Developing and validating a machine learning prognostic model for alerting to imminent deterioration of hospitalized patients with COVID-19.

Our study was aimed at developing and validating a new approach, embodied in a machine learning-based model, for sequentially monitoring hospitalized COVID-19 patients and directing professional attention to patients whose deterioration is imminent. Model development employed real-world patient data (598 prediction events for 210 patients), internal validation (315 prediction events for 97 patients), and external validation (1373 prediction events for 307 patients). Results show significant divergence in longitudinal values of eight routinely collected blood parameters appearing several days before deterioration. Our model uses these signals to predict the personal likelihood of transition from non-severe to severe status within well-specified short time windows. Internal validation of the model's prediction accuracy showed ROC AUC of 0.8 and 0.79 for prediction scopes of 48 or 96 h, respectively; external validation showed ROC AUC of 0.7 and 0.73 for the same prediction scopes. Results indicate the feasibility of predicting the forthcoming deterioration of non-severe COVID-19 patients by eight routinely collected blood parameters, including neutrophil, lymphocyte, monocyte, and platelets counts, neutrophil-to-lymphocyte ratio, CRP, LDH, and D-dimer. A prospective clinical study and an impact assessment will allow implementation of this model in the clinic to improve care, streamline resources and ease hospital burden by timely focusing the medical attention on potentially deteriorating patients.

A New Method for Optimizing Sepsis Therapy by Nivolumab and Meropenem Combination: Importance of Early Intervention and CTL Reinvigoration Rate as a Response Marker.

Background: Recently, there has been a growing interest in applying immune checkpoint blockers (ICBs), so far used to treat cancer, to patients with bacterial sepsis. We aimed to develop a method for predicting the personal benefit of potential treatments for sepsis, and to apply it to therapy by meropenem, an antibiotic drug, and nivolumab, a programmed cell death-1 (PD-1) pathway inhibitor. Methods: We defined an optimization problem as a concise framework of treatment aims and formulated a fitness function for grading sepsis treatments according to their success in accomplishing the pre-defined aims. We developed a mathematical model for the interactions between the pathogen, the cellular immune system and the drugs, whose simulations under diverse combined meropenem and nivolumab schedules, and calculation of the fitness function for each schedule served to plot the fitness landscapes for each set of treatments and personal patient parameters. Results: Results show that treatment by meropenem and nivolumab has maximum benefit if the interval between the onset of the two drugs does not exceed a dose-dependent threshold, beyond which the benefit drops sharply. However, a second nivolumab application, within 7-10 days after the first, can extinguish a pathogen which the first nivolumab application failed to remove. The utility of increasing nivolumab total dose above 6 mg/kg is contingent on the patient's personal immune attributes, notably, the reinvigoration rate of exhausted CTLs and the overall suppression rates of functional CTLs. A baseline pathogen load, higher than 5,000 CFU/µL, precludes successful nivolumab and meropenem combination therapy, whereas when the initial load is lower than 3,000 CFU/µL, meropenem monotherapy suffices for removing the pathogen. Discussion: Our study shows that early administration of nivolumab, 6 mg/kg, in combination with antibiotics, can alleviate bacterial sepsis in cases where antibiotics alone are insufficient and the initial pathogen load is not too high. The study pinpoints the role of precision medicine in sepsis, suggesting that personalized therapy by ICBs can improve pathogen elimination and dampen immunosuppression. Our results highlight the importance in using reliable markers for classifying patients according to their predicted response and provides a valuable tool in personalizing the drug regimens for patients with sepsis.

Accelerating the Development of Personalized Cancer Immunotherapy by Integrating Molecular Patients' Profiles with Dynamic Mathematical Models.

We review the evolution, achievements, and limitations of the current paradigm shift in medicine, from the "one-size-fits-all" model to "Precision Medicine." Precision, or personalized, medicine-tailoring the medical treatment to the personal characteristics of each patient-engages advanced statistical methods to evaluate the relationships between static patient profiling (e.g., genomic and proteomic), and a simple clinically motivated output (e.g., yes/no responder). Today, precision medicine technologies that have facilitated groundbreaking advances in oncology, notably in cancer immunotherapy, are approaching the limits of their potential, mainly due to the scarcity of methods for integrating genomic, proteomic and clinical patient information. A different approach to treatment personalization involves methodologies focusing on the dynamic interactions in the patient-disease-drug system, as portrayed in mathematical modeling. Achievements of this scientific approach, in the form of algorithms for predicting personal disease dynamics in individual patients under immunotherapeutic drugs, are reviewed as well. The contribution of the dynamic approaches to precision medicine is limited, at present, due to insufficient applicability and validation. Yet, the time is ripe for amalgamating together these two approaches, for maximizing their joint potential to personalize and improve cancer immunotherapy. We suggest the roadmap toward achieving this goal, technologically, and urge clinicians, pharmacologists, and computational biologists to join forces along the pharmaco-clinical track of this development.

Predicting response to pembrolizumab in metastatic melanoma by a new personalization algorithm.

BACKGROUND: At present, immune checkpoint inhibitors, such as pembrolizumab, are widely used in the therapy of advanced non-resectable melanoma, as they induce more durable responses than other available treatments. However, the overall response rate does not exceed 50% and, considering the high costs and low life expectancy of nonresponding patients, there is a need to select potential responders before therapy. Our aim was to develop a new personalization algorithm which could be beneficial in the clinical setting for predicting time to disease progression under pembrolizumab treatment. METHODS: We developed a simple mathematical model for the interactions of an advanced melanoma tumor with both the immune system and the immunotherapy drug, pembrolizumab. We implemented the model in an algorithm which, in conjunction with clinical pretreatment data, enables prediction of the personal patient response to the drug. To develop the algorithm, we retrospectively collected clinical data of 54 patients with advanced melanoma, who had been treated by pembrolizumab, and correlated personal pretreatment measurements to the mathematical model parameters. Using the algorithm together with the longitudinal tumor burden of each patient, we identified the personal mathematical models, and simulated them to predict the patient's time to progression. We validated the prediction capacity of the algorithm by the Leave-One-Out cross-validation methodology. RESULTS: Among the analyzed clinical parameters, the baseline tumor load, the Breslow tumor thickness, and the status of nodular melanoma were significantly correlated with the activation rate of CD8+ T cells and the net tumor growth rate. Using the measurements of these correlates to personalize the mathematical model, we predicted the time to progression of individual patients (Cohen's κ = 0.489). Comparison of the predicted and the clinical time to progression in patients progressing during the follow-up period showed moderate accuracy (R2 = 0.505). CONCLUSIONS: Our results show for the first time that a relatively simple mathematical mechanistic model, implemented in a personalization algorithm, can be personalized by clinical data, evaluated before immunotherapy onset. The algorithm, currently yielding moderately accurate predictions of individual patients' response to pembrolizumab, can be improved by training on a larger number of patients. Algorithm validation by an independent clinical dataset will enable its use as a tool for treatment personalization.

Alleviation of exhaustion-induced immunosuppression and sepsis by immune checkpoint blockers sequentially administered with antibiotics-analysis of a new mathematical model.

BACKGROUND: Sepsis-associated immune dysregulation, involving hyper-inflammation and immunosuppression, is common in intensive care patients, often leading to multiple organ dysfunction and death. The aim of this study was to identify the main driving force underlying immunosuppression in sepsis, and to suggest new therapeutic avenues for controlling this immune impairment and alleviating excessive pathogen load. METHODS: We developed two minimalistic (skeletal) mathematical models of pathogen-associated inflammation, which focus on the dynamics of myeloid, lymphocyte, and pathogen numbers in blood. Both models rely on the assumption that the presence of the pathogen causes a bias in hematopoietic stem cell differentiation toward the myeloid developmental line. Also in one of the models, we assumed that continuous exposure to pathogens induces lymphocyte exhaustion. In addition, we also created therapy models, both by antibiotics and by immunotherapy with PD-1/PD-L1 checkpoint inhibitors. Assuming realistic parameter ranges, we simulated the pathogen-associated inflammation models in silico with or without various antibiotic and immunotherapy schedules. RESULTS: Computer simulations of the two models show that the assumption of lymphocyte exhaustion is a prerequisite for attaining sepsis-associated immunosuppression, and that the ability of the innate and adaptive immune systems to control infections depends on the pathogen's replication rate. Simulation results further show that combining antibiotics with immune checkpoint blockers can suffice for defeating even an aggressive pathogen within a relatively short period. This is so as long as the drugs are administered soon after diagnosis. In contrast, when applied as monotherapies, antibiotics or immune checkpoint blockers fall short of eliminating aggressive pathogens in reasonable time. CONCLUSIONS: Our results suggest that lymphocyte exhaustion crucially drives immunosuppression in sepsis, and that one can efficiently resolve both immunosuppression and pathogenesis by timely coupling of antibiotics with an immune checkpoint blocker, but not by either one of these two treatment modalities alone. Following experimental validation, our model can be adapted to explore the potential of other therapeutic options in this field.

Extracellular inhibitors can attenuate tumorigenic Wnt pathway activity in adenomatous polyposis coli mutants: Predictions of a validated mathematical model.

BACKGROUND: Despite considerable investigational efforts, no method to overcome the pathogenesis caused by loss of function (LoF) mutations in tumor suppressor genes has been successfully translated to the clinic. The most frequent LoF mutation in human cancers is Adenomatous polyposis coli (APC), causing aberrant activation of the Wnt pathway. In nearly all colon cancer tumors, the APC protein is truncated, but still retains partial binding abilities. OBJECTIVE & METHODS: Here, we tested the hypothesis that extracellular inhibitors of the Wnt pathway, although acting upstream of the APC mutation, can restore normal levels of pathway activity in colon cancer cells. To this end, we developed and simulated a mathematical model for the Wnt pathway in different APC mutants, with or without the effects of the extracellular inhibitors, Secreted Frizzled-Related Protein1 (sFRP1) and Dickhopf1 (Dkk1). We compared our model predictions to experimental data in the literature. RESULTS: Our model accurately predicts T-cell factor (TCF) activity in mutant cells that vary in APC mutation. Model simulations suggest that both sFRP1 and DKK1 can reduce TCF activity in APC1638N/1572T and Apcmin/min mutants, but restoration of normal activity levels is possible only in the former. When applied in combination, synergism between the two inhibitors can reduce their effective doses to one-fourth of the doses required under single inhibitor application. Overall, re-establishment of normal Wnt pathway activity is predicted for every APC mutant in whom TCF activity is increased by up to 11 fold. CONCLUSIONS: Our work suggests that extracellular inhibitors can effectively restore normal Wnt pathway activity in APC-truncated cancer cells, even though these LoF mutations occur downstream of the inhibitory action. The insufficient activity of the truncated APC can be quantitatively balanced by the upstream intervention. This new concept of upstream intervention to control the effects of downstream mutations may be considered also for other partial LoF mutations in other signaling pathways.

Employing dynamical computational models for personalizing cancer immunotherapy.

INTRODUCTION: Recently, cancer immunotherapy has shown considerable success, but due to the complexity of the immune-cancer interactions, clinical outcomes vary largely between patients. A possible approach to overcome this difficulty may be to develop new methodologies for personal predictions of therapy outcomes, by the integration of patient data with dynamical mathematical models of the drug-affected pathophysiological processes. AREAS COVERED: This review unfolds the story of mathematical modeling in cancer immunotherapy, and examines the feasibility of using these models for immunotherapy personalization. The reviewed studies suggest that response to immunotherapy can be improved by patient-specific regimens, which can be worked out by personalized mathematical models. The studies further indicate that personalized models can be constructed and validated relatively early in treatment. EXPERT OPINION: The suggested methodology has the potential to raise the overall efficacy of the developed immunotherapy. If implemented already during drug development it may increase the prospects of the technology being approved for clinical use. However, schedule personalization, per se, does not comply with the current, 'one size fits all,' paradigm of clinical trials. It is worthwhile considering adjustment of the current paradigm to involve personally tailored immunotherapy regimens.

Predicting time to castration resistance in hormone sensitive prostate cancer by a personalization algorithm based on a mechanistic model integrating patient data.

BACKGROUND: Prostate cancer (PCa) is a leading cause of cancer death of men worldwide. In hormone-sensitive prostate cancer (HSPC), androgen deprivation therapy (ADT) is widely used, but an eventual failure on ADT heralds the passage to the castration-resistant prostate cancer (CRPC) stage. Because predicting time to failure on ADT would allow improved planning of personal treatment strategy, we aimed to develop a predictive personalization algorithm for ADT efficacy in HSPC patients. METHODS: A mathematical mechanistic model for HSPC progression and treatment was developed based on the underlying disease dynamics (represented by prostate-specific antigen; PSA) as affected by ADT. Following fine-tuning by a dataset of ADT-treated HSPC patients, the model was embedded in an algorithm, which predicts the patient's time to biochemical failure (BF) based on clinical metrics obtained before or early in-treatment. RESULTS: The mechanistic model, including a tumor growth law with a dynamic power and an elaborate ADT-resistance mechanism, successfully retrieved individual time-courses of PSA (R(2) = 0.783). Using the personal Gleason score (GS) and PSA at diagnosis, as well as PSA dynamics from 6 months after ADT onset, and given the full ADT regimen, the personalization algorithm accurately predicted the individual time to BF of ADT in 90% of patients in the retrospective cohort (R(2) = 0.98). CONCLUSIONS: The algorithm we have developed, predicting biochemical failure based on routine clinical tests, could be especially useful for patients destined for short-lived ADT responses and quick progression to CRPC. Prospective studies must validate the utility of the algorithm for clinical decision-making.

Complex pattern of interleukin-11-induced inflammation revealed by mathematically modeling the dynamics of C-reactive protein.

Inflammation underlies many diseases and is an undesired effect of several therapy modalities. Biomathematical modeling can help unravel the complex inflammatory processes and the mechanisms triggering their emergence. We developed a model for induction of C-reactive protein (CRP), a clinically reliable marker of inflammation, by interleukin (IL)-11, an approved cytokine for treatment of chemotherapy-induced thrombocytopenia. Due to paucity of information on the mechanisms underlying inflammation-induced CRP dynamics, our model was developed by systematically evaluating several models for their ability to retrieve variable CRP profiles observed in IL-11-treated breast cancer patients. The preliminary semi-mechanistic models were designed by non-linear mixed-effects modeling, and were evaluated by various performance criteria, which test goodness-of-fit, parsimony and uniqueness. The best-performing model, a robust population model with minimal inter-individual variability, uncovers new aspects of inflammation dynamics. It shows that CRP clearance is a nonlinear self-controlled process, indicating an adaptive anti-inflammatory reaction in humans. The model also reveals a dual IL-11 effect on CRP elevation, whereby the drug has not only a potent immediate influence on CRP incline, but also a long-term influence inducing elevated CRP levels for several months. Consistent with this, model simulations suggest that periodic IL-11 therapy may result in prolonged low-grade (chronic) inflammation post treatment. Future application of the model can therefore help design improved IL-11 regimens with minimized long-term CRP toxicity. Our study illuminates the dynamics of inflammation and its control, and provides a prototype for progressive modeling of complex biological processes in the medical realm and beyond.

The resonance phenomenon in population persistence: can the same theory guide both national security policies and personalized medicine?

The theory of resonance in population persistence proposes that the survival of a population that is exposed to externally inflicted loss processes (disturbances) during part of its life cycle is dependent on the relation between the average period of the disturbances and the average generation time of the population. This suggests that the size of a population can be controlled by manipulating the period between external disturbances. This theory, first formalized in a study of intertidal Red Sea mollusks exposed to periodic storms, has been found to apply to such seemingly disparate phenomena as the spread of a pathogen among susceptible individuals and the response of malignant cancer cells to chemotherapy. The current article provides a brief review of the evolution of the resonance theory into a tool that can be applied to designing vaccination policies - specifically, in preparedness for bio-terrorism attacks - and in personalized medicine. A personalized protocol based on the resonance theory was applied to a cancer patient, stabilizing his tumor progression, relieving his hematopoietic toxicity, and extending his survival.

Personalizing oncology treatments by predicting drug efficacy, side-effects, and improved therapy: mathematics, statistics, and their integration.

Despite its great promise, personalized oncology still faces many hurdles, and it is increasingly clear that targeted drugs and molecular biomarkers alone yield only modest clinical benefit. One reason is the complex relationships between biomarkers and the patient's response to drugs, obscuring the true weight of the biomarkers in the overall patient's response. This complexity can be disentangled by computational models that integrate the effects of personal biomarkers into a simulator of drug-patient dynamic interactions, for predicting the clinical outcomes. Several computational tools have been developed for personalized oncology, notably evidence-based tools for simulating pharmacokinetics, Bayesian-estimated tools for predicting survival, etc. We describe representative statistical and mathematical tools, and discuss their merits, shortcomings and preliminary clinical validation attesting to their potential. Yet, the individualization power of mathematical models alone, or statistical models alone, is limited. More accurate and versatile personalization tools can be constructed by a new application of the statistical/mathematical nonlinear mixed effects modeling (NLMEM) approach, which until recently has been used only in drug development. Using these advanced tools, clinical data from patient populations can be integrated with mechanistic models of disease and physiology, for generating personal mathematical models. Upon a more substantial validation in the clinic, this approach will hopefully be applied in personalized clinical trials, P-trials, hence aiding the establishment of personalized medicine within the main stream of clinical oncology.

Personalizing immunotherapy: Balancing predictability and precision.

Despite great expectations and research efforts, anticancer immunotherapy has not yet become a definitive cure. Perhaps, this is because past reductionist approaches were too simplistic for the patient-specific complex system of co-evolving tumor cells and host immunity. Recent efforts based on a systems-based approach promise improved clinical outcomes engendered by a dynamic modification of personalized therapeutic regimens.

Analyzing transformation of myelodysplastic syndrome to secondary acute myeloid leukemia using a large patient database.

One-third of patients with myelodysplastic syndrome (MDS) progress to secondary acute myeloid leukemia (sAML), with its concomitant poor prognosis. Recently, multiple mutations have been identified in association with MDS-to-sAMLtransition, but it is still unclear whether all these mutations are necessary for transformation. If multiple independent mutations are required for the transformation, sAML risk should increase with time from MDS diagnosis. In contrast, if a single critical biological event determines sAML transformation; its risk should be constant in time elapsing from MDS diagnosis. To elucidate this question, we studied a database of 1079 patients with MDS. We classified patients according to the International Prognostic Scoring System (IPSS), using either the French-American-British (FAB) or the World Health Organization (WHO) criteria, and statistically analyzed the resulting transformation risk curves of each group. The risk of transformation after MDS diagnosis remained constant in time within three out of four risk groups, and in all four risk groups, when patients were classified according to FAB or to the WHO-determined criteria, respectively. Further subdivision by blast percentage or cytogenetics had no influence on this result. Our analysis suggests that a single random biological event leads to transformation to sAML, thus calling for the exclusion of time since MDS diagnosis from the clinical decision-making process.

Reconsidering the paradigm of cancer immunotherapy by computationally aided real-time personalization.

Although therapeutic vaccination often induces markers of tumor-specific immunity, therapeutic responses remain rare. An improved understanding of patient-specific dynamic interactions of immunity and tumor progression, combined with personalized application of immune therapeutics would increase the efficacy of immunotherapy. Here, we developed a method to predict and enhance the individual response to immunotherapy by using personalized mathematical models, constructed in the early phase of treatment. Our approach includes an iterative real-time in-treatment evaluation of patient-specific parameters from the accruing clinical data, construction of personalized models and their validation, model-based simulation of subsequent response to ongoing therapy, and suggestion of potentially more effective patient-specific modified treatment. Using a mathematical model of prostate cancer immunotherapy, we applied our model to data obtained in a clinical investigation of an allogeneic whole-cell therapeutic prostate cancer vaccine. Personalized models for the patients who responded to treatment were derived and validated by data collected before treatment and during its early phase. Simulations, based on personalized models, suggested that an increase in vaccine dose and administration frequency would stabilize the disease in most patients. Together, our findings suggest that application of our method could facilitate development of a new paradigm for studies of in-treatment personalization of the immune agent administration regimens (P-trials), with treatment modifications restricted to an approved range, resulting in more efficacious immunotherapies.

A new validated mathematical model of the Wnt signalling pathway predicts effective combinational therapy by sFRP and Dkk.

The Wnt signalling pathway controls cell proliferation and differentiation, and its deregulation is implicated in different diseases including cancer. Learning how to manipulate this pathway could substantially contribute to the development of therapies. We developed a mathematical model describing the initial sequence of events in the Wnt pathway, from ligand binding to ß-catenin accumulation, and the effects of inhibitors, such as sFRPs (secreted Frizzled-related proteins) and Dkk (Dickkopf). Model parameters were retrieved from experimental data reported previously. The model was retrospectively validated by accurately predicting the effects of Wnt3a and sFRP1 on ß-catenin levels in two independent published experiments (R(2) between 0.63 and 0.91). Prospective validation was obtained by testing the model's accuracy in predicting the effect of Dkk1 on Wnt-induced ß-catenin accumulation (R(2)≈0.94). Model simulations under different combinations of sFRP1 and Dkk1 predicted a clear synergistic effect of these two inhibitors on ß-catenin accumulation, which may point towards a new treatment avenue. Our model allows precise calculation of the effect of inhibitors applied alone or in combination, and provides a flexible framework for identifying potential targets for intervention in the Wnt signalling pathway.

Strategies for cancer stem cell elimination: insights from mathematical modeling.

The cancer stem cell (CSC) hypothesis states that only a small fraction of a malignant cell population is responsible for tumor growth and relapse. Understanding the relationships between CSC dynamics and cancer progression may contribute to improvements in cancer treatment. Analysis of a simple discrete mathematical model has suggested that homeostasis in developing tissues is governed by a "quorum sensing" control mechanism, in which stem cells differentiate or proliferate according to feedback they receive from neighboring cell populations. Further analysis of the same model has indicated that excessive stem cell proliferation leading to malignant transformation mainly results from altered sensitivity to such micro-environmental signals. Our aim in this work is to expand the analysis to the dynamics of established populations of cancer cells and to examine possible therapeutic avenues for eliminating CSCs. The proposed model considers two populations of cells: CSCs, which can divide indefinitely, and differentiated cancer cells, which do not divide and have a limited lifespan. We assume that total cell density has negative feedback on CSC proliferation and that high CSC density activates CSC differentiation. We show that neither stimulation of CSC differentiation nor inhibition of CSC proliferation alone is sufficient for complete CSC elimination and cancer cure, since each of these two therapies affects a different subpopulation of CSCs. However, a combination of these two strategies can substantially reduce the population sizes and densities of all types of cancer cells. Therefore, we propose that in clinical trials, CSC differentiation therapy should only be examined in combination with chemotherapy. Our conclusions are corroborated by clinical experience with differentiating agents in acute promyelocytic leukemia and neuroblastoma.

An integrated disease/pharmacokinetic/pharmacodynamic model suggests improved interleukin-21 regimens validated prospectively for mouse solid cancers.

Interleukin (IL)-21 is an attractive antitumor agent with potent immunomodulatory functions. Yet thus far, the cytokine has yielded only partial responses in solid cancer patients, and conditions for beneficial IL-21 immunotherapy remain elusive. The current work aims to identify clinically-relevant IL-21 regimens with enhanced efficacy, based on mathematical modeling of long-term antitumor responses. For this purpose, pharmacokinetic (PK) and pharmacodynamic (PD) data were acquired from a preclinical study applying systemic IL-21 therapy in murine solid cancers. We developed an integrated disease/PK/PD model for the IL-21 anticancer response, and calibrated it using selected "training" data. The accuracy of the model was verified retrospectively under diverse IL-21 treatment settings, by comparing its predictions to independent "validation" data in melanoma and renal cell carcinoma-challenged mice (R(2)>0.90). Simulations of the verified model surfaced important therapeutic insights: (1) Fractionating the standard daily regimen (50 µg/dose) into a twice daily schedule (25 µg/dose) is advantageous, yielding a significantly lower tumor mass (45% decrease); (2) A low-dose (12 µg/day) regimen exerts a response similar to that obtained under the 50 µg/day treatment, suggestive of an equally efficacious dose with potentially reduced toxicity. Subsequent experiments in melanoma-bearing mice corroborated both of these predictions with high precision (R(2)>0.89), thus validating the model also prospectively in vivo. Thus, the confirmed PK/PD model rationalizes IL-21 therapy, and pinpoints improved clinically-feasible treatment schedules. Our analysis demonstrates the value of employing mathematical modeling and in silico-guided design of solid tumor immunotherapy in the clinic.

Dickkopf1 regulates fate decision and drives breast cancer stem cells to differentiation: an experimentally supported mathematical model.

BACKGROUND: Modulation of cellular signaling pathways can change the replication/differentiation balance in cancer stem cells (CSCs), thus affecting tumor growth and recurrence. Analysis of a simple, experimentally verified, mathematical model suggests that this balance is maintained by quorum sensing (QS). METHODOLOGY/PRINCIPAL FINDINGS: To explore the mechanism by which putative QS cellular signals in mammary stem cells (SCs) may regulate SC fate decisions, we developed a multi-scale mathematical model, integrating extra-cellular and intra-cellular signal transduction within the mammary tissue dynamics. Preliminary model analysis of the single cell dynamics indicated that Dickkopf1 (Dkk1), a protein known to negatively regulate the Wnt pathway, can serve as anti-proliferation and pro-maturation signal to the cell. Simulations of the multi-scale tissue model suggested that Dkk1 may be a QS factor, regulating SC density on the level of the whole tissue: relatively low levels of exogenously applied Dkk1 have little effect on SC numbers, whereas high levels drive SCs into differentiation. To verify these model predictions, we treated the MCF-7 cell line and primary breast cancer (BC) cells from 3 patient samples with different concentrations and dosing regimens of Dkk1, and evaluated subsequent formation of mammospheres (MS) and the mammary SC marker CD44(+)CD24(lo). As predicted by the model, low concentrations of Dkk1 had no effect on primary BC cells, or even increased MS formation among MCF-7 cells, whereas high Dkk1 concentrations decreased MS formation among both primary BC cells and MCF-7 cells. CONCLUSIONS/SIGNIFICANCE: Our study suggests that Dkk1 treatment may be more robust than other methods for eliminating CSCs, as it challenges a general cellular homeostasis mechanism, namely, fate decision by QS. The study also suggests that low dose Dkk1 administration may be counterproductive; we showed experimentally that in some cases it can stimulate CSC proliferation, although this needs validating in vivo.