Diffusion versus network models as descriptions for the spread of prion diseases in the brain.

In this paper we will discuss different modeling approaches for the spread of prion diseases in the brain. Firstly, we will compare reaction-diffusion models with models of epidemic diseases on networks. The solutions of the resulting reaction-diffusion equations exhibit traveling wave behavior on a one-dimensional domain, and the wave speed can be estimated. The models can be tested for diffusion-driven (Turing) instability, which could present a possible mechanism for the formation of plaques. We also show that the reaction-diffusion systems are capable of reproducing experimental data on prion spread in the mouse visual system. Secondly, we study classical epidemic models on networks, and use these models to study the influence of the network topology on the disease progression.

[1]  Subhasis Banerjee,et al.  Reaction-Diffusion Processes on Random and Scale-Free Networks , 2004 .

[2]  L. Gallos,et al.  Absence of kinetic effects in reaction-diffusion processes in scale-free networks. , 2004, Physical review letters.

[3]  Alessandro Vespignani,et al.  Epidemic dynamics and endemic states in complex networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  D. Dormont,et al.  Prions, BSE and food. , 2002, International journal of food microbiology.

[5]  S. Collins,et al.  Organ distribution of prion proteins in variant Creutzfeldt-Jakob disease. , 2003, The Lancet. Infectious diseases.

[6]  A. Aguzzi,et al.  Peripheral pathogenesis of prion diseases. , 2000, Microbes and infection.

[7]  V. Jansen,et al.  Designing drugs to stop the formation of prion aggregates and other amyloids. , 2000, Biophysical chemistry.

[8]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[9]  M. Eigen,et al.  Prionics or the kinetic basis of prion diseases. , 1996, Biophysical chemistry.

[10]  M. Beekes,et al.  Sequential appearance and accumulation of pathognomonic markers in the central nervous system of hamsters orally infected with scrapie. , 1996, The Journal of general virology.

[11]  Panos Argyrakis,et al.  Reaction-diffusion processes on correlated and uncorrelated scale-free networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  J. C. Cressoni,et al.  Thermo-kinetic model for Prion diseases , 2001 .

[13]  M. Elowitz,et al.  Protein Mobility in the Cytoplasm ofEscherichia coli , 1999, Journal of bacteriology.

[14]  H. Fraser,et al.  Enucleation after intraocular scrapie injection delays the spread of infection , 1989, Brain Research.

[15]  G. Krishnamoorthy,et al.  Cell type and spatial location dependence of cytoplasmic viscosity measured by time-resolved fluorescence microscopy. , 1997, Archives of biochemistry and biophysics.

[16]  Reka Albert,et al.  Mean-field theory for scale-free random networks , 1999 .

[17]  Stanley B. Prusiner,et al.  Nobel Lecture: Prions , 1998 .

[18]  Alessandro Vespignani,et al.  Velocity and hierarchical spread of epidemic outbreaks in scale-free networks. , 2003, Physical review letters.

[19]  P. Lantos,et al.  The spatial patterns of prion protein deposits in Creutzfeldt–Jakob disease: comparison with β-amyloid deposits in Alzheimer's disease , 2001, Neuroscience Letters.

[20]  David C. Krakauer,et al.  The spatial dynamics of prion disease , 1998, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[21]  H Fraser,et al.  Scrapie in the central nervous system: neuroanatomical spread of infection and Sinc control of pathogenesis. , 1992, The Journal of general virology.

[22]  J. Murray,et al.  A quantitative model for differential motility of gliomas in grey and white matter , 2000, Cell proliferation.

[23]  P. Lansbury,et al.  Models of amyloid seeding in Alzheimer's disease and scrapie: mechanistic truths and physiological consequences of the time-dependent solubility of amyloid proteins. , 1997, Annual review of biochemistry.

[24]  M A Nowak,et al.  Quantifying the kinetic parameters of prion replication. , 1999, Biophysical chemistry.