Fluctuation and noise propagation in phenotypic transition cascades of clonal populations

Inferring absolute cell numbers from relative proportion in stochastic models with cell plasticity

Quantifying dynamic changes in cell populations is crucial for a comprehensive understanding of biological processes such as cell proliferation, injury repair, and disease progression. However, compared to directly measuring the absolute cell numbers of specific subpopulations, relative proportion data demonstrate greater reproducibility and yield more stable, reliable outcomes. Therefore, inferring absolute cell numbers from relative proportion data may present a novel approach for effectively predicting changes in cell population sizes. To address this, we establish two mathematical mappings between cell proportions and population sizes using moment equations derived from stochastic cell-plasticity models. Notably, our findings indicate that one of these mappings does not require prior knowledge of the initial population size, highlighting the value of incorporating variance information into cell proportion data. We evaluated the robustness of our methods from multiple perspectives and extended their application to various biological mechanisms within the context of cell plasticity models. These methods help mitigate the limitations associated with the direct measurement of absolute cell counts through experimental techniques. Moreover, they provide new insights into leveraging the stochastic dynamics of cell populations to quantify interactions between different biomasses within the system.

Effect of dedifferentiation on noise propagation in cellular hierarchy

Many fast renewing tissues have a hierarchical structure. Tissue-specific stem cells are at the root of this cellular hierarchy, which give rive to a whole range of specialized cells via cellular differentiation. However, increasing evidence shows that the hierarchical structure can be broken due to cellular dedifferentiation in which cells at differentiated stages can revert to the stem cell stage. Dedifferentiation has significant impacts on many aspects of hierarchical tissues. Here we investigate the effect of dedifferentiation on noise propagation by developing a stochastic model composed of different cell types. The moment equations are derived, via which we systematically investigate how the noise in the cell number is changed by dedifferentiation. Our results suggest that dedifferentiation have different effects on the noises in the numbers of stem cells and nonstem cells. Specifically, the noise in the number of stem cells is significantly reduced by increasing dedifferentiation probability. Due to the dual effect of dedifferentiation on nonstem cells, however, more complex changes could happen to the noise in the number of nonstem cells by increasing dedifferentiation probability. Furthermore, it is found that even though dedifferentiation could turn part of the noise propagation process into a noise-amplifying step, it is very unlikely to turn the entire process into a noise-amplifying cascade.

Effects of bidirectional phenotype switching on signal noise in a bacterial community

Cells can sense and process various signals. Noise is inevitable in the cell signaling system. In a bacterial community, the mutual conversion between normal cells and persistent cells forms a bidirectional phenotype switching cascade, in which either one can be used as an upstream signal and the other as a downstream signal. In order to quantitatively describe the relationship between noise and signal amplification of each phenotype, the gain-fluctuation relationship is obtained by using the linear noise approximation of the master equation. Through the simulation of these theoretical formulas, it is found that the bidirectional phenotype switching can directly generate interconversion noise which is usually very small and almost negligible. In particular, the bidirectional phenotype switching can provide a global fluctuating environment, which will not only affect the values of noise and covariance, but also generate additional intrinsic noise. The additional intrinsic noise in each phenotype is the main part of the total noise and can be transmitted to the other phenotype. The transmitted noise is also a powerful supplement to the total noise. Therefore, the indirect impact of bidirectional phenotype switching is far greater than its direct impact, which may be one of the reasons why chronic infections caused by persistent cells are refractory to treat.

Noisy signal propagation and amplification in phenotypic transition cascade of colonic cells

Like genes and proteins, cells can use biochemical networks to sense and process information. The differentiation of the cell state in colonic crypts forms a typical unidirectional phenotypic transitional cascade, in which stem cells differentiate into the transit-amplifying cells (TACs), and TACs continue to differentiate into fully differentiated cells. In order to quantitatively describe the relationship between the noise of each compartment and the amplification of signals, the gain factor is introduced, and the gain-fluctuation relation is obtained by using the linear noise approximation of the master equation. Through the simulation of these theoretical formulas, the characters of noise propagation and amplification are studied. It is found that the transmitted noise is an important part of the total noise in each downstream cell. Therefore, a small number of downstream cells can only cause its small inherent noise, but the total noise may be very large due to the transmitted noise. The influence of the transmitted noise may be the indirect cause of colon cancer. In addition, the total noise of the downstream cells always has a minimum value. As long as a reasonable value of the gain factor is selected, the number of cells in colonic crypts will be controlled within the normal range. This may be a good method to intervene the uncontrollable growth of tumor cells and effectively control the deterioration of colon cancer.

Modeling of mesenchymal hybrid epithelial state and phenotypic transitions in EMT and MET processes of cancer cells

Based on the transcriptional regulatory mechanisms between microRNA-200 and transcription factor ZEB in an individual cancer cell, a minimal dynamic model is proposed to study the epithelial-mesenchymal transition (EMT) and mesenchymal-epithelial transition (MET) processes of cancer cells. It is shown that each cancer cell can exit in any of three phenotypic states: the epithelial (E) state, the mesenchymal (M) state, and the epithelial/mesenchymal (E/M) hybrid state, and the state of cancer cell can interconvert between different states. The phase diagram shows that there are monostable, bistable, and tristable phenotypic states regions in a parameters plane. It is found that different pathway in the phase diagram can correspond to the EMT or the MET process of cancer cells, and there are two possible EMT processes. It is important that the experimental phenomenon of E/M hybrid state appearing in the EMT process but rather in the MET process can be understood through different pathways in the phase diagram. Our numerical simulations show that the effects of noise are opposite to these of time delay on the expression of transcription factor ZEB, and there is competition between noise and time delay in phenotypic transitions process of cancer cells.

A kinetic model of multiple phenotypic states for breast cancer cells

Quantitative modeling of microscopic genes regulatory mechanisms in an individual cell is a crucial step towards understanding various macroscopic physiological phenomena of cell populations. Based on the regulatory mechanisms of genes zeb1 and cdh1 in the growth and development of breast cancer cells, we propose a kinetic model at the level of single cell. By constructing the effective landscape of underlying stationary probability for the genes expressions, it is found that (i) each breast cancer cell has three phenotypic states (i.e., the stem-like, basal, and luminal states) which correspond to three attractions of the probability landscape. (ii) The interconversions between phenotypic states can be induced by the noise intensity and the property of phenotypic switching is quantified by the mean first-passage time. (iii) Under certain conditions, the probabilities of each cancer cell appearing in the three states are consistent with the macroscopic phenotypic equilibrium proportions in the breast cancer SUM159 cell line. (iv) Our kinetic model involving the TGF-β signal can also qualitatively explain several macroscopic physiological phenomena of breast cancer cells, such as the "TGF-β paradox" in tumor therapy, the five clinical subtypes of breast cancer cells, and the effects of transient TGF-β on breast cancer metastasis.

Noise Decomposition Principle in a Coherent Feed-Forward Transcriptional Regulatory Loop

Coherent feed-forward loops exist extensively in realistic biological regulatory systems, and are common signaling motifs. Here, we study the characteristics and the propagation mechanism of the output noise in a coherent feed-forward transcriptional regulatory loop that can be divided into a main road and branch. Using the linear noise approximation, we derive analytical formulae for the total noise of the full loop, the noise of the branch, and the noise of the main road, which are verified by the Gillespie algorithm. Importantly, we find that (i) compared with the branch motif or the main road motif, the full motif can effectively attenuate the output noise level; (ii) there is a transition point of system state such that the noise of the main road is dominated when the underlying system is below this point, whereas the noise of the branch is dominated when the system is beyond the point. The entire analysis reveals the mechanism of how the noise is generated and propagated in a simple yet representative signaling module.

The overshoot and phenotypic equilibrium in characterizing cancer dynamics of reversible phenotypic plasticity

The paradigm of phenotypic plasticity indicates reversible relations of different cancer cell phenotypes, which extends the cellular hierarchy proposed by the classical cancer stem cell (CSC) theory. Since it is still questionable if the phenotypic plasticity is a crucial improvement to the hierarchical model or just a minor extension to it, it is worthwhile to explore the dynamic behavior characterizing the reversible phenotypic plasticity. In this study we compare the hierarchical model and the reversible model in predicting the cell-state dynamics observed in biological experiments. Our results show that the hierarchical model shows significant disadvantages over the reversible model in describing both long-term stability (phenotypic equilibrium) and short-term transient dynamics (overshoot) in cancer cell populations. In a very specific case in which the total growth of population due to each cell type is identical, the hierarchical model predicts neither phenotypic equilibrium nor overshoot, whereas the reversible model succeeds in predicting both of them. Even though the performance of the hierarchical model can be improved by relaxing the specific assumption, its prediction to the phenotypic equilibrium strongly depends on a precondition that may be unrealistic in biological experiments. Moreover, it still does not show as rich dynamics as the reversible model in capturing the overshoots of both CSCs and non-CSCs. By comparison, it is more likely for the reversible model to correctly predict the stability of the phenotypic mixture and various types of overshoot behavior.