[show abstract][hide abstract] ABSTRACT: To identify sources of inter-subject variation in vaccine responses, we performed high-frequency sampling of human peripheral blood cells post-vaccination, followed by a novel systems biology analysis. Functional principal component analysis was used to examine time varying B cell vaccine responses. In subjects vaccinated within the previous three years, 90% of transcriptome variation was explained by a single subject-specific mathematical pattern. Within individual vaccine response patterns, a common subset of 742 genes was strongly correlated with migrating plasma cells. Of these, 366 genes were associated with human plasmablasts differentiating in vitro. Additionally, subject-specific temporal transcriptome patterns in peripheral blood mononuclear cells identified migration of myeloid/dendritic cell lineage cells one day after vaccination. Upstream analyses of transcriptome changes suggested both shared and subject-specific transcription groups underlying larger patterns. With robust statistical methods, time-varying response characteristics of individual subjects were effectively captured along with a shared plasma cell gene signature.
[show abstract][hide abstract] ABSTRACT: The ELISPOT assay is often used for cell count determination in immunological studies. Automated methods are needed to estimate cell concentrations from spot counts obtained from the assay. Three major distributions are assumed for observational cell counts. For each assumed distribution, individual least squares (LS)/ maximum likelihood and/or individual robust least squares (RLS) are applied for parameter estimation. Distributions of study endpoints (derived variables), defined as percentages of antigen-specific memory cell per total immunoglobulin G (IgG), are investigated to provide a basis for hypothesis testing. We show, under some weak conditions, that the distribution of endpoint estimates across subjects is approximately the same within a group. Thus, the t -test or the Wilcoxon Rank Sum test can be applied to detect group differences. These methods are compared through simulations and application to real data.
Journal of Biopharmaceutical Statistics 07/2013; 23(4):921-936. · 0.73 Impact Factor
[show abstract][hide abstract] ABSTRACT: With the development of micron-scale imaging techniques, capillaries can be conveniently visualized using methods such as two-photon and whole mount microscopy. However, the presence of background staining, leaky vessels and the diffusion of small fluorescent molecules can lead to significant complexity in image analysis and loss of information necessary to accurately quantify vascular metrics. One solution to this problem is the development of accurate thresholding algorithms that reliably distinguish blood vessels from surrounding tissue. Although various thresholding algorithms have been proposed, our results suggest that without appropriate pre- or post-processing, the existing approaches may fail to obtain satisfactory results for capillary images that include areas of contamination. In this study, we propose a novel local thresholding algorithm, called directional histogram ratio at random probes (DHR-RP). This method explicitly considers the geometric features of tube-like objects in conducting image binarization, and has a reliable performance in distinguishing small vessels from either clean or contaminated background. Experimental and simulation studies suggest that our DHR-RP algorithm is superior over existing thresholding methods.
[show abstract][hide abstract] ABSTRACT: Recently, melanoma has become the most malignant and commonly occurring skin cancer. Melanoma is not only the major source (75%) of deaths related to skin cancer, but also it is hard to be treated by the conventional drugs. Recent research indicated that angiogenesis is an important factor for tumor initiation, expansion, and response to therapy. Thus, we proposed a novel multi-scale agent-based computational model that integrates the angiogenesis into tumor growth to study the response of melanoma cancer under combined drug treatment.
Our multi-scale agent-based model can simulate the melanoma tumor growth with angiogenesis under combined drug treatment. The significant synergistic effects between drug Dox and drug Sunitinib demonstrated the clinical potential to interrupt the communication between melanoma cells and its related vasculatures. Also, the sensitivity analysis of the model revealed that diffusivity related to the micro-vasculatures around tumor tissues closely correlated with the spread, oscillation and destruction of the tumor.
Simulation results showed that the 3D model can represent key features of melanoma growth, angiogenesis, and its related micro-environment. The model can help cancer researchers understand the melanoma developmental mechanism. Drug synergism analysis suggested that interrupting the communications between melanoma cells and the related vasculatures can significantly increase the drug efficacy against tumor cells.
Theoretical Biology and Medical Modelling 06/2013; 10(1):41. · 1.46 Impact Factor
[show abstract][hide abstract] ABSTRACT: We review mathematical modeling and related statistical issues of HIV dynamics primarily in response to antiretroviral drug therapy in this article. We start from a basic model of virus infection and then review a number of more advanced models with considering, e.g., pharmacokinetic factors, adherence and drug resistance. Specifically, we illustrate how mathematical models can be developed and parameterized to understand effects of long-term treatment and different treatment strategies on disease progression. In addition, we discuss a variety of parameter estimation methods for differential equation models that are applicable to either within- or between-host viral dynamics.
Advanced drug delivery reviews 04/2013; · 11.96 Impact Factor
[show abstract][hide abstract] ABSTRACT: Background Quantile and rank normalizations are two widely used pre-processingtechniques designed to remove technological noise presented ingenomic data. Subsequent statistical analysis such as genedifferential expression analysis is usually based on normalizedexpressions. In this study, we find that these normalizationprocedures can have a profound impact on differential expressionanalysis, especially in terms of testing power.Results We conduct theoretical derivations to show that the testing power ofdifferential expression analysis based on quantile or ranknormalized gene expressions can never reach 100% with fixed samplesize no matter how strong the gene differentiation effects are.We perform extensive simulation analyses and find theresults corroborate theoretical predictions.Conclusions Our finding may explain why genes with well documentedstrong differentiation are not always detected in microarrayanalysis. It provides new insights in microarray experimental design and will helppractitioners in selecting proper normalization procedures.
[show abstract][hide abstract] ABSTRACT: BACKGROUND: One of the fundamental problems in time course gene expression data analysis is to identify genes associatedwith a biological process or a particular stimulus of interest, like a treatment or virus infection. Most of theexisting methods for this problem are designed for data with longitudinal replicates. But in reality, many timecourse gene experiments have no replicates or only have a small number of independent replicates. RESULTS: We focus on the case without replicates and propose a new method for identifying differentially expressedgenes by incorporating the functional principal component analysis (FPCA) into a hypothesis testingframework. The data-driven eigenfunctions allow a flexible and parsimonious representation of time coursegene expression trajectories, leaving more degrees of freedom for the inference compared to that using aprespecified basis. Moreover, the information of all genes is borrowed for individual gene inferences. CONCLUSION: The proposed approach turns out to be more powerful in identifying time course differentially expressed genescompared to the existing methods. The improved performance is demonstrated through simulation studies anda real data application to the Saccharomyces cerevisiae cell cycle data.
[show abstract][hide abstract] ABSTRACT: Human CD4 T cell recall responses to influenza virus are strongly biased towards Type 1 cytokines, producing IFNγ, IL-2 and TNFα. We have now examined the effector phenotypes of CD4 T cells in more detail, particularly focusing on differences between recent versus long-term, multiply-boosted responses. Peptides spanning the proteome of temporally distinct influenza viruses were distributed into pools enriched for cross-reactivity to different influenza strains, and used to stimulate antigen-specific CD4 T cells representing recent or long-term memory. In the general population, peptides unique to the long-circulating influenza A/New Caledonia/20/99 (H1N1) induced Th1-like responses biased toward the expression of IFNγ(+)TNFα(+) CD4 T cells. In contrast, peptide pools enriched for non-cross-reactive peptides of the pandemic influenza A/California/04/09 (H1N1) induced more IFNγ(-)IL-2(+)TNFα(+) T cells, similar to the IFNγ(-)IL-2(+) non-polarized, primed precursor T cells (Thpp) that are a predominant response to protein vaccination. These results were confirmed in a second study that compared samples taken before the 2009 pandemic to samples taken one month after PCR-confirmed A/California/04/09 infection. There were striking increases in influenza-specific TNFα(+), IFNγ(+), and IL-2(+) cells in the post-infection samples. Importantly, peptides enriched for non-cross-reactive A/California/04/09 specificities induced a higher proportion of Thpp-like IFNγ(-)IL-2(+)TNFα(+) CD4 T cells than peptide pools cross-reactive with previous influenza strains, which induced more Th1 (IFNγ(+)TNFα(+)) responses. These IFNγ(-)IL-2(+)TNFα(+) CD4 T cells may be an important target population for vaccination regimens, as these cells are induced upon infection, may have high proliferative potential, and may play a role in providing future effector cells during subsequent infections.
PLoS ONE 01/2013; 8(3):e57275. · 3.73 Impact Factor
[show abstract][hide abstract] ABSTRACT: The strategies of structured treatment interruptions (STIs) of antiretroviral therapies have been proposed for clinical management of HIV infected patients, but clinical studies on STIs failed to achieve a consistent conclusion for this strategy. To evaluate the STI strategies, in particular, CD4(+) T cell count-guided STIs, and explain these controversial conclusions from different clinical studies, in this paper we propose to use piecewise HIV virus dynamic models to quantitatively explore the STI strategies and investigate their dynamic behaviors. Our analysis results indicate that CD4(+) T cell counts can be maintained above a safe level using the STI with a single threshold or a threshold window. Numerical simulations show that the CD4(+) T cell counts either fluctuate or approach a stable level for a patient, depending on the prescribed upper or lower threshold values. In particular, the CD4(+) T cell counts can be stabilized at a desired level if the threshold policy control is applied. The durations of drug-on and drug-off are very sensitive to the prescribed upper or lower threshold levels, which possibly explains why the on-off strategy with fixed schedule or an STI strategy with frequent switches are associated with the high rate of failure. Our findings suggest that it is critical to carefully choose the thresholds of CD4(+) T cell count and individualize the STIs for each individual patient based on initial CD4(+) T cell counts.
Journal of Theoretical Biology 05/2012; 308:123-34. · 2.35 Impact Factor
[show abstract][hide abstract] ABSTRACT: Although previous studies have found minimal changes in CD4 T cell responses after vaccination of adults with trivalent inactivated influenza vaccine, daily sampling and monitoring of the proliferation marker Ki-67 have now been used to reveal that a substantial fraction of influenza-specific CD4 T cells respond to vaccination. At 4-6 days after vaccination, there is a sharp rise in the numbers of Ki-67-expressing PBMC that produce IFNγ, IL-2 and/or TNFα in vitro in response to influenza vaccine or peptide. Ki-67(+) cell numbers then decline rapidly, and 10 days after vaccination, both Ki-67(+) and overall influenza-specific cell numbers are similar to pre-vaccination levels. These results provide a tool for assessing the quality and quantity of CD4 T cell responses to different influenza vaccines, and raise the possibility that the anti-influenza T cell memory response may be qualitatively altered by vaccination, even if the overall memory cell numbers do not change significantly.
[show abstract][hide abstract] ABSTRACT: Differential equations are extensively used for modeling dynamics of physical processes in many scientific fields such as engineering, physics, and biomedical sciences. Parameter estimation of differential equation models is a challenging problem because of high computational cost and high-dimensional parameter space. In this article, we propose a novel class of methods for estimating parameters in ordinary differential equation (ODE) models, which is motivated by HIV dynamics modeling. The new methods exploit the form of numerical discretization algorithms for an ODE solver to formulate estimating equations. First, a penalized-spline approach is employed to estimate the state variables and the estimated state variables are then plugged in a discretization formula of an ODE solver to obtain the ODE parameter estimates via a regression approach. We consider three different order of discretization methods, Euler's method, trapezoidal rule, and Runge-Kutta method. A higher-order numerical algorithm reduces numerical error in the approximation of the derivative, which produces a more accurate estimate, but its computational cost is higher. To balance the computational cost and estimation accuracy, we demonstrate, via simulation studies, that the trapezoidal discretization-based estimate is the best and is recommended for practical use. The asymptotic properties for the proposed numerical discretization-based estimators are established. Comparisons between the proposed methods and existing methods show a clear benefit of the proposed methods in regards to the trade-off between computational cost and estimation accuracy. We apply the proposed methods t an HIV study to further illustrate the usefulness of the proposed approaches.
[show abstract][hide abstract] ABSTRACT: During the human B cell (Bc) recall response, rapid cell division results in multiple Bc subpopulations. The TLR-9 agonist CpG oligodeoxynucleotide, combined with cytokines, causes Bc activation and division in vitro and increased CD27 surface expression in a sub-population of Bc. We hypothesized that the proliferating CD27(lo) subpopulation, which has a lower frequency of antibody-secreting cells (ASC) than CD27(hi) plasmablasts, provides alternative functions such as cytokine secretion, costimulation, or antigen presentation. We performed genome-wide transcriptional analysis of CpG activated Bc sorted into undivided, proliferating CD27(lo) and proliferating CD27(hi) subpopulations. Our data supported an alternative hypothesis, that CD27(lo) cells are a transient pre-plasmablast population, expressing genes associated with Bc receptor editing. Undivided cells had an active transcriptional program of non-ASC B cell functions, including cytokine secretion and costimulation, suggesting a link between innate and adaptive Bc responses. Transcriptome analysis suggested a gene regulatory network for CD27(lo) and CD27(hi) Bc differentiation.
[show abstract][hide abstract] ABSTRACT: The biological parameters that determine the distribution of virus-specific CD8(+) T cells during influenza infection are not all directly measurable by experimental techniques but can be inferred through mathematical modeling. Mechanistic and semimechanistic ordinary differential equations were developed to describe the expansion, trafficking, and disappearance of activated virus-specific CD8(+) T cells in lymph nodes, spleens, and lungs of mice during primary influenza A infection. An intensive sampling of virus-specific CD8(+) T cells from these three compartments was used to inform the models. Rigorous statistical fitting of the models to the experimental data allowed estimation of important biological parameters. Although the draining lymph node is the first tissue in which Ag-specific CD8(+) T cells are detected, it was found that the spleen contributes the greatest number of effector CD8(+) T cells to the lung, with rates of expansion and migration that exceeded those of the draining lymph node. In addition, models that were based on the number and kinetics of professional APCs fit the data better than those based on viral load, suggesting that the immune response is limited by Ag presentation rather than the amount of virus. Modeling also suggests that loss of effector T cells from the lung is significant and time dependent, increasing toward the end of the acute response. Together, these efforts provide a better understanding of the primary CD8(+) T cell response to influenza infection, changing the view that the spleen plays a minor role in the primary immune response.
The Journal of Immunology 09/2011; 187(9):4474-82. · 5.52 Impact Factor
[show abstract][hide abstract] ABSTRACT: Nonnucleoside reverse transcriptase inhibitors (NNRTIs) are potent and commonly prescribed antiviral agents used in combination therapy (CART) of human immunodeficiency virus type 1 (HIV-1) infection. The development of drug resistance is a major limitation of CART. Reverse transcriptase (RT) genotypes with the NNRTI resistance mutations K101E+G190S are highly resistant to efavirenz (EFV) and can develop during failure of EFV-containing regimens in patients. We have previously shown that virus with K101E+G190S mutations can replicate more efficiently in the presence of EFV than in its absence. In this study, we evaluated the underlying mechanism for drug-dependent stimulation, using a single-cycle cell culture assay in which EFV was added either during the infection or the virus production step. We determined that EFV stimulates K101E+G190S virus during early infection and does not affect late steps of virus replication, such as increasing the amount of active RT incorporated into virions. Additionally, we showed that another NNRTI, nevirapine (NVP), stimulated K101E+G190S virus replication during the early steps of infection similar to EFV, but that the newest NNRTI, etravirine (ETR), did not. We also showed that EFV stimulates K101E+Y188L and K101E+V106I virus, but not K101E+L100I, K101E+K103N, K101E+Y181C, or K101E+G190A virus, suggesting that the stimulation is mutation specific. Real-time PCR of reverse transcription intermediates showed that although the drug did not stimulate minus-strand transfer, it did stimulate minus-strand strong-stop DNA synthesis. Our results indicate that stimulation most likely occurs through a mechanism whereby NNRTIs stimulate priming or elongation of the tRNA.
Journal of Virology 08/2011; 85(20):10861-73. · 5.08 Impact Factor
[show abstract][hide abstract] ABSTRACT: Carboxy-fluorescein diacetate succinimidyl ester (CFSE) labeling is an important experimental tool for measuring cell responses to extracellular signals in biomedical research. However, changes of the cell cycle (e.g., time to division) corresponding to different stimulations cannot be directly characterized from data collected in CFSE-labeling experiments. A number of independent studies have developed mathematical models as well as parameter estimation methods to better understand cell cycle kinetics based on CFSE data. However, when applying different models to the same data set, notable discrepancies in parameter estimates based on different models has become an issue of great concern. It is therefore important to compare existing models and make recommendations for practical use. For this purpose, we derived the analytic form of an age-dependent multitype branching process model. We then compared the performance of different models, namely branching process, cyton, Smith-Martin, and a linear birth-death ordinary differential equation (ODE) model via simulation studies. For fairness of model comparison, simulated data sets were generated using an agent-based simulation tool which is independent of the four models that are compared. The simulation study results suggest that the branching process model significantly outperforms the other three models over a wide range of parameter values. This model was then employed to understand the proliferation pattern of CD4+ and CD8+ T cells under polyclonal stimulation.
Bulletin of Mathematical Biology 06/2011; 74(2):300-26. · 2.02 Impact Factor
[show abstract][hide abstract] ABSTRACT: Differential equation models are widely used for the study of natural phenomena in many fields. The study usually involves unknown factors such as initial conditions and/or parameters. It is important to investigate the impact of unknown factors (parameters and initial conditions) on model outputs in order to better understand the system the model represents. Apportioning the uncertainty (variation) of output variables of a model according to the input factors is referred to as sensitivity analysis. In this paper, we focus on the global sensitivity analysis of ordinary differential equation (ODE) models over a time period using the multivariate adaptive regression spline (MARS) as a meta model based on the concept of the variance of conditional expectation (VCE). We suggest to evaluate the VCE analytically using the MARS model structure of univariate tensor-product functions which is more computationally efficient. Our simulation studies show that the MARS model approach performs very well and helps to significantly reduce the computational cost. We present an application example of sensitivity analysis of ODE models for influenza infection to further illustrate the usefulness of the proposed method.
Bulletin of Mathematical Biology 06/2011; 74(1):73-90. · 2.02 Impact Factor
[show abstract][hide abstract] ABSTRACT: The rapid development of new biotechnologies allows us to deeply understand biomedical dynamic systems in more detail and at a cellular level. Many of the subject-specific biomedical systems can be described by a set of differential or difference equations that are similar to engineering dynamic systems. In this article, motivated by HIV dynamic studies, we propose a class of mixed-effects state-space models based on the longitudinal feature of dynamic systems. State-space models with mixed-effects components are very flexible in modeling the serial correlation of within-subject observations and between-subject variations. The Bayesian approach and the maximum likelihood method for standard mixed-effects models and state-space models are modified and investigated for estimating unknown parameters in the proposed models. In the Bayesian approach, full conditional distributions are derived and the Gibbs sampler is constructed to explore the posterior distributions. For the maximum likelihood method, we develop a Monte Carlo EM algorithm with a Gibbs sampler step to approximate the conditional expectations in the E-step. Simulation studies are conducted to compare the two proposed methods. We apply the mixed-effects state-space model to a data set from an AIDS clinical trial to illustrate the proposed methodologies. The proposed models and methods may also have potential applications in other biomedical system analyses such as tumor dynamics in cancer research and genetic regulatory network modeling.
[show abstract][hide abstract] ABSTRACT: Viral decay rates during efavirenz-based therapy were compared between human immunodeficiency virus (HIV)-infected patients without tuberculosis (n = 40) and those with tuberculosis coinfection who were receiving concurrent antituberculous therapy (n = 34). Phase I and II viral decay rates were similar in the 2 groups (P > .05). Overall, concurrent antituberculous therapy did not reduce the efficacy of the HIV treatment.
[show abstract][hide abstract] ABSTRACT: HIV dynamic studies have contributed significantly to the understanding of HIV pathogenesis and antiviral treatment strategies for AIDS patients. Establishing the relationship of virologic responses with clinical factors and covariates during long-term antiretroviral (ARV) therapy is important to the development of effective treatments. Medication adherence is an important predictor of the effectiveness of ARV treatment, but an appropriate determinant of adherence rate based on medication event monitoring system (MEMS) data is critical to predict virologic outcomes. The primary objective of this paper is to investigate the effects of a number of summary determinants of MEMS adherence rates on virologic response measured repeatedly over time in HIV-infected patients. We developed a mechanism-based differential equation model with consideration of drug adherence, interacted by virus susceptibility to drug and baseline characteristics, to characterize the long-term virologic responses after initiation of therapy. This model fully integrates viral load, MEMS adherence, drug resistance and baseline covariates into the data analysis. In this study we employed the proposed model and associated Bayesian nonlinear mixed-effects modeling approach to assess how to efficiently use the MEMS adherence data for prediction of virologic response, and to evaluate the predicting power of each summary metric of the MEMS adherence rates. In particular, we intend to address the questions: (i) how to summarize the MEMS adherence data for efficient prediction of virologic response after accounting for potential confounding factors such as drug resistance and covariates, and (ii) how to evaluate treatment effect of baseline characteristics interacted with adherence and other clinical factors. The approach is applied to an AIDS clinical trial involving 31 patients who had available data as required for the proposed model. Results demonstrate that the appropriate determinants of MEMS adherence rates are important in order to more efficiently predict virologic response, and investigations of adherence to ARV treatment would benefit from measuring not only adherence rate but also its summary metric assessment. Our study also shows that the mechanism-based dynamic model is powerful and effective to establish a relationship of virologic responses with medication adherence, virus resistance to drug and baseline covariates.
The Annals of Applied Statistics 01/2011; 5(1):551-577. · 2.24 Impact Factor
[show abstract][hide abstract] ABSTRACT: Gene regulation is a complicated process. The interaction of many genes and their products forms an intricate biological network. Identification of this dynamic network will help us understand the biological process in a systematic way. However, the construction of such a dynamic network is very challenging for a high-dimensional system. In this article we propose to use a set of ordinary differential equations (ODE), coupled with dimensional reduction by clustering and mixed-effects modeling techniques, to model the dynamic gene regulatory network (GRN). The ODE models allow us to quantify both positive and negative gene regulations as well as feedback effects of one set of genes in a functional module on the dynamic expression changes of the genes in another functional module, which results in a directed graph network. A five-step procedure, Clustering, Smoothing, regulation Identification, parameter Estimates refining and Function enrichment analysis (CSIEF) is developed to identify the ODE-based dynamic GRN. In the proposed CSIEF procedure, a series of cutting-edge statistical methods and techniques are employed, that include non-parametric mixed-effects models with a mixture distribution for clustering, nonparametric mixed-effects smoothing-based methods for ODE models, the smoothly clipped absolute deviation (SCAD)-based variable selection, and stochastic approximation EM (SAEM) approach for mixed-effects ODE model parameter estimation. The key step, the SCAD-based variable selection of the proposed procedure is justified by investigating its asymptotic properties and validated by Monte Carlo simulations. We apply the proposed method to identify the dynamic GRN for yeast cell cycle progression data. We are able to annotate the identified modules through function enrichment analyses. Some interesting biological findings are discussed. The proposed procedure is a promising tool for constructing a general dynamic GRN and more complicated dynamic networks.
Journal of the American Statistical Association 01/2011; 106(496):1242-1258. · 1.83 Impact Factor