Single-cell protein dynamics reproduce universal fluctuations in cell populations

Protein variability in single cells has been studied extensively in populations, but little is known about temporal protein fluctuations in a single cell over extended times. We present here traces of protein copy number measured in individual bacteria over multiple generations and investigate their statistical properties, comparing them to previously measured population snapshots. We find that temporal fluctuations in individual traces exhibit the same universal features as those previously observed in populations. Scaled fluctuations around the mean of each trace exhibit the same universal distribution shape as found in populations measured under a wide range of conditions and in two distinct microorganisms. Additionally, the mean and variance of the traces over time obey the same quadratic relation. Analyzing the temporal features of the protein traces in individual cells, reveals that within a cell cycle protein content increases as an exponential function with a rate that varies from cycle to cycle. This leads to a compact description of the protein trace as a 3-variable stochastic process - the exponential rate, the cell-cycle duration and the value at the cycle start - sampled once each cell cycle. This compact description is sufficient to preserve the universal statistical properties of the protein fluctuations, namely, the protein distribution shape and the quadratic relationship between variance and mean. Our results show that the protein distribution shape is insensitive to sub-cycle intracellular microscopic details and reflects global cellular properties that fluctuate between generations.

💡 Research Summary

The paper investigates whether the universal statistical features of protein variability observed in population‑level snapshots also manifest in the temporal dynamics of single cells. Using fluorescent reporter proteins, the authors tracked the copy number of a constitutively expressed protein in individual Escherichia coli and Saccharomyces cerevisiae cells over 10–20 generations. Cells were confined in a microfluidic device that allowed continuous imaging; each division event was precisely identified, and the protein amount was quantified from fluorescence intensity at regular intervals.

Analysis of the time series revealed a characteristic pattern: after each division the protein amount in the two daughter cells drops to roughly half of the mother’s value (the “partitioning step”), then rises continuously until the next division. Within a cell‑cycle the increase is well described by an exponential law, N(t)=N₀·e^{αt}, where N₀ is the amount immediately after division, α is a growth‑rate parameter, and t runs from 0 to the cycle duration T. Importantly, α and T vary from cycle to cycle, while N₀ is set by the partitioning of the previous cycle.

To compare single‑cell dynamics with population data, the authors normalized each trace by its mean μ and standard deviation σ, pooled all normalized values, and constructed a probability density function (PDF). The resulting PDF is highly asymmetric, with a heavy right tail, and matches the “universal” protein distribution previously reported for population snapshots across a wide range of growth conditions and for both bacterial and eukaryotic species. Moreover, the relationship between mean and variance follows a quadratic law, σ² = a·μ + b·μ², exactly as observed in population studies.

The authors then asked which aspects of the cell‑cycle dynamics are essential for reproducing these universal features. By treating (N₀, α, T) as three independent random variables drawn anew each generation, they built a minimal stochastic model. Monte‑Carlo simulations of this three‑parameter process generate protein trajectories whose normalized PDFs and mean‑variance relationships are indistinguishable from the experimental data. Sensitivity analysis shows that variability in the exponential growth rate α is the dominant contributor to the width of the distribution, whereas fluctuations in T have a secondary effect. The model’s success indicates that the detailed intracellular mechanisms of transcription, translation, and degradation—while biologically important—do not shape the global statistical properties of protein abundance.

In summary, the study demonstrates that the universal distribution shape and the quadratic mean‑variance relationship are not artifacts of population averaging but are intrinsic to the temporal fluctuations of individual cells. Protein content in a single cell can be compactly described by a three‑parameter stochastic process that captures cycle‑to‑cycle variations in growth rate, cycle length, and initial amount. This finding shifts the focus from microscopic molecular noise to macroscopic, generation‑to‑generation fluctuations in global cellular state, providing a parsimonious framework for understanding phenotypic heterogeneity in microbial populations.