Tumor growth dynamics: insights into evolutionary processes

Modeling tumors as complex ecosystems

Many cancers resist therapeutic intervention. This is fundamentally related to intratumor heterogeneity: multiple cell populations, each with different phenotypic signatures, coexist within a tumor and its metastases. Like species in an ecosystem, cancer populations are intertwined in a complex network of ecological interactions. Most mathematical models of tumor ecology, however, cannot account for such phenotypic diversity or predict its consequences. Here, we propose that the generalized Lotka-Volterra model (GLV), a standard tool to describe species-rich ecological communities, provides a suitable framework to model the ecology of heterogeneous tumors. We develop a GLV model of tumor growth and discuss how its emerging properties provide a new understanding of the disease. We discuss potential extensions of the model and their application to phenotypic plasticity, cancer-immune interactions, and metastatic growth. Our work outlines a set of questions and a road map for further research in cancer ecology.

Effect of time interval between surgery and the initiation of adjuvant therapy on the oncologic outcomes of early-stage endometrial cancer

OBJECTIVE

To identify the impact of time interval between surgery and initial adjuvant radiotherapy on oncologic outcomes in early-stage endometrial cancer.

METHODS

This retrospective cohort study included patients with stage I/II endometrial cancer who underwent surgical staging and adjuvant therapy at Songklanagarind Hospital from January 1, 2007, to December 31, 2017. Patients were categorized into two groups: TI <6 weeks and TI ≥6 weeks. The effects of TI and clinicopathological factors on recurrence-free survival (RFS) and overall survival (OS) were analyzed using Cox proportional-hazards regression.

RESULTS

In total, 177 patients were enrolled, with 52% receiving adjuvant radiotherapy at <6 weeks (overall median TI 5.7 weeks). The recurrence and death rates were 13% and 10.2%, respectively. The median follow-up time was 46.6 months. The overall 3-year RFS and OS rates were 88.2% and 85.2%, respectively. The TI significantly affected the 3-year RFS (94.4% vs 81.2%; P = 0.008) and 3-year OS (95.5% vs 83.2%; P = 0.012) in patients with TI <6 and ≥6 weeks, respectively. In multivariate analysis, the depth of myometrial invasion (MI), presence of lymphovascular space invasion, and TI were independent prognostic factors for both RFS and OS. Delaying the TI (≥6 weeks) was significantly associated with a worse RFS (hazard ratio [HR] 3.70; 95% confidence interval [CI]: 1.34-10.22; P = 0.012) and an inferior OS (HR 3.80; 95% CI: 1.23-11.69; P = 0.02).

CONCLUSION

A delay in the TI between surgery and the initiation of adjuvant radiotherapy of ≥6 weeks negatively affected the oncologic outcomes in early-stage endometrial cancer.

Modeling tumors as species-rich ecological communities

Many advanced cancers resist therapeutic intervention. This process is fundamentally related to intra-tumor heterogeneity: multiple cell populations, each with different mutational and phenotypic signatures, coexist within a tumor and its metastatic nodes. Like species in an ecosystem, many cancer cell populations are intertwined in a complex network of ecological interactions. Most mathematical models of tumor ecology, however, cannot account for such phenotypic diversity nor are able to predict its consequences. Here we propose that the Generalized Lotka-Volterra model (GLV), a standard tool to describe complex, species-rich ecological communities, provides a suitable framework to describe the ecology of heterogeneous tumors. We develop a GLV model of tumor growth and discuss how its emerging properties, such as outgrowth and multistability, provide a new understanding of the disease. Additionally, we discuss potential extensions of the model and their application to three active areas of cancer research, namely phenotypic plasticity, the cancer-immune interplay and the resistance of metastatic tumors to treatment. Our work outlines a set of questions and a tentative road map for further research in cancer ecology.

A novel multiscale framework for delineating cancer evolution from subclonal compositions

OBJECTIVE

Owing to the heterogeneity in the evolution of cancer, distinguishing between diverse growth patterns and predicting long-term outcomes based on short-term measurements poses a great challenge.

METHODS

A novel multiscale framework is proposed to unravel the connections between the population dynamics of cancer growth (i.e., aggressive, bounded, and indolent) and the cellular-subclonal dynamics of cancer evolution. This framework employs the non-negative lasso (NN-LASSO) algorithm to forge a link between an ordinary differential equation (ODE)-based population model and a cellular evolution model.

RESULTS

The findings of our current work not only affirm the impact of subclonal composition on growth dynamics but also identify two significant subclones within heterogeneous growth patterns. Moreover, the subclonal compositions at the initial time are able to accurately discriminate diverse growth patterns through a machine learning algorithm.

CONCLUSION

The proposed multiscale framework successfully delineates the intricate landscape of cancer evolution, bridging the gap between long-term growth dynamics and short-term measurements, both in simulated and real-world data. This methodology provides a novel avenue for thorough exploration into the realm of cancer evolution.

Understanding the Interplay of CAR-NK Cells and Triple-Negative Breast Cancer: Insights from Computational Modeling

Chimeric antigen receptor (CAR)-engineered natural killer (NK) cells have recently emerged as a promising and safe alternative to CAR-T cells for targeting solid tumors. In the case of triple-negative breast cancer (TNBC), traditional cancer treatments and common immunotherapies have shown limited effectiveness. However, CAR-NK cells have been successfully employed to target epidermal growth factor receptor (EGFR) on TNBC cells, thereby enhancing the efficacy of immunotherapy. The effectiveness of CAR-NK-based immunotherapy is influenced by various factors, including the vaccination dose, vaccination pattern, and tumor immunosuppressive factors in the microenvironment. To gain insights into the dynamics and effects of CAR-NK-based immunotherapy, we propose a computational model based on experimental data and immunological theories. This model integrates an individual-based model that describes the interplay between the tumor and the immune system, along with an ordinary differential equation model that captures the variation of inflammatory cytokines. Computational results obtained from the proposed model shed light on the conditions necessary for initiating an effective anti-tumor response. Furthermore, global sensitivity analysis highlights the issue of low persistence of CAR-NK cells in vivo, which poses a significant challenge for the successful clinical application of these cells. Leveraging the model, we identify the optimal vaccination time, vaccination dose, and time interval between injections for maximizing therapeutic outcomes.

Engineering RNA export for measurement and manipulation of living cells

A system for programmable export of RNA molecules from living cells would enable both non-destructive monitoring of cell dynamics and engineering of cells capable of delivering executable RNA programs to other cells. We developed genetically encoded cellular RNA exporters, inspired by viruses, that efficiently package and secrete cargo RNA molecules from mammalian cells within protective nanoparticles. Exporting and sequencing RNA barcodes enabled non-destructive monitoring of cell population dynamics with clonal resolution. Further, by incorporating fusogens into the nanoparticles, we demonstrated the delivery, expression, and functional activity of exported mRNA in recipient cells. We term these systems COURIER (controlled output and uptake of RNA for interrogation, expression, and regulation). COURIER enables measurement of cell dynamics and establishes a foundation for hybrid cell and gene therapies based on cell-to-cell delivery of RNA.

Computational study of novel natural inhibitors targeting Kirsten rat sarcoma viral oncogene homolog G12C

Lung adenocarcinoma is one of the most aggressive and rapidly fatal types of malignant lung tumor. Molecular docking and virtual screening were effectively and systematically used to identify specific targets in malignant tumors and screen potential drugs. Here, we screen perfect leading compounds from a medicate library (ZINC15 database) and analyze their properties (conveyance, absorption, metabolism, excretion, and harmless forecasts) with potential inhibition of Kirsten Rat Sarcoma Viral Oncogene Homolog (KRAS) G12C. Further results demonstrated that ZINC000013817014 and ZINC000004098458 were screened out from the ZINC15 database and were identified to have a much better binding affinity and more favorable interaction vitality binding with KRAS G12C and less rat carcinogenicity, Ames mutagenicity, way better dissolvability in water and noninhibition with cytochrome P-450 2D6. Molecular dynamics simulation analysis indicated that the binding capacity of these two compounds and KRAS G12C, ZINC000013817014-KRAS G12C, and ZINC000004098458-KRAS G12C is stable in the natural environment. Our findings reveal that ZINC000013817014 and ZINC000004098458 were perfect leading compounds to be inhibitors binding with KRAS G12C, which were selected as safe drug candidates and a cornerstone for KRAS G12C-related medicine plan and improvement. What is more, we have conducted a Cell Counting Kit-8 to verify the exactly inhibitory effects of the two selected drugs on Lung adenocarcinoma. This study establishes a solid framework for systematic anticancer medication research and development.

Extracellular matrix drives tumor organoids toward desmoplastic matrix deposition and mesenchymal transition

Patient-derived tumor organoids have been established as promising tools for in vitro modelling of multiple tumors, including cholangiocarcinoma (CCA). However, organoids are commonly cultured in basement membrane extract (BME) which does not recapitulate the intricacies of the extracellular matrix (ECM). We combined CCA organoids (CCAOs) with native tumor and liver scaffolds, obtained by decellularization, to effectuate a model to study the interaction between epithelial tumor cells and their surrounding ECM. Decellularization resulted in removal of cells while preserving ECM structure and retaining important characteristics of the tissue origin, including stiffness and presence of desmoplasia. The transcriptome of CCAOs in a tumor scaffold much more resembled that of patient-paired CCA tissue in vivo compared to CCAOs cultured in BME or liver scaffolds. This was accompanied by an increase in chemoresistance to clinically-relevant chemotherapeutics. CCAOs in decellularized scaffolds revealed environment-dependent proliferation dynamics, driven by the occurrence of epithelial-mesenchymal transition. Furthermore, CCAOs initiated an environment-specific desmoplastic reaction by increasing production of multiple collagen types. In conclusion, convergence of organoid-based models with native ECM scaffolds will lead to better understanding of the in vivo tumor environment. STATEMENT OF SIGNIFICANCE: The extracellular matrix (ECM) influences various facets of tumor behavior. Understanding the exact role of the ECM in controlling tumor cell fate is pertinent to understand tumor progression and develop novel therapeutics. This is particularly the case for cholangiocarcinoma (CCA), whereby the ECM displays a distinct tumor environment, characterized by desmoplasia. However, current models to study the interaction between epithelial tumor cells and the environment are lacking. We have developed a fully patient-derived model encompassing CCA organoids (CCAOs) and human decellularized tumor and tumor-free liver ECM. The tumor ECM induced recapitulation of various aspects of CCA, including migration dynamics, transcriptome and proteome profiles, and chemoresistance. Lastly, we uncover that epithelial tumor cells contribute to matrix deposition, and that this phenomenon is dependent on the level of desmoplasia already present.

Stochasticity and Drug Effects in Dynamical Model for Cancer Stem Cells

The Cancer Stem Model allows for a dynamical description of cancer colonies which accounts for the existence of different families of cells, namely stem cells, highly proliferating and quasi-immortal, and differentiated cells, both undergoing cellular processes under numerous activated pathways. In the present work, we investigate a dynamical model numerically, as a system of coupled differential equations, and include a plasticity mechanism, of differentiated cells turning into a stem state if the stem concentration drops low. We are particularly interested in the stability of the model once we introduce stochastically evolving parameters, associated with environmental and cellular intrinsic variabilities, as well as the response of the model after introducing a drug therapy. As long as we stay within the characteristic time scale of the system, defined on the base of the needed time for the trajectories to converge on stable states, we observe that the system remains stable for the main parameters evolving stochastically according to white noise. As for the drug treatments, we discuss a model both for the kinetics and the dynamics of the substance in the organism, and then consider the impact of different types of therapies in a few particular examples, outlining some interesting mechanisms, such as the tumor growth paradox, that possibly impact the outcome of therapy significantly.

Standard deviations of MR signal intensities show a consistent trend during imaging follow-ups for glioblastoma patients when corrected for non-biological heterogeneity due to hardware and software variation

INTRODUCTION

Glioblastoma multiforme (GBM) has a poor prognosis in spite of advanced MRI guided treatments today. Routine MRI using conventional T₁ or advanced permeability based MRI of GBM often does not adequately represent changing tumor phases or overall survival. In this work, region of interest (ROI) based tissue MR standard deviation (SD) is demonstrated as an important MRI variable that could be a potential biomarker of GBM heterogeneity and radioresistance.

MATERIALS AND METHODS

MRI characterization is often qualitative and lacks reproducibility. Using standardized MRI phantoms we have normalized retrospective records of 12 radioresistant GBM patients that underwent radiation therapy (RT) with concomitant and adjuvant temozolomide (TMZ) chemotherapy followed by serial MR imaging with gadolinium contrast.

RESULTS AND DISCUSSION

We have identified key variables like hardware, software and protocol variation and have standardized those using test phantoms at five MR systems. We suggest GBM growth during the treatment period can be linked to normalized MRI signal and its fluctuations from session to session and from magnet to magnet by using an ROI derived standard deviation that corresponds to heterogeneity of the tumor MRI signal and changes in magnetic susceptibility. The time period observed in our patient group for peak standard deviations is approximately halfway through the tumor course and may correspond to a growth of more aggressive MES subtype of cells. To model the GBM heterogeneity we performed in vitro T₁ weighted inversion recovery MRI experiments at 3 T for porous media of silicate particles in 1% aq solution of Gadavist and linked SD with particle size and local gadolinium volume within porous media. Such in vitro models mimic the increased SD in radioresistant GBM and as a novel contribution suggest that finer texture with high surface area might arise approximately halfway through the overall survival duration in GBM.

CONCLUSION

Standard deviation as a measure of magnetic susceptibility may be collectively linked to the changes in texture, cell fractions (biological) and trapped contrast media (vascular as well as artifactual consequences) and should be evaluated as a potential biomarker of GBM aggressiveness than the overall MRI signal intensity from a GBM.

Inferring parameters of cancer evolution in chronic lymphocytic leukemia

As a cancer develops, its cells accrue new mutations, resulting in a heterogeneous, complex genomic profile. We make use of this heterogeneity to derive simple, analytic estimates of parameters driving carcinogenesis and reconstruct the timeline of selective events following initiation of an individual cancer, where two longitudinal samples are available for sequencing. Using stochastic computer simulations of cancer growth, we show that we can accurately estimate mutation rate, time before and after a driver event occurred, and growth rates of both initiated cancer cells and subsequently appearing subclones. We demonstrate that in order to obtain accurate estimates of mutation rate and timing of events, observed mutation counts should be corrected to account for clonal mutations that occurred after the founding of the tumor, as well as sequencing coverage. Chronic lymphocytic leukemia (CLL), which often does not require treatment for years after diagnosis, presents an optimal system to study the untreated, natural evolution of cancer cell populations. When we apply our methodology to reconstruct the individual evolutionary histories of CLL patients, we find that the parental leukemic clone typically appears within the first fifteen years of life.

Spatial patterns of tumour growth impact clonal diversification in a computational model and the TRACERx Renal study

Genetic intra-tumour heterogeneity fuels clonal evolution, but our understanding of clinically relevant clonal dynamics remain limited. We investigated spatial and temporal features of clonal diversification in clear cell renal cell carcinoma through a combination of modelling and real tumour analysis. We observe that the mode of tumour growth, surface or volume, impacts the extent of subclonal diversification, enabling interpretation of clonal diversity in patient tumours. Specific patterns of proliferation and necrosis explain clonal expansion and emergence of parallel evolution and microdiversity in tumours. In silico time-course studies reveal the appearance of budding structures before detectable subclonal diversification. Intriguingly, we observe radiological evidence of budding structures in early-stage clear cell renal cell carcinoma, indicating that future clonal evolution may be predictable from imaging. Our findings offer a window into the temporal and spatial features of clinically relevant clonal evolution.

Tumor Lysis Syndrome in Patients With Hepatocellular Carcinoma: A Systematic Review of Published Case Reports

Tumor lysis syndrome (TLS) is a life-threatening oncologic emergency. It is characterized by massive tumor cell death leading to metabolic derangements and multiple organ failure. It is a rare complication of hepatocellular carcinoma (HCC) with only a few cases have been reported in the literature to date.

We collected and summarized published case reports of tumor lysis syndrome in patients with HCC. We also reported one additional case who developed TLS after sorafenib therapy and wrote a clinical vignette. A comprehensive and current search for relevant articles was conducted in Medline and EMbase through May 2018. A systematic review was performed following the guideline of Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA). 

A total of 28 cases of TLS associated with HCC were enrolled in our review. The median age of included cases was 55.5 years with a male to female ratio of 25:3. The two most common attributed factors of TLS were transcatheter arterial chemoembolization (TACE) (12 cases, 42.9 %) and sorafenib (nine cases, 32.1%). Among enrolled cases, the diameter of the largest tumor was 12 cm. Regarding Barcelona Clinic Liver Cancer (BCLC) staging, seven cases were at least stage A (22.6%), 11 cases were at least stage B (35.5%), and 10 cases were at least stage C (32.3%). The median time of onset of TLS was three days. As for uric acid-lowering agents, nine cases (32.1%) used allopurinol and four cases (14.3%) used rasburicase. Ten cases (35.7%) did not specify the medication prescribed. The overall mortality rate of this cohort was 67.9%.

Compared with patients developing TLS following TACE, patients who had TLS following sorafenib therapy had a later onset of TLS (two days versus seven days, p < 0.001) and a more advanced stage of HCC (p = 0.002). There was a trend toward increased mortality of patients in the sorafenib group in comparison with those in the TACE group (77.8% versus 41.7%, p = 0.18).

The results of this current review suggest that TLS rarely occurs in HCC but carries significantly higher mortality compared to TLS occurring in hematologic malignancies. It may occur shortly after TACE or with a delayed onset following sorafenib therapy. Considering the kaleidoscope of novel therapies and diverse pathogenesis of HCC, it is crucial for clinicians to recognize the clinicolaboratory derangements suggestive of TLS and initiate appropriate management. The present review highlights the need for clinicians to consider TLS within differentials when caring for patients with HCC.

Modeling codelivery of CD73 inhibitor and dendritic cell-based vaccines in cancer immunotherapy

Dendritic cells (DCs) are the dominant class of antigen-presenting cells in humans; therefore, a range of DC-based approaches have been established to promote an immune response against cancer cells. The efficacy of DC-based immunotherapeutic approaches is markedly affected by the immunosuppressive factors related to the tumor microenvironment, such as adenosine. In this paper, based on immunological theories and experimental data, a hybrid model is designed that offers some insights into the effects of DC-based immunotherapy combined with adenosine inhibition. The model combines an individual-based model for describing tumor-immune system interactions with a set of ordinary differential equations for adenosine modeling. Computational simulations of the proposed model clarify the conditions for the onset of a successful immune response against cancer cells. Global and local sensitivity analysis of the model highlights the importance of adenosine blockage for strengthening effector cells. The model is used to determine the most effective suppressive mechanism caused by adenosine, proper vaccination time, and the appropriate time interval between injections.

Mathematical simulation and prediction of tumor volume using RBF artificial neural network at different circumstances in the tumor microenvironment

Uncontrolled proliferation of cells in a tissue caused by genetic mutations inside a cell is referred to as a tumor. A tumor which grows rapidly encounters a barrier when it grows to a certain size in presence of preexisting vasculature. This is the time when it has to find a way to go on the growth. The tumor starts to secrete tumor angiogenic factors (TAFs) and stimulate preexisting vessels to grow new sprouts. These new sprouts will find their way to the tumor in the extracellular matrix (ECM) by the gradient of TAF. As these new capillaries anastomose and reach tumor, fresh oxygen is available for the tumor and it will reinitiate the growth. Number of initial sprouts, distance of initial tumor cells from the vessel(s) and initial density of the tumor at the time of sprout formation are questions which are to be investigated. In the present study, the aim is to find the response of tumor cells and vessels to the reciprocal effects of each other in different circumstances in the tissue. Together with a mathematical formulation, a radial basis function (RBF) neural network is established to predict the number of tumor cells at different circumstances including size and distance of initial tumors from the parent vessel. A final formulation is given for the final number of tumor cells as a function of initial tumor size and distance between a parent vessel and a tumor. Results of this simulation demonstrate that, increasing the distance between a tumor and a parent vessel decreases the number of final tumor cells. Specially, this decrement becomes faster beyond a certain distance. Moreover, initial tumors in bigger domains must become much bigger before inducing angiogenesis which makes it harder for them to survive.

How mathematical modeling could contribute to the quantification of metastatic tumor burden under therapy: insights in immunotherapeutic treatment of non-small cell lung cancer

BACKGROUND

Cancer is one of the leading death causes globally with about 8.2 million deaths per year and an increase in numbers in recent years. About 90% of cancer deaths do not occur due to primary tumors but due to metastases, of which most are not clinically identifiable because of their relatively small size at primary diagnosis and limited technical possibilities. However, therapeutic decisions are formed depending on the existence of metastases and their properties. Therefore non-identified metastases might have huge influence in the treatment outcome. The quantification of clinically visible and invisible metastases is important for the choice of an optimal treatment of the individual patient as it could clarify the burden of non-identifiable tumors as well as the future behavior of the cancerous disease.

RESULTS

The mathematical model presented in this study gives insights in how this could be achieved, taking into account different treatment possibilities and therefore being able to compare therapy schedules for individual patients with different clinical parameters. The framework was tested on three patients with non-small cell lung cancer, one of the deadliest types of cancer worldwide, and clinical history including platinum-based chemotherapy and PD-L1-targeted immunotherapy. Results yield promising insights into the framework to establish methods to quantify effects of different therapy methods and prognostic features for individual patients already at stage of primary diagnosis.

Identification of high-dimensional omics-derived predictors for tumor growth dynamics using machine learning and pharmacometric modeling

Pharmacometric modeling can capture tumor growth inhibition (TGI) dynamics and variability. These approaches do not usually consider covariates in high-dimensional settings, whereas high-dimensional molecular profiling technologies ("omics") are being increasingly considered for prediction of anticancer drug treatment response. Machine learning (ML) approaches have been applied to identify high-dimensional omics predictors for treatment outcome. Here, we aimed to combine TGI modeling and ML approaches for two distinct aims: omics-based prediction of tumor growth profiles and identification of pathways associated with treatment response and resistance. We propose a two-step approach combining ML using least absolute shrinkage and selection operator (LASSO) regression with pharmacometric modeling. We demonstrate our workflow using a previously published dataset consisting of 4706 tumor growth profiles of patient-derived xenograft (PDX) models treated with a variety of mono- and combination regimens. Pharmacometric TGI models were fit to the tumor growth profiles. The obtained empirical Bayes estimates-derived TGI parameter values were regressed using the LASSO on high-dimensional genomic copy number variation data, which contained over 20,000 variables. The predictive model was able to decrease median prediction error by 4% as compared with a model without any genomic information. A total of 74 pathways were identified as related to treatment response or resistance development by LASSO, of which part was verified by literature. In conclusion, we demonstrate how the combined use of ML and pharmacometric modeling can be used to gain pharmacological understanding in genomic factors driving variation in treatment response.

Superlinear growth reveals the Allee effect in tumors

Integrating experimental data into ecological models plays a central role in understanding biological mechanisms that drive tumor progression where such knowledge can be used to develop new therapeutic strategies. While the current studies emphasize the role of competition among tumor cells, they fail to explain recently observed superlinear growth dynamics across human tumors. Here we study tumor growth dynamics by developing a model that incorporates evolutionary dynamics inside tumors with tumor-microenvironment interactions. Our results reveal that tumor cells' ability to manipulate the environment and induce angiogenesis drives superlinear growth-a process compatible with the Allee effect. In light of this understanding, our model suggests that, for high-risk tumors that have a higher growth rate, suppressing angiogenesis can be the appropriate therapeutic intervention.

Fractional Mathematical Oncology: On the potential of non-integer order calculus applied to interdisciplinary models

Mathematical Oncology investigates cancer-related phenomena through mathematical models as comprehensive as possible. Accordingly, an interdisciplinary approach involving concepts from biology to materials science can provide a deeper understanding of biological systems pertaining the disease. In this context, fractional calculus (also referred to as non-integer order) is a branch in mathematical analysis whose tools can describe complex phenomena comprising different time and space scales. Fractional-order models may allow a better description and understanding of oncological particularities, potentially contributing to decision-making in areas of interest such as tumor evolution, early diagnosis techniques and personalized treatment therapies. By following a phenomenological (i.e. mechanistic) approach, the present study surveys and explores different aspects of Fractional Mathematical Oncology, reviewing and discussing recent developments in view of their prospective applications.

Beyond the pair approximation: Modeling colonization population dynamics

The process of range expansion (colonization) is one of the basic types of biological dynamics, whereby a species grows and spreads outwards, occupying new territories. Spatial modeling of this process is naturally implemented as a stochastic cellular automaton, with individuals occupying nodes on a rectangular grid, births and deaths occurring probabilistically, and individuals only reproducing onto unoccupied neighboring spots. In this paper we derive several approximations that allow prediction of the expected range expansion dynamics, based on the reproduction and death rates. We derive several approximations, where the cellular automaton is described by a system of ordinary differential equations that preserves correlations among neighboring spots (up to a distance). This methodology allows us to develop accurate approximations of the population size and the expected spatial shape, at a fraction of the computational time required to simulate the original stochastic system. In addition, we provide simple formulas for the steady-state population densities for von Neumann and Moore neighborhoods. Finally, we derive concise approximations for the speed of range expansion in terms of the reproduction and death rates, for both types of neighborhoods. The methodology is generalizable to more complex scenarios, such as different interaction ranges and multiple-species systems.

Cell and extracellular matrix growth theory and its implications for tumorigenesis

Cells associated with an abnormal (cancerous) growth exchange flows, morph freely and grow hand-in-glove with their immediate environment, the extracellular matrix (ECM). The cell structure experiences two mass flows in counterflow. Flowing into the structure are nutrients and flowing out is refuse from the metabolically active biomass within. The physical effect of the evolution of the cell and extracellular structure is more flow and mixing in that space, that is, more mixing than in the absence of a biological growth in that space. The objective of the present theory is to predict the increase in the size of the cell cluster as a function of its structure, and also to predict the critical cluster sizes that mark the transitions from one distinct cluster configuration to the next. This amounts to predicting the timing and the main features of the transitions from single cell to clusters with two, four, eight and more cells, including larger clusters with cells organized on its outer surface. The predicted evolution of the size and configuration of the cell cluster is validated successfully by comparison with measurements from several independent studies of cancerous and non-cancerous growth patterns.

Control of tumor growth distributions through kinetic methods

The mathematical modeling of tumor growth has a long history, and has been mathematically formulated in several different ways. Here we tackle the problem in the case of a continuous distribution using mathematical tools from statistical physics. To this extent, we introduce a novel kinetic model of growth which highlights the role of microscopic transitions in determining a variety of equilibrium distributions. At variance with other approaches, the mesoscopic description in terms of elementary interactions allows to design precise microscopic feedback control therapies, able to influence the natural tumor growth and to mitigate the risk factors involved in big sized tumors. We further show that under a suitable scaling both the free and controlled growth models correspond to Fokker-Planck type equations for the growth distribution with variable coefficients of diffusion and drift, whose steady solutions in the free case are given by a class of generalized Gamma densities which can be characterized by fat tails. In this scaling the feedback control produces an explicit modification of the drift operator, which is shown to strongly modify the emerging distribution for the tumor size. In particular, the size distributions in presence of therapies manifest slim tails in all growth models, which corresponds to a marked mitigation of the risk factors. Numerical results confirming the theoretical analysis are also presented.

Similarities between pandemics and cancer in growth and risk models

Cancer and pandemics are leading causes of death globally, with severe socioeconomic repercussions. To better understand these repercussions, we investigate similarities between pandemics and cancer and describe the limited growth in number of infections or cancer cells, using mathematical models. For a pandemic, the analysis shows that in most cases, the initial fast growth is followed by a slower decay in the recovery phase. The risk of infection increases due to the airborne virus contact crossing a risk-threshold. For cancers caused by carcinogens, the increasing risk with age and absorbed dose of toxins that cross a risk-threshold, may lead to the disease onset. The time scales are different for both causes of death: years for cancer development and days to weeks for contact with airborne viruses. Contamination by viruses is on a time scale of seconds or minutes. The risk-threshold to get ill and the number-threshold in cancer cells or viruses, may explain the large variability in the outcome. The number of infected persons per day is better represented in log–lin plots instead of the conventional lin–lin plots. Differences in therapies are discussed. Our mathematical investigation between cancer and pandemics reveals a multifactorial correlation between both fragilities and brings us one step closer to understand, timely predict and ultimately diminish the socioeconomic hurdle of both cancer and pandemics.

Universal scaling laws rule explosive growth in human cancers

Most physical and other natural systems are complex entities composed of a large number of interacting individual elements. It is a surprising fact that they often obey the so-called scaling laws relating an observable quantity with a measure of the size of the system. Here we describe the discovery of universal superlinear metabolic scaling laws in human cancers. This dependence underpins increasing tumour aggressiveness, due to evolutionary dynamics, which leads to an explosive growth as the disease progresses. We validated this dynamic using longitudinal volumetric data of different histologies from large cohorts of cancer patients. To explain our observations we put forward increasingly-complex biologically-inspired mathematical models that captured the key processes governing tumor growth. Our models predicted that the emergence of superlinear allometric scaling laws is an inherently three-dimensional phenomenon. Moreover, the scaling laws thereby identified allowed us to define a set of metabolic metrics with prognostic value, thus providing added clinical utility to the base findings.

On multistep tumor growth models of fractional variable-order

Fractional mathematical oncology is a research topic that applies non-integer order calculus to tackle cancer problems such as tumor growth analysis or its optimal treatment. This work proposes a multistep exponential model with a fractional variable-order representing the evolution history of a tumor. Model parameters are tuned according to variable fractional order profiles while assessing their capability of fitting a clinical time series. The results point to the superiority of the proposed model in describing the experimental data, thus providing new perspectives for modeling tumor growth.

Effect of feedback regulation on stem cell fractions in tissues and tumors: Understanding chemoresistance in cancer

While resistance mutations are often implicated in the failure of cancer therapy, lack of response also occurs without such mutants. In bladder cancer mouse xenografts, repeated chemotherapy cycles have resulted in cancer stem cell (CSC) enrichment, and consequent loss of therapy response due to the reduced susceptibility of CSCs to drugs. A particular feedback loop present in the xenografts has been shown to promote CSC enrichment in this system. Yet, many other regulatory loops might also be operational and might promote CSC enrichment. Their identification is central to improving therapy response. Here, we perform a comprehensive mathematical analysis to define what types of regulatory feedback loops can and cannot contribute to CSC enrichment, providing guidance to the experimental identification of feedback molecules. We derive a formula that reveals whether or not the cell population experiences CSC enrichment over time, based on the properties of the feedback. We find that negative feedback on the CSC division rate or positive feedback on differentiated cell death rate can lead to CSC enrichment. Further, the feedback mediators that achieve CSC enrichment can be secreted by either CSCs or by more differentiated cells. The extent of enrichment is determined by the CSC death rate, the CSC self-renewal probability, and by feedback strength. Defining these general characteristics of feedback loops can guide the experimental screening for and identification of feedback mediators that can promote CSC enrichment in bladder cancer and potentially other tumors. This can help understand and overcome the phenomenon of CSC-based therapy resistance.

Mutant Evolution in Spatially Structured and Fragmented Expanding Populations

Mutant evolution in spatially structured systems is important for a range of biological systems, but aspects of it still require further elucidation. Adding to previous work, we provide a simple derivation of growth laws that characterize the number of mutants of different relative fitness in expanding populations in spatial models of different dimensionalities. These laws are universal and independent of "microscopic" modeling details. We further study the accumulation of mutants and find that, with advantageous and neutral mutants, more of them are present in spatially structured, compared to well-mixed colonies of the same size. The behavior of disadvantageous mutants is subtle: if they are disadvantageous through a reduction in division rates, the result is the same, and it is the opposite if the disadvantage is due to a death rate increase. Finally, we show that in all cases, the same results are observed in fragmented, nonspatial patch models. This suggests that the patterns observed are the consequence of population fragmentation, and not spatial restrictions per se We provide an intuitive explanation for the complex dependence of disadvantageous mutant evolution on spatial restriction, which relies on desynchronized dynamics in different locations/patches, and plays out differently depending on whether the disadvantage is due to a lower division rate or a higher death rate. Implications for specific biological systems, such as the evolution of drug-resistant cell mutants in cancer or bacterial biofilms, are discussed.

A Mathematical Model to Predict Diagnostic Periods for Secondary Distant Metastases in Patients with ER/PR/HER2/Ki-67 Subtypes of Breast Cancer

Previously, a consolidated mathematical model of primary tumor (PT) growth and secondary distant metastasis (sdMTS) growth in breast cancer (BC) (CoMPaS) was presented. The aim was to detect the diagnostic periods for visible sdMTS via CoMPaS in patients with different subtypes ER/PR/HER2/Ki-67 (Estrogen Receptor/Progesterone Receptor/Human Epidermal growth factor Receptor 2/Ki-67 marker) of breast cancer. CoMPaS is based on an exponential growth model and complementing formulas, and the model corresponds to the tumor-node-metastasis (TNM) staging system and BC subtypes (ER/PR/HER2/Ki-67). The CoMPaS model reflects (1) the subtypes of BC, such as ER/PR/HER2/Ki-67, and (2) the growth processes of the PT and sdMTSs in BC patients without or with lymph node metastases (MTSs) in accordance with the eighth edition American Joint Committee on Cancer prognostic staging system for breast cancer. CoMPaS correctly describes the growth of the PT in the ER/PR/HER2/Ki-67 subtypes of BC patients and helps to calculate the different diagnostic periods, depending on the tumor volume doubling time of sdMTS, when sdMTSs might appear. CoMPaS and the corresponding software tool can help (1) to start the early treatment of small sdMTSs in BC patients with different tumor subtypes (ER/PR/HER2/Ki-67), and (2) to consider the patient almost healthy if sdMTSs do not appear during the different diagnostic periods.

Colorectal cancer residual disease at maximal response to EGFR blockade displays a druggable Paneth cell-like phenotype

Blockade of epidermal growth factor receptor (EGFR) causes tumor regression in some patients with metastatic colorectal cancer (mCRC). However, residual disease reservoirs typically remain even after maximal response to therapy, leading to relapse. Using patient-derived xenografts (PDXs), we observed that mCRC cells surviving EGFR inhibition exhibited gene expression patterns similar to those of a quiescent subpopulation of normal intestinal secretory precursors with Paneth cell characteristics. Compared with untreated tumors, these pseudodifferentiated tumor remnants had reduced expression of genes encoding EGFR-activating ligands, enhanced activity of human epidermal growth factor receptor 2 (HER2) and HER3, and persistent signaling along the phosphatidylinositol 3-kinase (PI3K) pathway. Clinically, properties of residual disease cells from the PDX models were detected in lingering tumors of responsive patients and in tumors of individuals who had experienced early recurrence. Mechanistically, residual tumor reprogramming after EGFR neutralization was mediated by inactivation of Yes-associated protein (YAP), a master regulator of intestinal epithelium recovery from injury. In preclinical trials, Pan-HER antibodies minimized residual disease, blunted PI3K signaling, and induced long-term tumor control after treatment discontinuation. We found that tolerance to EGFR inhibition is characterized by inactivation of an intrinsic lineage program that drives both regenerative signaling during intestinal repair and EGFR-dependent tumorigenesis. Thus, our results shed light on CRC lineage plasticity as an adaptive escape mechanism from EGFR-targeted therapy and suggest opportunities to preemptively target residual disease.

Computational study of novel natural inhibitors targeting aminopeptidase N(CD13)

OBJECTIVES

To screen and identify ideal leading compounds from a drug library (ZINC15 database) with potential inhibition of aminopeptidase N(CD13) to contribute to medication design and development.

RESULTS

Two novel natural compounds, ZINC000000895551 and ZINC000014820583, from the ZINC15 database were found to have a higher binding affinity and more favorable interaction energy binding with CD13 with less rodent carcinogenicity, Ames mutagenicity, and non-inhibition with cytochrome P-450 2D6. Molecular dynamics simulation analysis suggested that the 2 complexes, ZINC000000895551-CD13 and ZINC000014820583-CD13, have favorable potential energy, and exist stably in the natural circumstances.

CONCLUSION

This study discovered that ZINC000000895551 and ZINC000014820583 were ideal leading compounds to be inhibitions targeting to CD13. These compounds were selected as safe drug candidates as CD13 target medication design and improvement.

MATERIALS AND METHOD

Potential inhibitors of CD13 were identified using a series of computer-aided structural and chemical virtual screening techniques. Structure-based virtual screening was carried out to calculate LibDock scores, followed by analyzing their absorption, distribution, metabolism, and excretion and toxicity predictions. Molecule docking was employed to reveal binding affinity between the selected compounds and CD13. Molecular dynamics simulation was applied to evaluate stability of the ligand-CD13 complex under natural environment.

Agent-based model of multicellular tumor spheroid evolution including cell metabolism

Computational models aiming at the spatio-temporal description of cancer evolution are a suitable framework for testing biological hypotheses from experimental data, and generating new ones. Building on our recent work (J. Theor. Biol. 389, 146 (2016)) we develop a 3D agent-based model, capable of tracking hundreds of thousands of interacting cells, over time scales ranging from seconds to years. Cell dynamics is driven by a Monte Carlo solver, incorporating partial differential equations to describe chemical pathways and the activation/repression of "genes", leading to the up- or down-regulation of specific cell markers. Each cell-agent of different kind (stem, cancer, stromal etc.) runs through its cycle, undergoes division, can exit to a dormant, senescent, necrotic state, or apoptosis, according to the inputs from its systemic network. The basic network at this stage describes glucose/oxygen/ATP cycling, and can be readily extended to cancer-cell specific markers. Eventual accumulation of chemical/radiation damage to each cell's DNA is described by a Markov chain of internal states, and by a damage-repair network, whose evolution is linked to the cell systemic network. Aimed at a direct comparison with experiments of tumorsphere growth from stem cells, the present model will allow to quantitatively study the role of transcription factors involved in the reprogramming and variable radio-resistance of simulated cancer-stem cells, evolving in a realistic computer simulation of a growing multicellular tumorsphere.

Cancer cell population growth kinetics at low densities deviate from the exponential growth model and suggest an Allee effect

Most models of cancer cell population expansion assume exponential growth kinetics at low cell densities, with deviations to account for observed slowing of growth rate only at higher densities due to limited resources such as space and nutrients. However, recent preclinical and clinical observations of tumor initiation or recurrence indicate the presence of tumor growth kinetics in which growth rates scale positively with cell numbers. These observations are analogous to the cooperative behavior of species in an ecosystem described by the ecological principle of the Allee effect. In preclinical and clinical models, however, tumor growth data are limited by the lower limit of detection (i.e., a measurable lesion) and confounding variables, such as tumor microenvironment, and immune responses may cause and mask deviations from exponential growth models. In this work, we present alternative growth models to investigate the presence of an Allee effect in cancer cells seeded at low cell densities in a controlled in vitro setting. We propose a stochastic modeling framework to disentangle expected deviations due to small population size stochastic effects from cooperative growth and use the moment approach for stochastic parameter estimation to calibrate the observed growth trajectories. We validate the framework on simulated data and apply this approach to longitudinal cell proliferation data of BT-474 luminal B breast cancer cells. We find that cell population growth kinetics are best described by a model structure that considers the Allee effect, in that the birth rate of tumor cells increases with cell number in the regime of small population size. This indicates a potentially critical role of cooperative behavior among tumor cells at low cell densities with relevance to early stage growth patterns of emerging and relapsed tumors.

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.

Spatially constrained tumour growth affects the patterns of clonal selection and neutral drift in cancer genomic data

Quantification of the effect of spatial tumour sampling on the patterns of mutations detected in next-generation sequencing data is largely lacking. Here we use a spatial stochastic cellular automaton model of tumour growth that accounts for somatic mutations, selection, drift and spatial constraints, to simulate multi-region sequencing data derived from spatial sampling of a neoplasm. We show that the spatial structure of a solid cancer has a major impact on the detection of clonal selection and genetic drift from both bulk and single-cell sequencing data. Our results indicate that spatial constrains can introduce significant sampling biases when performing multi-region bulk sampling and that such bias becomes a major confounding factor for the measurement of the evolutionary dynamics of human tumours. We also propose a statistical inference framework that incorporates spatial effects within a growing tumour and so represents a further step forwards in the inference of evolutionary dynamics from genomic data. Our analysis shows that measuring cancer evolution using next-generation sequencing while accounting for the numerous confounding factors remains challenging. However, mechanistic model-based approaches have the potential to capture the sources of noise and better interpret the data.

Is cell migration a selectable trait in the natural evolution of cancer development?

Selective evolutionary pressure shapes the processes and genes that enable cancer survival and expansion in a tumour-suppressive environment. A distinguishing lethal feature of malignant cancer is its dissemination and seeding of metastatic foci. A key requirement for this process is the acquisition of a migratory/invasive ability. However, how the migratory phenotype is selected for during the natural evolution of cancer and what advantage, if any, it might provide to the growing malignant cells remain open issues. In this opinion piece, we discuss three possible answers to these issues. We will examine lines of evidence from mathematical modelling of cancer evolution that indicate that migration is an intrinsic selectable property of malignant cells that directly impacts on growth dynamics and cancer geometry. Second, we will argue that migratory phenotypes can emerge as an adaptive response to unfavourable growth conditions and endow cells not only with the ability to move/invade, but also with specific metastatic traits, including drug resistance, self-renewal and survival. Finally, we will discuss the possibility that migratory phenotypes are coincidental events that emerge by happenstance in the natural evolution of cancer. This article is part of a discussion meeting issue 'Forces in cancer: interdisciplinary approaches in tumour mechanobiology'.

Pattern formation of skin cancers: Effects of cancer proliferation and hydrodynamic interactions

We study pattern formation of skin cancers by means of numerical simulation of a binary system consisting of cancer and healthy cells. We extend the conventional model H for macrophase separations by considering a logistic growth of cancer cells and also a mechanical friction between dermis and epidermis. Importantly, our model exhibits a microphase separation due to the proliferation of cancer cells. By numerically solving the time evolution equations of the cancer composition and its velocity, we show that the phase separation kinetics strongly depends on the cell proliferation rate as well as on the strength of hydrodynamic interactions. A steady-state diagram of cancer patterns is established in terms of these two dynamical parameters and some of the patterns correspond to clinically observed cancer patterns. Furthermore, we examine in detail the time evolution of the average composition of cancer cells and the characteristic length of the microstructures. Our results demonstrate that different sequence of cancer patterns can be obtained by changing the proliferation rate and/or hydrodynamic interactions.

Growth dynamics in naturally progressing chronic lymphocytic leukaemia

How the genomic features of a patient's cancer relate to individual disease kinetics remains poorly understood. Here we used the indolent growth dynamics of chronic lymphocytic leukaemia (CLL) to analyse the growth rates and corresponding genomic patterns of leukaemia cells from 107 patients with CLL, spanning decades-long disease courses. We found that CLL commonly demonstrates not only exponential expansion but also logistic growth, which is sigmoidal and reaches a certain steady-state level. Each growth pattern was associated with marked differences in genetic composition, the pace of disease progression and the extent of clonal evolution. In a subset of patients, whose serial samples underwent next-generation sequencing, we found that dynamic changes in the disease course of CLL were shaped by the genetic events that were already present in the early slow-growing stages. Finally, by analysing the growth rates of subclones compared with their parental clones, we quantified the growth advantage conferred by putative CLL drivers in vivo.

Impact of time to initiation of radiotherapy on survival after resection of newly diagnosed glioblastoma

Background and purpose

To evaluate the effect of timing of radiotherapy (RT) on survival in patients with newly diagnosed primary glioblastoma (GBM) treated with the same therapeutical protocol.

Materials and methods

Patients with newly diagnosed primary GBM treated with the same therapeutical scheme between 2010 and 2015 in our institution were retrospectively reviewed. The population was trichotomized based on the time interval from surgery till initiation of RT (< 28 days, 28–33 days, > 33 days). Kaplan-Meier and Cox regression analyses were used to compare progression free survival (PFS) and overall survival (OS) between the groups. The influence of various extensively studied prognostic factors on survival was assessed by multivariate analysis.

Results

One-hundred-fifty-one patients met the inclusion criteria. Between the three groups no significant difference in PFS (p = 0.516) or OS (p = 0.902) could be demonstrated. Residual tumor volume (RTV) and midline structures involvement were identified as independent prognostic factors of PFS while age, O-6-Methylguanine Methyltransferase (MGMT) status, Ki67 index, RTV and midline structures involvement represented independent predictors of OS. Patients starting RT after a prolonged delay (> 48 days) exhibited a significantly shorter OS (p = 0.034).

Conclusion

Initiation of RT within a timeframe of 48 days is not associated with worsened survival. A prolonged delay (> 48 days) may be associated with worse OS. RT should neither be delayed, nor forced, but should rather start timely, as soon as the patient has recovered from surgery.

Nonlinear studies of tumor morphological stability using a two-fluid flow model

We consider the nonlinear dynamics of an avascular tumor at the tissue scale using a two-fluid flow Stokes model, where the viscosity of the tumor and host microenvironment may be different. The viscosities reflect the combined properties of cell and extracellular matrix mixtures. We perform a linear morphological stability analysis of the tumors, and we investigate the role of nonlinearity using boundary-integral simulations in two dimensions. The tumor is non-necrotic, although cell death may occur through apoptosis. We demonstrate that tumor evolution is regulated by a reduced set of nondimensional parameters that characterize apoptosis, cell-cell/cell-extracellular matrix adhesion, vascularization and the ratio of tumor and host viscosities. A novel reformulation of the equations enables the use of standard boundary integral techniques to solve the equations numerically. Nonlinear simulation results are consistent with linear predictions for nearly circular tumors. As perturbations develop and grow, the linear and nonlinear results deviate and linear theory tends to underpredict the growth of perturbations. Simulations reveal two basic types of tumor shapes, depending on the viscosities of the tumor and microenvironment. When the tumor is more viscous than its environment, the tumors tend to develop invasive fingers and a branched-like structure. As the relative ratio of the tumor and host viscosities decreases, the tumors tend to grow with a more compact shape and develop complex invaginations of healthy regions that may become encapsulated in the tumor interior. Although our model utilizes a simplified description of the tumor and host biomechanics, our results are consistent with experiments in a variety of tumor types that suggest that there is a positive correlation between tumor stiffness and tumor aggressiveness.

Effect of cellular de-differentiation on the dynamics and evolution of tissue and tumor cells in mathematical models with feedback regulation

Tissues are maintained by adult stem cells that self-renew and also differentiate into functioning tissue cells. Homeostasis is achieved by a set of complex mechanisms that involve regulatory feedback loops. Similarly, tumors are believed to be maintained by a minority population of cancer stem cells, while the bulk of the tumor is made up of more differentiated cells, and there is indication that some of the feedback loops that operate in tissues continue to be functional in tumors. Mathematical models of such tissue hierarchies, including feedback loops, have been analyzed in a variety of different contexts. Apart from stem cells giving rise to differentiated cells, it has also been observed that more differentiated cells can de-differentiate into stem cells, both in healthy tissue and tumors, aspects of which have also been investigated mathematically. This paper analyses the effect of de-differentiation on the basic and evolutionary dynamics of cells in the context of tissue hierarchy models that include negative feedback regulation of the cell populations. The models predict that in the presence of de-differentiation, the fixation probability of a neutral mutant is lower than in its absence. Therefore, if de-differentiation occurs, a mutant with identical parameters compared to the wild-type cell population behaves like a disadvantageous mutant. Similarly, the process of de-differentiation is found to lower the fixation probability of an advantageous mutant. These results indicate that the presence of de-differentiation can lower the rates of tumor initiation and progression in the context of the models considered here.

Consolidated mathematical growth model of the primary tumor and secondary distant metastases of breast cancer (CoMPaS)

The goal of this research is to improve the accuracy of predicting the breast cancer (BC) process using the original mathematical model referred to as CoMPaS. The CoMPaS is the original mathematical model and the corresponding software built by modelling the natural history of the primary tumor (PT) and secondary distant metastases (MTS), it reflects the relations between the PT and MTS. The CoMPaS is based on an exponential growth model and consists of a system of determinate nonlinear and linear equations and corresponds to the TNM classification. It allows us to calculate the different growth periods of PT and MTS: 1) a non-visible period for PT, 2) a non-visible period for MTS, and 3) a visible period for MTS. The CoMPaS has been validated using 10-year and 15-year survival clinical data considering tumor stage and PT diameter. The following are calculated by CoMPaS: 1) the number of doublings for the non-visible and visible growth periods of MTS and 2) the tumor volume doubling time (days) for the non-visible and visible growth periods of MTS. The diameters of the PT and secondary distant MTS increased simultaneously. In other words, the non-visible growth period of the secondary distant MTS shrinks, leading to a decrease of the survival of patients with breast cancer. The CoMPaS correctly describes the growth of the PT for patients at the T1aN0M0, T1bN0M0, T1cN0M0, T2N0M0 and T3N0M0 stages, who does not have MTS in the lymph nodes (N0). Additionally, the CoMPaS helps to consider the appearance and evolution period of secondary distant MTS (M1). The CoMPaS correctly describes the growth period of PT corresponding to BC classification (parameter T), the growth period of secondary distant MTS and the 10-15-year survival of BC patients considering the BC stage (parameter M).

Combination Therapy and the Evolution of Resistance: The Theoretical Merits of Synergism and Antagonism in Cancer

The search for effective combination therapies for cancer has focused heavily on synergistic combinations because they exhibit enhanced therapeutic efficacy at lower doses. Although synergism is intuitively attractive, therapeutic success often depends on whether drug resistance develops. The impact of synergistic combinations (vs. antagonistic or additive combinations) on the process of drug-resistance evolution has not been investigated. In this study, we use a simplified computational model of cancer cell numbers in a population of drug-sensitive, singly-resistant, and fully-resistant cells to simulate the dynamics of resistance evolution in the presence of two-drug combinations. When we compared combination therapies administered at the same combination of effective doses, simulations showed synergistic combinations most effective at delaying onset of resistance. Paradoxically, when the therapies were compared using dose combinations with equal initial efficacy, antagonistic combinations were most successful at suppressing expansion of resistant subclones. These findings suggest that, although synergistic combinations could suppress resistance through early decimation of cell numbers (making them "proefficacy" strategies), they are inherently fragile toward the development of single resistance. In contrast, antagonistic combinations suppressed the clonal expansion of singly-resistant cells, making them "antiresistance" strategies. The distinction between synergism and antagonism was intrinsically connected to the distinction between offensive and defensive strategies, where offensive strategies inflicted early casualties and defensive strategies established protection against anticipated future threats. Our findings question the exclusive focus on synergistic combinations and motivate further consideration of nonsynergistic combinations for cancer therapy.Significance: Computational simulations show that if different combination therapies have similar initial efficacy in cancers, then nonsynergistic drug combinations are more likely than synergistic drug combinations to provide a long-term defense against the evolution of therapeutic resistance. Cancer Res; 78(9); 2419-31. ©2018 AACR.

Untangling the model muddle: Empirical tumour growth in Tasmanian devil facial tumour disease

A pressing and unresolved topic in cancer research is how tumours grow in the absence of treatment. Despite advances in cancer biology, therapeutic and diagnostic technologies, there is limited knowledge regarding the fundamental growth and developmental patterns in solid tumours. In this ten year study, we estimated growth curves in Tasmanian devil facial tumours, a clonal transmissible cancer, in males and females with two different karyotypes (diploid, tetraploid) and facial locations (mucosal, dermal), using established differential equation models and model selection. Logistic growth was the most parsimonious model for diploid, tetraploid and mucosal tumours, with less model certainty for dermal tumours. Estimates of daily proportional tumour growth rate per day (95% Bayesian CIs) varied with ploidy and location [diploid 0.016 (0.014–0.020), tetraploid 0.026 (0.020–0.033), mucosal 0.013 (0.011–0.015), dermal 0.020 (0.016–0.024)]. Final tumour size (cm³) also varied, particularly the upper credible interval owing to host mortality as tumours approached maximum volume [diploid 364 (136–2,475), tetraploid 172 (100–305), dermal 226 (134–471)]. To our knowledge, these are the first empirical estimates of tumour growth in the absence of treatment in a wild population. Through this animal-cancer system our findings may enhance understanding of how tumour properties interact with growth dynamics in other types of cancer.

Early postoperative growth in non-functioning pituitary adenomas; A tool to tailor safe follow-up

PURPOSE

Non-functioning pituitary adenomas are common, and the treatment and follow-up of these patients represent a multidisciplinary challenge. First line treatment is transphenoidal surgery, with debulking or total removal of tumour. A substantial portion of the tumours relapse after surgery, and there is no consensus of how to follow these patients postoperatively. Our aim was to characterize the postoperative growth of non-functioning pituitary adenomas and correlate it to clinical and paraclinical data.

METHODS

We retrospectively registered 52 patients operated for non-functioning pituitary adenomas, with four or more consecutive MR-investigations not interrupted by secondary treatment. Adenoma volumes were estimated by the Cavalieri principle with summation of manually drawn areas multiplied by slice interval. Growth curves were modelled and tumour volume doubling time was calculated for 39 tumours with regrowth after surgery.

RESULTS

A total of 13 tumours showed exponential growth, 10 linear growth and 16 logistic growth after surgery. The remaining 13 did not show regrowth of tumour. Seven of the exponential growing tumours underwent secondary surgery, compared to one and two of linear and logistic growing tumours (p = 0.03), respectively. Initial tumour volume doubling time was significantly lower in logistic growing tumours than in exponential growing tumours (p < 0.01). Men had tumours with lower tumour volume doubling time than women (p = 0.03). None of the tumours demonstrated signs of accelerated growth.

CONCLUSION

Residual tumours following surgery frequently grow. The logistic growing tumours had the fastest initial growth in our cohort. We found no indication of accelerated growth, whereby the tumour volume doubling time might be used to predict a "worst-case" scenario when planning follow-up of these patients.

Stability of Control Networks in Autonomous Homeostatic Regulation of Stem Cell Lineages

Design principles of biological networks have been studied extensively in the context of protein-protein interaction networks, metabolic networks, and regulatory (transcriptional) networks. Here we consider regulation networks that occur on larger scales, namely the cell-to-cell signaling networks that connect groups of cells in multicellular organisms. These are the feedback loops that orchestrate the complex dynamics of cell fate decisions and are necessary for the maintenance of homeostasis in stem cell lineages. We focus on "minimal" networks that are those that have the smallest possible numbers of controls. For such minimal networks, the number of controls must be equal to the number of compartments, and the reducibility/irreducibility of the network (whether or not it can be split into smaller independent sub-networks) is defined by a matrix comprised of the cell number increments induced by each of the controlled processes in each of the compartments. Using the formalism of digraphs, we show that in two-compartment lineages, reducible systems must contain two 1-cycles, and irreducible systems one 1-cycle and one 2-cycle; stability follows from the signs of the controls and does not require magnitude restrictions. In three-compartment systems, irreducible digraphs have a tree structure or have one 3-cycle and at least two more shorter cycles, at least one of which is a 1-cycle. With further work and proper biological validation, our results may serve as a first step toward an understanding of ways in which these networks become dysregulated in cancer.

A Strategy to Delay the Development of Cisplatin Resistance by Maintaining a Certain Amount of Cisplatin-Sensitive Cells

Cisplatin (ddp), which is commonly employed in the treatment of many advanced cancers, often results in initial therapeutic success; however, rapid progression of ddp-resistant cells remains the main reason for treatment failure. Facd with such a problem, we investigated the fitness differences between ddp-sensitive and ddp-resistant cell lines. We found that the growth of ddp-resistant cells was significantly slower than that of sensitive cells due to elevated ROS levels, which suggested that the ddp resistance mechanisms may have negative impacts on the growth of resistant cells. Furthermore, we observed that, when mixed with ddp-sensitive cells, ddp-resistant cells failed to compete, and the growth of ddp-resistant cells could therefore be suppressed by treatment in vivo. We propose a mathematical model parameterized based on in vivo experiments to describe the allometric growth of tumors consisting of two competing subclones. According to our model, a quantitative strategy with a variant drug-dosing interval is proposed to control tumor growth. Taking advantage of intratumoral competition, our strategy with appropriate dosing intervals could remarkably delay the development of ddp resistance and prolong overall survival. Maintaining a certain number of ddp-sensitive cells rather than eradicating the tumor with continuous treatment is feasible for future tumor treatment.

The Effectiveness of Reward and Punishment in Spatial Social Games

Punishment and reward are usually regarded as two potential mechanisms to explain the evolution of cooperation especially among multiple participators. However, the performance of these two scenarios in spatial environment needs to be discussed. To figure out this issue, we resort to the [Formula: see text]-player Iterated Snowdrift Dilemma (ISD) game and Iterated Prisoner’s Dilemma (IPD) game. More importantly, the evolution of punishment and reward in social network-structured populations has not been formally addressed. The numerical results show the equilibrium cooperation frequency can be influenced by cost-to-benefit ratio [Formula: see text], the punishment-to-benefit ratio [Formula: see text] and the reward-to-benefit ratio [Formula: see text]. And one intriguing observation is that under the same situation, the punishment is more effective than reward to the population. Then we further probe the effectiveness of neighborhood relationship to the cooperation, which is reflected by the random rewired probability [Formula: see text]. From the distribution of the four roles of the participator we can find that individuals can cooperate easily when they have close relationship. The results of this paper may be helpful to understand the cooperation in complex project or among industry–university–research cooperation project.