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

Algorithms for the Uniqueness of the Longest Common Subsequence

Given several number sequences, determining the longest common subsequence is a classical problem in computer science. This problem has applications in bioinformatics, especially determining transposable genes. Nevertheless, related works only consider how to find one longest common subsequence. In this paper, we consider how to determine the uniqueness of the longest common subsequence. If there are multiple longest common subsequences, we also determine which number appears in all/some/none of the longest common subsequences. We focus on four scenarios: (1) linear sequences without duplicated numbers; (2) circular sequences without duplicated numbers; (3) linear sequences with duplicated numbers; (4) circular sequences with duplicated numbers. We develop corresponding algorithms and apply them to gene sequencing data.

Enhancement of Prebiotic Peptide Formation in Cyclic Environments

The dynamic behaviors of prebiotic reaction networks may be critically important to understanding how larger biopolymers could emerge, despite being unfavorable to form in water. We focus on understanding the dynamics of simple systems, prior to the emergence of replication mechanisms, and what role they may have played in biopolymer formation. We specifically consider the dynamics in cyclic environments using both model and experimental data. Cyclic environmental conditions prevent a system from reaching thermodynamic equilibrium, improving the chance of observing interesting kinetic behaviors. We used an approximate kinetic model to simulate the dynamics of trimetaphosphate (TP)-activated peptide formation from glycine in cyclic wet-dry conditions. The model predicts that environmental cycling allows trimer and tetramer peptides to sustain concentrations above the predicted fixed points of the model due to overshoot, a dynamic phenomenon. Our experiments demonstrate that oscillatory environments can shift product distributions in favor of longer peptides. However, experimental validation of certain behaviors in the kinetic model is challenging, considering that open systems with cyclic environmental conditions break many of the common assumptions in classical chemical kinetics. Overall, our results suggest that the dynamics of simple peptide reaction networks in cyclic environments may have been important for the formation of longer polymers on the early Earth. Similar phenomena may have also contributed to the emergence of reaction networks with product distributions determined not by thermodynamics, but rather by kinetics.

Cell population growth kinetics in the presence of stochastic heterogeneity of cell phenotype

Recent studies at individual cell resolution have revealed phenotypic heterogeneity in nominally clonal tumor cell populations. The heterogeneity affects cell growth behaviors, which can result in departure from the idealized uniform exponential growth of the cell population. Here we measured the stochastic time courses of growth of an ensemble of populations of HL60 leukemia cells in cultures, starting with distinct initial cell numbers to capture a departure from the uniform exponential growth model for the initial growth ("take-off"). Despite being derived from the same cell clone, we observed significant variations in the early growth patterns of individual cultures with statistically significant differences in growth dynamics, which could be explained by the presence of inter-converting subpopulations with different growth rates, and which could last for many generations. Based on the hypothesis of existence of multiple subpopulations, we developed a branching process model that was consistent with the experimental observations.

Order-of-mutation effects on cancer progression: models for myeloproliferative neoplasm

In some patients with myeloproliferative neoplasms (MPN), two genetic mutations are often found, JAK2 V617F and one in the TET2 gene. Whether or not one mutation is present will influence how the other subsequent mutation affects the regulation of gene expression. When both mutations are present, the order of their occurrence has been shown to influence disease progression and prognosis. We propose a nonlinear ordinary differential equation (ODE), Moran process, and Markov chain models to explain the non-additive and non-commutative mutation effects on recent clinical observations of gene expression patterns, proportions of cells with different mutations, and ages at diagnosis of MPN. These observations consistently shape our modeling framework. Our key proposal is that bistability in gene expression provides a natural explanation for many observed order-of-mutation effects. We also propose potential experimental measurements that can be used to confirm or refute predictions of our models.

Unified tumor growth mechanisms from multimodel inference and dataset integration

Mechanistic models of biological processes can explain observed phenomena and predict responses to a perturbation. A mathematical model is typically constructed using expert knowledge and informal reasoning to generate a mechanistic explanation for a given observation. Although this approach works well for simple systems with abundant data and well-established principles, quantitative biology is often faced with a dearth of both data and knowledge about a process, thus making it challenging to identify and validate all possible mechanistic hypothesis underlying a system behavior. To overcome these limitations, we introduce a Bayesian multimodel inference (Bayes-MMI) methodology, which quantifies how mechanistic hypotheses can explain a given experimental datasets, and concurrently, how each dataset informs a given model hypothesis, thus enabling hypothesis space exploration in the context of available data. We demonstrate this approach to probe standing questions about heterogeneity, lineage plasticity, and cell-cell interactions in tumor growth mechanisms of small cell lung cancer (SCLC). We integrate three datasets that each formulated different explanations for tumor growth mechanisms in SCLC, apply Bayes-MMI and find that the data supports model predictions for tumor evolution promoted by high lineage plasticity, rather than through expanding rare stem-like populations. In addition, the models predict that in the presence of cells associated with the SCLC-N or SCLC-A2 subtypes, the transition from the SCLC-A subtype to the SCLC-Y subtype through an intermediate is decelerated. Together, these predictions provide a testable hypothesis for observed juxtaposed results in SCLC growth and a mechanistic interpretation for tumor treatment resistance.

How the interplay among the tumor microenvironment and the gut microbiota influences the stemness of colorectal cancer cells

Colorectal cancer (CRC) remains the third most prevalent cancer disease and involves a multi-step process in which intestinal cells acquire malignant characteristics. It is well established that the appearance of distal metastasis in CRC patients is the cause of a poor prognosis and treatment failure. Nevertheless, in the last decades, CRC aggressiveness and progression have been attributed to a specific cell population called CRC stem cells (CCSC) with features like tumor initiation capacity, self-renewal capacity, and acquired multidrug resistance. Emerging data highlight the concept of this cell subtype as a plastic entity that has a dynamic status and can be originated from different types of cells through genetic and epigenetic changes. These alterations are modulated by complex and dynamic crosstalk with environmental factors by paracrine signaling. It is known that in the tumor niche, different cell types, structures, and biomolecules coexist and interact with cancer cells favoring cancer growth and development. Together, these components constitute the tumor microenvironment (TME). Most recently, researchers have also deepened the influence of the complex variety of microorganisms that inhabit the intestinal mucosa, collectively known as gut microbiota, on CRC. Both TME and microorganisms participate in inflammatory processes that can drive the initiation and evolution of CRC. Since in the last decade, crucial advances have been made concerning to the synergistic interaction among the TME and gut microorganisms that condition the identity of CCSC, the data exposed in this review could provide valuable insights into the biology of CRC and the development of new targeted therapies.

Inference on autoregulation in gene expression with variance-to-mean ratio

Some genes can promote or repress their own expressions, which is called autoregulation. Although gene regulation is a central topic in biology, autoregulation is much less studied. In general, it is extremely difficult to determine the existence of autoregulation with direct biochemical approaches. Nevertheless, some papers have observed that certain types of autoregulations are linked to noise levels in gene expression. We generalize these results by two propositions on discrete-state continuous-time Markov chains. These two propositions form a simple but robust method to infer the existence of autoregulation from gene expression data. This method only needs to compare the mean and variance of the gene expression level. Compared to other methods for inferring autoregulation, our method only requires non-interventional one-time data, and does not need to estimate parameters. Besides, our method has few restrictions on the model. We apply this method to four groups of experimental data and find some genes that might have autoregulation. Some inferred autoregulations have been verified by experiments or other theoretical works.

Cell Population Growth Kinetics in the Presence of Stochastic Heterogeneity of Cell Phenotype

Recent studies at individual cell resolution have revealed phenotypic heterogeneity in nominally clonal tumor cell populations. The heterogeneity affects cell growth behaviors, which can result in departure from the idealized exponential growth. Here we measured the stochastic time courses of growth of an ensemble of populations of HL60 leukemia cells in cultures, starting with distinct initial cell numbers to capture the departure from the exponential growth model in the initial growth phase. Despite being derived from the same cell clone, we observed significant variations in the early growth patterns of individual cultures with statistically significant differences in growth kinetics and the presence of subpopulations with different growth rates that endured for many generations. Based on the hypothesis of existence of multiple inter-converting subpopulations, we developed a branching process model that captures the experimental observations.

On tumoural growth and treatment under cellular dedifferentiation

Differentiated cancer cells may regain stem cell characteristics; however, the effects of such a cellular dedifferentiation on tumoural growth and treatment are currently understudied. Thus, we here extend a mathematical model of cancer stem cell (CSC) driven tumour growth to also include dedifferentiation. We show that dedifferentiation increases the likelihood of tumorigenesis and the speed of tumoural growth, both modulated by the proliferative potential of the non-stem cancer cells (NSCCs). We demonstrate that dedifferentiation also may lead to treatment evasion, especially when a treatment solely targets CSCs. Conversely, targeting both CSCs and NSCCs in parallel is shown to be more robust to dedifferentiation. Despite dedifferentiation, perturbing CSC-related parameters continues to exert the largest relative effect on tumoural growth; however, we show the existence of synergies between specific CSC- and NSCC-directed treatments which cause superadditive reductions of tumoural growth. Overall, our study demonstrates various effects of dedifferentiation on growth and treatment of tumoural lesions, and we anticipate our results to be helpful in guiding future molecular and clinical research on limiting tumoural growth in vivo.

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.

Alternative models of cancer stem cells: The stemness phenotype model, 10 years later

The classical cancer stem cell (CSCs) theory proposed the existence of a rare but constant subpopulation of CSCs. In this model cancer cells are organized hierarchically and are responsible for tumor resistance and tumor relapse. Thus, eliminating CSCs will eventually lead to cure of cancer. This simplistic model has been challenged by experimental data. In 2010 we proposed a novel and controversial alternative model of CSC biology (the Stemness Phenotype Model, SPM). The SPM proposed a non-hierarchical model of cancer biology in which there is no specific subpopulation of CSCs in tumors. Instead, cancer cells are highly plastic in term of stemness and CSCs and non-CSCs can interconvert into each other depending on the microenvironment. This model predicts the existence of cancer cells ranging from a pure CSC phenotype to pure non-CSC phenotype and that survival of a single cell can originate a new tumor. During the past 10 years, a plethora of experimental evidence in a variety of cancer types has shown that cancer cells are indeed extremely plastic and able to interconvert into cells with different stemness phenotype. In this review we will (1) briefly describe the cumulative evidence from our laboratory and others supporting the SPM; (2) the implications of the SPM in translational oncology; and (3) discuss potential strategies to develop more effective therapeutic regimens for cancer treatment.

Phenotypic Switching Resulting From Developmental Plasticity: Fixed or Reversible?

The prevalent view of developmental phenotypic switching holds that phenotype modifications occurring during critical windows of development are "irreversible" - that is, once produced by environmental perturbation, the consequent juvenile and/or adult phenotypes are indelibly modified. Certainly, many such changes appear to be non-reversible later in life. Yet, whether animals with switched phenotypes during early development are unable to return to a normal range of adult phenotypes, or whether they do not experience the specific environmental conditions necessary for them to switch back to the normal range of adult phenotypes, remains an open question. Moreover, developmental critical windows are typically brief, early periods punctuating a much longer period of overall development. This leaves open additional developmental time for reversal (correction) of a switched phenotype resulting from an adverse environment early in development. Such reversal could occur from right after the critical window "closes," all the way into adulthood. In fact, examples abound of the capacity to return to normal adult phenotypes following phenotypic changes enabled by earlier developmental plasticity. Such examples include cold tolerance in the fruit fly, developmental switching of mouth formation in a nematode, organization of the spinal cord of larval zebrafish, camouflage pigmentation formation in larval newts, respiratory chemosensitivity in frogs, temperature-metabolism relations in turtles, development of vascular smooth muscle and kidney tissue in mammals, hatching/birth weight in numerous vertebrates,. More extreme cases of actual reversal (not just correction) occur in invertebrates (e.g., hydrozoans, barnacles) that actually 'backtrack' along normal developmental trajectories from adults back to earlier developmental stages. While developmental phenotypic switching is often viewed as a permanent deviation from the normal range of developmental plans, the concept of developmental phenotypic switching should be expanded to include sufficient plasticity allowing subsequent correction resulting in the normal adult phenotype.

The invasion of de-differentiating cancer cells into hierarchical tissues

Many fast renewing tissues are characterized by a hierarchical cellular architecture, with tissue specific stem cells at the root of the cellular hierarchy, differentiating into a whole range of specialized cells. There is increasing evidence that tumors are structured in a very similar way, mirroring the hierarchical structure of the host tissue. In some tissues, differentiated cells can also revert to the stem cell phenotype, which increases the risk that mutant cells lead to long lasting clones in the tissue. However, it is unclear under which circumstances de-differentiating cells will invade a tissue. To address this, we developed mathematical models to investigate how de-differentiation is selected as an adaptive mechanism in the context of cellular hierarchies. We derive thresholds for which de-differentiation is expected to emerge, and it is shown that the selection of de-differentiation is a result of the combination of the properties of cellular hierarchy and de-differentiation patterns. Our results suggest that de-differentiation is most likely to be favored provided stem cells having the largest effective self-renewal rate. Moreover, jumpwise de-differentiation provides a wider range of favorable conditions than stepwise de-differentiation. Finally, the effect of de-differentiation on the redistribution of self-renewal and differentiation probabilities also greatly influences the selection for de-differentiation.

How can a tissue such as the blood system or the skin, which constantly produces a huge number of cells, avoids that errors accumulate in the cells over time? Such tissues are typically organized in cellular hierarchies, which induce a directional relation between different stages of cellular differentiation, minimizing the risk of retention of mutations. However, recent evidence also shows that some differentiated cells can de-differentiate into the stem cell phenotype. Why does de-differentiation arise in some tumors, but not in others? We developed a mathematical model to study the growth competition between de-differentiating mutant cell populations and non de-differentiating resident cell population. Our results suggest that the invasion of de-differentiation is jointly influenced by the cellular hierarchy (e.g. number of cell compartments, inherent cell division pattern) and the de-differentiation pattern, i.e. how exactly cells acquire their stem-cell like properties.