometry data showed no correlation between mitochondrial and cellular volume, but its analytical results are difficult to obtain.Source: Other Deterministic Dynamic Forms · p. 20
• A density-cutoff model can yield stationary mitochondrial-density distributions and transcriptional noise similar to the default model, but weakens mass–volume correlation.An example parameterization uses ρ− = 10 and ρ+ = 300, with α = β = 0.1 and γ = 3.6.Source: Other Deterministic Dynamic Forms · p. 20

Potential Experiments for Refinement

• The authors propose experiments to support the model or identify areas for refinement.Table IV describes potential experiments, roughly ranked by importance.Source: Potential Experiments for Refinement · p. 20, Table IV · p. 21
• The appendix derives an mRNA master equation and uses generating-function characteristics to obtain its time-dependent distribution.The authors then use stochastic simulation for the coupled mRNA–protein system, for which they report no general analytic solution.Source: mRNA & Protein Levels · pp. 21–23
• Simulations show pronounced protein-level effects from ATP-dependent transcription variability, including when translation rate is held constant.Higher degradation rates increased the intrinsic-noise contribution, while the dual-reporter trends changed little with constant translation rate.Source: mRNA & Protein Levels · p. 23