[show abstract][hide abstract] ABSTRACT: Breast cancer patients have an anomalously high rate of relapse many years-up to 25 years-after apparently curative surgery removed the primary tumour. Disease progression during the intervening years between resection and relapse is poorly understood. There is evidence that the disease persists as dangerous, tiny metastases that remain at a growth restricted, clinically undetectable size until a transforming event restarts growth. This is the starting point for our study, where patients who have metastases that are all tiny and growth-restricted are said to have cancer dormancy. Can long-term follow-up relapse data from breast cancer patients be used to extract knowledge about the progression of the undetected disease? Here, we evaluate whether this is the case by introducing and analysing four simple mathematical models of cancer dormancy. These models extend the common assumption that a random transforming event, such as a mutation, can restart growth of a tiny, growth-restricted metastasis; thereafter, cancer dormancy progresses to detectable metastasis. We find that physiopathological details, such as the number of random transforming events that metastases must undergo to escape from growth restriction, cannot be extracted from relapse data. This result is unsurprising. However, the same analysis suggested a natural question that does have a surprising answer: why are interesting trends in long-term relapse data not more commonly observed? Further, our models indicate that (a) therapies which induce growth restriction among metastases but do not prevent increases in metastases' tumourigenicity may introduce a time post-surgery when more patients are prone to relapse; and (b), if a number of facts about disease progression are first established, how relapse data might be used to estimate clinically relevant variables, such as the likely numbers of undetected growth-restricted metastases. This work is a necessary, early step in building a quantitative mechanistic understanding of cancer dormancy.
PLoS ONE 01/2013; 8(5):e62320. · 3.73 Impact Factor
[show abstract][hide abstract] ABSTRACT: Collective cell migration is a mode of movement crucial for morphogenesis and cancer metastasis. However, little is known about how migratory cells coordinate collectively. Here we show that mutual cell-cell attraction (named here coattraction) is required to maintain cohesive clusters of migrating mesenchymal cells. Coattraction can counterbalance the natural tendency of cells to disperse via mechanisms such as contact inhibition and epithelial-to-mesenchymal transition. Neural crest cells are coattracted via the complement fragment C3a and its receptor C3aR, revealing an unexpected role of complement proteins in early vertebrate development. Loss of coattraction disrupts collective and coordinated movements of these cells. We propose that coattraction and contact inhibition act in concert to allow cell collectives to self-organize and respond efficiently to external signals, such as chemoattractants and repellents.
[show abstract][hide abstract] ABSTRACT: The β-subunits of voltage-gated calcium channels regulate their functional expression and properties. Two mechanisms have been proposed for this, an effect on gating and an enhancement of expression. With respect to the effect on expression, β-subunits have been suggested to enhance trafficking by masking an unidentified endoplasmic reticulum (ER) retention signal. Here we have investigated whether, and how, β-subunits affect the level of Ca(V)2.2 channels within somata and neurites of cultured sympathetic neurons. We have used YFP-Ca(V)2.2 containing a mutation (W391A), that prevents binding of β-subunits to its I-II linker and found that expression of this channel was much reduced compared with WT CFP-Ca(V)2.2 when both were expressed in the same neuron. This effect was particularly evident in neurites and growth cones. The difference between the levels of YFP-Ca(V)2.2(W391A) and CFP-Ca(V)2.2(WT) was lost in the absence of co-expressed β-subunits. Furthermore, the relative reduction of expression of Ca(V)2.2(W391A) compared with the WT channel was reversed by exposure to two proteasome inhibitors, MG132 and lactacystin, particularly in the somata. In further experiments in tsA-201 cells, we found that proteasome inhibition did not augment the cell surface Ca(V)2.2(W391A) level but resulted in the observation of increased ubiquitination, particularly of mutant channels. In contrast, we found no evidence for selective retention of Ca(V)2.2(W391A) in the ER, in either the soma or growth cones. In conclusion, there is a marked effect of β-subunits on Ca(V)2.2 expression, particularly in neurites, but our results point to protection from proteasomal degradation rather than masking of an ER retention signal.
Journal of Biological Chemistry 01/2011; 286(11):9598-611. · 4.65 Impact Factor
[show abstract][hide abstract] ABSTRACT: We present statistical evidence and dynamical models for the management of conflict and a division of labor (task specialization) in a primate society. Two broad intervention strategy classes are observed--a dyadic strategy--pacifying interventions, and a triadic strategy--policing interventions. These strategies, their respective degrees of specialization, and their consequences for conflict dynamics can be captured through empirically-grounded mathematical models inspired by immuno-dynamics. The spread of aggression, analogous to the proliferation of pathogens, is an epidemiological problem. We show analytically and computationally that policing is an efficient strategy as it requires only a small proportion of a population to police to reduce conflict contagion. Policing, but not pacifying, is capable of effectively eliminating conflict. These results suggest that despite implementation differences there might be universal features of conflict management mechanisms for reducing contagion-like dynamics that apply across biological and social levels. Our analyses further suggest that it can be profitable to conceive of conflict management strategies at the behavioral level as mechanisms of social immunity.
PLoS ONE 01/2011; 6(8):e22709. · 3.73 Impact Factor
[show abstract][hide abstract] ABSTRACT: Background - Diatoms are unicellular algae, prolific in nearly all aqueous environments on earth. They are encased between two siliceous valves that each feature a variety of intricately patterned species-specific siliceous structures. How diatoms use biological and physical processes to form these tiny detailed structures is largely unknown. This work is concerned with the smallest regular structures in diatom valves, the pore occlusions, and the processes involved in their formation.Theory and method - We developed a discrete, free-boundary, reaction-diffusion computer model to assess a new physically motivated hypothesis: pore occlusion patterns in the genus Achnanthes are simply expressions of silica diffusion and deposition within a pore covered by a membrane (silicalemma), whose deformation interacts with the growth of the pore boundary to control the silica influx.Preliminary results and discussion - Simulations generate some promising pore features such as bifurcating and curved protrusions that grow towards one another, as seen in diatom pore occlusions. But they tend to be irregular and, to date, taking into account of smoothing and regularizing effects only partially symmetrized formations. Potential future work on this point is outlined.
Plant Ecology and Evolution 10/2010; 143(3):297-306. · 1.19 Impact Factor
[show abstract][hide abstract] ABSTRACT: Late relapse of breast cancer can occur more than 25 years after primary diagnosis. During the intervening years between initial treatment and relapse, occult cancers are maintained in an apparent state of dormancy that is poorly understood. In this study, we applied a probabilistic mathematical model to long-term follow-up studies of postresection patients to investigate the factors involved in mediating breast cancer dormancy. Our results suggest that long-term dormancy is maintained most often by just one growth-restricted dangerous micrometastasis. Analysis of the empirical data by Approximate Bayesian Computation indicated that patients in dormancy have between 1 and 5 micrometastases at 10 years postresection, when they escape growth restriction with a half-life of <69 years and are >0.4 mm in diameter. Before resection, primary tumors seed at most an average of 6 dangerous micrometastases that escape from growth restriction with a half-life of at least 12 years. Our findings suggest that effective preventive treatments will need to eliminate these small numbers of micrometastases, which may be preangiogenic and nonvascularized until they switch to growth due to one oncogenic mutation or tumor suppressor gene inactivation. In summary, breast cancer dormancy seems to be maintained by small numbers of sizeable micrometastases that escape from growth restriction with a half-life exceeding 12 years.
Cancer Research 06/2010; 70(11):4310-7. · 8.65 Impact Factor
[show abstract][hide abstract] ABSTRACT: Expression of the calcium channels CaV2.1 and CaV2.2 is markedly suppressed by co-expression with truncated constructs containing Domain I. This is the basis for the phenomenon
of dominant negative suppression observed for many of the episodic ataxia type 2 mutations in CaV2.1 that predict truncated channels. The process of dominant negative suppression has been shown previously to stem from interaction
between the full-length and truncated channels and to result in downstream consequences of the unfolded protein response and
endoplasmic reticulum-associated protein degradation. We have now identified the specific domain that triggers this effect.
For both CaV2.1 and CaV2.2, the minimum construct producing suppression was the cytoplasmic N terminus. Suppression was enhanced by tethering the
N terminus to the membrane with a CAAX motif. The 11-amino acid motif (including Arg52 and Arg54) within the N terminus, which we have previously shown to be required for G protein modulation, is also essential for dominant
negative suppression. Suppression is prevented by addition of an N-terminal tag (XFP) to the full-length and truncated constructs.
We further show that suppression of CaV2.2 currents by the N terminus-CAAX construct is accompanied by a reduction in CaV2.2 protein level, and this is also prevented by mutation of Arg52 and Arg54 to Ala in the truncated construct. Taken together, our evidence indicates that both the extreme N terminus and the Arg52, Arg54 motif are involved in the processes underlying dominant negative suppression.
Journal of Biological Chemistry 01/2010; 285(2):835-844. · 4.65 Impact Factor
[show abstract][hide abstract] ABSTRACT: Expression of the calcium channels Ca(V)2.1 and Ca(V)2.2 is markedly suppressed by co-expression with truncated constructs containing Domain I. This is the basis for the phenomenon of dominant negative suppression observed for many of the episodic ataxia type 2 mutations in Ca(V)2.1 that predict truncated channels. The process of dominant negative suppression has been shown previously to stem from interaction between the full-length and truncated channels and to result in downstream consequences of the unfolded protein response and endoplasmic reticulum-associated protein degradation. We have now identified the specific domain that triggers this effect. For both Ca(V)2.1 and Ca(V)2.2, the minimum construct producing suppression was the cytoplasmic N terminus. Suppression was enhanced by tethering the N terminus to the membrane with a CAAX motif. The 11-amino acid motif (including Arg(52) and Arg(54)) within the N terminus, which we have previously shown to be required for G protein modulation, is also essential for dominant negative suppression. Suppression is prevented by addition of an N-terminal tag (XFP) to the full-length and truncated constructs. We further show that suppression of Ca(V)2.2 currents by the N terminus-CAAX construct is accompanied by a reduction in Ca(V)2.2 protein level, and this is also prevented by mutation of Arg(52) and Arg(54) to Ala in the truncated construct. Taken together, our evidence indicates that both the extreme N terminus and the Arg(52), Arg(54) motif are involved in the processes underlying dominant negative suppression.
Journal of Biological Chemistry 11/2009; 285(2):835-44. · 4.65 Impact Factor
[show abstract][hide abstract] ABSTRACT: CaVbeta subunits of voltage-gated calcium channels contain two conserved domains, a src-homology-3 (SH3) domain and a guanylate kinase-like (GK) domain with an intervening HOOK domain. We have shown in a previous study that, although Gbetagamma-mediated inhibitory modulation of CaV2.2 channels did not require the interaction of a CaVbeta subunit with the CaValpha1 subunit, when such interaction was prevented by a mutation in the alpha1 subunit, G protein modulation could not be removed by a large depolarization and showed voltage-independent properties (Leroy et al., J Neurosci 25:6984-6996, 2005). In this study, we have investigated the ability of mutant and truncated CaVbeta subunits to support voltage-dependent G protein modulation in order to determine the minimal domain of the CaVbeta subunit that is required for this process. We have coexpressed the CaVbeta subunit constructs with CaV2.2 and alpha2delta-2, studied modulation by the activation of the dopamine D2 receptor, and also examined basal tonic modulation. Our main finding is that the CaVbeta subunit GK domains, from either beta1b or beta2, are sufficient to restore voltage dependence to G protein modulation. We also found that the removal of the variable HOOK region from beta2a promotes tonic voltage-dependent G protein modulation. We propose that the absence of the HOOK region enhances Gbetagamma binding affinity, leading to greater tonic modulation by basal levels of Gbetagamma. This tonic modulation requires the presence of an SH3 domain, as tonic modulation is not supported by any of the CaVbeta subunit GK domains alone.
Pflügers Archiv - European Journal of Physiology 02/2009; 457(4):743-56. · 4.87 Impact Factor
[show abstract][hide abstract] ABSTRACT: The behavior of organisms can contribute to the transformation of their environments. When organismal impacts on the environment feed back to influence organismal density, viability, fertility, or persistence, the environment can be construed as an extension of the organism. This process of fitness-enhancing environmental transformation has been called niche construction. We focus on the relationship of niche construction with species or strain diversity and on the variability of investment in niche construction versus reproduction. We demonstrate a fundamental dilemma of niche construction, whereby the construction of a shared resource leads to a tragedy of the commons, with competition tending to eliminate niche construction strategies. The ability to monopolize a niche, either through spatial proximity or through preferential exploitation, can stabilize niche construction and promote ecological coexistence among polymorphic constructors. We consider both sympatric and allopatric origins of niche construction. Under a variety of different construction mechanisms, variability in the investment in niche construction versus reproduction suggests reproductive altruism but is fully consistent with selfish behavior. We discuss the implications of niche-construction theory on the evolution of life cycles and development, behavioral plasticity, the division of labor, and long-term macroevolutionary trends.
The American Naturalist 01/2009; 173(1):26-40. · 4.55 Impact Factor
[show abstract][hide abstract] ABSTRACT: The role(s) of the novel stargazin-like gamma-subunit proteins remain controversial. We have shown previously that the neuron-specific gamma7 suppresses the expression of certain calcium channels, particularly Ca(V)2.2, and is therefore unlikely to operate as a calcium channel subunit. We now show that the effect of gamma7 on Ca(V)2.2 expression is via an increase in the degradation rate of Ca(V)2.2 mRNA and hence a reduction of Ca(V)2.2 protein level. Furthermore, exogenous expression of gamma7 in PC12 cells also decreased the endogenous Ca(V)2.2 mRNA level. Conversely, knockdown of endogenous gamma7 with short-hairpin RNAs produced a reciprocal enhancement of Ca(V)2.2 mRNA stability and an increase in endogenous calcium currents in PC12 cells. Moreover, both endogenous and expressed gamma7 are present on intracellular membranes, rather than the plasma membrane. The cytoplasmic C terminus of gamma7 is essential for all its effects, and we show that gamma7 binds directly via its C terminus to a heterogeneous nuclear ribonucleoprotein (hnRNP A2), which also binds to a motif in Ca(V)2.2 mRNA, and is associated with native Ca(V)2.2 mRNA in PC12 cells. The expression of hnRNP A2 enhances Ca(V)2.2 I(Ba), and this enhancement is prevented by a concentration of gamma7 that alone has no effect on I(Ba). The effect of gamma7 is selective for certain mRNAs because it had no effect on alpha2delta-2 mRNA stability, but it decreased the mRNA stability for the potassium-chloride cotransporter, KCC1, which contains a similar hnRNP A2 binding motif to that in Ca(V)2.2 mRNA. Our results indicate that gamma7 plays a role in stabilizing Ca(V)2.2 mRNA.
Journal of Neuroscience 11/2008; 28(42):10604-17. · 6.91 Impact Factor
[show abstract][hide abstract] ABSTRACT: Cancer arises through successive somatic mutations/epimutations of oncogenes and tumor-suppressor genes. Accurate estimates of the rates at which these (epi)mutations occur are a vital but missing link in our emerging quantitative understanding of tumorigenesis. Their absence has hindered arguments concerning the importance of genetic instability in tumorigenesis and the number of mutations that precede malignant conversion of healthy cell lineages. Herein, a novel method for calculating the in vivo mutation rate of the adenomatous polyposis coli (APC) tumor-suppressor gene is presented. The large majority of bowel cancers are thought to be initiated by a partial loss of APC function, with the age-onset pattern dramatically altered for the worse in familial adenomatous polyposis (FAP) because these patients harbor selected germline APC mutations. Colon cancer in the context of FAP can be thought of as occurring "one hit quicker" than in the sporadic setting. We were able to isolate and estimate the rate of the initiating APC mutation in sporadic cases using the age incidence of FAP to approximate the time taken for a cell lineage in a sporadic patient with one APC mutation to present clinically as a cancer. Our result of approximately 10(-5) mutations per allele per year, although higher than previous estimates, appears to be consistent with the mutational spectrum of APC. The quality of fit provided by this method supports the theory that FAP and sporadic bowel cancer follow the same genetic pathway and are separated by only one mutation.
American Journal Of Pathology 05/2008; 172(4):1062-8. · 4.52 Impact Factor
[show abstract][hide abstract] ABSTRACT: Most cancers occur with the same characteristic pattern of incidence. The simplicity of this pattern is in contrast to the perceived complexity of carcinogenesis. Therefore, age-onset statistics represent a tempting set of data and have provoked many bold but often misguided conclusions concerning the physiopathological mechanisms of cancer. Half a century has passed since the original multistage theory of Armitage and Doll. Although their basic notion of a healthy cell becoming malignant in several rate-limiting steps is still accepted, prevailing wisdom about the nature and number of these steps has never settled into a consensus. Why have we been unable to elucidate the quantitative dependence of cancer incidence on the molecular processes that feature in its aetiology? In this review we aim to provide answers for this question.
The lancet oncology 12/2007; 8(11):1030-8. · 14.47 Impact Factor
[show abstract][hide abstract] ABSTRACT: Reaction diffusion systems have been proposed as mechanisms for patterning during many stages of embryonic development. While much attention has been focused on the study of the steady state patterns formed and the robustness of pattern selection, much less is known about the time scales required for pattern formation. Studies of gradient formation by the diffusion of a single morphogen from a localized source have shown that patterning can occur on realistic time scales over distances of a millimeter or less. Reaction diffusion has the potential to give rise to patterns on a faster time scale, since all points in the domain can act as sources of morphogen. However, the speed at which patterning can occur has hitherto not been explored in depth. In this paper, we investigate this issue in specific reaction diffusion models and address the question of whether patterning via reaction diffusion is fast enough to be applicable to morphogenesis.
[show abstract][hide abstract] ABSTRACT: We present an analysis of a stochastic model of the vascular endothelial growth factor (VEGF) receptor. This analysis addresses the contribution of ligand-binding-induced oligomerization, activation of src-homology 2 domain-carrying kinases and receptor internalization in the overall behaviour of the VEGF/VEGF receptor (VEGFR) system. The analysis is based upon a generalization of a Wentzel-Kramers-Brillouin (WKB) approximation of the solution of the corresponding master equation. We predict that tumour-mediated overexpression of VEGFRs in the endothelial cells (ECs) of tumour-engulfed vessels leads to an increased sensitivity of the ECs to low concentrations of VEGF, thus endowing the tumour with increased resistance to anti-angiogenic treatment.
Journal of The Royal Society Interface 05/2007; 4(13):283-304. · 4.91 Impact Factor
[show abstract][hide abstract] ABSTRACT: Mutations involved in many cancers have been identified, but with some cancers requiring six or more mutations to take on their fully metastatic forms, the question remains whether all of these mutations can be acquired via a process of successive mutation, at a normal rate, and clonal expansion or whether heightened mutation rates are required. This issue has been debated for decades. Recently there has been much interest in forms of genomic instability such as chromosomal instability and microsatellite instability. It remains to definitively show whether or not these instabilities are very early causal events in tumorigenesis. This article reviews the evidence for and against genomic instability being an early causal event in tumorigenesis and surveys the mathematical modelling literature in this area. The focus is on chromosomal instability and microsatellite instability in colorectal cancer.
Physics of Life Reviews 01/2007; 4:116-127. · 6.58 Impact Factor
[show abstract][hide abstract] ABSTRACT: The mouse mutant ducky and its allele ducky(2J) represent a model for absence epilepsy characterized by spike-wave seizures and cerebellar ataxia. These mice have mutations in Cacna2d2, which encodes the alpha2delta-2 calcium channel subunit. Of relevance to the ataxic phenotype, alpha2delta-2 mRNA is strongly expressed in cerebellar Purkinje cells (PCs). The Cacna2d2(du2J) mutation results in a 2 bp deletion in the coding region and a complete loss of alpha2delta-2 protein. Here we show that du(2J)/du(2J) mice have a 30% reduction in somatic calcium current and a marked fall in the spontaneous PC firing rate at 22 degrees C, accompanied by a decrease in firing regularity, which is not affected by blocking synaptic input to PCs. At 34 degrees C, du(2J)/du(2J) PCs show no spontaneous intrinsic activity. Du(2J)/du(2J) mice also have alterations in the cerebellar expression of several genes related to PC function. At postnatal day 21, there is an elevation of tyrosine hydroxylase mRNA and a reduction in tenascin-C gene expression. Although du(2J)/+ mice have a marked reduction in alpha2delta-2 protein, they show no fall in PC somatic calcium currents or increase in cerebellar tyrosine hydroxylase gene expression. However, du(2J)/+ PCs do exhibit a significant reduction in firing rate, correlating with the reduction in alpha2delta-2. A hypothesis for future study is that effects on gene expression occur as a result of a reduction in somatic calcium currents, whereas effects on PC firing occur as a long-term result of loss of alpha2delta-2 and/or a reduction in calcium currents and calcium-dependent processes in regions other than the soma.
Journal of Neuroscience 12/2006; 26(48):12576-86. · 6.91 Impact Factor
[show abstract][hide abstract] ABSTRACT: In this paper, we develop stochastic models of receptor binding by a bivalent ligand. A detailed kinetic study allows us to analyse the role of cross-linking in cell activation by receptor oligomerization. We show how oligomer formation could act to buffer intracellular signalling against stochastic fluctuations. In addition, we put forward the hypothesis that formation of long linear oligomers increases the range of ligand concentration to which the cell is responsive, whereas formation of closed oligomers increases ligand concentration specificity. Thus, different physiological functions requiring different degrees of specificity to ligand concentration would favour formation of oligomers with different lengths and geometries. Furthermore, provided that ligand concentration specificity is taken as a design principle, our model enables us to estimate parameters, such as the minimum proportion of receptors, that must engage in oligomer formation in order to trigger a cellular response.
Journal of The Royal Society Interface 09/2006; 3(9):545-59. · 4.91 Impact Factor
[show abstract][hide abstract] ABSTRACT: We formulate models of the mechanism(s) by which B cell lymphoma cells stimulated with an antibody specific to the B cell receptor (IgM) become quiescent or apoptotic. In particular, we aim to reproduce experimental results by Marches et al. according to which the fate of the targeted cells (Daudi) depends on the levels of expression of p21(Waf1) (p21) cell-cycle inhibitor. A simple model is formulated in which the basic ingredients are p21 and caspase activity, and their mutual inhibition. We show that this model does not reproduce the experimental results and that further refinement is needed. A second model successfully reproduces the experimental observations, for a given set of parameter values, indicating a critical role for Myc in the fate decision process. We use bifurcation analysis and objective sensitivity analysis to assess the robustness of our results. Importantly, this analysis yields experimentally testable predictions on the role of Myc, which could have therapeutic implications.
Journal of Theoretical Biology 06/2006; 240(1):54-71. · 2.35 Impact Factor
[show abstract][hide abstract] ABSTRACT: All auxiliary alpha2delta subunits of voltage-gated Ca2+ (Ca(V)) channels contain an extracellular Von Willebrand factor-A (VWA) domain that, in alpha2delta-1 and -2, has a perfect metal-ion-dependent adhesion site (MIDAS). Modeling of the alpha2delta-2 VWA domain shows it to be highly likely to bind a divalent cation. Mutating the three key MIDAS residues responsible for divalent cation binding resulted in a MIDAS mutant alpha2delta-2 subunit that was still processed and trafficked normally when it was expressed alone. However, unlike WT alpha2delta-2, the MIDAS mutant alpha2delta-2 subunit did not enhance and, in some cases, further diminished Ca(V)1.2, -2.1, and -2.2 currents coexpressed with beta1b by using either Ba2+ or Na+ as a permeant ion. Furthermore, expression of the MIDAS mutant alpha2delta-2 reduced surface expression and strongly increased the perinuclear retention of Ca(V)alpha1 subunits at the earliest time at which expression was observed in both Cos-7 and NG108-15 cells. Despite the presence of endogenous alpha2delta subunits, heterologous expression of alpha2delta-2 in differentiated NG108-15 cells further enhanced the endogenous high-threshold Ca2+ currents, whereas this enhancement was prevented by the MIDAS mutations. Our results indicate that alpha2delta subunits normally interact with the Ca(V)alpha1 subunit early in their maturation, before the appearance of functional plasma membrane channels, and an intact MIDAS motif in the alpha2delta subunit is required to promote trafficking of the alpha1 subunit to the plasma membrane by an integrin-like switch. This finding provides evidence for a primary role of a VWA domain in intracellular trafficking of a multimeric complex, in contrast to the more usual roles in binding extracellular ligands in other exofacial VWA domains.
Proceedings of the National Academy of Sciences 09/2005; 102(32):11230-5. · 9.74 Impact Factor