Dynamics of a cytokine storm.

Six volunteers experienced severe inflammatory response during the Phase I clinical trial of a monoclonal antibody that was designed to stimulate a regulatory T cell response. Soon after the trial began, each volunteer experienced a "cytokine storm", a dramatic increase in cytokine concentrations. The monoclonal antibody, TGN1412, raised serum concentrations of both pro- and anti-inflammatory cytokines το very hiγh values during the first day, while lymphocyte and monocyte concentrations plummeted. Because the subjects were healthy and had no prior indications of immune deficiency, this event provided an unusual opportunity to study the dynamic interactions of cytokines and other measured parameters. Here, the response histories of nine cytokines have been modeled by a set of linear ordinary differential equations. A general search procedure identifies parameters of the model, whose response fits the data well during the five-day measurement period. The eighteenth-order model reveals plausible cause-and-effect relationships among the cytokines, showing how each cytokine induces or inhibits other cytokines. It suggests that perturbations in IL2, IL8, and IL10 have the most significant inductive effect, while IFN-γ and IL12 have the greatest inhibiting effect on other cytokine concentrations. Although TNF-α is a major pro-inflammatory factor, IFN-γ and three other cytokines have faster initial and median response to TGN1412 infusion. Principal-component analysis of the data reveals three clusters of similar cytokine responses: [TNF-α, IL1, IL10], [IFN-γ, IL2, IL4, IL8, and IL12], and [IL6]. IL1, IL6, IL10, and TNF-α have the highest degree of variability in response to uncertain initial conditions, exogenous effects, and parameter estimates. This study illuminates details of a cytokine storm event, and it demonstrates the value of linear modeling for interpreting complex, coupled biological system dynamics from empirical data.

The signatures of autozygosity among patients with colorectal cancer.

Previous studies have shown that among populations with a high rate of consanguinity, there is a significant increase in the prevalence of cancer. Single nucleotide polymorphism (SNP) array data (Affymetrix, 50K XbaI) analysis revealed long regions of homozygosity in genomic DNAs taken from tumor and matched normal tissues of colorectal cancer (CRC) patients. The presence of these regions in the genome may indicate levels of consanguinity in the individual's family lineage. We refer to these autozygous regions as identity-by-descent (IBD) segments. In this study, we compared IBD segments in 74 mostly Caucasian CRC patients (mean age of 66 years) to two control data sets: (a) 146 Caucasian individuals (mean age of 80 years) who participated in an age-related macular degeneration (AMD) study and (b) 118 cancer-free Caucasian individuals from the Framingham Heart Study (mean age of 67 years). Our results show that the percentage of CRC patients with IBD segments (>or=4 Mb length and 50 SNPs probed) in the genome is at least twice as high as the AMD or Framingham control groups. Also, the average length of these IBD regions in the CRC patients is more than twice the length of the two control data sets. Compared with control groups, IBD segments are found to be more common among individuals of Jewish background. We believe that these IBD segments within CRC patients are likely to harbor important CRC-related genes with low-penetrance SNPs and/or mutations, and, indeed, two recently identified CRC predisposition SNPs in the 8q24 region were confirmed to be homozygous in one particular patient carrying an IBD segment covering the region.

Mutation and control of the human immunodeficiency virus.

We examine the dynamics of infection by the human immunodeficiency virus (HIV), as well as therapies that minimize viral load, restore adaptive immunity, and use minimal dosage of anti-HIV drugs. Virtual therapies for wild-type infections are demonstrated; however, the HIV infection is never cured, requiring continued treatment to keep the condition in remission. With high viral turnover and mutation rates, drug-resistant strains of HIV evolve quickly. The ability of optimal therapy to contain drug-resistant strains is shown to depend upon the relative fitness of mutant strains.

Relationship of gene expression and chromosomal abnormalities in colorectal cancer.

Several studies have verified the existence of multiple chromosomal abnormalities in colon cancer. However, the relationships between DNA copy number and gene expression have not been adequately explored nor globally monitored during the progression of the disease. In this work, three types of array-generated data (expression, single nucleotide polymorphism, and comparative genomic hybridization) were collected from a large set of colon cancer patients at various stages of the disease. Probes were annotated to specific chromosomal locations and coordinated alterations in DNA copy number and transcription levels were revealed at specific positions. We show that across many large regions of the genome, changes in expression level are correlated with alterations in DNA content. Often, large chromosomal segments, containing multiple genes, are transcriptionally affected in a coordinated way, and we show that the underlying mechanism is a corresponding change in DNA content. This implies that whereas specific chromosomal abnormalities may arise stochastically, the associated changes in expression of some or all of the affected genes are responsible for selecting cells bearing these abnormalities for clonal expansion. Indeed, particular chromosomal regions are frequently gained and overexpressed (e.g., 7p, 8q, 13q, and 20q) or lost and underexpressed (e.g., 1p, 4, 5q, 8p, 14q, 15q, and 18) in primary colon tumors, making it likely that these changes favor tumorigenicity. Furthermore, we show that these aberrations are absent in normal colon mucosa, appear in benign adenomas (albeit only in a small fraction of the samples), become more frequent as disease advances, and are found in the majority of metastatic samples.

Smooth function approximation using neural networks.

An algebraic approach for representing multidimensional nonlinear functions by feedforward neural networks is presented. In this paper, the approach is implemented for the approximation of smooth batch data containing the function's input, output, and possibly, gradient information. The training set is associated to the network adjustable parameters by nonlinear weight equations. The cascade structure of these equations reveals that they can be treated as sets of linear systems. Hence, the training process and the network approximation properties can be investigated via linear algebra. Four algorithms are developed to achieve exact or approximate matching of input-output and/or gradient-based training sets. Their application to the design of forward and feedback neurocontrollers shows that algebraic training is characterized by faster execution speeds and better generalization properties than contemporary optimization techniques.

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.

Optimal enhancement of immune response.

MOTIVATION: Therapeutic enhancement of innate immune response to microbial attack is addressed as the optimal control of a dynamic system. Interactions between an invading pathogen and the innate immune system are characterized by four non-linear, ordinary differential equations that describe rates of change of pathogen, plasma cell, and antibody concentrations, and of an indicator of organic health. Without therapy, the dynamic model evidences sub-clinical or clinical decay, chronic stabilization, or unrestrained lethal growth of the pathogen; the response pattern depends on the initial concentration of pathogens in the simulated attack. In the model, immune response can be augmented by therapeutic agents that kill the pathogen directly, that stimulate the production of plasma cells or antibodies, or that enhance organ health. A previous paper demonstrated open-loop optimal control solutions that defeat the pathogen and preserve organ health, given initial conditions that otherwise would be lethal (Stengel et al. (2002)). Therapies based on separate and combined application of the agents were derived by minimizing a quadratic cost function that weighted both system response and control usage, providing implicit control over harmful side effects. RESULTS: We demonstrate the ability of neighboring-optimal feedback control to account for a range of unknown initial conditions and persistent input of pathogens by adjusting the therapy to account for perturbations from the nominal-optimal response history. We examine therapies that combine open-loop control of one agent with closed-loop control of another. We show that optimal control theory points the way toward new protocols for treatment and cure of human diseases. CONTACT: stengel@princeton.edu; rghiglia@princeton.edu; nkulkarn@princeton.edu