Shaping the AML Treatment Landscape:Modeling a Path through Plenty, Uncertainty, and Paucity

The last two decades have identified and characterized heterogeneities arising in the genetic structure of the bone marrow malignancy, acute myeloid leukemia (AML), to partly explain the variation in outcomes among similarly treated patients.[1] In high-income countries, treatment paradigms for AML have now shifted to include conventional chemotherapy and/or small molecule drugs directed against biological targets, deemed disease-defining.[1] [2] [3] Apart from the acute promyelocytic leukemia variant,[4] however, AML remains incurable for a significant number of patients within different disease subgroups. In addition, the incremental survival gain with small molecule drugs is relatively modest,[2] [3] [5] and the costs associated with therapy, supportive care, and disease-monitoring remain considerable. In low-and middle-income countries, financial constraints often render therapies, considered “standard-of-care” in higher income countries, prohibitively expensive.[6] Increasingly, the rarity of biological subtypes of AML[1] and the availability of multiple drugs targeting unique disease sub-types[2] [5] [7] [8] are also beginning to present challenges to the design of contemporaneous clinical trials. To optimize clinical benefits and the cost-effectiveness of therapy to patients and healthcare systems, as well as to address key clinical hypotheses, an innovative approach for hypothesis testing and identifying best therapy is, therefore, required.In recent years, the pharmaceutical industry and regulators have increasingly turned to modeling and simulation to investigate drug–drug interactions,[9] assess the exposure and toxicological impacts of various compounds,[10] [11] and reduce reliance on animal experiments for identifying new products.[12] In contrast, physicians have depended solely on the statistical output of adequately powered clinical trials to guide treatment decisions. The existence of clinical trial data and associated publicly available genomic datasets, along with increasingly sophisticated mathematical and computational methodologies, presents a significant opportunity to make progress in the challenging arena of AML therapeutics. Here, we highlight three problem areas relevant to the therapy or monitoring of AML that could benefit from an integrated biological and mathematical approach.<br/

Shaping the AML Treatment Landscape:Modeling a Path through Plenty, Uncertainty, and Paucity

The last two decades have identified and characterized heterogeneities arising in the genetic structure of the bone marrow malignancy, acute myeloid leukemia (AML), to partly explain the variation in outcomes among similarly treated patients.[1] In high-income countries, treatment paradigms for AML have now shifted to include conventional chemotherapy and/or small molecule drugs directed against biological targets, deemed disease-defining.[1] [2] [3] Apart from the acute promyelocytic leukemia variant,[4] however, AML remains incurable for a significant number of patients within different disease subgroups. In addition, the incremental survival gain with small molecule drugs is relatively modest,[2] [3] [5] and the costs associated with therapy, supportive care, and disease-monitoring remain considerable. In low-and middle-income countries, financial constraints often render therapies, considered “standard-of-care” in higher income countries, prohibitively expensive.[6] Increasingly, the rarity of biological subtypes of AML[1] and the availability of multiple drugs targeting unique disease sub-types[2] [5] [7] [8] are also beginning to present challenges to the design of contemporaneous clinical trials. To optimize clinical benefits and the cost-effectiveness of therapy to patients and healthcare systems, as well as to address key clinical hypotheses, an innovative approach for hypothesis testing and identifying best therapy is, therefore, required.In recent years, the pharmaceutical industry and regulators have increasingly turned to modeling and simulation to investigate drug–drug interactions,[9] assess the exposure and toxicological impacts of various compounds,[10] [11] and reduce reliance on animal experiments for identifying new products.[12] In contrast, physicians have depended solely on the statistical output of adequately powered clinical trials to guide treatment decisions. The existence of clinical trial data and associated publicly available genomic datasets, along with increasingly sophisticated mathematical and computational methodologies, presents a significant opportunity to make progress in the challenging arena of AML therapeutics. Here, we highlight three problem areas relevant to the therapy or monitoring of AML that could benefit from an integrated biological and mathematical approach.<br/

Signal propagation in sensing and reciprocating cellular systems with spatial and structural heterogeneity

International audienceSensing and reciprocating cellular systems (SARs) are important for the operation of many biological systems. Production in interferon (IFN) SARs is achieved through activation of the Jak-Stat pathway, and downstream upregulation of IFN regulatory factor (IRF)-7 and IFN transcription, but the role that high-and low-affinity IFNs play in this process remains unclear. We present a comparative between a minimal spatio-temporal partial differential equation model and a novel spatio-structural-temporal (SST) model for the consideration of receptor, binding, and metabolic aspects of SAR behaviour. Using the SST framework, we simulate single-and multi-cluster paradigms of IFN communication. Simulations reveal a cyclic process between the binding of IFN to the receptor, and the consequent increase in metabolism, decreasing the propensity for binding due to the internal feedback mechanism. One observes the effect of heterogeneity between cellular clusters, allowing them to individualise and increase local production, and within clusters, where we observe 'subpopular quiescence'; a process whereby intra-cluster subpopulations reduce their binding and metabolism such that other such subpopulations may augment their production. Finally, we observe the ability for low-affinity IFN to communicate a long range signal, where high affinity cannot, and the breakdown of this relationship through the introduction of cell motility. Biological systems may utilise cell motility where environments are unrestrictive and may use fixed system, with low affinity communication, where a localised response is desirable

Social Networking and Population Growth - A complex mathematical relationship

International audienceGrowth and disease transmission rates within human populations are continuously changing and will be of increasing importance over thecoming decades. The modelling of social network construction in pair- bonding species is, therefore, necessary for understanding how connectionbetween individuals influence these critical dyanmics. The established and accepted Ecological Constraints model hypothesises that nonlinear and constrained population growth occurs as a function of competition for limited ecological resources. Meanwhile, existing Markovian models of population growth have not yet explored the dynamics of pair formation within such species and, as such, the effect of these dynamics on population growth. These simpler Markovian models, however, have been rigorously analysed and present an appropriate framework for further mathematical exploration. We propose a novel nonlinear Markovian model to explore the effect of mutual pair-bonding on population growth and embed this model within the novel Dynamic Markovian Ecological Network (DyME-Net) model to explore how subdivision may overcome these nonlinearities. We explore the hypothesis that nonlinear population growth within pair-bonding species could be explained by the probabilistic functions of mate choice, even in the absence of ecological constraints

Computational Model of Heterogeneity in Melanoma:Designing Therapies and Predicting Outcomes

International audienceCutaneous melanoma is a highly invasive tumor and, despite the development of recent therapies, most patients with advanced metastatic melanoma have a poor clinical outcome. The most frequent mutations in melanoma affect the BRAF oncogene, a protein kinase of the MAPK signaling pathway. Therapies targeting both BRAF and MEK are effective for only 50% of patients and, almost systematically, generate drug resistance. Genetic and non-genetic mechanisms associated with the strong heterogeneity and plasticity of melanoma cells have been suggested to favor drug resistance but are still poorly understood. Recently, we have introduced a novel mathematical formalism allowing the representation of the relation between tumor heterogeneity and drug resistance and proposed several models for the development of resistance of melanoma treated with BRAF/MEK inhibitors. In this paper, we further investigate this relationship by using a new computational model that copes with multiple cell states identified by single cell mRNA sequencing data in melanoma treated with BRAF/MEK inhibitors. We use this model to predict the outcome of different therapeutic strategies. The reference therapy, referred to as “continuous” consists in applying one or several drugs without disruption. In “combination therapy”, several drugs are used sequentially. In “adaptive therapy” drug application is interrupted when the tumor size is below a lower threshold and resumed when the size goes over an upper threshold. We show that, counter-intuitively, the optimal protocol in combination therapy of BRAF/MEK inhibitors with a hypothetical drug targeting cell states that develop later during the tumor response to kinase inhibitors, is to treat first with this hypothetical drug. Also, even though there is little difference in the timing of emergence of the resistance between continuous and adaptive therapies, the spatial distribution of the different melanoma subpopulations is more zonated in the case of adaptive therapy

Computational Approaches and Analysis for a Spatio-Structural-Temporal Invasive Carcinoma Model

Spatio-temporal models have long been used to describe biological systems of cancer, but it has not been until very recently that increased attention has been paid to structural dynamics of the interaction between cancer populations and the molecular mechanisms associated with local invasion. One system that is of particular interest is that of the urokinase plasminogen activator (uPA) wherein uPA binds uPA receptors on the cancer cell surface, allowing plasminogen to be cleaved into plasmin, which degrades the extracellular matrix and this way leads to enhanced cancer cell migration. In this paper, we develop a novel numerical approach and associated analysis for spatio-structuro-temporal modelling of the uPA system for up to two-spatial and two-structural dimensions. This is accompanied by analytical exploration of the numerical techniques used in simulating this system, with special consideration being given to the proof of stability within numerical regimes encapsulating a central differences approach to approximating numerical gradients. The stability analysis performed here reveals instabilities induced by the coupling of the structural binding and proliferative processes. The numerical results expound how the uPA system aids the tumour in invading the local stroma, whilst the inhibitor to this system may impede this behaviour and encourage a more sporadic pattern of invasion.PostprintPeer reviewe