Spatial heterogeneity in drug concentrations can facilitate the emergence of resistance to cancer therapy

Mathematical modeling of the evolution of resistance and aggressiveness of high-grade serous ovarian cancer from patient CA-125 time series

A time-series analysis of serum Cancer Antigen 125 (CA-125) levels was performed in 791 patients with high-grade serous ovarian cancer (HGSOC) from the Australian Ovarian Cancer Study to evaluate the development of chemoresistance and response to therapy. To investigate chemoresistance and better predict the treatment effectiveness, we examined two traits: resistance (defined as the rate of CA-125 change when patients were treated with therapy) and aggressiveness (defined as the rate of CA-125 change when patients were not treated). We found that as the number of treatment lines increases, the data-based resistance increases (a decreased rate of CA-125 decay). We use mathematical models of two distinct cancer cell types, treatment-sensitive cells and treatment-resistant cells, to estimate the values and evolution of the two traits in individual patients. By fitting to individual patient HGSOC data, our models successfully capture the dynamics of the CA-125 level. The parameters estimated from the mathematical models show that patients with inferred low growth rates of treatment-sensitive cells and treatment-resistant cells (low model-estimated aggressiveness) and a high death rate of treatment-resistant cells (low model-estimated resistance) have longer survival time after completing their second-line of therapy. These findings show that mathematical models can characterize the degree of resistance and aggressiveness in individual patients, which improves our understanding of chemoresistance development and could predict treatment effectiveness in HGSOC patients.

Modeling spatial evolution of multi-drug resistance under drug environmental gradients

Multi-drug combinations to treat bacterial populations are at the forefront of approaches for infection control and prevention of antibiotic resistance. Although the evolution of antibiotic resistance has been theoretically studied with mathematical population dynamics models, extensions to spatial dynamics remain rare in the literature, including in particular spatial evolution of multi-drug resistance. In this study, we propose a reaction-diffusion system that describes the multi-drug evolution of bacteria based on a drug-concentration rescaling approach. We show how the resistance to drugs in space, and the consequent adaptation of growth rate, is governed by a Price equation with diffusion, integrating features of drug interactions and collateral resistances or sensitivities to the drugs. We study spatial versions of the model where the distribution of drugs is homogeneous across space, and where the drugs vary environmentally in a piecewise-constant, linear and nonlinear manner. Although in many evolution models, per capita growth rate is a natural surrogate for fitness, in spatially-extended, potentially heterogeneous habitats, fitness is an emergent property that potentially reflects additional complexities, from boundary conditions to the specific spatial variation of growth rates. Applying concepts from perturbation theory and reaction-diffusion equations, we propose an analytical metric for characterization of average mutant fitness in the spatial system based on the principal eigenvalue of our linear problem, λ1. This enables an accurate translation from drug spatial gradients and mutant antibiotic susceptibility traits to the relative advantage of each mutant across the environment. Our approach allows one to predict the precise outcomes of selection among mutants over space, ultimately from comparing their λ1 values, which encode a critical interplay between growth functions, movement traits, habitat size and boundary conditions. Such mathematical understanding opens new avenues for multi-drug therapeutic optimization.

The Impact of Inadequate Exposure to Epidermal Growth Factor Receptor-Tyrosine Kinase Inhibitors on the Development of Resistance in Non-Small-Cell Lung Cancer Cells

Epidermal growth factor receptor (EGFR)-mutant non-small-cell lung cancer (NSCLC) patients treated with EGFR-tyrosine kinase inhibitors (TKIs) inevitably develop resistance through several biological mechanisms. However, little is known on the molecular mechanisms underlying acquired resistance to suboptimal EGFR-TKI doses, due to pharmacodynamics leading to inadequate drug exposure. To evaluate the effects of suboptimal EGFR-TKI exposure on resistance in NSCLC, we obtained HCC827 and PC9 cell lines resistant to suboptimal fixed and intermittent doses of gefitinib and compared them to cells exposed to higher doses of the drug. We analyzed the differences in terms of EGFR signaling activation and the expression of epithelial-mesenchymal transition (EMT) markers, whole transcriptomes byRNA sequencing, and cell motility. We observed that the exposure to low doses of gefitinib more frequently induced a partial EMT associated with an induced migratory ability, and an enhanced transcription of cancer stem cell markers, particularly in the HCC827 gefitinib-resistant cells. Finally, the HCC827 gefitinib-resistant cells showed increased secretion of the EMT inducer transforming growth factor (TGF)-β1, whose inhibition was able to partially restore gefitinib sensitivity. These data provide evidence that different levels of exposure to EGFR-TKIs in tumor masses might promote different mechanisms of acquired resistance.

Competition for resources can reshape the evolutionary properties of spatial structure

Many evolving ecosystems have spatial structures that can be conceptualized as networks, with nodes representing individuals or homogeneous subpopulations and links the patterns of interaction and replacement between them. Prior models of evolution on networks do not take ecological niche differences and eco-evolutionary interplay into account. Here, we combine a resource competition model with evolutionary graph theory to study how heterogeneous topological structure shapes evolutionary dynamics under global frequency-dependent ecological interactions. We find that the addition of ecological competition for resources can produce a reversal of roles between amplifier and suppressor networks for deleterious mutants entering the population. Moreover, we show that this effect is a non-linear function of ecological niche overlap and discuss intuition for the observed dynamics using simulations and analytical approximations.

Redefining clinical practice through spatial profiling: a revolution in tissue analysis

Spatial biology, which combines molecular biology and advanced imaging, enhances our understanding of tissue cellular organisation. Despite its potential, spatial omics encounters challenges related to data complexity, computational requirements and standardisation of analysis. In clinical applications, spatial omics has the potential to revolutionise biomarker discovery, disease stratification and personalised treatments. It can identify disease-specific cell patterns, and could help risk stratify patients for clinical trials and disease-appropriate therapies. Although there are challenges in adopting it in clinical practice, spatial omics has the potential to significantly enhance patient outcomes. In this paper, we discuss the recent evolution of spatial biology, and its potential for improving our tissue level understanding and treatment of disease, to help advance precision and effectiveness in healthcare interventions.

Frequency-dependent ecological interactions increase the prevalence, and shape the distribution, of pre-existing drug resistance

The evolution of resistance remains one of the primary challenges for modern medicine from infectious diseases to cancers. Many of these resistance-conferring mutations often carry a substantial fitness cost in the absence of treatment. As a result, we would expect these mutants to undergo purifying selection and be rapidly driven to extinction. Nevertheless, pre-existing resistance is frequently observed from drug-resistant malaria to targeted cancer therapies in non-small cell lung cancer (NSCLC) and melanoma. Solutions to this apparent paradox have taken several forms from spatial rescue to simple mutation supply arguments. Recently, in an evolved resistant NSCLC cell line, we found that frequency-dependent ecological interactions between ancestor and resistant mutant ameliorate the cost of resistance in the absence of treatment. Here, we hypothesize that frequency-dependent ecological interactions in general play a major role in the prevalence of pre-existing resistance. We combine numerical simulations with robust analytical approximations to provide a rigorous mathematical framework for studying the effects of frequency-dependent ecological interactions on the evolutionary dynamics of pre-existing resistance. First, we find that ecological interactions significantly expand the parameter regime under which we expect to observe pre-existing resistance. Next, even when positive ecological interactions between mutants and ancestors are rare, these resistant clones provide the primary mode of evolved resistance because even weak positive interaction leads to significantly longer extinction times. We then find that even in the case where mutation supply alone is sufficient to predict pre-existing resistance, frequency-dependent ecological forces still contribute a strong evolutionary pressure that selects for increasingly positive ecological effects (negative frequency-dependent selection). Finally, we genetically engineer several of the most common clinically observed resistance mechanisms to targeted therapies in NSCLC, a treatment notorious for pre-existing resistance. We find that each engineered mutant displays a positive ecological interaction with their ancestor. As a whole, these results suggest that frequency-dependent ecological effects can play a crucial role in shaping the evolutionary dynamics of pre-existing resistance.

On minimising tumoural growth under treatment resistance

Drug resistance is a major challenge for curative cancer treatment, representing the main reason of death in patients. Evolutionary biology suggests pauses between treatment rounds as a way to delay or even avoid resistance emergence. Indeed, this approach has already shown promising preclinical and early clinical results, and stimulated the development of mathematical models for finding optimal treatment protocols. Due to their complexity, however, these models do not lend themself to a rigorous mathematical analysis, hence so far clinical recommendations generally relied on numerical simulations and ad-hoc heuristics. Here, we derive two mathematical models describing tumour growth under genetic and epigenetic treatment resistance, respectively, which are simple enough for a complete analytical investigation. First, we find key differences in response to treatment protocols between the two modes of resistance. Second, we identify the optimal treatment protocol which leads to the largest possible tumour shrinkage rate. Third, we fit the "epigenetic model" to previously published xenograft experiment data, finding excellent agreement, underscoring the biological validity of our approach. Finally, we use the fitted model to calculate the optimal treatment protocol for this specific experiment, which we demonstrate to cause curative treatment, making it superior to previous approaches which generally aimed at stabilising tumour burden. Overall, our approach underscores the usefulness of simple mathematical models and their analytical examination, and we anticipate our findings to guide future preclinical and, ultimately, clinical research in optimising treatment regimes.

Modeling the Effect of Spatial Structure on Solid Tumor Evolution and Circulating Tumor DNA Composition

Circulating tumor DNA (ctDNA) monitoring, while sufficiently advanced to reflect tumor evolution in real time and inform cancer diagnosis, treatment, and prognosis, mainly relies on DNA that originates from cell death via apoptosis or necrosis. In solid tumors, chemotherapy and immune infiltration can induce spatially variable rates of cell death, with the potential to bias and distort the clonal composition of ctDNA. Using a stochastic evolutionary model of boundary-driven growth, we study how elevated cell death on the edge of a tumor can simultaneously impact driver mutation accumulation and the representation of tumor clones and mutation detectability in ctDNA. We describe conditions in which invasive clones are over-represented in ctDNA, clonal diversity can appear elevated in the blood, and spatial bias in shedding can inflate subclonal variant allele frequencies (VAFs). Additionally, we find that tumors that are mostly quiescent can display similar biases but are far less detectable, and the extent of perceptible spatial bias strongly depends on sequence detection limits. Overall, we show that spatially structured shedding might cause liquid biopsies to provide highly biased profiles of tumor state. While this may enable more sensitive detection of expanding clones, it could also increase the risk of targeting a subclonal variant for treatment. Our results indicate that the effects and clinical consequences of spatially variable cell death on ctDNA composition present an important area for future work.

Advancements in Preclinical Models of Pancreatic Cancer

ABSTRACT

Pancreatic cancer remains one of the deadliest of all cancer types with a 5-year overall survival rate of just 12%. Preclinical models available for understanding the disease pathophysiology have evolved significantly in recent years. Traditionally, commercially available 2-dimensional cell lines were developed to investigate mechanisms underlying tumorigenesis, metastasis, and drug resistance. However, these cells grow as monolayer cultures that lack heterogeneity and do not effectively represent tumor biology. Developing patient-derived xenografts and genetically engineered mouse models led to increased cellular heterogeneity, molecular diversity, and tissues that histologically represent the original patient tumors. However, these models are relatively expensive and very timing consuming. More recently, the advancement of fast and inexpensive in vitro models that better mimic disease conditions in vivo are on the rise. Three-dimensional cultures like organoids and spheroids have gained popularity and are considered to recapitulate complex disease characteristics. In addition, computational genomics, transcriptomics, and metabolomic models are being developed to simulate pancreatic cancer progression and predict better treatment strategies. Herein, we review the challenges associated with pancreatic cancer research and available analytical models. We suggest that an integrated approach toward using these models may allow for developing new strategies for pancreatic cancer precision medicine.

Integrated PK/PD Modeling Relates Smoothened Inhibitor Biomarkers to The Heterogeneous Intratumor Disposition of Cetuximab in Pancreatic Cancer Tumor Models

Therapeutic antibodies have shown little efficacy in the treatment of pancreatic ductal adenocarcinomas (PDAC). Tumor desmoplasia, hypovascularity, and poor perfusion result in insufficient tumor cell exposure, contributing to treatment failure. Smoothened inhibitors of hedgehog signaling (sHHi) increase PDAC tumor permeability, perfusion, and drug delivery, and provide a tool to develop a quantitative, mechanistic understanding as to how the temporal dynamics of tumor priming can impact intratumor distribution of monoclonal antibodies (mAb). A linked pharmacokinetic (PK)/pharmacodynamic (PD) model was developed to integrate the plasma and tumor PK of a sHHi priming agent with its effects upon downstream stromal biomarkers Gli1, hyaluronic acid, and interstitial fluid pressure in PDAC patient-derived xenograft (PDX) tumors. In parallel, in situ tumor concentrations of cetuximab (CTX: anti-epidermal growth factor receptor; EGFR) were quantified as a marker for tumor delivery of mAb or antibody-drug conjugates. A minimal, physiologically-based pharmacokinetic (mPBPK) model was constructed to link sHHi effects upon mechanistic effectors of tumor barrier compromise with the intratumor distribution of CTX, and CTX occupancy of EGFR in tumors. Integration of the mPBPK model of mAb deposition and intratumor distribution with the PK/PD model of tumor responses to priming not only identified physiological parameters that are critical for tumor antibody distribution, but also provides insight into dosing regimens that could achieve maximal tumor disposition of therapeutic antibodies under conditions of transient PDAC tumor permeability barrier compromise that mechanistically-diverse tumor priming strategies may achieve.

Modeling spatial evolution of multi-drug resistance under drug environmental gradients

Multi-drug combinations to treat bacterial populations are at the forefront of approaches for infection control and prevention of antibiotic resistance. Although the evolution of antibiotic resistance has been theoretically studied with mathematical population dynamics models, extensions to spatial dynamics remain rare in the literature, including in particular spatial evolution of multi-drug resistance. In this study, we propose a reaction-diffusion system that describes the multi-drug evolution of bacteria, based on a rescaling approach (Gjini and Wood, 2021). We show how the resistance to drugs in space, and the consequent adaptation of growth rate is governed by a Price equation with diffusion. The covariance terms in this equation integrate features of drug interactions and collateral resistances or sensitivities to the drugs. We study spatial versions of the model where the distribution of drugs is homogeneous across space, and where the drugs vary environmentally in a piecewise-constant, linear and nonlinear manner. Applying concepts from perturbation theory and reaction-diffusion equations, we propose an analytical characterization of average mutant fitness in the spatial system based on the principal eigenvalue of our linear problem. This enables an accurate translation from drug spatial gradients and mutant antibiotic susceptibility traits, to the relative advantage of each mutant across the environment. Such a mathematical understanding allows to predict the precise outcomes of selection over space, ultimately from the fundamental balance between growth and movement traits, and their diversity in a population.

Modeling the effect of spatial structure on solid tumor evolution and ctDNA composition

Circulating tumor DNA (ctDNA) monitoring, while sufficiently advanced to reflect tumor evolution in real time and inform on cancer diagnosis, treatment, and prognosis, mainly relies on DNA that originates from cell death via apoptosis or necrosis. In solid tumors, chemotherapy and immune infiltration can induce spatially variable rates of cell death, with the potential to bias and distort the clonal composition of ctDNA. Using a stochastic evolutionary model of boundary-driven growth, we study how elevated cell death on the edge of a tumor can simultaneously impact driver mutation accumulation and the representation of tumor clones and mutation detectability in ctDNA. We describe conditions in which invasive clones end up over-represented in ctDNA, clonal diversity can appear elevated in the blood, and spatial bias in shedding can inflate subclonal variant allele frequencies (VAFs). Additionally, we find that tumors that are mostly quiescent can display similar biases, but are far less detectable, and the extent of perceptible spatial bias strongly depends on sequence detection limits. Overall, we show that spatially structured shedding might cause liquid biopsies to provide highly biased profiles of tumor state. While this may enable more sensitive detection of expanding clones, it could also increase the risk of targeting a subclonal variant for treatment. Our results indicate that the effects and clinical consequences of spatially variable cell death on ctDNA composition present an important area for future work.

Multiscale modeling of drug resistance in glioblastoma with gene mutations and angiogenesis

Drug resistance is a prominent impediment to the efficacy of targeted therapies across various cancer types, including glioblastoma (GBM). However, comprehending the intricate intracellular and extracellular mechanisms underlying drug resistance remains elusive. Empirical investigations have elucidated that genetic aberrations, such as gene mutations, along with microenvironmental adaptation, notably angiogenesis, act as pivotal drivers of tumor progression and drug resistance. Nonetheless, mathematical models frequently compartmentalize these factors in isolation. In this study, we present a multiscale agent-based model of GBM, encompassing cellular dynamics, intricate signaling pathways, gene mutations, angiogenesis, and therapeutic interventions. This integrative framework facilitates an exploration of the interplay between genetic mutations and the vascular microenvironment in shaping the dynamic evolution of tumors during treatment with tyrosine kinase inhibitor. Our simulations unveil that mutations influencing the migration and proliferation of tumor cells expedite the emergence of phenotype heterogeneity, thereby exacerbating tumor invasion under both treated and untreated conditions. Moreover, angiogenesis proximate to the tumor fosters a protumoral milieu, augmenting mutation-induced drug resistance by increasing the survival rate of tumor cells. Collectively, our findings underscore the dual roles of intrinsic genetic mutations and extrinsic microenvironmental adaptations in steering tumor growth and drug resistance. Finally, we substantiate our model predictions concerning the impact of gene mutations and angiogenesis on the responsiveness of targeted therapies by integrating single-cell RNA-seq, spatial transcriptomics, bulk RNA-seq, and clinical data from GBM patients. The multidimensional approach enhances our understanding of the complexities governing drug resistance in glioma and offers insights into potential therapeutic strategies.

The uncertain role of substandard and falsified medicines in the emergence and spread of antimicrobial resistance

Approximately 10% of antimicrobials used by humans in low- and middle-income countries are estimated to be substandard or falsified. In addition to their negative impact on morbidity and mortality, they may also be important drivers of antimicrobial resistance. Despite such concerns, our understanding of this relationship remains rudimentary. Substandard and falsified medicines have the potential to either increase or decrease levels of resistance, and here we discuss a range of mechanisms that could drive these changes. Understanding these effects and their relative importance will require an improved understanding of how different drug exposures affect the emergence and spread of resistance and of how the percentage of active pharmaceutical ingredients in substandard and falsified medicines is temporally and spatially distributed.

Bacterial motility can govern the dynamics of antibiotic resistance evolution

Spatial heterogeneity in antibiotic concentrations is thought to accelerate the evolution of antibiotic resistance, but current theory and experiments have overlooked the effect of cell motility on bacterial adaptation. Here, we study bacterial evolution in antibiotic landscapes with a quantitative model where bacteria evolve under the stochastic processes of proliferation, death, mutation and migration. Numerical and analytical results show that cell motility can both accelerate and decelerate bacterial adaptation by affecting the degree of genotypic mixing and ecological competition. Moreover, we find that for sufficiently high rates, cell motility can limit bacterial survival, and we derive conditions for all these regimes. Similar patterns are observed in more complex scenarios, namely where bacteria can bias their motion in chemical gradients (chemotaxis) or switch between motility phenotypes either stochastically or in a density-dependent manner. Overall, our work reveals limits to bacterial adaptation in antibiotic landscapes that are set by cell motility.

Diverse mutant selection windows shape spatial heterogeneity in evolving populations

Mutant selection windows (MSWs), the range of drug concentrations that select for drug-resistant mutants, have long been used as a model for predicting drug resistance and designing optimal dosing strategies in infectious disease. The canonical MSW model offers comparisons between two subtypes at a time: drug-sensitive and drug-resistant. In contrast, the fitness landscape model with N alleles, which maps genotype to fitness, allows comparisons between N genotypes simultaneously, but does not encode continuous drug response data. In clinical settings, there may be a wide range of drug concentrations selecting for a variety of genotypes. Therefore, there is a need for a more robust model of the pathogen response to therapy to predict resistance and design new therapeutic approaches. Fitness seascapes, which model genotype-by-environment interactions, permit multiple MSW comparisons simultaneously by encoding genotype-specific dose-response data. By comparing dose-response curves, one can visualize the range of drug concentrations where one genotype is selected over another. In this work, we show how N-allele fitness seascapes allow for N*2N-1 unique MSW comparisons. In spatial drug diffusion models, we demonstrate how fitness seascapes reveal spatially heterogeneous MSWs, extending the MSW model to more accurately reflect the selection fo drug resistant genotypes. Furthermore, we find that the spatial structure of MSWs shapes the evolution of drug resistance in an agent-based model. Our work highlights the importance and utility of considering dose-dependent fitness seascapes in evolutionary medicine.

Quantitative analysis of drug distribution in heterogeneous tissues using dual-stacking capillary electrophoresis-mass spectrometry

BACKGROUND AND PURPOSE

Intratumour heterogeneity frequently leads to drug resistance, which is a major issue in drug discovery. Drug distribution is one of the key factors for elucidating the resistance mechanism; however, quantitative and regional drug measurement is challenging. Here, we developed a novel ultra-sensitive analytical method and applied it to HER3-targeting antibody-drug conjugate patritumab deruxtecan (HER3-DXd), aiming to explore its payload (DXd) distribution within heterogeneous tissues.

EXPERIMENTAL APPROACH

The developed analytical method is named LDMS-CE-MS, a capillary electrophoresis-mass spectrometry (CE-MS) coupled with a novel sample preconcentration/separation method called "large-volume dual-sample stacking by micelle collapse and sweeping (LDMS)". First, the analytical performance of LDMS-CE-MS for DXd detection was evaluated. Subsequently, we evaluated the bystander effect of HER3-DXd, where tumour tissues were excised from xenograft models and clinical specimens after administration of HER3-DXd. HER3-high expression, adjacent, and HER3-low expression regions were then sampled by laser microdissection to quantify the released DXd.

KEY RESULTS

LDMS concentrated DXd by 1000-fold and separated it from the hydrophilic bio-matrix through continuous capture and release by the charged micelles, allowing quantification at sub-attomole-level. DXd concentrations decreased in the order of antigen-high expression > adjacent > antigen-low expression regions in the tumour xenograft model, whereas in clinical specimens, adjacent and antigen-high expression regions had approximately the same concentration. These distributions represent a bystander effect.

CONCLUSIONS AND IMPLICATIONS

Our LDMS-CE-MS successfully visualized the attomole-level drug distributions in heterogeneous clinical specimens. This new platform opens a new era of quantitative pharmacokinetic analysis, facilitating drug discovery and development.

Mapping lesion-specific response and progression dynamics and inter-organ variability in metastatic colorectal cancer

Achieving systemic tumor control across metastases is vital for long-term patient survival but remains intractable in many patients. High lesion-level response heterogeneity persists, conferring many dissociated responses across metastatic lesions. Most studies of metastatic disease focus on tumor molecular and cellular features, which are crucial to elucidating the mechanisms underlying lesion-level variability. However, our understanding of lesion-specific heterogeneity on the macroscopic level, such as lesion dynamics in growth, response, and progression during treatment, remains rudimentary. This study investigates lesion-specific response heterogeneity through analyzing 116,542 observations of 40,612 lesions in 4,308 metastatic colorectal cancer (mCRC) patients. Despite significant differences in their response and progression dynamics, metastatic lesions converge on four phenotypes that vary with anatomical site. Importantly, we find that organ-level progression sequence is closely associated with patient long-term survival, and that patients with the first lesion progression in the liver often have worse survival. In conclusion, our study provides insights into lesion-specific response and progression heterogeneity in mCRC and creates impetus for metastasis-specific therapeutics.

Quantification of spatial pharmacogene expression heterogeneity in breast tumors

BACKGROUND

Chemotherapeutic drug concentrations vary across different regions of tumors and this is thought to be involved in development of chemotherapy resistance. Insufficient drug delivery to some regions of the tumor may be due to spatial differences in expression of genes involved in the disposition, transport, and detoxification of drugs (pharmacogenes). Therefore, in this study, we analyzed the spatial expression of 286 pharmacogenes in six breast cancer tissues using the recently developed Visium spatial transcriptomics platform to (1) determine if these pharmacogenes are expressed heterogeneously across tumor tissue and (2) to determine which pharmacogenes have the most spatial expression heterogeneity.

METHODS AND RESULTS

The spatial transcriptomics technology sequences the transcriptome of 55 um diameter barcoded sections (spots) across a tissue sample. We analyzed spatial gene expression profiles of four biobank-sourced breast tumor samples in addition to two breast tumor sample datasets from 10× Genomics. We define heterogeneity as the interquartile range of read counts. Collectively, we identified 8887 spots in tumor regions, 3814 in stroma, 44 in lymphocytes, and 116 in normal regions based on pathologist annotation of the tissues. We showed statistically significant differences in expression of pharmacogenes in tumor regions compared to surrounding non-tumor regions. We also observed that the most heterogeneously expressed genes within tumor regions were involved in reactive oxygen species (ROS) handling and detoxification mechanisms. GPX4, GSTP1, MGST3, SOD1, CYP4Z1, CYB5R3, GSTK1, and NAT1 showed the most heterogeneous expression within tumor regions.

CONCLUSIONS

The heterogeneous expression of these pharmacogenes may have important implications for cancer therapy due to their ability to impact drug distribution and efficacy throughout the tumor. Our results suggest that chemoresistance caused by expression of GPX4, GSTP1, MGST3, and SOD1 may be intrinsic, not acquired, since the heterogeneity is not specific to chemotherapy-treated samples or cell type. Additionally, we identified candidate chemoresistance pharmacogenes that can be further tested through focused follow-up studies.

Synergistic cytotoxicity of perifosine and ABT-737 to colon cancer cells

An acidic environment and hypoxia within the tumour are hallmarks of cancer that contribute to cell resistance to therapy. Deregulation of the PI3K/Akt pathway is common in colon cancer. Numerous Akt-targeted therapies are being developed, the activity of Akt-inhibitors is, however, strongly pH-dependent. Combination therapy thus represents an opportunity to increase their efficacy. In this study, the cytotoxicity of the Akt inhibitor perifosine and the Bcl-2/Bcl-xL inhibitor ABT-737 was tested in colon cancer HT-29 and HCT-116 cells cultured in monolayer or in the form of spheroids. The efficacy of single drugs and their combination was analysed in different tumour-specific environments including acidosis and hypoxia using a series of viability assays. Changes in protein content and distribution were determined by immunoblotting and a "peeling analysis" of immunohistochemical signals. While the cytotoxicity of single agents was influenced by the tumour-specific microenvironment, perifosine and ABT-737 in combination synergistically induced apoptosis in cells cultured in both 2D and 3D independently on pH and oxygen level. Thus, the combined therapy of perifosine and ABT-737 could be considered as a potential treatment strategy for colon cancer.

Drug-Resistant Cancer Treatment Strategies Based on the Dynamics of Clonal Evolution and PKPD Modeling of Drug Combinations

A method for determining a dosage strategy is proposed to combat drug resistance in tumor progression. The method is based on a dynamic model for the clonal evolution of cancerous cells and considers the Pharmacokinetic/Pharmacodynamic (PKPD) modeling of combination therapy. The proposed mathematical representation models the dynamic and kinetic effects of multiple drugs on the number of cells while considering potential mutations and assuming that no cross-resistance arises. An optimization problem is then proposed to minimize the total number of cancerous cells in a finite treatment period given a limited number of treatments. The dosage schedule, including the amount of each drug to be administered and the timing, is found by solving the optimization problem. This treatment schedule is constrained to achieve a target minimum effectiveness, while also ensuring that the concentration of the drugs, individually and totally, does not exceed a prescribed toxicity threshold. The proposed optimization problem is represented as a Complementary Geometric Programming (CGP) problem. The results show that the solution of the optimization problem for combination therapy is the dosing schedule that leads to tumor eradication at the end of the treatment period. The results also investigate the tumor dynamics for all mutation types when undergoing treatment, showing that single drug therapies can fail to combat the emergence of resistance, while optimized combination therapies can reduce the amount of all mutation types during the course of treatment, thereby combating resistance.

Midlife brain metastases in the United States: Is male at risk?

Background

Population‐based estimates of the impact of gender throughout the whole course of brain metastases (BMs) at the time of diagnosis of systemic malignancies are insufficient. We aimed to discover the influence of gender on the presence of BMs in newly diagnosed malignancies and the survival of those patients on a population‐based level.

Methods

Midlife patients (40 years ≤ age ≤60 years) with newly diagnosed malignancies and BMs at the time of diagnosis were abstracted from the Surveillance, Epidemiology, and End Results (SEER) database of the National Cancer Institute. Clinical variables adjusted patient data. The LASSO regression was performed to exclude the possibility of collinearity. Univariable and multivariable logistic regression analyses were applied to find independent predictors for the presence of BMs, while univariable and multivariable Cox proportional hazard regression analyses were used to determine prognosticators of survival. K‐M curves were used to perform the survival analysis.

Result

276,327 population‐based samples met inclusion criteria between 2014 and 2016, and 5747 (2.08%) patients were diagnosed with BMs at the time of diagnosis of systematic malignancies. Among all midlife patients with cancer, 44.02% (121,634) were male, while 51.68% (2970) were male among patients with BMs at the time of diagnosis. The most frequent tumor type was breast cancer (23.11%), and lung cancer had the highest incidence proportion of BMs among the entire cohort (19.34%). The multivariable logistic regression model suggested that female (vs. male, odds ratio [OR] 1.07, 95% CI: 1.01–1.14, p < 0.001) was associated with a higher risk of the presence of BMs at the time of diagnosis. Moreover, in the multivariable Cox model for all‐cause mortality in individuals with BMs at diagnosis, female (vs. male, hazard ratio [HR], 0.86, 95% CI, 0.80–0.92, p < 0.001) was shown to have a lower risk of decreased all‐cause mortality.

Conclusion

The middle‐aged females were at increased risk of developing BMs, while the middle‐aged males with BMs were at higher risk of having poorer survival.

Spatial segregation and cooperation in radially expanding microbial colonies under antibiotic stress

Antibiotic resistance in microbial communities reflects a combination of processes operating at different scales. In this work, we investigate the spatiotemporal dynamics of bacterial colonies comprised of drug-resistant and drug-sensitive cells undergoing range expansion under antibiotic stress. Using the opportunistic pathogen Enterococcus faecalis with plasmid-encoded β-lactamase, we track colony expansion dynamics and visualize spatial patterns in fluorescently labeled populations exposed to antibiotics. We find that the radial expansion rate of mixed communities is approximately constant over a wide range of drug concentrations and initial population compositions. Imaging of the final populations shows that resistance to ampicillin is cooperative, with sensitive cells surviving in the presence of resistant cells at otherwise lethal concentrations. The populations exhibit a diverse range of spatial segregation patterns that depend on drug concentration and initial conditions. Mathematical models indicate that the observed dynamics are consistent with global cooperation, despite the fact that β-lactamase remains cell-associated. Experiments confirm that resistant colonies provide a protective effect to sensitive cells on length scales multiple times the size of a single colony, and populations seeded with (on average) no more than a single resistant cell can produce mixed communities in the presence of the drug. While biophysical models of drug degradation suggest that individual resistant cells offer only short-range protection to neighboring cells, we show that long-range protection may arise from synergistic effects of multiple resistant cells, providing surprisingly large protection zones even at small population fractions.

Analyze impact of tumor-associated kinetics on antibody delivery in solid tumors with a physiologically based pharmacokinetics/pharmacodynamics model

Monoclonal antibody (mAb)-based drugs are critical anti-cancer therapies. Unfortunately, therapeutic efficacy can be compromised by spatially heterogeneous intratumoral Ab deposition. Binding-site barriers arising from Ab and tumor-associated kinetics often underlie this phenomenon. Quantitative insight into these issues may lead to more efficient drug delivery. Difficulties in addressing this issue include (1) lack of techniques to quantify critical kinetic events, (2) lack of a pharmacokinetic/pharmacodynamic (PK/PD) model to assess important parameters for specific tumor types, and (3) uncertainty or variability of critical kinetic factors even within a single tumor type. This study developed a mechanism-based PK/PD model to profile heterogeneous distribution of Ab within tumors and tested this model using real-life experimental data. Model simulations incorporating several uncertainties were used to determine how mAb and tumor-associated kinetics influence receptor occupancy. Simulations were also used to predict the potential impact of these findings in preclinical tumor models and human tumors. We found significant differences in tumor-associated kinetics between groups in which mAb therapy was effective versus groups in which it was ineffective. These kinetic differences included rates of tumor-associated antigen (TAA) degradation, TAA expression, apparent flow rates of interstitial fluid, and ratios of Ab-TAA complex internalization to TAA degradation. We found less significant differences in mAb kinetics, including rates of clearance or affinity for target antigens. In conclusion, our mechanism-based PK/PD model suggests that TAA-associated kinetic factors participate more significantly than those associated with the Ab in generating barriers to mAb delivery and distribution in tumors.

Understanding patterns of HIV multi-drug resistance through models of temporal and spatial drug heterogeneity

Triple-drug therapies have transformed HIV from a fatal condition to a chronic one. These therapies should prevent HIV drug resistance evolution, because one or more drugs suppress any partially resistant viruses. In practice, such therapies drastically reduced, but did not eliminate, resistance evolution. In this article, we reanalyze published data from an evolutionary perspective and demonstrate several intriguing patterns about HIV resistance evolution - resistance evolves (1) even after years on successful therapy, (2) sequentially, often via one mutation at a time and (3) in a partially predictable order. We describe how these observations might emerge under two models of HIV drugs varying in space or time. Despite decades of work in this area, much opportunity remains to create models with realistic parameters for three drugs, and to match model outcomes to resistance rates and genetic patterns from individuals on triple-drug therapy. Further, lessons from HIV may inform other systems.

Coupled Source-Sink Habitats Produce Spatial and Temporal Variation of Cancer Cell Molecular Properties as an Alternative to Branched Clonal Evolution and Stem Cell Paradigms

Intratumoral molecular cancer cell heterogeneity is conventionally ascribed to the accumulation of random mutations that occasionally generate fitter phenotypes. This model is built upon the “mutation-selection” paradigm in which mutations drive ever-fitter cancer cells independent of environmental circumstances. An alternative model posits spatio-temporal variation (e.g., blood flow heterogeneity) drives speciation by selecting for cancer cells adapted to each different environment. Here, spatial genetic variation is the consequence rather than the cause of intratumoral evolution. In nature, spatially heterogenous environments are frequently coupled through migration. Drawing from ecological models, we investigate adjacent well-perfused and poorly-perfused tumor regions as “source” and “sink” habitats, respectively. The source habitat has a high carrying capacity resulting in more emigration than immigration. Sink habitats may support a small (“soft-sink”) or no (“hard-sink”) local population. Ecologically, sink habitats can reduce the population size of the source habitat so that, for example, the density of cancer cells directly around blood vessels may be lower than expected. Evolutionarily, sink habitats can exert a selective pressure favoring traits different from those in the source habitat so that, for example, cancer cells adjacent to blood vessels may be suboptimally adapted for that habitat. Soft sinks favor a generalist cancer cell type that moves between the environment but can, under some circumstances, produce speciation events forming source and sink habitat specialists resulting in significant molecular variation in cancer cells separated by small distances. Finally, sink habitats, with limited blood supply, may receive reduced concentrations of systemic drug treatments; and local hypoxia and acidosis may further decrease drug efficacy allowing cells to survive treatment and evolve resistance. In such cases, the sink transforms into the source habitat for resistant cancer cells, leading to treatment failure and tumor progression. We note these dynamics will result in spatial variations in molecular properties as an alternative to the conventional branched evolution model and will result in cellular migration as well as variation in cancer cell phenotype and proliferation currently described by the stem cell paradigm.

Inter-Metastatic Heterogeneity of Tumor Marker Expression and Microenvironment Architecture in a Preclinical Cancer Model

BACKGROUND

Preclinical drug development studies rarely consider the impact of a candidate drug on established metastatic disease. This may explain why agents that are successful in subcutaneous and even orthotopic preclinical models often fail to demonstrate efficacy in clinical trials. It is reasonable to anticipate that sites of metastasis will be phenotypically unique, as each tumor will have evolved heterogeneously with respect to gene expression as well as the associated phenotypic outcome of that expression. The objective for the studies described here was to gain an understanding of the tumor heterogeneity that exists in established metastatic disease and use this information to define a preclinical model that is more predictive of treatment outcome when testing novel drug candidates clinically.

METHODS

Female NCr nude mice were inoculated with fluorescent (mKate), Her2/neu-positive human breast cancer cells (JIMT-mKate), either in the mammary fat pad (orthotopic; OT) to replicate a primary tumor, or directly into the left ventricle (intracardiac; IC), where cells eventually localize in multiple sites to create a model of established metastasis. Tumor development was monitored by in vivo fluorescence imaging (IVFI). Subsequently, animals were sacrificed, and tumor tissues were isolated and imaged ex vivo. Tumors within organ tissues were further analyzed via multiplex immunohistochemistry (mIHC) for Her2/neu expression, blood vessels (CD31), as well as a nuclear marker (Hoechst) and fluorescence (mKate) expressed by the tumor cells.

RESULTS

Following IC injection, JIMT-1mKate cells consistently formed tumors in the lung, liver, brain, kidney, ovaries, and adrenal glands. Disseminated tumors were highly variable when assessing vessel density (CD31) and tumor marker expression (mkate, Her2/neu). Interestingly, tumors which developed within an organ did not adopt a vessel microarchitecture that mimicked the organ where growth occurred, nor did the vessel microarchitecture appear comparable to the primary tumor. Rather, metastatic lesions showed considerable variability, suggesting that each secondary tumor is a distinct disease entity from a microenvironmental perspective.

CONCLUSIONS

The data indicate that more phenotypic heterogeneity in the tumor microenvironment exists in models of metastatic disease than has been previously appreciated, and this heterogeneity may better reflect the metastatic cancer in patients typically enrolled in early-stage Phase I/II clinical trials. Similar to the suggestion of others in the past, the use of models of established metastasis preclinically should be required as part of the anticancer drug candidate development process, and this may be particularly important for targeted therapeutics and/or nanotherapeutics.

Evolution in alternating environments with tunable interlandscape correlations

Natural populations are often exposed to temporally varying environments. Evolutionary dynamics in varying environments have been extensively studied, although understanding the effects of varying selection pressures remains challenging. Here, we investigate how cycling between a pair of statistically related fitness landscapes affects the evolved fitness of an asexually reproducing population. We construct pairs of fitness landscapes that share global fitness features but are correlated with one another in a tunable way, resulting in landscape pairs with specific correlations. We find that switching between these landscape pairs, depending on the ruggedness of the landscape and the interlandscape correlation, can either increase or decrease steady-state fitness relative to evolution in single environments. In addition, we show that switching between rugged landscapes often selects for increased fitness in both landscapes, even in situations where the landscapes themselves are anticorrelated. We demonstrate that positively correlated landscapes often possess a shared maximum in both landscapes that allows the population to step through sub-optimal local fitness maxima that often trap single landscape evolution trajectories. Finally, we demonstrate that switching between anticorrelated paired landscapes leads to ergodic-like dynamics where each genotype is populated with nonzero probability, dramatically lowering the steady-state fitness in comparison to single landscape evolution.

The Role of Intratumor Heterogeneity in the Response of Metastatic Non-Small Cell Lung Cancer to Immune Checkpoint Inhibitors

Immune checkpoint inhibitors (ICIs) represent one of the most promising therapeutic approaches in metastatic non-small cell lung cancer (M-NSCLC). Unfortunately, approximately 50–75% of patients do not respond to this treatment modality. Intratumor heterogeneity (ITH) at the genetic and phenotypic level is considered as a major cause of anticancer therapy failure, including resistance to ICIs. Recent observations suggest that spatial heterogeneity in the composition and spatial organization of the tumor microenvironment plays a major role in the response of M-NSCLC patients to ICIs. In this mini review, we first present a brief overview of the use of ICIs in M-NSCLC. We then discuss the role of genetic and non-genetic ITH on the efficacy of ICIs in patients with M-NSCLC.

The Moran process on 2-chromatic graphs

Resources are rarely distributed uniformly within a population. Heterogeneity in the concentration of a drug, the quality of breeding sites, or wealth can all affect evolutionary dynamics. In this study, we represent a collection of properties affecting the fitness at a given location using a color. A green node is rich in resources while a red node is poorer. More colors can represent a broader spectrum of resource qualities. For a population evolving according to the birth-death Moran model, the first question we address is which structures, identified by graph connectivity and graph coloring, are evolutionarily equivalent. We prove that all properly two-colored, undirected, regular graphs are evolutionarily equivalent (where “properly colored” means that no two neighbors have the same color). We then compare the effects of background heterogeneity on properly two-colored graphs to those with alternative schemes in which the colors are permuted. Finally, we discuss dynamic coloring as a model for spatiotemporal resource fluctuations, and we illustrate that random dynamic colorings often diminish the effects of background heterogeneity relative to a proper two-coloring.

Heterogeneity in environmental conditions can have profound effects on long-term evolutionary outcomes in structured populations. We consider a population evolving on a colored graph, wherein the color of a node represents the resources at that location. Using a combination of analytical and numerical methods, we quantify the effects of background heterogeneity on a population’s dynamics. In addition to considering the notion of an “optimal” coloring with respect to mutant invasion, we also study the effects of dynamic spatial redistribution of resources as the population evolves. Although the effects of static background heterogeneity can be quite striking, these effects are often attenuated by the movement (or “flow”) of the underlying resources.

Kernel Fusion Method for Detecting Cancer Subtypes via Selecting Relevant Expression Data

Recently, cancer has been characterized as a heterogeneous disease composed of many different subtypes. Early diagnosis of cancer subtypes is an important study of cancer research, which can be of tremendous help to patients after treatment. In this paper, we first extract a novel dataset, which contains gene expression, miRNA expression, and isoform expression of five cancers from The Cancer Genome Atlas (TCGA). Next, to avoid the effect of noise existing in 60, 483 genes, we select a small number of genes by using LASSO that employs gene expression and survival time of patients. Then, we construct one similarity kernel for each expression data by using Chebyshev distance. And also, We used SKF to fused the three similarity matrix composed of gene, Iso, and miRNA, and finally clustered the fused similarity matrix with spectral clustering. In the experimental results, our method has better P-value in the Cox model than other methods on 10 cancer data from Jiang Dataset and Novel Dataset. We have drawn different survival curves for different cancers and found that some genes play a key role in cancer. For breast cancer, we find out that HSPA2A, RNASE1, CLIC6, and IFITM1 are highly expressed in some specific groups. For lung cancer, we ensure that C4BPA, SESN3, and IRS1 are highly expressed in some specific groups. The code and all supporting data files are available from https://github.com/guofei-tju/Uncovering-Cancer-Subtypes-via-LASSO.

Opportunities for Quantitative Translational Modeling in Oncology

A 2-day meeting was held by members of the UK Quantitative Systems Pharmacology Network () in November 2018 on the topic of Translational Challenges in Oncology. Participants from a wide range of backgrounds were invited to discuss current and emerging modeling applications in nonclinical and clinical drug development, and to identify areas for improvement. This resulting perspective explores opportunities for impactful quantitative pharmacology approaches. Four key themes arose from the presentations and discussions that were held, leading to the following recommendations: Evaluate the predictivity and reproducibility of animal cancer models through precompetitive collaboration. Apply mechanism of action (MoA) based mechanistic models derived from nonclinical data to clinical trial data. Apply MoA reflective models across trial data sets to more robustly quantify the natural history of disease and response to differing interventions. Quantify more robustly the dose and concentration dependence of adverse events through mathematical modelling techniques and modified trial design.

Population structure across scales facilitates coexistence and spatial heterogeneity of antibiotic-resistant infections

Antibiotic-resistant infections are a growing threat to human health, but basic features of the eco-evolutionary dynamics remain unexplained. Most prominently, there is no clear mechanism for the long-term coexistence of both drug-sensitive and resistant strains at intermediate levels, a ubiquitous pattern seen in surveillance data. Here we show that accounting for structured or spatially-heterogeneous host populations and variability in antibiotic consumption can lead to persistent coexistence over a wide range of treatment coverages, drug efficacies, costs of resistance, and mixing patterns. Moreover, this mechanism can explain other puzzling spatiotemporal features of drug-resistance epidemiology that have received less attention, such as large differences in the prevalence of resistance between geographical regions with similar antibiotic consumption or that neighbor one another. We find that the same amount of antibiotic use can lead to very different levels of resistance depending on how treatment is distributed in a transmission network. We also identify parameter regimes in which population structure alone cannot support coexistence, suggesting the need for other mechanisms to explain the epidemiology of antibiotic resistance. Our analysis identifies key features of host population structure that can be used to assess resistance risk and highlights the need to include spatial or demographic heterogeneity in models to guide resistance management.

Mathematical Approach to Differentiate Spontaneous and Induced Evolution to Drug Resistance During Cancer Treatment

Purpose

Drug resistance is a major impediment to the success of cancer treatment. Resistance is typically thought to arise from random genetic mutations, after which mutated cells expand via Darwinian selection. However, recent experimental evidence suggests that progression to drug resistance need not occur randomly, but instead may be induced by the treatment itself via either genetic changes or epigenetic alterations. This relatively novel notion of resistance complicates the already challenging task of designing effective treatment protocols.

Materials and Methods

To better understand resistance, we have developed a mathematical modeling framework that incorporates both spontaneous and drug-induced resistance.

Results

Our model demonstrates that the ability of a drug to induce resistance can result in qualitatively different responses to the same drug dose and delivery schedule. We have also proven that the induction parameter in our model is theoretically identifiable and propose an in vitro protocol that could be used to determine a treatment’s propensity to induce resistance.

Using Selection by Nonantibiotic Stressors to Sensitize Bacteria to Antibiotics

Evolutionary adaptation of bacteria to nonantibiotic selective forces, such as osmotic stress, has been previously associated with increased antibiotic resistance, but much less is known about potentially sensitizing effects of nonantibiotic stressors. In this study, we use laboratory evolution to investigate adaptation of Enterococcus faecalis, an opportunistic bacterial pathogen, to a broad collection of environmental agents, ranging from antibiotics and biocides to extreme pH and osmotic stress. We find that nonantibiotic selection frequently leads to increased sensitivity to other conditions, including multiple antibiotics. Using population sequencing and whole-genome sequencing of single isolates from the evolved populations, we identify multiple mutations in genes previously linked with resistance to the selecting conditions, including genes corresponding to known drug targets or multidrug efflux systems previously tied to collateral sensitivity. Finally, we hypothesized based on the measured sensitivity profiles that sequential rounds of antibiotic and nonantibiotic selection may lead to hypersensitive populations by harnessing the orthogonal collateral effects of particular pairs of selective forces. To test this hypothesis, we show experimentally that populations evolved to a sequence of linezolid (an oxazolidinone antibiotic) and sodium benzoate (a common preservative) exhibit increased sensitivity to more stressors than adaptation to either condition alone. The results demonstrate how sequential adaptation to drug and nondrug environments can be used to sensitize bacteria to antibiotics and highlight new potential strategies for exploiting shared constraints governing adaptation to diverse environmental challenges.

Drug-Induced Resistance in Micrometastases: Analysis of Spatio-Temporal Cell Lineages

Resistance to anti-cancer drugs is a major cause of treatment failure. While several intracellular mechanisms of resistance have been postulated, the role of extrinsic factors in the development of resistance in individual tumor cells is still not fully understood. Here we used a hybrid agent-based model to investigate how sensitive tumor cells develop drug resistance in the heterogeneous tumor microenvironment. We characterized the spatio-temporal evolution of lineages of the resistant cells and examined how resistance at the single-cell level contributes to the overall tumor resistance. We also developed new methods to track tumor cell adaptation, to trace cell viability trajectories and to examine the three-dimensional spatio-temporal lineage trees. Our findings indicate that drug-induced resistance can result from cells adaptation to the changes in drug distribution. Two modes of cell adaptation were identified that coincide with microenvironmental niches—areas sheltered by cell micro-communities (protectorates) or regions with limited drug penetration (refuga or sanctuaries). We also recognized that certain cells gave rise to lineages of resistant cells (precursors of resistance) and pinpointed three temporal periods and spatial locations at which such cells emerged. This supports the hypothesis that tumor micrometastases do not need to harbor cell populations with pre-existing resistance, but that individual tumor cells can adapt and develop resistance induced by the drug during the treatment.

Preparation and anti-cancer activity of transferrin/folic acid double-targeted graphene oxide drug delivery system

In this study, a transferrin/folic acid double-targeting graphene oxide drug delivery system loaded with doxorubicin was designed. Graphene oxide was prepared by ultrasound improved Hummers method and was modified with Pluronic F68, folic acid, and transferrin to decrease its toxicity and to allow dual-targeting. The results show that the double target drug delivery system (TFGP*DOX) has good and controllable drug delivery performance with no toxicity. Moreover, TFGP*DOX has a better inhibitory effect on SMMC-7721 cells than does a single target drug delivery system (FGP*DOX). The results of drug release analysis and cell inhibition studies showed that TFGP*DOX has a good sustained release function that can reduce the drug release rate in blood circulation over time and improve the local drug concentration in or near a targeted tumor. Therefore, the drug loading system (TFGP*DOX) has potential application value in the treatment of hepatocellular carcinoma.

Hyperthermia and smart drug delivery systems for solid tumor therapy

Chemotherapy is a cornerstone of cancer therapy. Irrespective of the administered drug, it is crucial that adequate drug amounts reach all cancer cells. To achieve this, drugs first need to be absorbed, then enter the blood circulation, diffuse into the tumor interstitial space and finally reach the tumor cells. Next to chemoresistance, one of the most important factors for effective chemotherapy is adequate tumor drug uptake and penetration. Unfortunately, most chemotherapeutic agents do not have favorable properties. These compounds are cleared rapidly, distribute throughout all tissues in the body, with only low tumor drug uptake that is heterogeneously distributed within the tumor. Moreover, the typical microenvironment of solid cancers provides additional hurdles for drug delivery, such as heterogeneous vascular density and perfusion, high interstitial fluid pressure, and abundant stroma. The hope was that nanotechnology will solve most, if not all, of these drug delivery barriers. However, in spite of advances and decades of nanoparticle development, results are unsatisfactory. One promising recent development are nanoparticles which can be steered, and release content triggered by internal or external signals. Here we discuss these so-called smart drug delivery systems in cancer therapy with emphasis on mild hyperthermia as a trigger signal for drug delivery.

Geostatistical visualization of ecological interactions in tumors

Recent advances in our understanding of cancer progression have highlighted the roles played by molecular heterogeneity and by the tumor microenvironment in driving drug resistance and metastasis. The coupling of single-cell measurement technologies with algorithms, such as t-sne and SPADE, have enabled deep investigation of tumor heterogeneity. However, such techniques only capture molecular heterogeneity and do not enable the quantification nor visualization of intercellular interactions. They additionally do not allow the visualization of ecological niches that are critical to understanding tumor behavior. Novel computational tools to quantify and visualize spatial patterns in the tumor microenvironment are critically needed. Here, we take a tumor ecology perspective to examine how predation, mutualism, commensalism, and parasitism may impact tumor development and spatial patterning. We additionally quantify local spatial heterogeneity and the emergent global spatial behavior of the models using geostatistics. By visualizing emergent spatial patterns we demonstrate the potential utility of a geostatistical analysis in differentiating amongst cell-cell interactions in the tumor microenvironment. These studies introduce both an ecological framework for characterizing intercellular interactions in cancer and a novel way of quantifying and visualizing spatial patterns in cancer.

Stochastic fluctuations in apoptotic threshold of tumour cells can enhance apoptosis and combat fractional killing

Fractional killing, which is a significant impediment to successful chemotherapy, is observed even in a population of genetically identical cancer cells exposed to apoptosis-inducing agents. This phenomenon arises not from genetic mutation but from cell-to-cell variation in the activation timing and level of the proteins that regulates apoptosis. To understand the mechanism behind the phenomenon, we formulate complex fractional killing processes as a first-passage time (FPT) problem with a stochastically fluctuating boundary. Analytical calculations are performed for the FPT distribution in a toy model of stochastic p53 gene expression, where the cancer cell is killed only when the p53 expression level crosses an active apoptotic threshold. Counterintuitively, we find that threshold fluctuations can effectively enhance cellular killing by significantly decreasing the mean time that the p53 protein reaches the threshold level for the first time. Moreover, faster fluctuations lead to the killing of more cells. These qualitative results imply that fluctuations in threshold are a non-negligible stochastic source, and can be taken as a strategy for combating fractional killing of cancer cells.

Genotype-Fitness Maps of EGFR-Mutant Lung Adenocarcinoma Chart the Evolutionary Landscape of Resistance for Combination Therapy Optimization

Cancer evolution poses a central obstacle to cure, as resistant clones expand under therapeutic selection pressures. Genome sequencing of relapsed disease can nominate genomic alterations conferring resistance but sample collection lags behind, limiting therapeutic innovation. Genome-wide screens offer a complementary approach to chart the compendium of escape genotypes, anticipating clinical resistance. We report genome-wide open reading frame (ORF) resistance screens for first- and third-generation epidermal growth factor receptor (EGFR) inhibitors and a MEK inhibitor. Using serial sampling, dose gradients, and mathematical modeling, we generate genotype-fitness maps across therapeutic contexts and identify alterations that escape therapy. Our data expose varying dose-fitness relationship across genotypes, ranging from complete dose invariance to paradoxical dose dependency where fitness increases in higher doses. We predict fitness with combination therapy and compare these estimates to genome-wide fitness maps of drug combinations, identifying genotypes where combination therapy results in unexpected inferior effectiveness. These data are applied to nominate combination optimization strategies to forestall resistant disease.

Tumor Priming by SMO Inhibition Enhances Antibody Delivery and Efficacy in a Pancreatic Ductal Adenocarcinoma Model

Despite frequent overexpression of numerous growth factor receptors by pancreatic ductal adenocarcinomas (PDAC), such as EGFR, therapeutic antibodies have not proven effective. Desmoplasia, hypovascularity, and hypoperfusion create a functional drug delivery barrier that contributes to treatment resistance. Drug combinations that target tumor/stroma interactions could enhance tumor deposition of therapeutic antibodies, although clinical trials have yet to support this strategy. We hypothesize that macromolecular or nanoparticulate therapeutic agents may best exploit stroma-targeting "tumor priming" strategies, based on the fundamental principles of the Enhanced Permeability and Retention phenomenon. Therefore, we investigated the molecular and pharmacologic tumor responses to NVP-LDE225, an SMO inhibitor of sonic hedgehog signaling (sHHI), of patient-derived xenograft models that recapitulate the desmoplasia and drug delivery barrier properties of PDAC. Short-term sHHI exposure mediated dose- and time-dependent changes in tumor microvessel patency, extracellular matrix architecture, and interstitial pressure, which waned with prolonged sHHI exposure, and increased nanoparticulate permeability probe deposition in multiple PDAC patient-derived xenograft isolates. During sHHI-mediated priming, deposition and intratumor distribution of both a nontargeted mAb and a mAb targeting EGFR, cetuximab, were enhanced. Sequencing the sHH inhibitor with cetuximab administration resulted in marked tumor growth inhibition compared with cetuximab alone. These studies suggest that PDAC drug delivery barriers confound efforts to employ mAb against targets in PDAC, and that short-term, intermittent exposure to stromal modulators can increase tumor cell exposure to therapeutic antibodies, improving their efficacy, and potentially minimize adverse effects that may accompany longer-term, continuous sHHI treatment.

Interplay of Darwinian Selection, Lamarckian Induction and Microvesicle Transfer on Drug Resistance in Cancer

Development of drug resistance in cancer has major implications for patients’ outcome. It is related to processes involved in the decrease of drug efficacy, which are strongly influenced by intratumor heterogeneity and changes in the microenvironment. Heterogeneity arises, to a large extent, from genetic mutations analogously to Darwinian evolution, when selection of tumor cells results from the adaptation to the microenvironment, but could also emerge as a consequence of epigenetic mutations driven by stochastic events. An important exogenous source of alterations is the action of chemotherapeutic agents, which not only affects the signalling pathways but also the interactions among cells. In this work we provide experimental evidence from in vitro assays and put forward a mathematical kinetic transport model to describe the dynamics displayed by a system of non-small-cell lung carcinoma cells (NCI-H460) which, depending on the effect of a chemotherapeutic agent (doxorubicin), exhibits a complex interplay between Darwinian selection, Lamarckian induction and the nonlocal transfer of extracellular microvesicles. The role played by all of these processes to multidrug resistance in cancer is elucidated and quantified.

Growth-dependent drug susceptibility can prevent or enhance spatial expansion of a bacterial population

As a population wave expands, organisms at the tip typically experience plentiful nutrients while those behind the front become nutrient-depleted. If the environment also contains a gradient of some inhibitor (e.g. a toxic drug), a tradeoff exists: the nutrient-rich tip is more exposed to the inhibitor, while the nutrient-starved region behind the front is less exposed. Here we show that this can lead to complex dynamics when the organism's response to the inhibitory substance is coupled to nutrient availability. We model a bacterial population which expands in a spatial gradient of antibiotic, under conditions where either fast-growing bacteria at the wave's tip, or slow-growing, resource-limited bacteria behind the front are more susceptible to the antibiotic. We find that growth-rate dependent susceptibility can have strong effects on the dynamics of the expanding population. If slow-growing bacteria are more susceptible, the population wave advances far into the inhibitory zone, leaving a trail of dead bacteria in its wake. In contrast, if fast-growing bacteria are more susceptible, the wave is blocked at a much lower concentration of antibiotic, but a large population of live bacteria remains behind the front. Our results may contribute to understanding the efficacy of different antimicrobials for spatially structured microbial populations such as biofilms, as well as the dynamics of ecological population expansions more generally.

Competing evolutionary paths in growing populations with applications to multidrug resistance

Investigating the emergence of a particular cell type is a recurring theme in models of growing cellular populations. The evolution of resistance to therapy is a classic example. Common questions are: when does the cell type first occur, and via which sequence of steps is it most likely to emerge? For growing populations, these questions can be formulated in a general framework of branching processes spreading through a graph from a root to a target vertex. Cells have a particular fitness value on each vertex and can transition along edges at specific rates. Vertices represent cell states, say genotypes or physical locations, while possible transitions are acquiring a mutation or cell migration. We focus on the setting where cells at the root vertex have the highest fitness and transition rates are small. Simple formulas are derived for the time to reach the target vertex and for the probability that it is reached along a given path in the graph. We demonstrate our results on several scenarios relevant to the emergence of drug resistance, including: the orderings of resistance-conferring mutations in bacteria and the impact of imperfect drug penetration in cancer.

How long does it take for a treatment naive, growing bacterial colony to be able to survive exposure to a cocktail of antibiotics? En route to multidrug resistance, what order did the drugs become impotent in? Questions such as these that pertain to the emergence of a significant cell type in a growing population arise frequently. They are often investigated via mathematical modelling but biologically insightful results are challenging to obtain. Here we outline a general framework of a stochastically growing population spreading through a graph to study such questions and provide simple formulas as answers. The significant cell type appears upon the population reaching a target vertex. Due to their simplicity, the derived formulas are widely accessible and can be used to guide and develop intuition on a range of biological scenarios. We demonstrate this on several settings including: how a region where drugs cannot penetrate affects the emergence of resistance, and, the ordering of mutations that leads to drugs being ineffective.

Clinical Cancer Nanomedicine

Nanotechnology offers new solutions for the development of cancer therapeutics that display improved efficacy and safety. Although several nanotherapeutics have received clinical approval, the most promising nanotechnology applications for patients still lie ahead. Nanoparticles display unique transport, biological, optical, magnetic, electronic, and thermal properties that are not apparent on the molecular or macroscale, and can be utilized for therapeutic purposes. These characteristics arise because nanoparticles are in the same size range as the wavelength of light and display large surface area to volume ratios. The large size of nanoparticles compared to conventional chemotherapeutic agents or biological macromolecule drugs also enables incorporation of several supportive components in addition to active pharmaceutical ingredients. These components can facilitate solubilization, protection from degradation, sustained release, immunoevasion, tissue penetration, imaging, targeting, and triggered activation. Nanoparticles are also processed differently in the body compared to conventional drugs. Specifically, nanoparticles display unique hemodynamic properties and biodistribution profiles. Notably, the interactions that occur at the bio-nano interface can be exploited for improved drug delivery. This review discusses successful clinically approved cancer nanodrugs as well as promising candidates in the pipeline. These nanotherapeutics are categorized according to whether they predominantly exploit multifunctionality, unique electromagnetic properties, or distinct transport characteristics in the body. Moreover, future directions in nanomedicine such as companion diagnostics, strategies for modifying the microenvironment, spatiotemporal nanoparticle transitions, and the use of extracellular vesicles for drug delivery are also explored.