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There are various cases of animal movement where behaviour broadly switches between two modes of operation, corresponding to a long distance movement state and a resting or local movement state. Here a mathematical description of this process is formulated, adapted from Friedrich et. al. (2006). The approach allows the specification any running or waiting time distribution along with any angular and speed distributions. The resulting system of partial integro-differential equations are tumultuous and therefore it is necessary to both simplify and derive summary statistics. An expression for the mean squared displacement is derived which shows good agreement with experimental data from the bacterium Escherichia coli and the gull Larus fuscus. Finally a large time diffusive approximation is considered via a Cattaneo approximation (Hillen, 2004). This leads to the novel result that the effective diffusion constant is dependent on the mean and variance of the running time distribution but only on the mean of the waiting time distribution., 16 pages, 6 figures

The motile behaviour of bacteria underlies many important aspects of their actions, including pathogenicity, foraging efficiency, and ability to form biofilms. In this thesis, we apply mathematical modelling and analysis to various aspects of the planktonic motility of flagellated bacteria, guided by experimental observations. We use data obtained by tracking free-swimming Rhodobacter sphaeroides under a microscope, taking advantage of the availability of a large dataset acquired using a recently developed, high-throughput protocol. A novel analysis method using a hidden Markov model for the identification of reorientation phases in the tracks is described. This is assessed and compared with an established method using a computational simulation study, which shows that the new method has a reduced error rate and less systematic bias. We proceed to apply the novel analysis method to experimental tracks, demonstrating that we are able to successfully identify reorientations and record the angle changes of each reorientation phase. The analysis pipeline developed here is an important proof of concept, demonstrating a rapid and cost-effective protocol for the investigation of myriad aspects of the motility of microorganisms. In addition, we use mathematical modelling and computational simulations to investigate the effect that the microscope sampling rate has on the observed tracking data. This is an important, but often overlooked aspect of experimental design, which affects the observed data in a complex manner. Finally, we examine the role of rotational diffusion in bacterial motility, testing various models against the analysed data. This provides strong evidence that R. sphaeroides undergoes some form of active reorientation, in contrast to the mainstream belief that the process is passive.

Choroid plexus tumours (CPTs) account for 2-5% of brain tumours in children. They can spread along the neuraxis and can recur after treatment. Little is known about the molecular mechanisms underlying their formation and only few high fidelity mouse models of p53-deficient malignant CPTs are available.We show here that c-MYC overexpression in the choroid plexus epithelium induces T-cell inflammation-dependent choroid plexus papillomas in a mouse model. We demonstrate that c-MYC is expressed in a substantial proportion of human choroid plexus tumours and that this subgroup of tumours is characterised by an inflammatory transcriptome and significant inflammatory infiltrates. In compound mutant mice, overexpression of c-MYC in an immunodeficient background led to a decreased incidence of CPP and reduced tumour bulk. Finally, reduced tumour size was also observed upon T-cell depletion in CPP-bearing mice. Our data raise the possibility that benign choroid plexus tumours expressing c-MYC could be amenable to medical therapy with anti-inflammatory drugs.

Table S1. Characteristics of CPT developing in the transgenic mouse model. Each tumour was histologically classified according to stratification of cells, loss of papillary architecture/solid growth and cellular & nuclear pleomorphism (- mild, moderate or severe). For mitotic activity mild = 5/10 HPF. Based on the WHO criteria the tumours were classified as either CPP (with mild features) or ACPP (with moderate features). None of the tumours fulfilled the criteria to be classified as CPC. Abbreviations: Het – heterozygous; Hom – heterozygous; Symp – symptomatic; End – end of experiment following 20, 5-6 or 9-12 months of observation (as applicable); F – female; M – male; FV – fourth ventricle; LV – lateral ventricle; CPP – choroid plexus papilloma; ACPP – atypical choroid plexus papilloma; Mod – moderate; Sev – severe. * All mice are of genotype RosaMyc;c-MycSTOPFlox. (DOCX 27 kb)

Table S2. Patient demographics and tumour characteristics. Paediatric and adult patients were included and the tumours samples were of all three histological grades (CPP, ACPP and CPC). Abbreviations: F – female; M – male; FV – fourth ventricle; LV – lateral ventricle; TV – third ventricle; met – metastasis; CPP – choroid plexus papilloma; ACPP – atypical choroid plexus papilloma; IHC – immunohistochemistry. For recurrence, Y = yes; for c-MYC expression, F = focal (10-50%); D = diffuse (>50%). * & ** are tumour tissue from same respective patients. *** is an autopsy case. (DOCX 22 kb)

Table S2. Patient demographics and tumour characteristics. Paediatric and adult patients were included and the tumours samples were of all three histological grades (CPP, ACPP and CPC). Abbreviations: F – female; M – male; FV – fourth ventricle; LV – lateral ventricle; TV – third ventricle; met – metastasis; CPP – choroid plexus papilloma; ACPP – atypical choroid plexus papilloma; IHC – immunohistochemistry. For recurrence, Y = yes; for c-MYC expression, F = focal (10-50%); D = diffuse (>50%). * & ** are tumour tissue from same respective patients. *** is an autopsy case. (DOCX 22 kb)

Table S1. Characteristics of CPT developing in the transgenic mouse model. Each tumour was histologically classified according to stratification of cells, loss of papillary architecture/solid growth and cellular & nuclear pleomorphism (- mild, moderate or severe). For mitotic activity mild = 5/10 HPF. Based on the WHO criteria the tumours were classified as either CPP (with mild features) or ACPP (with moderate features). None of the tumours fulfilled the criteria to be classified as CPC. Abbreviations: Het – heterozygous; Hom – heterozygous; Symp – symptomatic; End – end of experiment following 20, 5-6 or 9-12 months of observation (as applicable); F – female; M – male; FV – fourth ventricle; LV – lateral ventricle; CPP – choroid plexus papilloma; ACPP – atypical choroid plexus papilloma; Mod – moderate; Sev – severe. * All mice are of genotype RosaMyc;c-MycSTOPFlox. (DOCX 27 kb)

Choroid plexus tumours (CPTs) account for 2-5% of brain tumours in children. They can spread along the neuraxis and can recur after treatment. Little is known about the molecular mechanisms underlying their formation and only few high fidelity mouse models of p53-deficient malignant CPTs are available.We show here that c-MYC overexpression in the choroid plexus epithelium induces T-cell inflammation-dependent choroid plexus papillomas in a mouse model. We demonstrate that c-MYC is expressed in a substantial proportion of human choroid plexus tumours and that this subgroup of tumours is characterised by an inflammatory transcriptome and significant inflammatory infiltrates. In compound mutant mice, overexpression of c-MYC in an immunodeficient background led to a decreased incidence of CPP and reduced tumour bulk. Finally, reduced tumour size was also observed upon T-cell depletion in CPP-bearing mice. Our data raise the possibility that benign choroid plexus tumours expressing c-MYC could be amenable to medical therapy with anti-inflammatory drugs.