Tumor selective, replication competent viruses are being tested for cancer gene therapy. This approach introduces a new therapeutic paradigm due to potential replication of the therapeutic agent and induction of a tumor-specific immune response. However, the experimental outcomes are quite variable, even when studies utilize highly inbred strains of mice and the same cell line and virus. Recognizing that virotherapy is an exercise in population dynamics, we utilize mathematical modeling to understand the variable outcomes observed when B16ova malignant melanoma tumors are treated with vesicular stomatitis virus in syngeneic, fully immunocompetent mice. We show how variability in the initial tumor size and the actual amount of virus delivered to the tumor have critical roles on the outcome of therapy. Virotherapy works best when tumors are small, and a robust innate immune response can lead to superior tumor control. Strategies that reduce tumor burden without suppressing the immune response and methods that maximize the amount of virus delivered to the tumor should optimize tumor control in this model system.

Replication-competent viruses are being tested as tumor therapy agents. The fundamental premise of this therapy is the selective infection of the tumor cell population with the amplification of the virus. Spread of the virus in the tumor ultimately should lead to eradication of the cancer. Tumor virotherapy is unlike any other form of cancer therapy as the outcome depends on the dynamics that emerge from the interaction between the virus and tumor cell populations both of which change in time. We explore these interactions using a model that captures the salient biological features of this system in combination with in vivo data. Our results show that various therapeutic outcomes are possible ranging from tumor eradication to oscillatory behavior. Data from in vivo studies support these conclusions and validate our modeling approach. Such realistic models can be used to understand experimental observations, explore alternative therapeutic scenarios and develop techniques to optimize therapy.

Cancer virotherapy represents a dynamical system that requires mathematical modeling for complete understanding of the outcomes. The combination of virotherapy with radiation (radiovirotherapy) has been recently shown to successfully eliminate tumors when virotherapy alone failed. However, it introduces a new level of complexity. We have developed a mathematical model, based on population dynamics, that captures the essential elements of radiovirotherapy. The existence of corresponding equilibrium points related to complete cure, partial cure, and therapy failure is proved and discussed. The parameters of the model were estimated by fitting to experimental data. By using simulations we analyzed the influence of parameters that describe the interaction between virus and tumor cell on the outcome of the therapy. Furthermore, we evaluated relevant therapeutic scenarios for radiovirotherapy, and offered elements for optimization.

Our current understanding of molecular mechanisms of cellular regulation still does not support quantitative predictions of the overall growth kinetics of normal or malignant tissues. However, discernment of the role of growth-factor mediated cell-cell communication in tissue kinetics is possible by the use of simple mathematical models. Here we discuss the design and use of mathematical models in quantifying the contribution of autocrine and paracrine (i.e., humoral) interactions to the kinetics of tissue growth. We present models that include a humorally mediated regulatory feedback among cells built into phenomenological mathematical models of growth. Application of these models to data exemplifies the finite contributions of positive feedback in cell-cell interactions to the overall tissue growth. In addition, we propose a perturbation approach to allow separation of cell-cell interactions dependent on the perturbing agent (such as hormone antagonists in hormone-dependent tissues) from cell-cell interactions independent of it.

Calbindin-D28K is a biologically important protein required for normal neural function and for the transport of calcium in epithelial cells of the intestine and kidney. We have used fluorescence and circular dichroism (CD) spectroscopy to characterize the effects of calcium binding on the structure and stability of calbindin. Ca2+ titration monitored by fluorescence spectroscopy reveals the presence of two classes of calcium-binding sites with association constants ∼107.5 and ∼108.9 M−1. CD spectra in the far-UV spectral range show minor changes upon Ca2+ titration, implying that the secondary structure of calbindin-D28K is not greatly affected. On the basis of the CD spectra in the near-UV spectral range, we conclude that the tertiary structure is more sensitive to Ca2+ addition. The most significant change occurs between pCa 7.0 and pCa 8.0. The variations in the protein thermostability are correlated with those in the near-UV CD spectra. The enthalpy changes upon heat denaturation of calbindin in the apo-state are characteristic of proteins containing several weakly interacting domains with similar thermodynamical properties. Thus, calcium binding by calbindin-D28K largely affects the local structure around the aromatic residues and the thermal stability of the protein; the changes in the secondary structure are insignificant.

The thyroidal sodium iodide symporter (NIS) in combination with various radioactive isotopes has shown promise as a therapeutic gene in various tumor models. Therapy depends on adequate retention of the isotope in the tumor. We hypothesized that in the absence of iodide organification, isotope trapping is a dynamic process either due to slow efflux or re-uptake of the isotope by cells expressing NIS. Iodide efflux is slower in ARH-77 and K-562 cells expressing NIS compared to a thyroid cell line. Isotope retention half times varied linearly with the number of cells expressing NIS. With sufficient NIS expression, iodide efflux is a zero-order process. Efflux kinetics in the presence or absence of perchlorate also supports the hypothesis that iodide re-uptake occurs and contributes to the retention of the isotope in tumor cells. Iodide organification was insignificant. In vivo studies in tumors composed of mixed cell populations confirmed these observations.

A two-compartment model of cancer cells population dynamics proposed by Gyllenberg and Webb includes transition rates between proliferating and quiescent cells as non-specified functions of the total population, N. We define the net inter-compartmental transition rate function: Φ(N). We assume that the total cell population follows the Gompertz growth model, as it is most often empirically found and derive Φ(N). The Gyllenberg–Webb transition functions are shown to be characteristically related through Φ(N). Effectively, this leads to a hybrid model for which we find the explicit analytical solutions for proliferating and quiescent cell populations, and the relations among model parameters. Several classes of solutions are examined. Our model predicts that the number of proliferating cells may increase along with the total number of cells, but the proliferating fraction appears to be a continuously decreasing function. The net transition rate of cells is shown to retain direction from the proliferating into the quiescent compartment. The death rate parameter for quiescent cell population is shown to be a factor in determining the proliferation level for a particular Gompertz growth curve.

We consider a novel numerical characterization of proteomics maps based on the construction of a graph obtained by connecting all protein spots in a proteomics map that are at distance equal to, or smaller than, a critical distance Dc. We refer to the so constructed graph as a cluster graph and we calculate four associated characteristic matrices, previously considered in the literature: (1) the Euclidean-distance matrix ED; (2) the neighborhood-distance matrix ND; (3) the path-distance matrix based on the shortest paths between connected spots PD; and (4) the quotient matrix Q, the elements of which are given as the quotient of the corresponding elements of ED and ND matrices. Numerical descriptors for proteomics maps include in particular the leading eigenvalue of the Q matrix and the family of associated “higher order” matrices defined as powers of Q. These map descriptors show considerable sensitivity to perturbations of proteomics maps by toxicants.

Killer Ig-like receptors (KIRs) are expressed on CD4(+)CD28(null) T cells, a highly oligoclonal subset of T cells that is expanded in patients with rheumatoid arthritis. It is unclear at what stage of development these T cells acquire KIR expression. To determine whether KIR expression is a consequence of clonal expansion and replicative senescence, multiple CD4(+)CD28(null) T cell clones expressing the in vivo dominant TCR beta-chain sequences were identified in three patients and analyzed for their KIR gene expression pattern. Based on sharing of TCR sequences, the clones were grouped into five clone families. The repertoire of KIRs was diverse, even within each clone family; however, the gene expression was not random. Three particular receptors, KIR2DS2, KIR2DL2, and KIR3DL2, had significant differences in gene expression frequencies between the clone families. These data suggest that KIRs are successively acquired after TCR rearrangement, with each clone family developing a dominant expression pattern. The patterns did not segregate with the individual from whom the clones were derived, indicating that peripheral selection in the host environment was not a major shaping force. Several models were examined using a computer algorithm that was designed to simulate the expression of KIRs at various times during T cell proliferation. The computer simulations favored a model in which KIR gene expression is inducible for a limited time during the initial stages of clonal expansion.

DREAM, an EF-hand protein, associates with and modulates the activity of presenilins and Kv4 potassium channels in neural and cardiac tissues and represses prodynorphin andc-fos gene expression by binding to DNA response elements in these genes. Information concerning the metal-binding properties of DREAM and the consequences of metal binding on protein structure are important in understanding how this protein functions in cells. We now show that DREAM binds 1 mol of calcium/mol of protein with relatively high affinity and another 3 mol of calcium with lower affinity. DREAM binds 1 mol of magnesium/mol of protein. DREAM, pre-loaded with 1 mol of calcium, binds 1 mol of magnesium, thus demonstrating that the magnesium-binding site is distinct from the high affinity calcium-binding site. Analysis of metal binding to mutant DREAM protein constructs localizes the high affinity calcium-binding site and the magnesium-binding site to EF-hands 3 or 4. Binding of calcium but not magnesium changes the conformation, stability, and α-helical content of DREAM. Calcium, but not magnesium, reduces the affinity of apo-DREAM for specific DNA response elements in the prodynorphin andc-fos genes. We conclude that DREAM binds calcium and magnesium and that calcium, but not magnesium, modulates DREAM structure and function.

Choline acetyltransferase (ChAT; EC ) catalyzes the reversible synthesis of acetylcholine (ACh) from acetyl CoA and choline at cholinergic synapses. Mutations in genes encoding ChAT affecting motility exist in Caenorhabditis elegans and Drosophila, but no CHAT mutations have been observed in humans to date. Here we report that mutations in CHAT cause a congenital myasthenic syndrome associated with frequently fatal episodes of apnea (CMS-EA). Studies of the neuromuscular junction in this disease show a stimulation-dependent decrease of the amplitude of the miniature endplate potential and no deficiency of the ACh receptor. These findings point to a defect in ACh resynthesis or vesicular filling and to CHAT as one of the candidate genes. Direct sequencing of CHAT reveals 10 recessive mutations in five patients with CMS-EA. One mutation (523insCC) is a frameshifting null mutation. Three mutations (I305T, R420C, and E441K) markedly reduce ChAT expression in COS cells. Kinetic studies of nine bacterially expressed ChAT mutants demonstrate that one mutant (E441K) lacks catalytic activity, and eight mutants (L210P, P211A, I305T, R420C, R482G, S498L, V506L, and R560H) have significantly impaired catalytic efficiencies.

Glucosamine (GlcN) modulates fluoropyrimidine metabolism and enhances cytotoxicity of 5-fluorouridine (FUrd), but not of 5-fluorouracil (FUra), in human tumor models. To elucidate the underlying metabolic differences between FUra and FUrd, by the use of F-19 and P-31 NMR spectroscopy we studied these drugs in multicell tumor spheroids (MTS) formed by human colon carcinoma cells HT-29. This experimental system allowed detailed kinetic measurements of anabolic intracellular phosphates and fluorophosphates over periods of up to 2 days. Time-dependent NMR data were reduced and interpreted by the use of nonlinear compartmental models which yielded numerical values for the empirical rate constants characterizing mass transfer among the compartments. An analysis of these rate constants indicated qualitative and quantitative differences in the metabolism of FUra and FUrd and in the effects of GlcN on these drugs. The enhanced generation of FUDP-hexoses was a predicted effect of GlcN, but inhibited formation of fluorouridine diphosphates and fluorouridine triphosphates in FUra-treated MTS, and the magnitude of stimulation of fluoropyrimidine incorporation into macromolecules in FUrd-treated MTS were not predicted, Copyright (C) 1999 John Wiley & Sons, Ltd.

The Gompertz law of growth has puzzled scientists for decades: while it successfully described growth kinetics of various biological systems (e.g., tumor growth), its foundation has remained unclear. In this paper I recognize the Gompertzian growth as founded on self-similarity, which is so abundant in natural phenomena that it justifiably represents a fundamental natural paradigm. The self-similarity leads to an allometric principle: the sizes of a given biological system at different times are related by a simple power law. The stated relation can be also viewed as basic functional growth equation with unique nonconstant solutions being the Gompertz and the exponential functions. This equation also provides the description of growth and regression dynamics in terms of a difference equation which already has found practical application in characterizing tumor growth kinetics.

The paper discusses the applicability of some empirical and functional mathematical models of tumor growth to multicell tumor spheroids which are a three-dimensional experimental paradigm of prevascular tumors. A new mathematical model based on receptor-mediated regulation of growth is developed and tested and two additional functional models (autostimulation, competing populations) are analyzed. It is demonstrated that these models, defined by two autonomous differential equations, can describe spontaneous tumor regression. The concept of tumor magnification factor, a quantifier of positive feedback mechanisms, is elaborated.