Mathematical modelling of biosystems

This volume is an interdisciplinary book which introduces, in a very readable way, state-of-the-art research in the fundamental topics of mathematical modelling of Biosystems. These topics include the study of Biological Growth and its mechanisms, the coupling of pattern to form via theorems of Differential Geometry, the human immunodeficiency virus dynamics, and the inverse folding problem and the possibility of analysing true protein backbone flexibility. The Biclustering techniques for the organization of microarray data are covered, along with the analytical approach to the modelling of biomolecular structure via Steiner trees, the action of biocides on resistance mechanisms of mutated and phenotypic bacteria strains, and a description of the fundamental processes for the distribution and abundances of species towards a unified theory of Ecology. A special introduction to Protein Physics aims to explain the all-or-none first order phase transitions from native to denatured states.

[1]  M. Peifer,et al.  Wingless signaling: The inconvenient complexities of life , 1998, Current Biology.

[2]  E. Brouzes,et al.  Interplay of mechanical deformation and patterned gene expression in developing embryos. , 2004, Current opinion in genetics & development.

[3]  J Witek,et al.  Residual HIV-1 RNA in blood plasma of patients taking suppressive highly active antiretroviral therapy. , 1999, JAMA.

[4]  D Ambrosi,et al.  The role of stress in the growth of a multicell spheroid , 2004, Journal of mathematical biology.

[5]  A. Perelson,et al.  Rapid turnover of plasma virions and CD4 lymphocytes in HIV-1 infection , 1995, Nature.

[6]  J. Gerhart,et al.  Cells, embryos, and evolution: toward a cellular and developmental understanding of phenotypic variation and evolutionary adaptability , 1997 .

[7]  M. Hirsch,et al.  Infection of monocyte/macrophages by human T lymphotropic virus type III. , 1986, The Journal of clinical investigation.

[8]  R. Siliciano,et al.  The challenge of viral reservoirs in HIV-1 infection. , 2002, Annual review of medicine.

[9]  A. Perelson,et al.  Dynamics of HIV infection of CD4+ T cells. , 1993, Mathematical biosciences.

[10]  A. Perelson Modelling viral and immune system dynamics , 2002, Nature Reviews Immunology.

[11]  H. Gershengorn,et al.  Predicting the unpredictable: Transmission of drug-resistant HIV , 2001, Nature Medicine.

[12]  Alan S. Perelson,et al.  Effect of drug efficacy and the eclipse phase of the viral life cycle on estimates of HIV viral dynamic parameters. , 2001 .

[13]  S D Kemp,et al.  Resistance to ddI and sensitivity to AZT induced by a mutation in HIV-1 reverse transcriptase. , 1991, Science.

[14]  J. Kahn,et al.  Predicting the transmission of drug-resistant HIV: comparing theory with data. , 2003, The Lancet. Infectious diseases.

[15]  L M Wahl,et al.  Adherence and drug resistance: predictions for therapy outcome , 2000, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[16]  Terri Wrin,et al.  Persistence of drug-resistant HIV-1 after a structured treatment interruption and its impact on treatment response , 2003, AIDS.

[17]  Ben D MacArthur,et al.  Residual stress generation and necrosis formation in multi-cell tumour spheroids , 2004, Journal of mathematical biology.

[18]  Anthony S Fauci,et al.  HIV and AIDS: 20 years of science , 2003, Nature Medicine.

[19]  Giuseppe Saccomandi,et al.  A Molecular-Statistical Basis for the Gent Constitutive Model of Rubber Elasticity , 2002 .

[20]  I. Klapper Biological Applications of the Dynamics of Twisted Elastic Rods , 1996 .

[21]  R. Cameron,et al.  Nonlinear Integral Equations , 1964 .

[22]  M A Nowak,et al.  Virus dynamics and drug therapy. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[23]  D. Ho,et al.  The HIV-1 Vaccine Race , 2002, Cell.

[24]  D. Montefiori,et al.  Structured antiretroviral treatment interruptions in chronically HIV-1-infected subjects , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[25]  A S Perelson,et al.  Drug concentration heterogeneity facilitates the evolution of drug resistance. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[26]  Alain Goriely,et al.  On the Dynamics of Elastic Strips , 2001, J. Nonlinear Sci..

[27]  Marcelo Epstein,et al.  Thermomechanics of volumetric growth in uniform bodies , 2000 .

[28]  C. Boucher,et al.  Clinical data sets of human immunodeficiency virus type 1 reverse transcriptase-resistant mutants explained by a mathematical model , 1997, Journal of virology.

[29]  Ray W. Ogden,et al.  Growth in soft biological tissue and residual stress development , 2006 .

[30]  John W. Mellors,et al.  Prognosis in HIV-1 Infection Predicted by the Quantity of Virus in Plasma , 1996, Science.

[31]  D. Stainier,et al.  Developmental biology: Twisting the body into shape , 2003, Nature.

[32]  A S Perelson,et al.  Modeling plasma virus concentration during primary HIV infection. , 2000, Journal of theoretical biology.

[33]  Antonio DiCarlo,et al.  Growth and balance , 2002 .

[34]  E. Davidson Genomic Regulatory Systems , 2001 .

[35]  J. Taipale,et al.  The Hedgehog and Wnt signalling pathways in cancer , 2001, Nature.

[36]  L A Taber,et al.  Theoretical study of stress-modulated growth in the aorta. , 1996, Journal of theoretical biology.

[37]  Stephen M. Klisch,et al.  A Theory of Volumetric Growth for Compressible Elastic Biological Materials , 2001 .

[38]  A. Wodarz,et al.  A genetic hierarchy controlling cell polarity , 2003, Nature Cell Biology.

[39]  Megan F. Cole,et al.  Core Transcriptional Regulatory Circuitry in Human Embryonic Stem Cells , 2005, Cell.

[40]  Strickland,et al.  A Model of Phyllotaxis. , 1998, Journal of theoretical biology.

[41]  R. Nusse Cell biology: Relays at the membrane , 2005, Nature.

[42]  Irene K. Moore,et al.  A genomic code for nucleosome positioning , 2006, Nature.

[43]  S Bonhoeffer,et al.  Production of resistant HIV mutants during antiretroviral therapy. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[44]  J. Lockhart An analysis of irreversible plant cell elongation. , 1965, Journal of theoretical biology.

[45]  M. Martindale,et al.  An ancient role for nuclear β-catenin in the evolution of axial polarity and germ layer segregation , 2003, Nature.

[46]  M Hubbard,et al.  Axial forces and normal distributed loads in twining stems of morning glory. , 1991, Journal of biomechanics.

[47]  J. Lisziewicz,et al.  Structured treatment interruptions to control HIV-1 infection , 2000, The Lancet.

[48]  D J Cosgrove,et al.  Cell wall yield properties of growing tissue : evaluation by in vivo stress relaxation. , 1985, Plant physiology.

[49]  T. Lecuit,et al.  Spatial control of actin organization at adherens junctions by a synaptotagmin-like protein , 2006, Nature.

[50]  Hulin Wu,et al.  Modeling Long-Term HIV Dynamics and Antiretroviral Response: Effects of Drug Potency, Pharmacokinetics, Adherence, and Drug Resistance , 2005, Journal of acquired immune deficiency syndromes.

[51]  A. Perelson,et al.  Optimizing within-host viral fitness: infected cell lifespan and virion production rate. , 2004, Journal of theoretical biology.

[52]  A. Perelson,et al.  A model of HIV-1 pathogenesis that includes an intracellular delay. , 2000, Mathematical biosciences.

[53]  A. Ghani,et al.  Adherence to antiretroviral therapy and its impact on clinical outcome in HIV-infected patients , 2005, Journal of The Royal Society Interface.

[54]  Oliver A. Shergold,et al.  The uniaxial stress versus strain response of pig skin and silicone rubber at low and high strain rates , 2006 .

[55]  L. Preziosi,et al.  Modelling Solid Tumor Growth Using the Theory of Mixtures , 2001, Mathematical medicine and biology : a journal of the IMA.

[56]  B. Shilo,et al.  Spitz and Wingless, emanating from distinct borders, cooperate to establish cell fate across the Engrailed domain in the Drosophila epidermis. , 1997, Development.

[57]  D. Richman,et al.  HIV with reduced sensitivity to zidovudine (AZT) isolated during prolonged therapy. , 1989, Science.

[58]  D. Kirschner,et al.  Predicting differential responses to structured treatment interruptions during HAART , 2004, Bulletin of mathematical biology.

[59]  B. Shraiman,et al.  Mechanical feedback as a possible regulator of tissue growth. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[60]  F. W. Cummings,et al.  On the origin of pattern and form in early Metazoans. , 2006, The International journal of developmental biology.

[61]  T. Merigan,et al.  Treatment of human immunodeficiency virus infection with saquinavir, zidovudine, and zalcitabine. AIDS Clinical Trials Group. , 1996, The New England journal of medicine.

[62]  M. Stevenson HIV-1 pathogenesis , 2003, Nature Medicine.

[63]  Alain Goriely,et al.  Tendril Perversion in Intrinsically Curved Rods , 2002, J. Nonlinear Sci..

[64]  G. Friedland,et al.  Attaining higher goals in HIV treatment: the central importance of adherence. , 1999, AIDS.

[65]  N. Mendelson Helical Bacillus subtilis macrofibers: morphogenesis of a bacterial multicellular macroorganism. , 1978, Proceedings of the National Academy of Sciences of the United States of America.

[66]  Dominik Wodarz,et al.  Immune responses and the emergence of drug–resistant virus strains in vivo , 2004, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[67]  S. Carroll,et al.  From DNA to Diversity: Molecular Genetics and the Evolution of Animal Design , 2000 .

[68]  H. Frieboes,et al.  An integrated computational/experimental model of tumor invasion. , 2006, Cancer research.

[69]  Allan J. Hance,et al.  HIV Drug Resistance , 2004 .

[70]  S. Deeks,et al.  Treatment of antiretroviral-drug-resistant HIV-1 infection , 2003, The Lancet.

[71]  Joel E Gallant,et al.  Association between adherence to antiretroviral therapy and human immunodeficiency virus drug resistance. , 2003, Clinical infectious diseases : an official publication of the Infectious Diseases Society of America.

[72]  R. Gulick New antiretroviral drugs. , 2003, Clinical microbiology and infection : the official publication of the European Society of Clinical Microbiology and Infectious Diseases.

[73]  D L S McElwain,et al.  New insights into vascular collapse and growth dynamics in solid tumors. , 2004, Journal of theoretical biology.

[74]  D. Richman,et al.  Sexual transmission and propagation of SIV and HIV in resting and activated CD4+ T cells. , 1999, Science.

[75]  L. Taber Biomechanics of Growth, Remodeling, and Morphogenesis , 1995 .

[76]  Natalia L. Komarova,et al.  Computational Biology of Cancer: Lecture Notes and Mathematical Modeling , 2005 .

[77]  F. W. Cummings,et al.  A model of morphogenesis , 2003, physics/0308030.

[78]  L A Taber,et al.  Biomechanical growth laws for muscle tissue. , 1998, Journal of theoretical biology.

[79]  R. Jain,et al.  Solid stress generated by spheroid growth estimated using a linear poroelasticity model. , 2003, Microvascular research.

[80]  Alan N. Gent,et al.  Elastic instabilities in rubber , 2005 .

[81]  D. Ho,et al.  Viral Counts Count in HIV Infection , 1996, Science.

[82]  N. Tapon,et al.  Rho, Rac and Cdc42 GTPases regulate the organization of the actin cytoskeleton. , 1997, Current opinion in cell biology.

[83]  Z. Feng,et al.  A Two-Strain Tuberculosis Model with Age of Infection , 2002, SIAM J. Appl. Math..

[84]  A. Turing The chemical basis of morphogenesis , 1952, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.

[85]  T. Lecuit,et al.  Compartmentalized morphogenesis in epithelia: From cell to tissue shape , 2005, Developmental dynamics : an official publication of the American Association of Anatomists.

[86]  G. Coté,et al.  Biochemistry of Phosphoinositides , 1993 .

[87]  James A. Cuff,et al.  A Bivalent Chromatin Structure Marks Key Developmental Genes in Embryonic Stem Cells , 2006, Cell.

[88]  Sonya J Snedecor,et al.  Comparison of three kinetic models of HIV-1 infection: implications for optimization of treatment. , 2003, Journal of theoretical biology.

[89]  A. Gent A New Constitutive Relation for Rubber , 1996 .

[90]  W. Silk,et al.  An electronic device for continuous, in vivo measurement of forces exerted by twining vines. , 1997, American journal of botany.

[91]  M A Nowak,et al.  Competition between zidovudine‐sensitive and zidovudine‐resistant strains of HIV , 1992, AIDS.

[92]  P. Robson,et al.  Transcriptional Regulation of Nanog by OCT4 and SOX2* , 2005, Journal of Biological Chemistry.

[93]  M. Sacks Biaxial Mechanical Evaluation of Planar Biological Materials , 2000 .

[94]  John W. Mellors,et al.  New Real-Time Reverse Transcriptase-Initiated PCR Assay with Single-Copy Sensitivity for Human Immunodeficiency Virus Type 1 RNA in Plasma , 2003, Journal of Clinical Microbiology.

[95]  A. Hall,et al.  Rho GTPases and the actin cytoskeleton. , 1998, Science.

[96]  Stella Pelengaris,et al.  c-MYC: more than just a matter of life and death , 2002, Nature Reviews Cancer.

[97]  D. Kirschner,et al.  A model for treatment strategy in the chemotherapy of AIDS. , 1996, Bulletin of mathematical biology.

[98]  C. Darwin The Movements and Habits of Climbing Plants , 1875, Nature.

[99]  R. Siliciano,et al.  Long-term follow-up studies confirm the stability of the latent reservoir for HIV-1 in resting CD4+ T cells , 2003, Nature Medicine.

[100]  R Gordon,et al.  How to observe surface contraction waves on axolotl embryos. , 1996, The International journal of developmental biology.

[101]  A S Perelson,et al.  Modeling HIV infection of CD4+ T-cell subpopulations. , 1994, Journal of theoretical biology.

[102]  Paolo A. Netti,et al.  Solid stress inhibits the growth of multicellular tumor spheroids , 1997, Nature Biotechnology.

[103]  J. Coffin,et al.  HIV population dynamics in vivo: implications for genetic variation, pathogenesis, and therapy , 1995, Science.

[104]  A S Perelson,et al.  Improved estimates for HIV-1 clearance rate and intracellular delay. , 1999, AIDS.

[105]  A. Trkola,et al.  HIV RNA in plasma rebounds within days during structured treatment interruptions , 2003, AIDS.

[106]  N. Holbrook,et al.  The importance of frictional interactions in maintaining the stability of the twining habit. , 2005, American journal of botany.

[107]  A. Perelson,et al.  Influence of delayed viral production on viral dynamics in HIV-1 infected patients. , 1998, Mathematical biosciences.

[108]  H. Maruta,et al.  G proteins, phosphoinositides, and actin‐cytoskeleton in the control of cancer growth , 1999, Microscopy research and technique.

[109]  S D Kemp,et al.  Multiple mutations in HIV-1 reverse transcriptase confer high-level resistance to zidovudine (AZT). , 1989, Science.

[110]  On the eversion of compressible elastic cylinders , 1997 .

[111]  H. Bode,et al.  Formation of the head organizer in hydra involves the canonical Wnt pathway , 2005, Development.

[112]  S. J. Clark,et al.  High levels of HIV-1 in plasma during all stages of infection determined by competitive PCR. , 1993, Science.

[113]  Goriely,et al.  New Amplitude Equations for Thin Elastic Rods. , 1996, Physical review letters.

[114]  G. Mitchison,et al.  Phyllotaxis and the Fibonacci Series , 1977, Science.

[115]  Thomas A. Milne,et al.  A PHD finger of NURF couples histone H3 lysine 4 trimethylation with chromatin remodelling , 2006, Nature.

[116]  Alan S. Perelson,et al.  Mathematical Analysis of HIV-1 Dynamics in Vivo , 1999, SIAM Rev..

[117]  R. Ogden Non-Linear Elastic Deformations , 1984 .

[118]  Daniel Coombs,et al.  An age-structured model of hiv infection that allows for variations in the production rate of viral particles and the death rate of productively infected cells. , 2004, Mathematical biosciences and engineering : MBE.

[119]  D. Livingston Cancer: Chromosome defects in the colon , 2001, Nature.

[120]  Christof Niehrs,et al.  Casein kinase 1 γ couples Wnt receptor activation to cytoplasmic signal transduction , 2005, Nature.

[121]  S. Antman Nonlinear problems of elasticity , 1994 .

[122]  A. Stein The deformation of a rod of growing biological material under longitudinal compression , 1995 .

[123]  D Bilder,et al.  Cooperative regulation of cell polarity and growth by Drosophila tumor suppressors. , 2000, Science.

[124]  Sébastien Neukirch,et al.  Mechanics of climbing and attachment in twining plants. , 2006, Physical review letters.

[125]  R. Siliciano,et al.  Viral Dynamics in HIV-1 Infection , 1998, Cell.

[126]  J. Ortega Augmented growth equation for cell wall expansion. , 1985, Plant physiology.

[127]  Gérard A. Maugin,et al.  Pseudo-plasticity and Pseudo-inhomogeneity Effects in Materials Mechanics , 2003 .

[128]  Simon L. Peyton Jones Haskell 98 Libraries: CPU Time , 2003, J. Funct. Program..

[129]  J. Lisziewicz,et al.  Latent infection of CD4+ T cells provides a mechanism for lifelong persistence of HIV-1, even in patients on effective combination therapy , 1999, Nature Medicine.

[130]  F. W. Cummings Interaction of morphogens with geometry , 2005 .