Inducing catastrophe in malignant growth

B. Roy Frieden College of Optical Sciences, University of Arizona, Tucson, AZ 85721, USA Email: roy.frieden{at}optics.arizona.edu Received on February 29, 2008. Revised on May 14, 2008. Accepted on June 2, 2008. Mathematical catastrophe theory is used to describe cancer growthduring any time-dependent program a(t) of therapeutic activity.The program may be actively imposed, e.g. as chemotherapy, oroccur passively as an immune response. With constant therapya(t), the theory predicts that cancer mass p(t) grows in timet as a cosine-modulated power law, with power = 1.618···,the Fibonacci constant. The cosine modulation predicts the familiarrelapses and remissions of cancer growth. These fairly wellagree with clinical data on breast cancer recurrences followingmastectomy. Two such studies of 3183 Italian women consistentlyshow an immune system's average activity level of about a =2.8596 for the women. Fortunately, an optimum time-varying therapyprogram a(t) is found that effects a gradual approach to fullremission over time, i.e. to a chronic disease. Both activitya(t) and cancer mass p(t) monotonically decrease with time,the activity a(t) as 1/(ln t) and mass remission as t94{ –0.382}. These predicted growth effects have a biological basisin the known presence of multiple alleles during cancer growth.     

The regulation of an age-structured population by a fatal disease

Present address: AgResearch (Grasslands), Tennent Drive. Private Bag 11008, Palmerston North, New Zealand A model describing the effect of a fatal disease on an age-structuredpopulation which would otherwise grow is presented and analysed.If the disease is capable of regulating host numbers, thereis an endemic steady age distribution (SAD), for which an analyticexpression is obtained under some simplifying assumptions. Theability of the disease to regulate the population depends ona parameter R(), which is defined in terms of the given age-dependentbirth and death rates, and where is the age-dependent disease-induceddeath rate. If R() < 1 the endemic SAD is attained, whileR()> 1 means the disease cannot control the population'ssize. The number R(0) is the expected number of offspring producedby each individual in the absence of the disease; for a growingpopulation we require R(0) > 1. A stability analysis is alsoperformed and it is conjectured that the endemic SAD is locallyasymptotically stable whenever it is attained. This is demonstratedexplicitly for a very simple example where all rates are takenas constant.     

Higher-dimensional separation principle for the analysis of relaxation oscillations in nonlinear systems: application to a model of HIV infection

Author to whom all correspondence should be addressed In this paper, geometric and singular perturbation argumentsare utilized to develop a separation condition for the identificationof limit cycles in higher-dimensional (n 4) dynamical systemscharacterized by highly diversified time responses, in whichthere exists an (n - 3)-dimensional subsystem which quicklyreaches a quasi-steady state. The condition, which has beenused up to now to analyze relaxation oscillation in slow-fastsystems, is extended to accommodate dynamical systems in whichmore state variables are involved in a special manner whichstill allows for the use of singular perturbation techniques.Application is then made to a model of human immunodeficiencyvirus infection in T helper (T_H) cell clones with limiting restingT_H cell supply.     

Delay effect in a model for virus replication

E-Mail: MAJUDYTH{at}SMTPGWY.POLYU.EDU.HK As biology becomes more quantitative, it appears that the increasinguse of mathematics in this area is inevitable. In 1996, Nowak& Bangham (1996, Science 272, 74–79) proposed threemathematical models to explore the relation between antiviralimmune responses, virus load, and virus diversity. In this paperwe investigate the delay effect in a model which considers theinteraction between a replicating virus and host cells. We assumethat there is a finite time lag between infection of a celland the emission of viral particles. Even with the introductionof this delay, the steady states of the model—as suggestedby Nowak & Bangham—remain stable. The result alsogives a condition for how the parameter values should be chosenwhen analysing clinical data so that the model remains tenable.     

The basic reproduction ratio for a model of directly transmitted infections considering the virus charge and the immunological response

Correspondent author email: hyunyang{at}ime.unicamp.br In order to describe mathematically the transmission of microparasites,especially directly transmitted infections, it is usual to setup differential equations assuming the mass action law and ahomogeneously mixed population. In this paper we analyze sucha model taking into account heterogeneity with respect to theinfectivity, that is, the variability in the evolution of theinteraction between parasite and the human host during the infectiousperiod. The well established biological phenomenon of initialincrease in parasite abundance followed by its decrease, dueto the interaction between the host's immunological responseand the parasite, has thus been taken into account The variableamount of microparasites eliminated by an infectious individual,and the different (heterogeneous) immunological response buildup by the host when in interaction with parasite are presentin the model. The analytical expression for the basic reproductionratio is derived through stability analysis.     

Andrology: Insulin-like growth factor-I and {alpha}2-macroglobulin in seminal plasma correlate with semen quality

Insulin-like growth factor-I (IGF-I) and ₂-macroglobulin (₂-M)are believed to be involved in the development of germ cells.IGF-I is mainly controlled by concentrations of human growthhormone (HGH), influences cell proliferation and differentiationand its action is mediated by insulin-like growth factor-bindingproteins (IGFBP), placental protein 14 (PP14) and prostate-specificantigen (PSA). ₂-M acts as a broad spectrum proteinase inhibitorand a binding protein for many cytokines and hormones, e.g.inhibin and activin. This study was designed to identify concentrationsof these molecules in seminal plasma in normal semen samplesof healthy men, correlations with semen quality, the relationshipof IGF-I and ₂-M with factors affecting male fertility, andwhether vasectomy influences the concentrations of these molecules.Concentrations of IGF-I and₂-M in human seminal plasma wererelated to semen quality, basal concentrations of HGH, testosterone,IGFBP-3, soluble fibronectin receptor (sFNR), PSA and PP14 inseminal plasma and to serum concentrations of luteinizing hormone(LH) and follicle stimulating hormone (FSH). Commercially availableassays were used to analyse 69 semen samples of various qualityand 11 post-vasectomy samples. IGF-I concentrations in seminalplasma were significantly correlated with the percentage ofmorphologically normal spermatozoa (r = 0.748, P = 0.00001)and sperm concentration (r = 0301, P = 0.011), but negativelycorrelated with serum FSH (r = –0.506, P = 0.00006) andPSA in seminal plasma (r = –0388, P = 0.0009). Total ₂-Mwas significantly correlated with sperm count (r = 0.423, P= 0.0005), percentage of progressively motile spermatozoa (r= 0.444, P = 0.00019), quality of motility (sperm motile efficiency,r = 802, P = 0.00001) and straight line velocity (r = 0.411,P = 0.0013). Correlation between the sperm concentration andHGH in seminal plasma was weak (r = 0.287, P = 0.015). Vasectomyreduced the concentration of total ₂-M (P = 0.00008) and HGH(P = 0.0068) in the seminal plasma; IGF-I was also reduced aftervasectomy when the total ejaculate amount was considered. ThusIGF-I and ₂-M are significant for the germ cell development:IGF-I hi the maturation of spermatozoa and ₂-M in progressivemotility.     

How seasonal temperature variations may influence the structure of annual squid populations

Email: ericg{at}stams.strath.ac.uk Email: s.desclers{at}ic.ac.uk Previous laboratory studies have established that temperatureis highly influential in affecting both the growth and lifespan of Cephalopoda. A major unresolved question is how suchsensitivity to environmental factors may determine populationstructure. Extending a hypothesis first advanced by Forsythe(1993, in: Recent Advances in Fisheries Biology (T. Okutani,R. K. O'Dor, & T. Kubdera, eds.), Tokyo, Tokai UniversityPress), we formulate a simple individual-level model which incorporatesa two-stage growth response for squid hatchlings exposed tocontinuous seasonal fluctuations of temperature. We show thatin seasonally fluctuating temperatures such a growth ‘duality’can directly affect the size distribution of squid over theyear and we demonstrate how in seasonally warming waters thismechanism may lead to younger individuals surpassing the sizeof older individuals. By postulating that development statuscan be inferred directly from size, we go on to propose a circle-mapmodel of the whole squid life cycle. Numerical investigationsinto the iterative dynamics support the hypothesis that theprogeny from such a population can rapidly separate to a lownumber of tightly synchronized cohorts within a few generations.     

Expression of melatoninergic receptors in human placental choriocarcinoma cell lines

BACKGROUND: Melatonin crosses the placenta and enters the fetalcirculation. Moreover, experimental data suggest a possibleinfluence of melatonin on placental function and fetal developmentin humans. To date, the expression and role of melatonin receptorsin human placenta choriocarcinoma cell lines and in human termplacental tissues remain to be elucidated. METHODS AND RESULTS:Results from RT–PCR, western blotting and confocal microscopydemonstrated that the MT1, MT2 and ROR1 melatonin receptorsare expressed in the human term placental tissues and in choriocarcinomacell lines JEG-3 and BeWo. Furthermore, enzyme-linked immunosorbentassay showed that 6-chloromelatonin (a melatonin agonist) inhibits,in a dose-dependent manner, forskolin-stimulated hCG- secretionin JEG-3 (P < 0.001) and BeWo (P < 0.05) cells but hadno effect on basal human chorionic gonadotrophin (hCG-) levels.This effect of 6-chloromelatonin on forskolin-stimulated HCG-secretion was abolished by pertussis toxin (PTX), suggestingthat melatonin regulates hCG- production by an action involvingan inhibitory Gi/o protein. In PTX-treated BeWo cells, 6-chloromelatoninstimulated basal hCG- secretion (P < 0.001). CONCLUSION:These results demonstrate, for the first time, the expressionof melatonin receptors in human term placental tissues and inchoriocarcinoma cells and suggest a possible paracrine/autocrinefunction for melatonin in human placenta.     

Molecular mechanisms underlying IFN-{gamma}-mediated tumor growth inhibition induced during tumor growth inhibition induced during tumor immunotherapy with rIL-12

The present studnt Investigates the molecular by which IFN-produced as a result of in vitroIL-12 addministration exertsits anty-tumor,rIL-12 was administered three or five times intomice bearing CDA1M fibrosarcoma, OV-HM ovarian carcinoma orMCH-1-A1 fibosarcoma. This regimen induced complete regressionof CSA1M and OV-HM tumors but only transient growth inhibitionof MCH-1-A1 tumors. The anty-tumor effects of Il-12 were associatatedwith enhanced induction of IFN-becouse these effects were abrogatedby pretreatment of hosts with anti-IFN- antibody.Exposure inin vitro of the three types of tumor cells to rIFN- resultedin moderate to potent inhibition of tumor cell growth.IFNstimulatedthe expression of mRNAs for an inducible type of NO synthasa(INOS)in CSA1M cells and indoleamine 2,3-dioxygenasa (IDO),an enzyme capable of degrading tryptophan, in OV-HM cells ,but induced only marginal levels of these mRNAs in MCH-I-ALcells. In association withiNOS gene expression, INF--stimulatedCSA1M cells produced a large amount of NO which functioned toinhibit their own growth in vitro. Although OV-HM and MCH-1-A1cells did not produce NO, they also exhibited NO susceptibility.Whereasthe tumor masses from IL-12-treated CSA1M-bearing mice inducedhigher levels of INOS (for CSA1M) or IDO and iNOS (for OV-HM)mRNAs,the MCH-1-A1 tumor mass expressed lower levels of iNOS mRNAalone.Moreover, massive infiltration of CD4⁺and CD8⁺ T cellsand Mac-1⁺ cells was seen only in the CSA1M and OV-HM tumors.Thus, these results indicate that IFN- produced after IL-12treatment induces the expression of various genes with potentialto modulate tumor cells and growth by acting directly on tumorecells or stimulating tumor-infiltrating lymphold cells and thatthe effectiveness of IL12 therapy is assoiated with the operation if these mechanisms.     

DNA adduct formation by 7-methoxy-2-nitro-naphtho[2,1-b]furan (R7000), an extremely potent mutagen

The effects on DNA, in bacteria, of 7-methoxy-2-nitronaphtho[2,1-b]furan(R7000), a very potent genotoxic product from the 2-nitronaphthofuranseries, were investigated with two different approaches: (i)measurement of the binding of the radiolabelled mutagen to DNAand (ii) detection by the ‘³²P-postlabelling’ methodof DNA adducts following treatment with unlabelled mutagens.The covalent binding of R7000 to DNA in Escherichia coli wasdemonstrated by both methods, and in the latter case it wasfound to involve the formation of nine different adducts. Formationof adducts by R7000 was shown to require metabolic activationof the compound. Deceased      

Therapy burden, drug resistance, and optimal treatment regimen for cancer chemotherapy

Email: boldrini{at}ime.unicamp.brAuthor to whom correspondence should be addressed. Email: michel{at}Incc.br Three nonlinear models of tumour cell growth under continuousdelivery of cycle nonspecific anticancer agents are studied.A dynamical optimization problem with the objective of minimizingthe final level of tumour cells is posed for these mathematicalsetups. The simplest setup does not possess toxicity constraints,whereas the other setups contain a dynamical equation describingthe therapy burden as a toxicity criterion. In addition, thethird setting contains the dynamics of drug resistant cells.A discussion conceming the optimal strategies of the respectivemodels is performed.     

Lck dependence of signaling pathways activated by {gamma}irradiation and CD3{varepsilon} engagement in RAG-1-/-immature thymocytes

The src family tyrosine kinase, Lck, transduces signals fromthe pre-TCR complex which regulate the development and expansionof CD4/CD8 double-positive (DP) thymocytes from CD25⁺ CD4/CD8double-negative progenitors. We and others have recently shownthat sublethal irradiation bypasses the need for TCRßexpression to promote the development and expansion of DP thymocytesin acid or recombinase-activating gene (RAG)-deficient mice.Here we demonstrate that -irradiation activates an Lck-dependentsignaling process in Immature thymocytes similar to that initiatedphysiologically by the pre-TCR complex.     

Immunoglobulin gene rearrangement in B cell deficient mice generated by targeted deletion of the JH locus

B lymphocyte differentiation is characterized by an orderedseries of Ig gene assembly and expression events. In the majorityof normal B cells, assembly and expression of Ig heavy (H) chaingenes precedes that of light (L) chain genes. To determine therole of the Ig heavy chain protein in B cell development andL chain gene rearrangement, we have generated mice that cannotassemble Ig H chain genes as a result of targeted deletion ofthe J_H gene segments in embryonic stem cells. Mice homozygousfor this deletion are devoid of slg⁺ B cells in the bone marrowand periphery. B cell differentiation in these mice is blockedat the large, CD43⁺ precursor stage. However, these precursorB cells do assemble L chain genes at a low level in the absenceof µ H chain proteins. These data demonstrate that rearrangementand expression of the µ H chain gene is not absolutelyrequired for L chain gene rearrangement in vivo. Expressionof µ chains may facilitate either efficient L chain generearrangement or the survival of cells that have rearrangedlight chain genes by promoting the differentiation of large,CD43⁺ to small, CD43^– pre-B cells.     

Identification of a chemotactic sensitivity in a coupled system

Email: renee.fister{at}murraystate.edu Corresponding author. Email: maeve.mccarthy{at}murraystate.edu Received on July 16, 2007. Revised on March 24, 2008. Accepted on June 7, 2008. Chemotaxis is the process by which cells behave in a way thatfollows the chemical gradient. Applications to bacteria growth,tissue inflammation and vascular tumours provide a focus onoptimization strategies. Experiments can characterize the formof possible chemotactic sensitivities. This paper addressesthe recovery of the chemotactic sensitivity from these experimentswhile allowing for non-linear dependence of the parameter onthe state variables. The existence of solutions to the forwardproblem is analysed. The identification of a chemotactic parameteris determined by inverse problem techniques. Tikhonov regularizationis investigated and appropriate convergence results are obtained.Numerical results of concentration-dependent chemotactic termsare explored.     

Two-dimensional models of tumour angiogenesis and anti-angiogenesis strategies

Author to whom correspondence should be sent; present address: Department of Mathematics and Computer Science, University of Dundee, Dundee, DD1 4HN, UK There is a very strong link between the vascularization of atumour and the spread of the disease, both locally and to distantsites (Gimbrone et al., 1974, J. Natl. Cancer Inst. 52, 413–27;Muthukkaruppan et al, 1982, J. Natl. Cancer Inst. 69, 699–704;Ellis & Fiddler, 1995, Lancet 346, 388–9). A tumourbecomes vascularized by a process known as angiogenesis. Tumourangiogenesis is initiated by the release of diffusible substancesby the tumour, whereby neighbouring capillary vessels are stimulatedto grow and eventually penetrate the tumour. Anti-angiogenesishas been proposed as a potential strategy for the treatmentof cancer (Folkman, 1995, Nature Med. 1, 21–31; Harriset al, 1996, Breast Cancer Res. Treat. 38, 97–108). Inthis paper, a mathematical model of the development of the tumourvasculature is presented. By suitable manipulation of the modelparameters, we simulate various anti-angiogenesis strategiesand we examine the roles that haptotaxis and chemotaxis mayplay during the growth of the neovasculature. The model is simulatedin two space dimensions (on a square domain) so that it is,in theory, experimentally reproducible and any predictions ofthe model can therefore be tested.