You will be presented with the abstract, introduction, and discussion section from a biomedical research article. Your task is to create a summary that a layperson can understand, capturing the essence of the research article. Keep essential scientific terms, but ensure that the language remains clear and the concepts are explained in an uncomplicated manner.

Title: Dynamic Rendering of the Heterogeneous Cell Response to Anticancer Treatments}
Article:
Abstract:
The antiproliferative response to anticancer treatment is the result of concurrent responses in all cell cycle phases, extending over several cell generations, whose complexity is not captured by current methods. In the proposed experimental/computational approach, the contemporary use of time-lapse live cell microscopy and flow cytometric data supported the computer rendering of the proliferative process through the cell cycle and subsequent generations during/after treatment. The effects of treatments were modelled with modules describing the functional activity of the main pathways causing arrest, repair and cell death in each phase. A framework modelling environment was created, enabling us to apply different types of modules in each phase and test models at the complexity level justified by the available data. We challenged the method with time-course measures taken in parallel with flow cytometry and time-lapse live cell microscopy in X-ray-treated human ovarian cancer cells, spanning a wide range of doses. The most suitable model of the treatment, including the dose-response of each effect, was progressively built, combining modules with a rational strategy and fitting simultaneously all data of different doses and platforms. The final model gave for the first time the complete rendering in silico of the cycling process following X-ray exposure, providing separate and quantitative measures of the dose-dependence of G1, S and G2M checkpoint activities in subsequent generations, reconciling known effects of ionizing radiations and new insights in a unique scenario.
Introduction:
Anticancer research spans a wide range of scales, from the microscopic/molecular up to the macroscopic level of clinical assessment of treatment efficacy. On an intermediate scale of preclinical testing in vitro and in vivo, cancer research maintains the need to evaluate the antiproliferative activity of old and new treatment options in cancer cell populations. In fact, even for new drugs, assessment of activity against a molecular target does not guarantee antiproliferative activity and control of expansion – if not eradication – of cancer cells, which is clearly the primary goal of any treatment. However, the impressive advances in the molecular understanding of cancer( s) have not been accompanied by a deeper comprehension of proliferation in treated samples, often simplistically estimated with scores based on treated/control ratios. These do not catch the complexity of the phenomena in play, leaving unanswered several questions, from the contribution of inter-cell heterogeneity to the origin of dose-dependence, from the dynamics of the response of checkpoint controls to the overlapping of cytostatic and cytotoxic phenomena[1]–[3]. In particular, biomedical research is now acknowledging the importance of cell-to-cell diversity and dynamic variability for protein levels[4]–[7] and response to environmental interactions[8] or treatments[9], even within populations of genetically identical cells. This calls for a probabilistic view of the single cell response representing a change of perspective compared to exclusively molecularly-driven research, often dominated by a deterministic-mechanistic view according to which a drug makes a given effect or not, without specifying the probabilities of the events and their dose-dependence. Mathematical modelling is increasingly adopted to tackle biological complexity, together with experimental procedures producing appropriate quantitative data, for in silico rendering of biological structures and processes in different fields and scales, from X-ray crystallography to medical imaging[10]–. The question is normally tackled by adopting a computational model of the biological phenomenon, whose inputs are meaningful biological parameters and outputs are measurable quantities. For instance, in the crystallography field a model of the diffraction keeps the 3D structure of a molecule as input and gives as output the data that a molecule's crystal would produce when challenged in X-ray diffraction experiments. The model can be used in two ways: to infer the 3D structure from experimental data( optimization problem) or to simulate the expected data from hypothetical 3D structures( simulation)[15]. Adopting a conceptually similar approach, we present here a mixed experimental/computational method( Figure 1) to render the process of proliferation at the cell population level, using a computational model whose input parameters are simple descriptors of the functional activities of the main intracellular molecular controls of the cell cycle and whose outputs can be directly fitted to data obtained by time-lapse live cell microscopy( TL) and DNA flow cytometry( FC). The two platforms convey complementary information, FC focusing on cell distributions in G1, S, G2M cell cycle phases, TL on lineage trees following cells in subsequent generations. Valuable examples of modelling proliferation over subsequent generations can be found in the immunological field, were data from cells labelled with suitable trackers are exploited to follow lymphocyte expansion after introduction of stimuli triggering their entry in cycle[16],[17]. These models usually do not include cell cycle phases. On the other hand, models based on cell cycle phases were used[18],[19] and adapted to model treatment[20] not distinguishing generations, although effects of treatment were observed not only in cells directly exposed but also to their descendants[21],[22]. In this paper we attempt to build a model deciphering the effects of treatment including both cell cycle phases and subsequent generations, exploiting together FC and TL data. By modelling proliferation at the cell population level it was possible to incorporate different kinds of heterogeneity in the structure of the model, both for untreated and treated cell populations. For untreated cells, intercell heterogeneity was included by distinguishing G1, S and G2M phases and introducing frequency distributions of the duration of each phase. After treatment, observations demonstrate that some cells die other survive, some are blocked in a given phase, and among them some die and others cycle and reach subsequent generations and so on. In this case the heterogeneity is rendered by the model parameters themselves, which are probabilities or rates of occurrence of each phenomenon in play and were applied to the cell cohorts arriving at each checkpoint at a given time. A multi-phase and multi-generation model for proliferation in the absence of treatment was already presented[23] showing the feasibility to reproduce proliferation at a deeper level than models explaining simply the time course of the overall cell number or equivalent measures, or cell phase percentages alone or cell generations alone. This model was here modified to include the effects of a treatment. Our previous attempts in treatment modelling were based on “single-cycle” models, where cells after division re-enter in the same cycle and generations were mixed, and on FC data, alone or coupled with absolute cell counts, with simplified descriptions of the time-dependence of checkpoint activities, and trial-and-error simulations[24]. These treatment models were revised and modules rendering the main effects of treatments were included in each phase and generation of the multi-phase and multi-generation model. This eventually enabled us to explain most of time-dependences required in the previous treatment models as different effects in subsequent generations. Moreover, a non-linear fitting procedure was included and, correspondingly, the experimental design was strongly enriched, with the inclusion of TL data, for different treatment doses. Setting the method obliged us to study and solve a number of related subproblems, concerning the data structure, the cell cycle model and the optimization( Figure 1). A robust rendering of the proliferation process up to the fourth generation was achieved, designing a formal workflow for model building and fitting, considering contemporaneously data from treatments at different doses and exploiting cross-validation between FC and TL datasets. This approach was used here to disclose the details of the proliferation of a cancer cell population after X-ray exposure, leading to a measure of the dose- and time-dependence of the main checkpoint activities and of the balance between recycling and death over three cell generations after treatment. Reconstruction of the process was then used for in silico experiments, evaluating the consequences of default or potentiation of specific checkpoints on the overall effect of treatment.
Discussion:
Mathematical modelling of biological or biomedical systems is now facing the challenge of quantitative rendering of the biological phenomena, taking into consideration the vast amounts of data produced by experimental biomedicine, with appreciation of the biological complexity, with its dynamics, and the processes of measure, with their strengths and limitations. Also in cancer research the demand for proper quantitative interpretation of the processes in play is rising[31],[32]. The method we propose enables a detailed study of the mechanisms concurring to build the response to anticancer treatment at the “cell population” level, where measures were made on single cells and on a statistically representative number of them, accounting for inter-cell variability. This provides a different view respect to that obtained with bulk measures on cell homogenates, representing “average” quantities, unpredictably weighted by the relative numerosity of cell subsets with different amounts of the measured quantity. At the cell population level, we may exploit a very rich amount of information, coming from established or new techniques. It remains a challenge to find the way to organize all that we can measure, and possibly put together complementary information from different techniques, in order to give sense to the observed heterogeneity. This challenge must be addressed, if we really aim to reach an unbiased picture of the behaviour of a multicellular system, from in vitro cultures to in vivo organs or tumours. We demonstrated that it is possible to integrate FC and TL platforms via in silico rendering of the dynamics of the underlying cell cycle progression. This was achieved with a flexible model-building environment, which enabled us to challenge a variety of tentative models in a manageable time. Once the model of unperturbed proliferation was established, we progressed to study how the system responds to a hypothetical treatment. Different types of modules were implemented in the model, miming the activity of cell cycle controls at increasing levels of complexity. The user can select a specific effect and look at its consequences in simulated experiments. Wishing to build a model for a real treatment, we strengthened the parameter estimation by fitting data from different treatment levels( four X-ray doses in our example) simultaneously and optimizing the dose-response for each parameter, with simple regularity assumptions. This combination of data from different doses and platforms provided internal cross-validation to exclude the existence of multiple solutions in models including several variable parameters. Our optimization procedure initially establishes a relatively simple model with a unique best fit solution, which was then cautiously refined, up to the definition of a final model, by which the data of all doses were fitted with average errors 1. 6%( FC cell cycle percentages) and 3. 6%( TL cell generation numbers)( Figure 4). The final model provided a unifying view of the effects of radiation that puts in order and defines the relative importance at the different doses of the main phenomena in play, which are described separately in the literature[21],[22],[33],[34]( supplementary Text S5). Study of the final model disclosed the dynamics of checkpoint activities and their dose-dependence, showing up basic differences between G1 and G2M checkpoint responses that were not perceivable by simple data inspection. In particular, G2M-blocked cells were eventually able to recover from the block and divide even after treatment with 10 Gy, while at this dose the majority of G1-blocked cells eventually died there. The response was not restricted to gen0 cells, but cell cycle progression was also hampered in gen1 and gen2. Our results strongly support the concept of a limited efficiency of a single checkpoint to process the damage[35], suggesting that cycling of individual cells may be subsequently hampered in different phases. The model was also used as a basis to explore, with in silico experiments, the consequences of default or potentiation of specific checkpoints, which in principle could become feasible with new, molecularly targeted co-treatments, or may occur in tumours with particular genetic defects. Obviously, the real response to treatment is even more complex than the proposed model. It does not include, for instance, possible correlations between sibling cells for probabilities of specific outcomes, or signalling between cells or spatial issues driving neighbour cells towards a common fate. Still our model works at a quite high complexity level, including details of the effects in each phase and generation at different treatment doses. This was made possible avoiding over-parametrization only through fitting of a very rich and complex data set. Further details would require more parameters and additional data, which are not precluded in future studies.
The antiproliferative response to anticancer treatment is the result of concurrent effects in all cell cycle phases , where molecular control pathways ( checkpoints ) are activated and cells may be arrested to repair DNA damage or killed if not able to succeed in the repair process . The complexity and inter-cell variability of these phenomena are not captured by the available methods , and the origin of the dose-dependence of the response remains elusive . In this work , we present an experimental-computational method that discloses and measures the individual responses of cell cycle controls in each phase and generation . We demonstrate that the method , exploiting jointly data sets obtained by flow cytometry and time-lapse in vivo imaging with a suitable experimental design , is able to achieve a full reconstruction in silico of the actual movement of cell cohorts following X-ray exposure , providing separate and quantitative measures of the dose-dependence of G1 , S and G2M checkpoint activities in subsequent generations . Best fit parameters values are actual measures of the probability of activation of the specific pathways of arrest , repair or death within the cell population , linking the molecular scale to the “macroscopic” response , with full appreciation of its dynamics and inter-cell heterogeneity .