A prelude to the fractional calculus applied to tumor dynamic

In order to refine the solution given by the classical logistic equation and extend its range of applications in the study of tumor dynamics, we propose and solve a generalization of this equation, using the so-called Fractional Calculus, i.e., we replace the ordinary derivative of order 1, in one version of the usual equation, by a non-integer derivative of order 0 < α < 1, and recover the classical solution as a particular case. Finally, we analyze the applicability of this model to describe the growth of cancer tumors.

Das transformadas integrais ao cálculo fracionário aplicado à equação logística

Pós-graduação em Biometria - IBB

Cálculo fracionário aplicado em dinâmica tumoral: método da Transformada Diferencial generalizada

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Mathematical Models of Tumor-Immune System Dynamics

"This collection of papers offers a broad synopsis of state-of-the-art mathematical methods used in modeling the interaction between tumors and the immune system. These papers were presented at the four-day workshop on Mathematical Models of Tumor-Immune System Dynamics held in Sydney, Australia from January 7th to January 10th, 2013. The workshop brought together applied mathematicians, biologists, and clinicians actively working in the field of cancer immunology to share their current research and to increase awareness of the innovative mathematical tools that are applicable to the growing field of cancer immunology. Recent progress in cancer immunology and advances in immunotherapy suggest that the immune system plays a fundamental role in host defense against tumors and could be utilized to prevent or cure cancer. Although theoretical and experimental studies of tumor-immune system dynamics have a long history, there are still many unanswered questions about the mechanisms that govern the interaction between the immune system and a growing tumor. The multidimensional nature of these complex interactions requires a cross-disciplinary approach to capture more realistic dynamics of the essential biology. The papers presented in this volume explore these issues and the results will be of interest to graduate students and researchers in a variety of fields within mathematical and biological sciences."--Publisher website

Taxol Suppresses Dynamics of Individual Microtubules in Living Human Tumor Cells

Microtubules are intrinsically dynamic polymers, and their dynamics play a crucial role in mitotic spindle assembly, the mitotic checkpoint, and chromosome movement. We hypothesized that, in living cells, suppression of microtubule dynamics is responsible for the ability of taxol to inhibit mitotic progression and cell proliferation. Using quantitative fluorescence video microscopy, we examined the effects of taxol (30–100 nM) on the dynamics of individual microtubules in two living human tumor cell lines: Caov-3 ovarian adenocarcinoma cells and A-498 kidney carcinoma cells. Taxol accumulated more in Caov-3 cells than in A-498 cells. At equivalent intracellular taxol concentrations, dynamic instability was inhibited similarly in the two cell lines. Microtubule shortening rates were inhibited in Caov-3 cells and in A-498 cells by 32 and 26%, growing rates were inhibited by 24 and 18%, and dynamicity was inhibited by 31 and 63%, respectively. All mitotic spindles were abnormal, and many interphase cells became multinucleate (Caov-3, 30%; A-498, 58%). Taxol blocked cell cycle progress at the metaphase/anaphase transition and inhibited cell proliferation. The results indicate that suppression of microtubule dynamics by taxol deleteriously affects the ability of cancer cells to properly assemble a mitotic spindle, pass the metaphase/anaphase checkpoint, and produce progeny.

Large-scale molecular dynamics simulations of HLA-A*0201 complexed with a tumor-specific antigenic peptide:can the α3 and β2m domains be neglected?

Large-scale massively parallel molecular dynamics (MD) simulations of the human class I major histo-compatibility complex (MHC) protein HLA-A*0201 bound to a decameric tumor-specific antigenic peptide GVY-DGREHTV were performed using a scalable MD code on high-performance computing platforms. Such computational capabilities put us in reach of simulations of various scales and complexities. The supercomputing resources available Large-scale massively parallel molecular dynamics (MD) simulations of the human class I major histocompatibility complex (MHC) protein HLA-A*0201 bound to a decameric tumor-specific antigenic peptide GVYDGREHTV were performed using a scalable MD code on high-performance computing platforms. Such computational capabilities put us in reach of simulations of various scales and complexities. The supercomputing resources available for this study allow us to compare directly differences in the behavior of very large molecular models; in this case, the entire extracellular portion of the peptide–MHC complex vs. the isolated peptide binding domain. Comparison of the results from the partial and the whole system simulations indicates that the peptide is less tightly bound in the partial system than in the whole system. From a detailed study of conformations, solvent-accessible surface area, the nature of the water network structure, and the binding energies, we conclude that, when considering the conformation of the α1–α2 domain, the α3 and β2m domains cannot be neglected. © 2004 Wiley Periodicals, Inc. J Comput Chem 25: 1803–1813, 2004

Tissue-engineered 3D tumor angiogenesis models : potential technologies for anti-cancer drug discovery

Angiogenesis is indispensable for solid tumor expansion, and thus it has become a major target of cancer research and anti-cancer therapies. Deciphering the arcane actions of various cell populations during tumor angiogenesis requires sophisticated research models, which could capture the dynamics and complexity of the process. There is a continuous need for improvement of existing research models, which engages interdisciplinary approaches of tissue engineering with life sciences. Tireless efforts to develop a new model to study tumor angiogenesis result in innovative solutions, which bring us one step closer to decipher the dubious nature of cancer. This review aims to overview the recent developments, current limitations and future challenges in three-dimensional tissue-engineered models for the study of tumor angiogenesis and for the purpose of elucidating novel targets aimed at anti-cancer drug discovery.

An Antitubulin Agent BCFMT Inhibits Proliferation of Cancer Cells and Induces Cell Death by Inhibiting Microtubule Dynamics

Using cell based screening assay, we identified a novel anti-tubulin agent (Z)-5-((5-(4-bromo-3-chlorophenyl)furan-2-yl)methylene)-2-thioxothiazoli din-4-one (BCFMT) that inhibited proliferation of human cervical carcinoma (HeLa) (IC50, 7.2 +/- 1.8 mu M), human breast adenocarcinoma (MCF-7) (IC50, 10.0 +/- 0.5 mu M), highly metastatic breast adenocarcinoma (MDA-MB-231) (IC50, 6.0 +/- 1 mu M), cisplatin-resistant human ovarian carcinoma (A2780-cis) (IC50, 5.8 +/- 0.3 mu M) and multi-drug resistant mouse mammary tumor (EMT6/AR1) (IC50, 6.5 +/- 1 mu M) cells. Using several complimentary strategies, BCFMT was found to inhibit cancer cell proliferation at G2/M phase of the cell cycle apparently by targeting microtubules. In addition, BCFMT strongly suppressed the dynamics of individual microtubules in live MCF-7 cells. At its half maximal proliferation inhibitory concentration (10 mu M), BCFMT reduced the rates of growing and shortening phases of microtubules in MCF-7 cells by 37 and 40%, respectively. Further, it increased the time microtubules spent in the pause (neither growing nor shortening detectably) state by 135% and reduced the dynamicity (dimer exchange per unit time) of microtubules by 70%. In vitro, BCFMT bound to tubulin with a dissociation constant of 8.3 +/- 1.8 mu M, inhibited tubulin assembly and suppressed GTPase activity of microtubules. BCFMT competitively inhibited the binding of BODIPY FL-vinblastine to tubulin with an inhibitory concentration (K-i) of 5.2 +/- 1.5 mu M suggesting that it binds to tubulin at the vinblastine site. In cultured cells, BCFMT-treatment depolymerized interphase microtubules, perturbed the spindle organization and accumulated checkpoint proteins (BubR1 and Mad2) at the kinetochores. BCFMT-treated MCF-7 cells showed enhanced nuclear accumulation of p53 and its downstream p21, which consequently activated apoptosis in these cells. The results suggested that BCFMT inhibits proliferation of several types of cancer cells including drug resistance cells by suppressing microtubule dynamics and indicated that the compound may have chemotherapeutic potential.

Forced Dissociation of Selectin-ligand Complexes Using Steered Molecular Dynamics Simulation

Selectin-ligand interactions are crucial to such biological processes as inflammatory cascade or tumor metastasis. How transient formation and dissociation of selectin-ligand bonds in blood flow are coupled to molecular conformation at atomic level, however, has not been well understood. In this study, steered molecular dynamics (SMD) simulations were used to elucidate the intramolecular and intermolecular conformational evolutions involved in forced dissociation of three selectin-ligand systems: the construct consisting of P-selectin lectin (Lec) and epidermal growth factor (EGF)-like domains (P-LE) interacting with synthesized sulfoglycopeptide or SGP-3, P-LE with sialyl Lewis X (sLeX), and E-LE with sLeX. SMD simulations were based on newly built-up force field parameters including carbohydrate units and sulfated tyrosine(s) using an analogy approach. The simulations demonstrated that the complex dissociation was coupled to the molecular extension. While the intramolecular unraveling in P-LESGP-3 system mainly resulted from the destroy of the two anti-parallel sheets of EGF domain and the breakage of hydrogen-bond cluster at the Lec-EGF interface, the intermolecular dissociation was mainly determined by separation of fucose (FUC) from Ca2+ ion in all three systems. Conformational changes during forced dissociations depended on pulling velocities and forces, as well as on how the force was applied. This work provides an insight into better understanding of conformational changes and adhesive functionality of selectin-ligand interactions under external forces.

Snap-shot multispectral imaging of vascular dynamics in a mouse window-chamber model.

Understanding tumor vascular dynamics through parameters such as blood flow and oxygenation can yield insight into tumor biology and therapeutic response. Hyperspectral microscopy enables optical detection of hemoglobin saturation or blood velocity by either acquiring multiple images that are spectrally distinct or by rapid acquisition at a single wavelength over time. However, the serial acquisition of spectral images over time prevents the ability to monitor rapid changes in vascular dynamics and cannot monitor concurrent changes in oxygenation and flow rate. Here, we introduce snap shot-multispectral imaging (SS-MSI) for use in imaging the microvasculature in mouse dorsal-window chambers. By spatially multiplexing spectral information into a single-image capture, simultaneous acquisition of dynamic hemoglobin saturation and blood flow over time is achieved down to the capillary level and provides an improved optical tool for monitoring rapid in vivo vascular dynamics.

Gelsolin induces colorectal tumor cell invasion via modulation of the urokinase-type plasminogen activator cascade

Gelsolin is a cytoskeletal protein which participates in actin filament dynamics and promotes cell motility and plasticity. Although initially regarded as a tumor suppressor, gelsolin expression in certain tumors correlates with poor prognosis and therapy-resistance. In vitro, gelsolin has anti-apoptotic and pro-migratory functions and is critical for invasion of some types of tumor cells. We found that gelsolin was highly expressed at tumor borders infiltrating into adjacent liver tissues, as examined by immunohistochemistry. Although gelsolin contributes to lamellipodia formation in migrating cells, the mechanisms by which it induces tumor invasion are unclear. Gelsolin's influence on the invasive activity of colorectal cancer cells was investigated using overexpression and small interfering RNA knockdown. We show that gelsolin is required for invasion of colorectal cancer cells through matrigel. Microarray analysis and quantitative PCR indicate that gelsolin overexpression induces the upregulation of invasion-promoting genes in colorectal cancer cells, including the matrix-degrading urokinase-type plasminogen activator (uPA). Conversely, gelsolin knockdown reduces uPA levels, as well as uPA secretion. The enhanced invasiveness of gelsolin-overexpressing cells was attenuated by treatment with function-blocking antibodies to either uPA or its receptor uPAR, indicating that uPA/uPAR activity is crucial for gelsolin-dependent invasion. In summary, our data reveals novel functions of gelsolin in colorectal tumor cell invasion through its modulation of the uPA/uPAR cascade, with potentially important roles in colorectal tumor dissemination to metastatic sites.

KATNAL1 regulation of sertoli cell microtubule dynamics is essential for spermiogenesis and male fertility

Spermatogenesis is a complex process reliant upon interactions between germ cells (GC) and supporting somatic cells. Testicular Sertoli cells (SC) support GCs during maturation through physical attachment, the provision of nutrients, and protection from immunological attack. This role is facilitated by an active cytoskeleton of parallel microtubule arrays that permit transport of nutrients to GCs, as well as translocation of spermatids through the seminiferous epithelium during maturation. It is well established that chemical perturbation of SC microtubule remodelling leads to premature GC exfoliation demonstrating that microtubule remodelling is an essential component of male fertility, yet the genes responsible for this process remain unknown. Using a random ENU mutagenesis approach, we have identified a novel mouse line displaying male-specific infertility, due to a point mutation in the highly conserved ATPase domain of the novel KATANIN p60-related microtubule severing protein Katanin p60 subunit A-like1 (KATNAL1). We demonstrate that Katnal1 is expressed in testicular Sertoli cells (SC) from 15.5 days post-coitum (dpc) and that, consistent with chemical disruption models, loss of function of KATNAL1 leads to male-specific infertility through disruption of SC microtubule dynamics and premature exfoliation of spermatids from the seminiferous epithelium. The identification of KATNAL1 as an essential regulator of male fertility provides a significant novel entry point into advancing our understanding of how SC microtubule dynamics promotes male fertility. Such information will have resonance both for future treatment of male fertility and the development of non-hormonal male contraceptives.

Hypoxia response element-driven cytosine deaminase/5-fluorocytosine gene therapy system:a highly effective approach to overcome the dynamics of tumour hypoxia and enhance the radiosensitivity of prostate cancer cells in vitro

BACKGROUND: We proposed to exploit hypoxia-inducible factor (HIF)-1alpha overexpression in prostate tumours and use this transcriptional machinery to control the expression of the suicide gene cytosine deaminase (CD) through binding of HIF-1alpha to arrangements of hypoxia response elements. CD is a prodrug activation enzyme, which converts inactive 5-fluorocytosine to active 5-fluorouracil (5-FU), allowing selective killing of vector containing cells.

METHODS: We developed a pair of vectors, containing either five or eight copies of the hypoxia response element (HRE) isolated from the vascular endothelial growth factor (pH5VCD) or glycolytic enzyme glyceraldehyde-3-phosphate dehydrogenase (pH8GCD) gene, respectively. The kinetics of the hypoxic induction of the vectors and sensitization effects were evaluated in 22Rv1 and DU145 cells in vitro.

RESULTS: The CD protein as selectively detected in lysates of transiently transfected 22Rv1 and DU145 cells following hypoxic exposure. This is the first evidence of GAPDH HREs being used to control a suicide gene therapy strategy. Detectable CD levels were sustained upon reoxygenation and prolonged hypoxic exposures. Hypoxia-induced chemoresistance to 5-FU was overcome in both cell lines treated with this suicide gene therapy approach. Hypoxic transfectants were sensitized to prodrug concentrations that were ten-fold lower than those that are clinically relevant. Moreover, the surviving fraction of reoxygenated transfectants could be further reduced with the concomitant delivery of clinically relevant single radiation doses.

CONCLUSIONS: This strategy thus has the potential to sensitize the hypoxic compartment of prostate tumours and improve the outcome of current therapies.

The dynamics of murid gammaherpesvirus 4 within wild, sympatric populations of bank voles and wood mice

Murid gammaherpesvirus 4 (MuHV-4) is widely used as a small animal model for understanding gammaherpesvirus infections in man. However, there have been no epidemiological studies of the virus in wild populations of small mammals. As MuHV-4 both infects cells associated with the respiratory and immune systems and attempts to evade immune control via various molecular mechanisms, infection may reduce immunocompetence with potentially serious fitness consequences for individuals. Here we report a longitudinal study of antibody to MuHV-4 in a mixed assemblage of bank voles (Clethrionomys glareolus) and wood mice (Apodemus sylvaticus) in the UK. The study was conducted between April 2001 and March 2004. Seroprevalence was higher in wood mice than bank voles, supporting earlier work that suggested wood mice were the major host even though the virus was originally isolated from a bank vole. Analyses of both the probability of having antibodies and the probability of initial seroconversion indicated no clear seasonal pattern or relationship with host density. Instead, infection risk was most closely associated with individual characteristics, with heavier males having the highest risk. This may reflect individual variation in susceptibility, potentially related to variability in the ability to mount an effective immune response.

Study of nuclear receptor dynamics by BRET

Les récepteurs nucléaires (RN) sont des facteurs de transcription ligand dépendants qui contrôlent une grande variété de processus biologiques de la physiologie humaine, ce qui a fait d'eux des cibles pharmacologiques privilégiées pour de nombreuses maladies. L'un de ces récepteurs, le récepteur de l’œstrogène alpha (ERα), peut activer la prolifération cellulaire dans certaines sections de l'épithélium mammaire tandis qu’un autre, le récepteur de l'acide rétinoïque alpha (RARα), peut provoquer un arrêt de la croissance et la différenciation cellulaire. La signalisation de ces deux récepteurs peut être altérée dans le cancer du sein, contribuant à la tumorigénèse mammaire. L’activité d’ERα peut être bloquée par les anti-oestrogènes (AE) pour inhiber la prolifération des cellules tumorales mammaires. Par contre, l’activation des voies de RARα avec des rétinoïdes dans un contexte clinique a rencontré peu de succès. Ceci pourrait résulter du manque de spécificité des ligands testés pour RARα et/ou de leur activité seulement dans certains sous-types de tumeurs mammaires. Puisque les récepteurs nucléaires forment des homo- et hétéro-dimères, nous avons cherché à développer de nouveaux essais pharmacologiques pour étudier l'activité de complexes dimériques spécifiques, leur dynamique d’association et la structure quaternaire des récepteurs des œstrogènes. Nous décrivons ici une nouvelle technique FRET, surnommée BRET avec renforcement de fluorescence par transferts combinés (BRETFect), qui permet de détecter la formation de complexes de récepteurs nucléaires ternaires. Le BRETFect peut suivre l'activation des hétérodimères ERα-ERβ et met en évidence un mécanisme allostérique d'activation que chaque récepteur exerce sur son partenaire de dimérisation. L'utilisation de BRETFect en combinaison avec le PCA nous a permis d'observer la formation de multimères d’ERα fonctionnels dans des cellules vivantes pour la première fois. La formation de multimères est favorisée par les AE induisant la dégradation du récepteur des oestrogènes, ce qui pourrait contribuer à leurs propriétés spécifiques. Ces essais de BRET apportent une nette amélioration par rapport aux tests de vecteurs rapporteur luciférase classique, en fournissant des informations spécifiques aux récepteurs en temps réel sans aucune interférence par d'autres processus tels que la transcription et de la traduction. L'utilisation de ces tests nous a permis de caractériser les propriétés de modulation de l’activité des récepteurs nucléaires d’une nouvelle classe de molécules hybrides qui peuvent à la fois lier ERa ou RAR et inhiber les HDACs, conduisant au développement de nouvelles molécules prometteuses bifonctionnelles telles que la molécule hybride RAR-agoniste/HDACi TTNN-HA.