Mechanism-based Mathematical Model Research Articles

Sialic Acid Mediated Endothelial and Hepatic Uptake: A Mechanism based Mathematic Model Elucidating the Complex Pharmacokinetics and Pharmacodynamics of Efmarodocokin Alfa, a Variably Glycosylated Fusion Protein

Sialic acid (SA) is crucial for protecting glycoproteins from clearance. Efmarodocokin alfa (IL-22Fc), a fusion protein agonist that links IL-22 to the crystallizable fragment (Fc) of human IgG4, contains 8 N-glycosylation sites and exhibits heterogeneous and variable terminal sialylation biodistribution. This presents a unique challenge for Pharmacokinetic (PK) and Pharmacodynamic (PD) analysis and cross-species translation. In this study, we sought to understand how varying SA levels and heterogeneous distribution contribute to IL-22Fc's complex PKPD properties. We initially used homogenous drug material with varying SA levels to examine PKPD in mice. Population PKPD analysis based on mouse data revealed that SA was a critical covariate simultaneously accounting for the substantial between subject variability (BSV) in clearance (CL), distribution clearance (CLd), and volume of distribution (Vd). In addition to the well-established mechanism by which SA inhibits ASGPR activity, we hypothesized a novel mechanism by which decrease in SA increases the drug uptake by endothelial cells. This decrease in SA, leading to more endothelial uptake, was supported by the neonatal Fc receptor (FcRn) dependent cell-based transcytosis assay. The population analysis also suggested in vivo EC50 (IL-22Fc stimulating Reg3β) was independent on SA, while the in-vitro assay indicated a contradictory finding of SA-in vitro potency relationship. We created a mechanism based mathematical (MBM) PKPD model incorporating the decrease in SA mediated endothelial and hepatic uptake, and successfully characterized the SA influence on IL-22Fc PK, as well as the increased PK exposure being responsible for increased PD. Thereby, the MBM model supported that SA has no direct impact on EC50, aligning with the population PKPD analysis. Subsequently, using the MBM PKPD model, we employed 5 subpopulation simulations to reconstitute the heterogeneity of drug material. The simulation accurately predicted the PKPD of heterogeneously and variably sialylated drug in mouse, monkey and human. The successful prospective validation confirmed the MBM's ability to predict IL-22Fc PK across variable SA levels, homogenous to heterogeneous material, and across species (R2=0.964 for clearance prediction). Our model prediction suggests an average of 1 mol/mol SA increase leads to a 50% increase in drug exposure. This underlines the significance of controlling sialic acid levels during lot-to-lot manufacturing.

A mechanism-based pathway toward administering highly active N-phage cocktails.

Bacteriophage (phage) therapy is being explored as a possible response to the antimicrobial resistance public health emergency. Administering a mixture of different phage types as a cocktail is one proposed strategy for therapeutic applications, but the optimal method for formulating phage cocktails remains a major challenge. Each phage strain has complex pharmacokinetic/pharmacodynamic (PK/PD) properties which depend on the nano-scale size, target-mediated, self-dosing nature of each phage strain, and rapid selection of resistant subpopulations. The objective of this study was to explore the pharmacodynamics (PD) of three unique and clinically relevant anti-Pseudomonas phages after simulation of dynamic dosing strategies. The Hollow Fiber Infection Model (HFIM) is an in vitro system that mimics in vivo pharmacokinetics (PK) with high fidelity, providing an opportunity to quantify phage and bacteria concentration profiles over clinical time scales with rich sampling. Exogenous monotherapy-bolus (producing max concentrations of Cmax = 7 log10 PFU/mL) regimens of phages LUZ19, PYO2, and E215 produced Pseudomonas aeruginosa nadirs of 0, 2.14, or 2.99 log10 CFU/mL after 6 h of treatment, respectively. Exogenous combination therapy bolus regimens (LUZ19 + PYO2 or LUZ19 + E215) resulted in bacterial reduction to <2 log10 CFU/mL. In contrast, monotherapy as a continuous infusion (producing a steady-state concentration of Css,avg = 2 log10PFU/mL) was less effective at reducing bacterial densities. Specifically, PYO2 failed to reduce bacterial density. Next, a mechanism-based mathematical model was developed to describe phage pharmacodynamics, phage-phage competition, and phage-dependent adaptive phage resistance. Monte Carlo simulations supported bolus dose regimens, predicting lower bacterial counts with bolus dosing as compared to prolonged phage infusions. Together, in vitro and in silico evaluation of the time course of phage pharmacodynamics will better guide optimal patterns of administration of individual phages as a cocktail.

Mechanism-based mathematical modeling of ethanol and acamprosate effects on the stress circuit chemistry and the functional dynamics of the HPA axis

Mechanism-based mathematical modeling of ethanol and acamprosate effects on the stress circuit chemistry and the functional dynamics of the HPA axis

Model-Agnostic Personalized Knowledge Adaptation for Soft Exoskeleton Robot

Personalized control strategies can improve the overall performance of exoskeleton robots by providing adaptive assistance to different individuals. However, current personalized strategies require accurate models or large amounts of training data, which are not suitable for soft exoskeletons due to human-robot interaction uncertainties and low data acquisition efficiency. This paper presents a framework of Model-Agnostic Personalized Knowledge Adaptation (MPKA) consisting of two modules of Soft-to-Rigid Kinematics Model (SRKM) and Data-Driven Personalized Adaptation (DDPA) to generate a personalized strategy. Specifically, the first SRKM module is used to simplify and convert uncertain and time-varying HRI model to a certain and fixed model. The second DDPA module is used to accelerate model adaptation to new individuals using meta-learning with less data, based on the learned knowledge from the previous subjects. The experiments were conducted on three different sized platforms, four healthy and one post-stroke subjects, respectively. The results demonstrate that the MPKA can generate personalized models for new individuals more rapidly with less data than a pre-trained neural network, and the personalized models can obtain better control accuracy by over 62% than mechanism-based mathematical model. The proposed method has the potential to provide personalized rehabilitation strategies, which can improve effectiveness of rehabilitation.

Computational Model of Noradrenaline Modulation of Astrocyte Responses to Synaptic Activity

The mathematical modeling of synaptically connected neuronal networks is an established instrument for gaining insights into dynamics of neuronal ensembles and information processing in the nervous system. Recently, calcium signaling in astrocytes—glial cells controlling local tissue metabolism and synapse homeostasis—and its corresponding downstream effect on synaptic plasticity and neuromodulation appeared in the limelight of modeling studies. Here, we used mechanism-based mathematical modeling to disentangle signaling pathways and feedback loops in the astrocytic calcium response to noradrenaline, an important neuromodulator marking periods of heightened alertness and arousal. The proposed model is based on an experiment-based 2D representation of astrocyte morphology, discrete random glutamate synapses with placement probability defined by the morphology pattern, and spatially heterogeneous noradrenaline sources, reflecting axonal varicosities of the adrenergic axons. Both glutamate and noradrenaline drive Ca2+ dynamics in the astrocyte in an additive or synergistic manner. Our simulations replicate the global activation of astrocytes by noradrenaline and predict the generation of high-frequency Ca2+ waves in a dose-dependent manner and the preferred Ca2+ wave origination near noradrenaline release sites if they colocalise with high-density clusters of glutamate synapses. We tested positive feedback loops between noradrenaline release and glutamate spillover directly or mediated by gliotransmitter release from the activated astrocyte. The simulations suggest that the coupled stochastic drive by glutamate and noradrenaline release converges on the graded modulation of the IP3 level, which is translated into whole-cell Ca2+ waves of different frequencies. Thus, the proposed approach is supported by experimental data and can be used to address situations inaccessible directly by experiment, and is a starting point for a more detailed model that includes other signaling mechanisms providing negative feedback.

Abstract 2736: Forecasting treatment response to neoadjuvant therapy in triple-negative breast cancer via an image-guided digital twin

Abstract Introduction: Patients with locally advanced, triple-negative breast cancer (TNBC) typically receive neoadjuvant therapy (NAT) to downstage the tumor and to improve the outcome of subsequent breast conservation surgery. There are currently no methods to accurately predict how a TNBC patient will respond to NAT before surgery. In this work, we applied a digital twin framework to address this unmet clinical need, by integrating quantitative magnetic resonance imaging (MRI) data with mechanism-based mathematical modeling. Methods: Multiparametric MRI was acquired in patients (N = 50) before, after 2 and 4 cycles of Adriamycin/Cyclophosphamide (A/C), and again after 12 cycles of Paclitaxel as part of the ARTEMIS (NCT02276433) trial. Within each imaging session, dynamic contrast-enhanced (DCE) MRI, diffusion-weighted imaging (DWI), and a pre-contrast T1-map were acquired. The images were processed by a pipeline consisting of motion correction, multiparametric image alignment, inter-visit image registration to align the tumor and surrounding breast tissue, tissue segmentation, and estimation of tumor cellularity from DWI. A mechanism-based mathematical model, a reaction-diffusion equation, is used to characterize the mobility of tumor cells via diffusion damped by mechanical tissue properties, tumor proliferation via logistic growth, and treatment-induced cell death via the delivery and decay of therapies. For each patient, pre-treatment images were used for model initialization. The model calibration and prediction were implemented with two strategies: 1) using images acquired during the A/C for calibration and predicting up to the end of A/C, and 2) using images acquired during and after the A/C for calibration and predicting up to the end of NAT. For strategy 1), we evaluated the model by comparing its predicted tumor volume and total tumor cellularity to the imaging measurements at the end of A/C. For strategy 2), we evaluated the model by comparing its predicted final response to the post-surgical pathological findings. Results: For strategy 1), our framework predicted the change of tumor volume and total tumor cellularity with Pearson correlation coefficients of 0.91 and 0.89, respectively. Regarding strategy 2), our framework achieved an area under the receiver operator characteristic curve of 0.88 for distinguishing pCR from non-pCR. As a comparison, imaging measurement of tumor volume at the end of A/C achieved an AUC of 0.79. Conclusion: Our approach successfully captures the patient-specific dynamics of TNBC response to NAT and provides an improved prediction of final response, which demonstrates the potential of a digital twin framework to be a powerful tool for predicting response to NAT. Once validated, the method will provide a unique opportunity for optimizing treatment plans on a patient-specific basis. Citation Format: Chengyue Wu, Angela M. Jarrett, Zijian Zhou, Nabil Elshafeey, Beatriz E. Adrada, Rosalind P. Candelaria, Rania Mohamed, Medine Boge, Lei Huo, Jason White, Debu Tripathy, Vicente Valero, Jennifer Litton, Clinton Yam, Jong Bum Son, Jingfei Ma, Gaiane M. Rauch, Thomas E. Yankeelov. Forecasting treatment response to neoadjuvant therapy in triple-negative breast cancer via an image-guided digital twin [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 2736.

Applications of Quantitative Systems Pharmacology (QSP) in Drug Development for NAFLD and NASH and Its Regulatory Application

Nonalcoholic steatohepatitis (NASH) is a widely prevalent disease, but approved pharmaceutical treatments are not available. As such, there is great activity within the pharmaceutical industry to accelerate drug development in this area and improve the quality of life and reduce mortality for NASH patients. The use of quantitative systems pharmacology (QSP) can help make this overall process more efficient. This mechanism-based mathematical modeling approach describes both the pathophysiology of a disease and how pharmacological interventions can modify pathophysiologic mechanisms. Multiple capabilities are provided by QSP modeling, including the use of model predictions to optimize clinical studies. The use of this approach has grown over the last 20 years, motivating discussions between modelers and regulators to agree upon methodologic standards. These include model transparency, documentation, and inclusion of clinical pharmacodynamic biomarkers. Several QSP models have been developed that describe NASH pathophysiology to varying extents. One specific application of NAFLDsym, a QSP model of NASH, is described in this manuscript. Simulations were performed to help understand if patient behaviors could help explain the relatively high rate of fibrosis stage reductions in placebo cohorts. Simulated food intake and body weight fluctuated periodically over time. The relatively slow turnover of liver collagen allowed persistent reductions in predicted fibrosis stage despite return to baseline for liver fat, plasma ALT, and the NAFLD activity score. Mechanistic insights such as this that have been derived from QSP models can help expedite the development of safe and effective treatments for NASH patients.

Abstract P1-08-08: Forecasting treatment response to neoadjuvant systemic therapy in triple negative breast cancer viamathematical modeling and quantitative MRI

Abstract Introduction:. Patients with locally advanced triple-negative breast cancer (TNBC) typically receive neoadjuvant therapy (NAT) to downstage the tumor and to improve the outcome of the subsequent breast conservation surgery. A critical unmet need is the lack of a method to accurately predict how a patient with TNBC will respond to NAT before surgery. In this work, we applied a clinical-computational framework to predict response of TNBC early in the course of NAT, by integrating quantitative MRI with mechanism-based mathematical modeling. Methods:. Patients and Data. Multiparametric quantitative MRI was acquired in patients (n = 46) before, and after 2 and 4 cycles of Adriamycin/Cyclophosphamide (A/C) regimen as part of the MD Anderson Cancer Center TNBC Moonshot Program. Within each imaging session, dynamic contrast-enhanced (DCE-), diffusion-weighted imaging (DWI), and a pre-contrast T1-map were acquired. Image processing. The processing pipeline consisted of three components. First, the images within each visit were registered to account for patient motion, and the parametric maps from the DCE and DWI images were computed. Second, inter-visit image registration was achieved by a non-rigid registration applied on breast, with a rigid penalty applied on the tumor region to preserve its size and shape. Third, post-processing was performed for preparation of modeling, including segmentation of the breast contour and tissues, and calculation of voxel-wise cellularity within tumors. Mathematical modeling. A predictive model was developed based on a reaction-diffusion equation (Eq. 1). The mobility of tumor cells is represented by diffusion coupled to mechanical properties of the tissue (Eq. 2), and the proliferation of the tumor is described with logistic growth. The injection and decay of administered therapies, inducing tumor cell death, is also represented in the model (Eq. 3). The variables and parameters used are listed in Table 1. Eq. 1: ∂N(x,t)/∂t = ∇⋅(D(x,t) ∇N(x,t)) + k(x) (1 - N(x,t)/θ)N(x,t) - (λ1(x,t) + λ2(x,t))N(x,t). Eq. 2: D(x,t) = D0 e-γσ(x,t). Eq. 3: λn(x,t) = αne-βn t C(x,t), n = 1, 2. For each patient, the domain and initial condition were generated from the pre-treatment images, and the images acquired during NAT were used for patient-specific calibration of parameters. The calibrated model was then used to predict the response to be observed at the end of NAT. We evaluated the model by comparing its predictions of tumor volume, longest axis, voxel-wise cellularity, and total tumor cellularity to the imaging measurements at the end of A/C. Results:. Our model predicted the tumor volume, total cellularity, and longest axis with a Pearson correlation coefficient (PCC) of 0.85, 0.80, and 0.60, respectively. The accuracy of voxel-wise cellularity achieved a PCC with the median (range) of 0.89 (0.77 - 0.93) between the prediction and the actual measurement. Moreover, we set criteria of 70% shrinkage of tumor volume to define response versus non-response cases, with which our model achieved a differentiation sensitivity/specificity of 0.90/0.73. Discussion:. Preliminary results of our study demonstrate the potential of the clinical-computational framework as a powerful tool for predicting response to NAT. Once validated, the method could also assist in optimizing treatment plans on a patient specific basis, or guiding patient selection in trials for novel NAT regimens. Table 1. Summary of the variables and parameters in the modelQuantitiesDefinition AssignmentDomainsΩbreast tissue domainGenerated from pre-treatment MRITEnd time point of NAT procedureDetermined from NAT schedulexCoordinate in breast tissueAssociated with spatial domain, ΩttimeAssociated with temporal domain, [0, T]VariablesN(x,t)Tumor cell numberInitialized from pre-treatment ADC, computed via Eq. 1D(x,t)Diffusive mobility of tumor cellsComputed via Eq. 2λn(x,t)Death rate induced by nth type of drugComputed via Eq. 3, n = 1 and 2 for A/Cσ(x,t)Von Mises stressComputed from gradient of N(x,t), based on Hormuth et al., 2018C(x,t)Spatiotemporal distribution of drugsAssigned based on NAT schedule and DCE imagesParametersk(x)Proliferation rate of tumor cellsLocally calibratedθTumor cells carry capacityGlobally calibratedαnEfficacy rate of nth type of drugGlobally calibratedβnDecay rate of of nth type of drugGlobally calibratedD0Diffusion coefficient of tumor cells in the absence of mechanical restrictionsGlobally calibratedγStress-tumor cell diffusion coupling constantAssigned based on Hormuth et al., 2018 Citation Format: Chengyue Wu, Angela M. Jarrett, Zijian Zhou, Nabil Elshafeey, Beatriz E. Adrada, Rosalind P. Candelaria, Rania M. Mohamed, Medine Boge, Lei Huo, Jason White, Debu Tripathy, Vicente Valero, Jennifer Litton, Stacy Moulder, Clinton Yam, Jong Bum Son, Jingfei Ma, Gaiane M. Rauch, Thomas E. Yankeelov. Forecasting treatment response to neoadjuvant systemic therapy in triple negative breast cancer viamathematical modeling and quantitative MRI [abstract]. In: Proceedings of the 2021 San Antonio Breast Cancer Symposium; 2021 Dec 7-10; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2022;82(4 Suppl):Abstract nr P1-08-08.

Abstract P5-05-06: Metformin concentration is a deciding factor of its pro- or anti-tumor function in triple negative breast cancer

Abstract We have previously reported that triple negative (TN) breast cancer (BC), an aggressive subtype of BC, has high dependency for mitochondrial fatty acid oxidation (FAO). We have also reported that FAO activates c-Src, one of the frequently upregulated oncopathways in TNBC. Our mechanism-based mathematical model of cancer metabolism by coupling the master gene regulators (AMPK, HIF-1) suggested that the combination of mitochondrial electron transport chain (ETC) and FAO repressions acquire the highest efficacy in suppressing the bioenergetics (i.e., cellular ATP production) of the TNBC cells. Biguanides such as metformin are one of the most widely administered anti-diabetic agents. Phenformin, a biguanide derivative similar to metformin, has greater potency than metformin. Both these drugs have been widely studied for their antitumor activities but showed only limited clinical advantages in BC. Biguanides can suppress oxidative phosphorylation (OXPHOS) by inhibiting the complex-I activity of mitochondrial ETC. However, biguanides also activate the energy sensor AMPK and phosphorylate its downstream protein ACC. Since ACC inhibits the transport of fatty acids to mitochondria, its phosphorylation can lead to FAO activation. Thus, biguanides can play opposing roles in mitochondrial metabolism (suppression of ETC and activation of FAO). Here we have analyzed the significance of these opposing roles of biguanides in TNBC metabolism and oncopathway activation. Molecular biology and RNASeq analyses suggest that while higher concentrations of biguanides suppress ETC activity and Src pathway despite the activation of AMPK, lower concentrations of biguanides activate FAO-driven ETC and Src pathway in TNBC cells. To understand the translational significance of this observation, we have performed preclinical studies using TNBC organoids and patient-derived xenografts (PDX) models. Combination therapy with metformin and FAO inhibitor, etomoxir significantly improved the antitumor activity compared to the single drug therapy. For a better clinically relevant approach, we did preclinical studies using the combination of metformin and Src inhibitor, dasatinib in TNBC organoids and PDX models. As expected, the combination of metformin and dasatinib synergistically inhibited tumor growth and enhanced the overall survival of the mice. Our observations suggested that the tumor bioavailability of biguanides is critical for its anti-tumor activity, especially in FAO-dependent tumors like TNBC. Using metabolomic, genomic and preclinical experiments, we are currently evaluating the translational potential of this findings in FAO-dependent TNBCs. Citation Format: Jun Hyoung Park, Dongya Jia, Sukjin Yang, Kwang Hwa Jung, Abha Tiwari, Debasmita Dutta, Meron Ghidey, Nagireddy Putluri, Cristian Coarfa, Chad Creighton, José N. Onuchic, Benny A Kaipparettu. Metformin concentration is a deciding factor of its pro- or anti-tumor function in triple negative breast cancer [abstract]. In: Proceedings of the 2021 San Antonio Breast Cancer Symposium; 2021 Dec 7-10; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2022;82(4 Suppl):Abstract nr P5-05-06.

KLF4 Induces Mesenchymal-Epithelial Transition (MET) by Suppressing Multiple EMT-Inducing Transcription Factors.

Simple SummaryCancer is expected to be the leading cause of death due to noncommunicable diseases in the 21st century. Cancer-related mortality is largely due to metastasis. Cancer cells undergoing metastasis exhibit Epithelial–Mesenchymal Plasticity where they can transition from an epithelial to mesenchymal (EMT) or from a mesenchymal to epithelial (MET) phenotype. These transitions are crucial for the success of various stages of metastasis. Both these processes are modulated by multiple EMT-inducing and MET-inducing factors acting in concert. While EMT inducers are well-recognized, MET inducers are relatively poorly investigated. Here, we investigated the role of KLF4 through mechanism-based mathematical models and transcriptomic data analysis and identified it to be a potential MET inducer by suppressing one or more EMT inducers directly and/or indirectly.Epithelial–Mesenchymal Plasticity (EMP) refers to reversible dynamic processes where cells can transition from epithelial to mesenchymal (EMT) or from mesenchymal to epithelial (MET) phenotypes. Both these processes are modulated by multiple transcription factors acting in concert. While EMT-inducing transcription factors (TFs)—TWIST1/2, ZEB1/2, SNAIL1/2/3, GSC, and FOXC2—are well-characterized, the MET-inducing TFs are relatively poorly understood (OVOL1/2 and GRHL1/2). Here, using mechanism-based mathematical modeling, we show that transcription factor KLF4 can delay the onset of EMT by suppressing multiple EMT-TFs. Our simulations suggest that KLF4 overexpression can promote a phenotypic shift toward a more epithelial state, an observation suggested by the negative correlation of KLF4 with EMT-TFs and with transcriptomic-based EMT scoring metrics in cancer cell lines. We also show that the influence of KLF4 in modulating the EMT dynamics can be strengthened by its ability to inhibit cell-state transitions at the epigenetic level. Thus, KLF4 can inhibit EMT through multiple parallel paths and can act as a putative MET-TF. KLF4 associates with the patient survival metrics across multiple cancers in a context-specific manner, highlighting the complex association of EMP with patient survival.

Mathematical modelling of the hematopoietic stem cell-niche system: Clonal dominance based on stem cell fitness.

Human blood cell production is maintained by hematopoietic stem cells (HSC) which give rise to all types of mature blood cells. Experimental observation of HSC in their physiologic bone-marrow microenvironment, the so-called stem cell niche, is challenging. Therefore, the details of HSC dynamics and the cellular interactions in the stem cell niche remain elusive. Mutations that lead to a competitive advantage are the cause of clinical challenges when treating HSC-derived malignancies such as acute myeloid leukemia or the myeloproliferative neoplasms (MPNs). To investigate the significance of the interaction between the HSC and the stem cell niche in these malignancies, we propose and analyse a mechanism-based mathematical model of HSC dynamics within the bone-marrow microenvironment. The model is based on the central hypothesis that HSC self-renewal depends on the niche. In the model, the interaction of HSC with specific niches located in the bone marrow are key to the indefinite HSC renewal necessary for long-term maintenance of blood cell production. We formulate a general model of n distinct clones that differ with respect to cell properties. We identify an attractive trapping region and compute and classify all steady states. A concept of HSC fitness naturally arises from the model analysis. HSC fitness is found to determine the asymptotic behaviour of the model, as the HSC clone with the highest fitness is related to the unique locally stable steady state. Based on biological assumptions about HSC, we propose two reduced models of different complexity. A thorough mathematical analysis reveals that both reduced models have the same asymptotic behaviour as the full model. We compare the simpler of the two models, a logistic equation of the disease burden, to clinical data of MPN-patients. The reduced model is found to agree well with data and suggests a simple interpretation and possible prediction of patient prognosis. The proposed mathematical model and the reduced forms have the potential to provide insights into the regulation of HSC dynamics and blood cell formation, and ultimately for future advances in treatment of hematologic malignancies.

Multi-Stability and Consequent Phenotypic Plasticity in AMPK-Akt Double Negative Feedback Loop in Cancer Cells.

Adaptation and survival of cancer cells to various stress and growth factor conditions is crucial for successful metastasis. A double-negative feedback loop between two serine/threonine kinases AMPK (AMP-activated protein kinase) and Akt can regulate the adaptation of breast cancer cells to matrix-deprivation stress. This feedback loop can significantly generate two phenotypes or cell states: matrix detachment-triggered pAMPKhigh/ pAktlow state, and matrix (re)attachment-triggered pAkthigh/ pAMPKlow state. However, whether these two cell states can exhibit phenotypic plasticity and heterogeneity in a given cell population, i.e., whether they can co-exist and undergo spontaneous switching to generate the other subpopulation, remains unclear. Here, we develop a mechanism-based mathematical model that captures the set of experimentally reported interactions among AMPK and Akt. Our simulations suggest that the AMPK-Akt feedback loop can give rise to two co-existing phenotypes (pAkthigh/ pAMPKlow and pAMPKhigh/pAktlow) in specific parameter regimes. Next, to test the model predictions, we segregated these two subpopulations in MDA-MB-231 cells and observed that each of them was capable of switching to another in adherent conditions. Finally, the predicted trends are supported by clinical data analysis of The Cancer Genome Atlas (TCGA) breast cancer and pan-cancer cohorts that revealed negatively correlated pAMPK and pAkt protein levels. Overall, our integrated computational-experimental approach unravels that AMPK-Akt feedback loop can generate multi-stability and drive phenotypic switching and heterogeneity in a cancer cell population.

Hybrid E/M Phenotype(s) and Stemness: A Mechanistic Connection Embedded in Network Topology.

Metastasis remains an unsolved clinical challenge. Two crucial features of metastasizing cancer cells are (a) their ability to dynamically move along the epithelial–hybrid–mesenchymal spectrum and (b) their tumor initiation potential or stemness. With increasing functional characterization of hybrid epithelial/mesenchymal (E/M) phenotypes along the spectrum, recent in vitro and in vivo studies have suggested an increasing association of hybrid E/M phenotypes with stemness. However, the mechanistic underpinnings enabling this association remain unclear. Here, we develop a mechanism-based mathematical modeling framework that interrogates the emergent nonlinear dynamics of the coupled network modules regulating E/M plasticity (miR-200/ZEB) and stemness (LIN28/let-7). Simulating the dynamics of this coupled network across a large ensemble of parameter sets, we observe that hybrid E/M phenotype(s) are more likely to acquire stemness relative to “pure” epithelial or mesenchymal states. We also integrate multiple “phenotypic stability factors” (PSFs) that have been shown to stabilize hybrid E/M phenotypes both in silico and in vitro—such as OVOL1/2, GRHL2, and NRF2—with this network, and demonstrate that the enrichment of hybrid E/M phenotype(s) with stemness is largely conserved in the presence of these PSFs. Thus, our results offer mechanistic insights into recent experimental observations of hybrid E/M phenotype(s) that are essential for tumor initiation and highlight how this feature is embedded in the underlying topology of interconnected EMT (Epithelial-Mesenchymal Transition) and stemness networks.

Evaluating patient-specific neoadjuvant regimens for breast cancer via a mathematical model constrained by quantitative magnetic resonance imaging data

The ability to accurately predict response and then rigorously optimize a therapeutic regimen on a patient-specific basis, would transform oncology. Toward this end, we have developed an experimental-mathematical framework that integrates quantitative magnetic resonance imaging (MRI) data into a biophysical model to predict patient-specific treatment response of locally advanced breast cancer to neoadjuvant therapy. Diffusion-weighted and dynamic contrast-enhanced MRI data is collected prior to therapy, after 1 cycle of therapy, and at the completion of the first therapeutic regimen. The model is initialized and calibrated with the first 2 patient-specific MRI data sets to predict response at the third, which is then compared to patient outcomes (N = 18). The model's predictions for total cellularity, total volume, and the longest axis at the completion of the regimen are significant within expected measurement precision (P< 0.05) and strongly correlated with measured response (P < 0.01). Further, we use the model to investigate, in silico, a range of (practical) alternative treatment plans to achieve the greatest possible tumor control for each individual in a subgroup of patients (N = 13). The model identifies alternative dosing strategies predicted to achieve greater tumor control compared to the standard of care for 12 of 13 patients (P < 0.01). In summary, a predictive, mechanism-based mathematical model has demonstrated the ability to identify alternative treatment regimens that are forecasted to outperform the therapeutic regimens the patients clinically. This has important implications for clinical trial design with the opportunity to alter oncology care in the future.

Integrating Quantitative Assays with Biologically Based Mathematical Modeling for Predictive Oncology.

SummaryWe provide an overview on the use of biological assays to calibrate and initialize mechanism-based models of cancer phenomena. Although artificial intelligence methods currently dominate the landscape in computational oncology, mathematical models that seek to explicitly incorporate biological mechanisms into their formalism are of increasing interest. These models can guide experimental design and provide insights into the underlying mechanisms of cancer progression. Historically, these models have included a myriad of parameters that have been difficult to quantify in biologically relevant systems, limiting their practical insights. Recently, however, there has been much interest calibrating biologically based models with the quantitative measurements available from (for example) RNA sequencing, time-resolved microscopy, and in vivo imaging. In this contribution, we summarize how a variety of experimental methods quantify tumor characteristics from the molecular to tissue scales and describe how such data can be directly integrated with mechanism-based models to improve predictions of tumor growth and treatment response.

Pharmacodynamic modeling of synergistic birinapant/paclitaxel interactions\xa0in pancreatic cancer cells

BackgroundFor most patients, pancreatic adenocarcinoma responds poorly to treatment, and novel therapeutic approaches are needed. Standard-of-care paclitaxel (PTX), combined with birinapant (BRP), a bivalent mimetic of the apoptosis antagonist SMAC (second mitochondria-derived activator of caspases), exerts synergistic killing of PANC-1 human pancreatic adenocarcinoma cells.MethodsTo investigate potential mechanisms underlying this synergistic pharmacodynamic interaction, data capturing PANC-1 cell growth, apoptosis kinetics, and cell cycle distribution were integrated with high-quality IonStar-generated proteomic data capturing changes in the relative abundance of more than 3300 proteins as the cells responded to the two drugs, alone and combined.ResultsPTX alone (15 nM) elicited dose-dependent G2/M-phase arrest and cellular polyploidy. Combined BRP/PTX (150/15 nM) reduced G2/M by 35% and polyploid cells by 45%, and increased apoptosis by 20%. Whereas BRP or PTX alone produced no change in the pro-apoptotic protein pJNK, and a slight increase in the anti-apoptotic protein Bcl2, the drug combination increased pJNK and decreased Bcl2 significantly compared to the vehicle control. A multi-scale, mechanism-based mathematical model was developed to investigate integrated birinapant/paclitaxel effects on temporal profiles of key proteins involved in kinetics of cell growth, death, and cell cycle distribution.ConclusionsThe model, consistent with the observed reduction in the Bcl2/BAX ratio, suggests that BRP-induced apoptosis of mitotically-arrested cells is a major contributor to the synergy between BRP and PTX. Coupling proteomic and cellular response profiles with multi-scale pharmacodynamic modeling provides a quantitative mechanistic framework for evaluating pharmacodynamically-based drug-drug interactions in combination chemotherapy, and could potentially guide the development of promising drug regimens.

Mathematical Modeling of MPNs Offers Understanding and Decision Support for Personalized Treatment.

(1) Background: myeloproliferative neoplasms (MPNs) are slowly developing hematological cancers characterized by few driver mutations, with JAK2V617F being the most prevalent. (2) Methods: using mechanism-based mathematical modeling (MM) of hematopoietic stem cells, mutated hematopoietic stem cells, differentiated blood cells, and immune response along with longitudinal data from the randomized Danish DALIAH trial, we investigate the effect of the treatment of MPNs with interferon-α2 on disease progression. (3) Results: At the population level, the JAK2V617F allele burden is halved every 25 months. At the individual level, MM describes and predicts the JAK2V617F kinetics and leukocyte- and thrombocyte counts over time. The model estimates the patient-specific treatment duration, relapse time, and threshold dose for achieving a good response to treatment. (4) Conclusions: MM in concert with clinical data is an important supplement to understand and predict the disease progression and impact of interventions at the individual level.

Using machine learning to optimize antibiotic combinations: dosing strategies for meropenem and polymyxin B against carbapenem-resistant Acinetobacter baumannii

ObjectivesIncreased rates of carbapenem-resistant strains of Acinetobacter baumannii have forced clinicians to rely upon last-line agents, such as the polymyxins, or empirical, unoptimized combination therapy. Therefore, the objectives of this study were: (a) to evaluate the in vitro pharmacodynamics of meropenem and polymyxin B (PMB) combinations against A. baumannii; (b) to utilize a mechanism-based mathematical model to quantify bacterial killing; and (c) to develop a genetic algorithm (GA) to define optimal dosing strategies for meropenem and PMB. MethodsA. baumannii (N16870; MICmeropenem = 16 mg/L, MICPMB = 0.5 mg/L) was studied in the hollow-fibre infection model (initial inoculum 108 cfu/mL) over 14 days against meropenem and PMB combinations. A mechanism-based model of the data and population pharmacokinetics of each drug were used to develop a GA to define the optimal regimen parameters. ResultsMonotherapies resulted in regrowth to ~1010 cfu/mL by 24 h, while combination regimens employing high-intensity PMB exposure achieved complete bacterial eradication (0 cfu/mL) by 336 h. The mechanism-based model demonstrated an SC50 (PMB concentration for 50% of maximum synergy on meropenem killing) of 0.0927 mg/L for PMB-susceptible subpopulations versus 3.40 mg/L for PMB-resistant subpopulations. The GA had a preference for meropenem regimens that improved the %T > MIC via longer infusion times and shorter dosing intervals. The GA predicted that treating 90% of simulated subjects harbouring a 108 cfu/mL starting inoculum to a point of 100 cfu/mL would require a regimen of meropenem 19.6 g/day 2 h prolonged infusion (2 hPI) q5h + PMB 5.17 mg/kg/day 2 hPI q6h (where the 0 h meropenem and PMB doses should be ‘loaded’ with 80.5% and 42.2% of the daily dose, respectively). ConclusionThis study provides a methodology leveraging in vitro experimental data, a mathematical pharmacodynamic model, and population pharmacokinetics provide a possible avenue to optimize treatment regimens beyond the use of the ‘traditional’ indices of antibiotic action.

Strain-Specific Immune Response to Influenza Virus Infection

A major question in influenza infection pathology is whether viruses of varying virulence invoke distinct immune responses. While efforts have attempted to mathematically characterize the host immune response to influenza virus infection, there has been no previous exploration of strain-specific infection dynamics. Here, a mechanism-based mathematical model is developed and used to compare the immune dynamics invoked by deadly H5N1 and moderately pathogenic H1N1 viruses. Results suggest that the kinetics of the immune response, specifically those related to the virus as well as those involved in interferon production, differ between H1N1 and H5N1 infections. The ability to predict strain differences could aid in clinical understanding of infection severity and take a step towards future application of patient-specific treatment profiles.

Analytical model for the bond stress-slip relationship of deformed bars in normal strength concrete

The lateral confinement provided by concrete cover and stirrups has a significant influence on the bond behavior of reinforcing bars. This paper presents a systematical study on the local bond stress-slip behavior of deformed steel bars based on test results of beam-end specimens and test data reported in the literature. The bond-slip mechanism is discussed in detail and a parameter K representing the confining ability of concrete cover and stirrups is proposed. Through parameter K the bond failure mode can be predicted. With K as the governing parameter, a mathematical model for peak slip is proposed. The proposed model enables a smooth transition from splitting failure to pull-out failure. Furthermore, the nonlinear characteristics of bond stress-slip curves under splitting failure mode, which has not been well recognized in previous studies, are thoroughly discussed. By dividing the post-peak bond stress into two components, a mechanism-based mathematical model for the nonlinear descending branch of bond-slip curves is formulated. Finally, a bond-slip model for deformed steel bars is proposed, which is applicable for both splitting failure and pull-out failure modes. Comparisons with experimental results available in the literature show that the proposed model can provide good predictions for the bond-slip behavior of deformed steel bars with varying confinement levels.