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In vitro selection of functional RNAs from large random sequence pools has led to the identification of many ligand-binding and catalytic RNAs. However, the structural diversity in random pools is not well understood. Such an understanding is a prerequisite for designing sequence pools to increase the probability of finding complex functional RNA by in vitro selection techniques. Toward this goal, we have generated by computer five random pools of RNA sequences of length up to 100 nt to mimic experiments and characterized the distribution of associated secondary structural motifs using sets of possible RNA tree structures derived from graph theory techniques. Our results show that such random pools heavily favor simple topological structures: For example, linear stem-loop and low-branching motifs are favored rather than complex structures with high-order junctions, as confirmed by known aptamers. Moreover, we quantify the rise of structural complexity with sequence length and report the dominant class of tree motifs (characterized by vertex number) for each pool. These analyses show not only that random pools do not lead to a uniform distribution of possible RNA secondary topologies; they point to avenues for designing pools with specific simple and complex structures in equal abundance in the goal of broadening the range of functional RNAs discovered by in vitro selection. Specifically, the optimal RNA sequence pool length to identify a structure with x stems is 20x.

Several real-time PCR (rtPCR) quantification techniques are currently used to determine the expression levels of individual genes from rtPCR data in the form of fluorescence intensities. In most of these quantification techniques, it is assumed that the efficiency of rtPCR is constant. Our analysis of rtPCR data shows, however, that even during the exponential phase of rtPCR, the efficiency of the reaction is not constant, but is instead a function of cycle number. In order to understand better the mechanisms belying this behavior, we have developed a mathematical model of the annealing and extension phases of the PCR process. Using the model, we can simulate the PCR process over a series of reaction cycles. The model thus allows us to predict the efficiency of rtPCR at any cycle number, given a set of initial conditions and parameter values, which can mostly be estimated from biophysical data. The model predicts a precipitous decrease in cycle efficiency when the product concentration reaches a sufficient level for template-template reannealing to compete with primer-template annealing; this behavior is consistent with available experimental data. The quantitative understanding of rtPCR provided by this model can allow us to develop more accurate methods to quantify gene expression levels from rtPCR data. ß 2005 Wiley Periodicals, Inc.

Cancer is a highly heterogeneous disease, exhibiting spatial and temporal variations that pose challenges for designing robust therapies. Here, we propose the VEPART (Virtual Expansion of Populations for Analyzing Robustness of Therapies) technique as a platform that integrates experimental data, mathematical modeling, and statistical analyses for identifying robust optimal treatment protocols. VEPART begins with time course experimental data for a sample population, and a mathematical model fit to aggregate data from that sample population. Using nonparametric statistics, the sample population is amplified and used to create a large number of virtual populations. At the final step of VEPART, robustness is assessed by identifying and analyzing the optimal therapy (perhaps restricted to a set of clinically realizable protocols) across each virtual population. As proof of concept, we have applied the VEPART method to study the robustness of treatment response in a mouse model of melanoma subject to treatment with immunostimulatory oncolytic viruses and dendritic cell vaccines. Our analysis (i) showed that every scheduling variant of the experimentally used treatment protocol is fragile (nonrobust) and (ii) discovered an alternative region of dosing space (lower oncolytic virus dose, higher dendritic cell dose) for which a robust optimal protocol exists.robust therapies | cancer treatment | mathematical modeling | virotherapy | immunotherapy H eterogeneity is a defining feature of cancer (1, 2). Interpatient heterogeneity manifests clinically in variable disease progression and treatment response between patients with the same diagnosis, whereas intrapatient heterogeneity describes variations that exist between tumor cells in a single patient. Intrapatient heterogeneity can be broken down further into intratumor heterogeneity, intrametastatic heterogeneity, intermetastatic heterogeneity, and temporal heterogeneity (2, 3). Intratumor heterogeneity is evident through the presence of multiple genetic subclones within a primary tumor (2), which have even been shown to exist in spatially distinct regions of the primary tumor (4). Intrametastatic heterogeneity is similar to intratumor heterogeneity, but describes heterogeneity within a single metastatic lesion instead of within the primary tumor (2). Intermetastatic heterogeneity, on the other hand, describes variations in subclones between different metastases in the same patient (2). Finally, temporal heterogeneity is defined as changes that take place in the tumor over time, whether they are a result of genomic instability, natural selection, non-Darwinian evolution, or selective pressures imposed by treatment (4-6). Note that, in each case, heterogeneity need not be genetic but may also be epigenetic, phenotypic, or microenvironmental (2, 7, 8).For decades, cancer patients have been treated using standard of care, meaning they receive the best known treatment that has been deemed as efficacious and safe in epidemiological studies (9). However, in the face of such int...

Practically, all chemotherapeutic agents lead to drug resistance. Clinically, it is a challenge to determine whether resistance arises prior to, or as a result of, cancer therapy. Further, a number of different intracellular and microenvironmental factors have been correlated with the emergence of drug resistance. With the goal of better understanding drug resistance and its connection with the tumor microenvironment, we have developed a hybrid discrete-continuous mathematical model. In this model, cancer cells described through a particle-spring approach respond to dynamically changing oxygen and DNA damaging drug concentrations described through partial differential equations. We thoroughly explored the behavior of our self-calibrated model under the following common conditions: a fixed layout of the vasculature, an identical initial configuration of cancer cells, the same mechanism of drug action, and one mechanism of cellular response to the drug. We considered one set of simulations in which drug resistance existed prior to the start of treatment, and another set in which drug resistance is acquired in response to treatment. This allows us to compare how both kinds of resistance influence the spatial and temporal dynamics of the developing tumor, and its clonal diversity. We show that both pre-existing and acquired resistance can give rise to three biologically distinct parameter regimes: successful tumor eradication, reduced effectiveness of drug during the course of treatment (resistance), and complete treatment failure. When a drug resistant tumor population forms from cells that acquire resistance, we find that the spatial component of our model (the microenvironment) has a significant impact on the transient and long-term tumor behavior. On the other hand, when a resistant tumor population forms from pre-existing resistant cells, the microenvironment only has a minimal transient impact on treatment response. Finally, we present evidence that the microenvironmental niches of low drug/sufficient oxygen and low drug/low oxygen play an important role in tumor cell survival and tumor expansion. This may play role in designing new therapeutic agents or new drug combination schedules.

Oncolytic viruses (OVs) are used to treat cancer, as they selectively replicate inside of and lyse tumor cells. The efficacy of this process is limited and new OVs are being designed to mediate tumor cell release of cytokines and co-stimulatory molecules, which attract cytotoxic T cells to target tumor cells, thus increasing the tumor-killing effects of OVs. To further promote treatment efficacy, OVs can be combined with other treatments, such as was done by Huang et al., who showed that combining OV injections with dendritic cell (DC) injections was a more effective treatment than either treatment alone. To further investigate this combination, we built a mathematical model consisting of a system of ordinary differential equations and fit the model to the hierarchical data provided from Huang et al. We used the model to determine the effect of varying doses of OV and DC injections and to test alternative treatment strategies. We found that the DC dose given in Huang et al. was near a bifurcation point and that a slightly larger dose could cause complete eradication of the tumor. Further, the model results suggest that it is more effective to treat a tumor with immunostimulatory oncolytic viruses first and then follow-up with a sequence of DCs than to alternate OV and DC injections. This protocol, which was not considered in the experiments of Huang et al., allows the infection to initially thrive before the immune response is enhanced. Taken together, our work shows how the ordering, temporal spacing, and dosage of OV and DC can be chosen to maximize efficacy and to potentially eliminate tumors altogether.

The holy grail of computational tumor modeling is to develop a simulation tool that can be utilized in the clinic to predict neoplastic progression and propose individualized optimal treatment strategies. In order to develop such a predictive model, one must account for many of the complex processes involved in tumor growth. One interaction that has not been incorporated into computational models of neoplastic progression is the impact that organ-imposed physical confinement and heterogeneity have on tumor growth. For this reason, we have taken a cellular automaton algorithm that was originally designed to simulate spherically symmetric tumor growth and generalized the algorithm to incorporate the effects of tissue shape and structure. We show that models that do not account for organ/tissue geometry and topology lead to false conclusions about tumor spread, shape and size. The impact that confinement has on tumor growth is more pronounced when a neoplasm is growing close to, versus far from, the confining boundary. Thus, any clinical simulation tool of cancer progression must not only consider the shape and structure of the organ in which a tumor is growing, but must also consider the location of the tumor within the organ if it is to accurately predict neoplastic growth dynamics.

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