When the optimal is not the best: parameter estimation in complex biological models

Background: The vast computational resources that became available during the past decade enabled the development and simulation of increasingly complex mathematical models of cancer growth. These models typically involve many free parameters whose determination is a substantial obstacle to model development. Direct measurement of biochemical parameters in vivo is often difficult and sometimes impracticable, while fitting them under data-poor conditions may result in biologically implausible values. Results: We discuss different methodological approaches to estimate parameters in complex biological models. We make use of the high computational power of the Blue Gene technology to perform an extensive study of the parameter space in a model of avascular tumor growth. We explicitly show that the landscape of the cost function used to optimize the model to the data has a very rugged surface in parameter space. This cost function has many local minima with unrealistic solutions, including the global minimum corresponding to the best fit. Conclusions: The case studied in this paper shows one example in which model parameters that optimally fit the data are not necessarily the best ones from a biological point of view. To avoid force-fitting a model to a dataset, we propose that the best model parameters should be found by choosing, among suboptimal parameters, those that match criteria other than the ones used to fit the model. We also conclude that the model, data and optimization approach form a new complex system, and point to the need of a theory that addresses this problem more generally

Interplay between distribution of live cells and growth dynamics of solid tumours

Experiments show that simple diffusion of nutrients and waste molecules is not sufficient to explain the typical multilayered structure of solid tumours, where an outer rim of proliferating cells surrounds a layer of quiescent but viable cells and a central necrotic region. These experiments challenge models of tumour growth based exclusively on diffusion. Here we propose a model of tumour growth that incorporates the volume dynamics and the distribution of cells within the viable cell rim. The model is suggested by in silico experiments and is validated using in vitro data. The results correlate with in vivo data as well, and the model can be used to support experimental and clinical oncology

Tumor growth instability and the onset of invasion

Motivated by experimental observations, we develop a mathematical model of chemotactically directed tumor growth. We present an analytical study of the model as well as a numerical one. The mathematical analysis shows that: (i) tumor cell proliferation by itself cannot generate the invasive branching behaviour observed experimentally, (ii) heterotype chemotaxis provides an instability mechanism that leads to the onset of tumor invasion and (iii) homotype chemotaxis does not provide such an instability mechanism but enhances the mean speed of the tumor surface. The numerical results not only support the assumptions needed to perform the mathematical analysis but they also provide evidence of (i), (ii) and (iii). Finally, both the analytical study and the numerical work agree with the experimental phenomena.Comment: 12 pages, 8 figures, revtex

The transcriptomic evolution of mammalian pregnancy:gene expression innovations in endometrial stromal fibroblasts

The endometrial stromal fibroblast (ESF) is a cell type present in the uterine lining of therian mammals. In the stem lineage of eutherian mammals, ESF acquired the ability to differentiate into decidual cells in order to allow embryo implantation. We call the latter cell type “neo-ESF” in contrast to “paleo-ESF” which is homologous to eutherian ESF but is not able to decidualize. In this study, we compare the transcriptomes of ESF from six therian species: Opossum (Monodelphis domestica; paleo-ESF), mink, rat, rabbit, human (all neo-ESF), and cow (secondarily nondecidualizing neo-ESF). We find evidence for strong stabilizing selection on transcriptome composition suggesting that the expression of approximately 5,600 genes is maintained by natural selection. The evolution of neo-ESF from paleo-ESF involved the following gene expression changes: Loss of expression of genes related to inflammation and immune response, lower expression of genes opposing tissue invasion, increased markers for proliferation as well as the recruitment of FOXM1, a key gene transiently expressed during decidualization. Signaling pathways also evolve rapidly and continue to evolve within eutherian lineages. In the bovine lineage, where invasiveness and decidualization were secondarily lost, we see a re-expression of genes found in opossum, most prominently WISP2, and a loss of gene expression related to angiogenesis. The data from this and previous studies support a scenario, where the proinflammatory paleo-ESF was reprogrammed to express anti-inflammatory genes in response to the inflammatory stimulus coming from the implanting conceptus and thus paving the way for extended, trans-cyclic gestation

Ranking ligand affinity for the DNA minor groove by experiment and simulation

The structural and thermodynamic basis for the strength and selectivity of the interactions of minor-groove binders (MGBs) with DNA is not fully understood. In 2003 we reported the first example of a thiazole containing MGB that bound in a phase shifted pattern that spanned 6 base-pairs rather than the usual 4 (for tricyclic distamycin-like compounds). Since then, using DNA footprinting, nuclear magnetic resonance spectroscopy, isothermal titration calorimetry and molecular dynamics, we have established that the flanking bases around the central 4 being read by the ligand have subtle effects on recognition. We have investigated the effect of these flanking sequences on binding and the reasons for the differences and established a computational method to rank ligand affinity against varying DNA sequences

The pressure-volume-temperature relationship of cellulose

Pressure–volume–temperature (PVT) mea- surements of a-cellulose with different water contents, were performed at temperatures from 25 to 180 °C and pressures from 19.6 to 196 MPa. PVT measurements allowed observation of the combined effects of pressure and temperature on the specific volume during cellulose thermo-compression. All isobars showed a decrease in cellulose specific volume with temperature. This densification is associated with a transition process of the cellulose, occurring at a temperature defined by the inflection point Tt of the isobar curve. Tt decreases from 110 to 40 °C with pressure and is lower as moisture content increases. For isobars obtained at high pressures and high moisture contents, after attaining a minimum, an increase in volume is observed with temperature that may be related to free water evaporation. PVT a-cellulose experimental data was compared with predicted values from a regression analysis of the Tait equations of state, usually applied to synthetic polymers. Good correla- tions were observed at low temperatures and low pressures. The densification observed from the PVT experimental data, at a temperature that decreases with pressure, could result from a sintering phenomenon, but more research is needed to actually understand the cohesion mechanism under these conditions

Prognostic factors for tumour response, progression-free survival and toxicity in metastatic colorectal cancer patients given irinotecan (CPT-11) as second-line chemotherapy after 5FU failure

Our purpose was to determine, in patients with metastatic colorectal carcinoma treated with irinotecan single-agent after 5-FU failure, the most significant predictive parameters for tumour response, progression-free survival and toxicity. Between October 1992 and April 1995, 455 patients with 5-FU resistant metastatic colorectal carcinoma entered four consecutive phase II trials. The first two studies assessed tumour response, the other two were randomized studies which assessed the efficacy of racecadotril to prevent irinotecan-induced diarrhoea. Due to homogeneous main eligibility criterias, data from those studies could be pooled for statistical analysis. Potential clinical and biological predictive factors (PF) for toxicity, tumour growth control, e.g. response or stabilization and progression-free survival (PFS), were studied in multivariate analysis. 363 patients were evaluable for response, 432 were evaluable for PFS, 368 for neutropenia and 416 for delayed diarrhoea, respectively. Normal baseline haemoglobin level (Hb), time since diagnosis of colorectal carcinoma, grade 3 or 4 neutropenia or diarrhoea at first cycle and a low number of organs involved were the most PF for tumour growth control (P< 0.05). Significant prognostic variables for PFS were WHO Performance Status, liver and lymph-node involvement, time since diagnosis, age and CEA value (P≤ 0.02). Six groups of patients based on the number of unfavourable prognostic factors are presented. Baseline bilirubin, haemoglobin level, number of organs involved and time from diagnosis were PF for neutropenia; PS, serum creatinine, leukocyte count, time from 5-FU progression and prior abdominopelvic irradiation were PF for delayed diarrhoea (P≤ 0.05). These PF should help clinicians to anticipate for a given patient the probability to observe a response/stabilization or a toxicity. These results should also be prospectively confirmed in ongoing or future trials using irinotecan, both as a single agent and in combination with other drugs. © 2000 Cancer Research Campaig

Attitudes of Physicians Toward Risk Assessment and Use of Granulocyte-Colony Stimulating Factor (G-Csf) As Primary Prophylaxis (Pp) in Patients (Pts) Receiving Chemotherapy with an Intermediate Risk of Febrile Neutropenia (Fn)

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