Pulse HIV Vaccination: Feasibility for Virus Eradication and Optimal Vaccination Schedule

We modify the classical virus dynamics model by incorporating an immune response with fixed or fluctuating vaccination frequencies and dosages to obtain a system of impulsive differential equations for the virus dynamics of both the wild-type and mutant strains. This model framework permits us to obtain precise conditions for the virus elimination, which are much more feasible compared with existing results, which require frequent vaccine administration with large dosage. We also consider the corresponding impulsive optimal control problem to describe when and how much of the vaccine should be administered in order to maximize levels of healthy CD4⁺ T cells and immune response cells. A gradient-based optimization method is applied to obtain the optimal schedule numerically. For a case study when the CTL vaccine is administered in a period of one year, our numerical studies support the optimal vaccination schedule consisting of vaccine administration three times, with the first dosage strong (to boost the immune system), followed by a second dosage shortly after (to strengthen the immune response) and then the third and final dosage long after (to ensure the immune system can handle viruses rebound).     

Evolution of Resistance to Targeted Anti-Cancer Therapies during Continuous and Pulsed Administration Strategies

The discovery of small molecules targeted to specific oncogenic pathways has revolutionized anti-cancer therapy. However, such therapy often fails due to the evolution of acquired resistance. One long-standing question in clinical cancer research is the identification of optimum therapeutic administration strategies so that the risk of resistance is minimized. In this paper, we investigate optimal drug dosing schedules to prevent, or at least delay, the emergence of resistance. We design and analyze a stochastic mathematical model describing the evolutionary dynamics of a tumor cell population during therapy. We consider drug resistance emerging due to a single (epi)genetic alteration and calculate the probability of resistance arising during specific dosing strategies. We then optimize treatment protocols such that the risk of resistance is minimal while considering drug toxicity and side effects as constraints. Our methodology can be used to identify optimum drug administration schedules to avoid resistance conferred by one (epi)genetic alteration for any cancer and treatment type.     

Synergy between chemotherapeutic agents and CTLA-4 blockade in preclinical tumor models

Ipilimumab, a cytotoxic T-lymphocyte antigen-4 (CTLA-4) binding agent, has proven to be an effective monotherapy for metastatic melanoma and has shown antitumor activity in trials when administered with other therapeutic agents. We hypothesized that the combination of ipilimumab with chemotherapeutic agents, such as ixabepilone, paclitaxel, etoposide, and gemcitabine, may produce therapeutic synergy based on distinct but complementary mechanisms of action for each drug and unique cellular targets. This concept was investigated using a mouse homolog of ipilimumab in preclinical murine tumor models, including SA1N fibrosarcoma, EMT-6 mammary carcinoma, M109 lung carcinoma, and CT-26 colon carcinoma. Results of CTLA-4 blockade in combination with one of various chemotherapeutic agents demonstrate that synergy occurs in settings where either agent alone was not effective in inducing tumor regression. Furthermore, when combined with CTLA-4 blockade, ixabepilone, etoposide, and gemcitabine elicited prolonged antitumor effects in some murine models with induction of a memory immune response. Future investigations are warranted to determine which specific chemo-immunotherapy combinations, if any, will produce synergistic antitumor effects in the clinical setting.     

Exploring the role of the immune response in preventing antibiotic resistance

For many bacterial infections, drug resistant mutants are likely present by the time antibiotic treatment starts. Nevertheless, such infections are often successfully cleared. It is commonly assumed that this is due to the combined action of drug and immune response, the latter facilitating clearance of the resistant population. However, most studies of drug resistance emergence during antibiotic treatment focus almost exclusively on the dynamics of bacteria and the drug and neglect the contribution of immune defenses. Here, we develop and analyze several mathematical models that explicitly include an immune response. We consider different types of immune responses and investigate how each impacts the emergence of resistance. We show that an immune response that retains its strength despite a strong drug-induced decline of bacteria numbers considerably reduces the emergence of resistance, narrows the mutant selection window, and mitigates the effects of non-adherence to treatment. Additionally, we show that compared to an immune response that kills bacteria at a constant rate, one that trades reduced killing at high bacterial load for increased killing at low bacterial load is sometimes preferable. We discuss the predictions and hypotheses derived from this study and how they can be tested experimentally.     

Engineering bacteria toward tumor targeting for cancer treatment: current state and perspectives

One of the primary limitations of cancer therapy is lack of selectivity of therapeutic agents to tumor cells. Current efforts are focused on discovering and developing anticancer agents that selectively target only tumor cells and spare normal cells to improve the therapeutic index. The use of preferentially replicating bacteria as an oncolytic agent is one of the innovative approaches for the treatment of cancer. This is based on the observation that some obligate or facultative anaerobic bacteria are capable of multiplying selectively in tumors and inhibiting their growth. Meanwhile, bacteria have been demonstrated to colonize and destroy tumor, and have emerged as biological gene vectors to tumor microenvironment. To improve the efficacy and safety of the bacterial therapy, a further understanding of bacteria between with immune system is required. Furthermore, we want to evaluate how bacterial infection facilitates the “bystander effect” of chemotherapeutic agent and assess if it can be used for additional antitumor effect when combined with chemotherapy. This study may not only evaluate therapeutic efficacy of bacteria for the treatment of cancer but also elucidate the mechanisms underlying antitumor activities mediated by bacteria, which involve host immune responses and the cellular molecular responses.     

Optimization of interleukin-21 immunotherapeutic strategies

The recently discovered interleukin-21 (IL-21) shows strong tumor attenuation in preclinical studies, and is considered a promising cancer immunotherapy agent. Yet, to exploit its potential, therapeutic strategies must be designed to achieve adequate balance between several conflicting aspects. A mathematical model describing the IL-21-antitumor effects provided the basis for application of the optimization methodology, aimed at finding improved immunotherapeutic regimens. Both dosages and inter-dosing intervals were optimized while considering maximal efficacy, determined by reduction of tumor burden, and minimal toxicity, estimated by cumulative IL-21 doses applied. Simulations allowed to compute the optimal regimen and explore its dependence on the weights of the target function. Optimized schedules lead to substantial cancer regression even with relatively low drug concentrations. Collectively, administration times shifted towards treatment onset, and IL-21 intensities sequentially decreased. Interestingly, there was a certain window in which deviations in the total IL-21 dosage administered largely influenced tumor elimination. The findings emphasize the importance of early tumor detection and the critical consequence of the inter-dosing interval on therapeutic efficacy, as supported by similar research involving chemotherapy. Our work provides initial basis for identifying clinically applicable IL-21 therapeutic strategies with improved efficacy/toxicity ratios.     

Identification of metabolism-associated molecular subtype in ovarian cancer

Ovarian cancer (OC) is the most lethal gynaecological cancer with genomic complexity and extensive heterogeneity. This study aimed to characterize the molecular features of OC based on the gene expression profile of 2752 previously characterized metabolism-relevant genes and provide new strategies to improve the clinical status of patients with OC. Finally, three molecular subtypes (C1, C2 and C3) were identified. The C2 subtype displayed the worst prognosis, upregulated immune-cell infiltration status and expression level of immune checkpoint genes, lower burden of copy number gains and losses and suboptimal response to targeted drug bevacizumab. The C1 subtype showed downregulated immune-cell infiltration status and expression level of immune checkpoint genes, the lowest incidence of BRCA mutation and optimal response to targeted drug bevacizumab. The C3 subtype had an intermediate immune status, the highest incidence of BRCA mutation and a secondary optimal response to bevacizumab. Gene signatures of C1 and C2 subtypes with an opposite expression level were mainly enriched in proteolysis and immune-related biological process. The C3 subtype was mainly enriched in the T cell-related biological process. The prognostic and immune status of subtypes were validated in the Gene Expression Omnibus (GEO) dataset, which was predicted with a 45-gene classifier. These findings might improve the understanding of the diversity and therapeutic strategies for OC.     

Optimizing the concentration and bolus of a drug delivered by continuous infusion

We consider treatment regimes in which an agent is administered continuously at a specified concentration until either a response is achieved or a predetermined maximum infusion time is reached. Response is an event defined to characterize therapeutic efficacy. A portion of the maximum planned total amount administered is given as an initial bolus. For such regimes, the amount of the agent received by the patient depends on the time to response. An additional complication when response is evaluated periodically rather than continuously is that the response time is interval censored. We address the problem of designing a clinical trial in which such response time data and a binary indicator of toxicity are used together to jointly optimize the concentration and the size of the bolus. We propose a sequentially adaptive Bayesian design that chooses the optimal treatment for successive patients by maximizing the posterior mean utility of the joint efficacy-toxicity outcome. The methodology is illustrated by a trial in which tissue plasminogen activator is infused intraarterially as rapid treatment for acute ischemic stroke.     

Optimal adjustment of the human circadian clock in the real world

Which suggestions for behavioral modifications, based on mathematical models, are most likely to be followed in the real world? We address this question in the context of human circadian rhythms. Jet lag is a consequence of the misalignment of the body’s internal circadian (~24-hour) clock during an adjustment to a new schedule. Light is the clock’s primary synchronizer. Previous research has used mathematical models to compute light schedules that shift the circadian clock to a new time zone as quickly as possible. How users adjust their behavior when provided with these optimal schedules remains an open question. Here, we report data collected by wearables from more than 100 travelers as they cross time zones using a smartphone app, Entrain. We find that people rarely follow the optimal schedules generated through mathematical modeling entirely, but travelers who better followed the optimal schedules reported more positive moods after their trips. Using the data collected, we improve the optimal schedule predictions to accommodate real-world constraints. We also develop a scheduling algorithm that allows for the computation of approximately optimal schedules "on-the-fly" in response to disruptions. User burnout may not be critically important as long as the first parts of a schedule are followed. These results represent a crucial improvement in making the theoretical results of past work viable for practical use and show how theoretical predictions based on known human physiology can be efficiently used in real-world settings.     

Stochastic optimal therapy for enhanced immune response

Therapeutic enhancement of humoral immune response to microbial attack is addressed as the stochastic optimal control of a dynamic system. Without therapy, the modeled immune response depends upon the initial concentration of pathogens in a simulated attack. Immune response can be augmented by agents that kill the pathogen directly, that stimulate the production of plasma cells or antibodies, or that enhance organ health. Using a generic mathematical model of immune response to the infection (i.e., of the dynamic state of the system), previous papers demonstrated optimal (open-loop) and neighboring-optimal (closed-loop) control solutions that defeat the pathogen and preserve organ health, given initial conditions that otherwise would be lethal [Optimal Contr. Appl. Methods 23 (2002) 91, Bioinformatics 18 (2002) 1227]. Therapies based on separate and combined application of the agents were derived by minimizing a quadratic cost function that weighted both system response and drug usage, providing implicit control over harmful side effects. Here, we focus on the effects that corrupted or incomplete measurements of the dynamic state may have on neighboring-optimal feedback control. Imperfect measurements degrade the precision of feedback adjustments to therapy; however, optimal state estimation allows the feedback strategy to be implemented with incomplete measurements and minimizes the expected effects of measurement error. Complete observability of the perturbed state for this four state example is provided by measurement of four of the six possible pairs of two variables, either set of three variables, or all four variables. The inclusion of state estimation extends the applicability of optimal control theory for developing new therapeutic protocols to enhance immune response.     

A theory of drug tolerance and dependence II: the mathematical model

The preceding paper presented a model of drug tolerance and dependence. The model assumes the development of tolerance to a repeatedly administered drug to be the result of a regulated adaptive process. The oral detection and analysis of exogenous substances is proposed to be the primary stimulus for the mechanism of drug tolerance. Anticipation and environmental cues are in the model considered secondary stimuli, becoming primary in dependence and addiction or when the drug administration bypasses the natural-oral-route, as is the case when drugs are administered intravenously. The model considers adaptation to the effect of a drug and adaptation to the interval between drug taking autonomous tolerance processes. Simulations with the mathematical model demonstrate the model's behaviour to be consistent with important characteristics of the development of tolerance to repeatedly administered drugs: the gradual decrease in drug effect when tolerance develops, the high sensitivity to small changes in drug dose, the rebound phenomenon and the large reactions following withdrawal in dependence. The present paper discusses the mathematical model in terms of its design. The model is a nonlinear, learning feedback system, fully satisfying control theoretical principles. It accepts any form of the stimulus-the drug intake-and describes how the physiological processes involved affect the distribution of the drug through the body and the stability of the regulation loop. The mathematical model verifies the proposed theory and provides a basis for the implementation of mathematical models of specific physiological processes.     

Optimal Control in a Model of Dendritic Cell Transfection Cancer Immunotherapy

We construct a population dynamics model of the competition among immune system cells and generic tumor cells. Then, we apply the theory of optimal control to find the optimal schedule of injection of autologous dendritic cells used as immunotherapeutic agent.The optimization method works for a general ODE system and can be applied to find the optimal schedule in a variety of medical treatments that have been described by a mathematical model.     

A Mathematical Model of Cell Cycle Effects in Gastric Cancer Chemotherapy

A mathematical model is presented to investigate the relationship between drug order and treatment response in gastric cancer chemotherapy involving a taxane (either paclitaxel or docetaxel) coupled with flavopiridol. To model treatment effects, we simulate treatment by bolus injection and employ a pulsing condition to indicate cell kill as well as instantaneous changes to the cell’s transition rates. Cell population growth is described using an ordinary differential equation model whereby we examine the treatment effects upon cells in various stages of the cell cycle. Ultimately, the results generated support prior clinical investigations which indicate that for an enhanced synergistic effect, flavopiridol must be administered following taxane therapy.     

Targeting drug delivery to the lungs by inhalation

Most drugs targeted to the respiratory tract are used for their local action. For example, ephidrine for nasal decongestion, beta-2 agonists for bronchodilatation, and inhaled steroids to suppress the inflammation seen in asthmatic airways. Since the drug is delivered directly to its required site, only a small quantity is needed for an adequate therapeutic response, and consequently there is a low incidence of systemic side effects compared with oral or intravenous administration. More recently, it has become apparent that the lining of the respiratory tract, from nasal mucosa to airways and alveoli, may be used for the absorption of a drug for its systemic effect. This route of administration may be particularly attractive if it avoids the metabolic destruction encountered when some drugs are administered by alternative routes (for instance, peptides and proteins are rapidly destroyed by peptidases when Oven by the oral route). If there is a lack ofclinical response to an aerosolized drug, it is important to question whether the drug has failed or whether delivery to the site of action is inadequate. To deliver therapeutic agents by inhalation to the lower respiratory tract, inhaled drug particles must have appropriate aerodynamic characteristics. In addition, the anatomy and pathophysiology of the patient's respiratory tract, mode of inhalation through the inhaler, and the characteristics of the inhalational device itself, may significantly affect drug deposition.     

Optimal controls for a model with pharmacokinetics maximizing bone marrow in cancer chemotherapy

A mathematical model for the depletion of bone marrow under cancer chemotherapy is analyzed as an optimal control problem. The control represents the drug dosage of a single chemotherapeutic agent and pharmacokinetic equations which model its plasma concentration are included. The drug dosages enter the objective linearly. It is shown that optimal controls are bang-bang, i.e. alternate the drug dosages at full dose with rest-periods in between, and that singular controls which correspond to treatment schedules with varying dosages at less than maximum rate are not optimal. Numerical simulations are given to illustrate the effect of the pharmacokinetic equations on the dosages.     

Dynamics and potential impact of the immune response to chronic myelogenous leukemia

Recent mathematical models have been developed to study the dynamics of chronic myelogenous leukemia (CML) under imatinib treatment. None of these models incorporates the anti-leukemia immune response. Recent experimental data show that imatinib treatment may promote the development of anti-leukemia immune responses as patients enter remission. Using these experimental data we develop a mathematical model to gain insights into the dynamics and potential impact of the resulting anti-leukemia immune response on CML. We model the immune response using a system of delay differential equations, where the delay term accounts for the duration of cell division. The mathematical model suggests that anti-leukemia T cell responses may play a critical role in maintaining CML patients in remission under imatinib therapy. Furthermore, it proposes a novel concept of an “optimal load zone” for leukemic cells in which the anti-leukemia immune response is most effective. Imatinib therapy may drive leukemic cell populations to enter and fall below this optimal load zone too rapidly to sustain the anti-leukemia T cell response. As a potential therapeutic strategy, the model shows that vaccination approaches in combination with imatinib therapy may optimally sustain the anti-leukemia T cell response to potentially eradicate residual leukemic cells for a durable cure of CML. The approach presented in this paper accounts for the role of the anti-leukemia specific immune response in the dynamics of CML. By combining experimental data and mathematical models, we demonstrate that persistence of anti-leukemia T cells even at low levels seems to prevent the leukemia from relapsing (for at least 50 months). As a consequence, we hypothesize that anti-leukemia T cell responses may help maintain remission under imatinib therapy. The mathematical model together with the new experimental data imply that there may be a feasible, low-risk, clinical approach to enhancing the effects of imatinib treatment.     

Small heat shock protein as a multifunctional scaffold: integrated tumor targeting and caspase imaging within a single cage

Protein cages have the potential to serve as biomaterials for the targeted therapeutic and imaging systems. As an effort to exploit small heat shock protein (Hsp) cages as multifunctional biomaterials, we demonstrate that chemically and genetically modified Hsp cages permeate the cells via cancer cell binding and subsequent endocytic internalization and can image caspase activity in the live cells. Moreover, we report here that these functional Hsp cages can be specifically accumulated to tumor tissues of tumor-bearing mice when administered intravenously through the lateral tail vein. These tumor-targeting properties could be explained by the prolonged in vivo circulation and enhanced permeability and retention (EPR) effect as well as the ligand-mediated binding to cancer cells. Furthermore, when combined with the caspase sensing ability, our Hsp cage allows us to monitor the therapeutic evaluation after anticancer drug treatment by imaging the caspase activity within tumors. Therefore, we demonstrate that the Hsp cages have multifunctional scaffolds amenable to genetic and chemical modifications without loss of the cagelike architecture and can be exploited as biomedical materials including drug or imaging agent carriers.     

To inhibit or to boost the ATP/P2RX7 pathway to fight cancer—that is the question

Despite new biological insights and recent therapeutic advances, many tumors remain at baseline during treatments. Therefore, there is an urgent need to find new therapeutic strategies to improve the care of patients with solid tumors. P2RX7 receptor (P2XR7), an ATP-gated ion channel characterized by its ability to form large pore within the cell membrane, is described by most of the investigators as a “chef d’orchestre” of the antitumor immune response. The purpose of this review is to detail the recent information concerning different cellular mechanisms linking P2RX7 to hallmarks of cancer and to discuss different progresses in elucidating how activation of the ATP/P2RX7/NLRP3/IL-18 pathway is a very promising approach to fight cancer progression by increasing antitumor immune responses.     

A coupled discrete/continuum model for describing cancer-therapeutic transport in the lung

We propose a computational simulation framework for describing cancer-therapeutic transport in the lung. A discrete vascular graph model (VGM) is coupled to a double-continuum model (DCM) to determine the amount of administered therapeutic agent that will reach the cancer cells. An alveolar cell carcinoma is considered. The processes in the bigger blood vessels (arteries, arterioles, venules and veins) are described by the VGM. The processes in the alveolar capillaries and the surrounding tissue are represented by a continuum approach for porous media. The system of equations of the coupled discrete/continuum model contains terms that account for degradation processes of the therapeutic agent, the reduction of the number of drug molecules by the lymphatic system and the interaction of the drug with the tissue cells. The functionality of the coupled discrete/continuum model is demonstrated in example simulations using simplified pulmonary vascular networks, which are designed to show-off the capabilities of the model rather than being physiologically accurate.     

Calcium signaling and the therapeutic targeting of cancer cells

The calcium signal is implicated in a variety of processes important in tumor progression (e.g. proliferation and invasiveness). The calcium signal has also been shown to be important in other processes important in cancer progression including the development of resistance to current cancer therapies. In this review, we discuss how Ca²⁺ channels, pumps and exchangers may be drug targets in some cancer types. We consider what factors should be taken into account when considering an optimal Ca²⁺ channel, pump or exchanger as a candidate for further assessment as a novel drug target in cancer. We also present and summarize how some therapies for the treatment of cancer intersect with Ca²⁺ signaling and how pharmacological manipulation of the machinery of Ca²⁺ signaling could promote the effectiveness of some therapies. We also review new therapeutic opportunities for Ca²⁺ signal modulators in the context of the tumor microenvironment.