Molecular basis of high viscosity in concentrated antibody solutions: Strategies for high concentration drug product development

mAbs

Volumn 8, Issue 2, 2016, Pages 216-228

  Tomar, Dheeraj S ^a   Kumar, Sandeep ^a   Singh, Satish K ^a   Goswami, Sumit ^a   Li, Li ^a  

^a PFIZER INC   (United States)

Author keywords

Electrostatics; High concentration; Hydrophobicity; Intermolecular interactions; Monoclonal antibody solution; Networks; Viscosity

Indexed keywords

ANTIBODY; MONOCLONAL ANTIBODY;

CHEMICAL INTERACTION; COMPLEMENTARITY DETERMINING REGION; DIFFUSION COEFFICIENT; DIPOLE; FLOW MEASUREMENT; FRICTION; INTERMOLECULAR INTERACTION; MOLECULAR CROWDING; MOLECULAR DYNAMICS; PROCESS OPTIMIZATION; REVIEW; STATIC ELECTRICITY; VISCOSITY; ZETA POTENTIAL; ANIMAL; CHEMICAL MODEL; CHEMISTRY; HUMAN;

ANIMALS; ANTIBODIES, MONOCLONAL; HUMANS; MODELS, CHEMICAL; VISCOSITY;

EID: 84964543165     PISSN: 19420862     EISSN: 19420870     Source Type: Journal    
DOI: 10.1080/19420862.2015.1128606     Document Type: Review

References (92)

1. MillerKL, LanthierM.Regulatory watch: Innovation in biologic new molecular entities: 1986-2014. Nat Rev Drug Discov2015; 14:83; PMID:25633785; http://dx.doi.org/10.1038/nrd4535
2. IMS Health. Global Spending on Medicines. http://www.imshealth.com/deployedfiles/imshealth/Global/Content/Corporate/IMS%20Health%20Institute/Reports/Global_Use_of_Meds_Outlook_2017/Biologics_Market.pdf. July 13. 2015
3. MullardA.2014FDA drug approvals. Nat Rev Drug Discov2015; 14:77-81; PMID:25633781; http://dx.doi.org/10.1038/nrd4545
4. USFDA. What Are "Biologics" Questions and Answers. http://www.fda.gov/AboutFDA/CentersOffices/OfficeofMedicalProductsandTo bacco/CBER/ucm133077.htm. July 8, 2015
5. NelsonAL, DhimoleaE, ReichertJM.Development trends for human monoclonal antibody therapeutics. Nat Rev Drug Discov2010; 9:767-74; PMID:20811384; http://dx.doi.org/10.1038/nrd3229
6. WeinerLM, SuranaR, WangS.Monoclonal antibodies: versatile platforms for cancer immunotherapy. Nat Rev Immunol2010; 10:317-27; PMID:20414205; http://dx.doi.org/10.1038/nri2744
7. ScottAM, WolchokJD, OldLJ.Antibody therapy of cancer. Nat Rev Cancer2012; 12:278-87; PMID:22437872; http://dx.doi.org/10.1038/nrc3236
8. ReichertJM, RosensweigCJ, FadenLB, DewitzMC.Monoclonal antibody successes in the clinic. Nat Biotechnol2005; 23:1073-8; PMID:16151394; http://dx.doi.org/10.1038/nbt0905-1073
9. ButtelIC, ChamberlainP, ChowersY, EhmannF, GreinacherA, JefferisR, KramerD, KropshoferH, LloydP, LubinieckiA, et al.Taking immunogenicity assessment of therapeutic proteins to the next level. Biologicals2011; 39:100-9; PMID:21353596; http://dx.doi.org/10.1016/j.biologicals.2011.01.006
10. ShireSJ, ShahrokhZ, LiuJ.Challenges in the development of high protein concentration formulations. J Pharm Sci2004; 93:1390-402; PMID:15124199; http://dx.doi.org/10.1002/jps.20079
11. BookbinderLH, HoferA, HallerMF, ZepedaML, KellerGA, LimJE, EdgingtonTS, ShepardHM, PattonJS, FrostGI.A recombinant human enzyme for enhanced interstitial transport of therapeutics. J Controlled Release2006; 114:230-41; PMID:16876899; http://dx.doi.org/10.1016/j.jconrel.2006.05.027
12. FriessH, LangrehrJ, OettleH, RaedleJ, NiedergethmannM, DittrichC, HossfeldD, StogerH, NeynsB, HerzogP, et al.A randomized multi-center phase II trial of the angiogenesis inhibitor Cilengitide (EMD 121974) and gemcitabine compared with gemcitabine alone in advanced unresectable pancreatic cancer. BMC Cancer2006; 6:285; PMID:17156477; http://dx.doi.org/10.1186/1471-2407-6-285
13. RathoreN, PranayP, BernackiJ, EuB, JiW, WallsE.Characterization of protein rheology and delivery forces for combination products. J Pharmaceutical Sci2012; 101:4472-80; PMID:22941931; http://dx.doi.org/10.1002/jps.23297
14. GoswamiS, WangW, ArakawaT, OhtakeS.Developments and challenges for mAb-βased therapeutics. Antibodies2013; 2:452-500; http://dx.doi.org/10.3390/antib2030452
15. ShireSJ.Formulation and manufacturability of biologics. Curr Opin Biotechnol2009; 20:708-14; PMID:19880308; http://dx.doi.org/10.1016/j.copbio.2009.10.006
16. FischerI, SchmidtA, BryantA, BesheerA.Calculation of injection forces for highly concentrated protein solutions. International journal of pharmaceutics2015; 493:70-4; PMID:26211901; http://dx.doi.org/10.1016/j.ijpharm.2015.07.054
17. AllmendingerA, FischerS, HuwylerJ, MahlerHC, SchwarbE, ZarragaIE, MuellerR.Rheological characterization and injection forces of concentrated protein formulations: an alternative predictive model for non-Newtonian solutions. Eur J Pharm Biopharm2014; 87:318-28; PMID:24560966; http://dx.doi.org/10.1016/j.ejpb.2014.01.009
18. PathakJA, SologurenRR, NarwalR.Do clustering monoclonal antibody solutions really have a concentration dependence of viscosity?Biophys J2013; 104:913-23; PMID:23442970; http://dx.doi.org/10.1016/j.bpj.2013.01.007
19. BergJC.An Introduction to Interfaces and Colloids, the bridge to nanoscience. World Scientific Publishing Company Private Limited2010
20. LaufferMA.Motion in viscous liquids: Simplified derivations of the Stokes and Einstein equations. J Chem Edu1981; 58:250; http://dx.doi.org/10.1021/ed058p250
21. JunkM, IllnerR.A new derivation of Jeffery’s equation. J Math Fluid Mech2007; 9:455-88; http://dx.doi.org/10.1007/s00021-005-0208-0
22. ZhouHX, RivasG, MintonAP.Macromolecular crowding and confinement: biochemical, biophysical, and potential physiological consequences. Ann Rev Biophys2008; 37:375-97; PMID:18573087; http://dx.doi.org/10.1146/annurev.biophys.37.032807.125817
23. MooneyM.The viscosity of a concentrated suspension of spherical particles. J Colloid Sci1951; 6:162-70; http://dx.doi.org/10.1016/00958522(51)90036-0
24. RossPD, MintonAP.Hard quasispherical model for the viscosity of hemoglobin solutions. Biochem Biophys Res Commun1977; 76:971-6; PMID:20088; http://dx.doi.org/10.1016/0006-291X(77)90950-0
25. LiuJ, NguyenMD, AndyaJD, ShireSJ.Reversible self-association increases the viscosity of a concentrated monoclonal antibody in aqueous solution. J Pharm Sci2005; 94:1928-40; PMID:16052543; http://dx.doi.org/10.1002/jps.20347
26. CreightonTE.The physical and chemical basis of molecular biology. Helvetian Press, 2010
27. SimhaR.Effect of concentration on the viscosity of dilute solutions. Transactions N York Acad Sci1949; 11:96; http://dx.doi.org/10.1111/j.2164-0947.1949.tb00137.x
28. HugginsML.The viscosity of dilute solutions of long-chain molecules. IV. dependence on concentration. J Am Chem Society1942; 64:2716-8; http://dx.doi.org/10.1021/ja01263a056
29. AragonS.A precise boundary element method for macromolecular transport properties. J Computational Chem2004; 25:1191-205; PMID:15116362; http://dx.doi.org/10.1002/jcc.20045
30. RutgersIR.Relative viscosity and concentration. Rheol Acta1962; 2:305-48; http://dx.doi.org/10.1007/BF01976051
31. SudduthRD. Ageneralized model to predict the viscosity of solutions with suspended particles. I. J Applied Polymer Sci1993; 48:25-36; http://dx.doi.org/10.1002/app.1993.070480104
32. IsraelachviliJN.Intermolecular and surface forces. Elsevier2011
33. NicoudL, OwczarzM, ArosioP, MorbidelliM.A multiscale view of therapeutic protein aggregation: A colloid science perspective. Biotechnol J2015; 10:367-78; PMID:25772395; http://dx.doi.org/10.1002/biot.201400858
34. LaueT.Proximity energies: a framework for understanding concentrated solutions. J Mol Recognition2012; 25:165-73; PMID:22407980; http://dx.doi.org/10.1002/jmr.2179
35. HardingSE, JohnsonP.The concentration-dependence of macromolecular parameters. Biochem J1985; 231:543-7; PMID:4074322; http://dx.doi.org/10.1042/bj2310543
36. YadavS, ShireSJ, KaloniaDS.Factors affecting the viscosity in high concentration solutions of different monoclonal antibodies. J Pharm Sci2010; 99:4812-29; PMID:20821382; http://dx.doi.org/10.1002/jps.22190
37. JayaramanJ, WuJ, BrunelleMC, CruzAM, GoldbergDS, LoboB, ShahA, TessierPM.Plasmonic measurements of monoclonal antibody self-association using self-interaction nanoparticle spectroscopy. Biotechnol Bioeng2014; 111:1513-1520
38. SaitoS, HasegawaJ, KobayashiN, KishiN, UchiyamaS, FukuiK.Behavior of monoclonal antibodies: relation between the second virial coefficient (B (2)) at low concentrations and aggregation propensity and viscosity at high concentrations. Pharm Res2012; 29:397-410; PMID:21853361; http://dx.doi.org/10.1007/s11095-011-0563-x
39. ConnollyBD, PetryC, YadavS, DemeuleB, CiaccioN, MooreJM, ShireSJ, GokarnYR.Weak interactions govern the viscosity of concentrated antibody solutions: high-throughput analysis using the diffusion interaction parameter. Biophys J2012; 103:69-78; PMID:22828333; http://dx.doi.org/10.1016/j.bpj.2012.04.047
40. BinabajiE, MaJ, ZydneyAL.Intermolecular interactions and the viscosity of highly concentrated monoclonal antibody solutions. Pharm Res2015; 32(9):3102; PMID:25832501
41. LilyestromWG, YadavS, ShireSJ, SchererTM.Monoclonal antibody self-association, cluster formation, and rheology at high concentrations. J Phys Chem B2013; 117:6373-84; PMID:23560896; http://dx.doi.org/10.1021/jp4008152
42. BuckPM, ChaudhriA, KumarS, SinghSK.Highly viscous antibody solutions are a consequence of network formation caused by domaindomain electrostatic complementarities: insights from coarse-grained simulations. Mol Pharm2015; 12:127-39; PMID:25383990; http://dx.doi.org/10.1021/mp500485w
43. SalujaA, BadkarAV, ZengDL, KaloniaDS.Ultrasonic rheology of a monoclonal antibody (IgG2) solution: implications for physical stability of proteins in high concentration formulations. J Pharm Sci2007; 96:3181-95; PMID:17588261; http://dx.doi.org/10.1002/jps.20970
44. SalujaA, BadkarAV, ZengDL, NemaS, KaloniaDS.Ultrasonic storage modulus as a novel parameter for analyzing protein-protein interactions in high protein concentration solutions: correlation with static and dynamic light scattering measurements. Biophys J2007; 92:234-44; PMID:17028129; http://dx.doi.org/10.1529/biophysj.106.095174
45. PrausnitzJ.The fallacy of misplaced concreteness. Biophys J2015; 108:453-4; PMID:25650910; http://dx.doi.org/10.1016/j.bpj.2014.11.3486
46. SarangapaniP, JonesRL, HudsonS, PathakJA.The pH and co1ncentration dependence of protein-protein interactions, conformation, and viscosity in crowded protein solutions. Biophys J2013; 106:665a-6a; http://dx.doi.org/10.1016/j.bpj.2013.11.3685
47. Sarangapani PrasadS, Hudson StevenD, Jones RonaldL, Douglas JackF, Pathak JaiA.Critical examination of the colloidal particle model of globular proteins. Biophys J2015; 108:724-37; PMID:25650939; http://dx.doi.org/10.1016/j.bpj.2014.11.3483
48. NicoudL, LattuadaM, YatesA, MorbidelliM.Impact of aggregate formation on the viscosity of protein solutions. Soft Matter2015; 11:5513-22; PMID:26061258; http://dx.doi.org/10.1039/C5SM00513B
49. BarnettGV, QiW, AminS, Neil LewisE, RobertsCJ.Aggregate structure, morphology and the effect of aggregation mechanisms on viscosity at elevated protein concentrations. Biophy Chem2015; 207:21-9; PMID:26284891; http://dx.doi.org/10.1016/j.bpc.2015.07.002
50. AminS, BarnettGV, PathakJA, RobertsCJ, SarangapaniPS.Protein aggregation, particle formation, characterization & rheology. Curr Opin Colloid Interface Sci2014; 19:438-49; http://dx.doi.org/10.1016/j.cocis.2014.10.002
51. VoynovV, ChennamsettyN, KayserV, HelkB, TroutBL.Predictive tools for stabilization of therapeutic proteins. MAbs2009; 1:580-2; PMID:20068399; http://dx.doi.org/10.4161/mabs.1.6.9773
52. ChennamsettyN, VoynovV, KayserV, HelkB, TroutBL.Design of therapeutic proteins with enhanced stability. Proc Natl Acad Sci U S A2009; 106:11937-42; PMID:19571001; http://dx.doi.org/10.1073/pnas.0904191106
53. BrandtJP, PatapoffTW, AragonSR.Construction, MD simulation, and hydrodynamic validation of an all-atom model of a monoclonal IgG antibody. Biophys J2010; 99:905-13; PMID:20682269; http://dx. doi.org/10.1016/j.bpj.2010.05.003
54. WangX, KumarS, BuckPM, SinghSK. Impact of de-glycosylation and thermal stress on conformational stability of a full length murine IgG2a monoclonal antibody: Observations from molecular dynamics simulations. Proteins2012; 81:443-460
55. KortkhonjiaE, BrandmanR, ZhouJZ, VoelzVA, ChornyI, KabakoffB, PatapoffTW, DillKA, SwartzTE.Probing antibody internal dynamics with fluorescence anisotropy and molecular dynamics simulations. MAbs2013; 5:306-22; PMID:23396076; http://dx.doi.org/10.4161/mabs.23651
56. LapelosaM, PatapoffTW, ZarragaIE.Molecular simulations of the pairwise interaction of monoclonal antibodies. J Phys Chem B2014; 118:13132-41; PMID:25350229; http://dx.doi.org/10.1021/jp508729z
57. SaundersMG, VothGA.Coarse-graining methods for computational biology. Ann Rev Biophy2013; 42:73-93; PMID:23451897; http://dx.doi.org/10.1146/annurev-βiophys-083012-130348
58. TakadaS.Coarse-grained molecular simulations of large biomolecules. Curr Opin Struct Biol2012; 22:130-7; PMID:22365574; http://dx.doi.org/10.1016/j.sbi.2012.01.010
59. KamerlinSC, VicatosS, DrygaA, WarshelA.Coarse-grained (multiscale) simulations in studies of biophysical and chemical systems. Ann Rev Phys Chem2011; 62:41-64; PMID:21034218; http://dx.doi.org/10.1146/annurev-physchem-032210-103335
60. ChaudhriA, ZarragaIE, KamerzellTJ, BrandtJP, PatapoffTW, ShireSJ, VothGA.Coarse-grained modeling of the self-association of therapeutic monoclonal antibodies. J Phys Chem B2012; 116:8045-57; PMID:22694284; http://dx.doi.org/10.1021/jp301140u
61. ChaudhriA, ZarragaIE, YadavS, PatapoffTW, ShireSJ, VothGA.The role of amino acid sequence in the self-association of therapeutic monoclonal antibodies: insights from coarse-grained modeling. J Phys Chem B2013; 117:1269-79; PMID:23316912; http://dx.doi.org/10.1021/jp3108396
62. MarrinkSJ, RisseladaHJ, YefimovS, TielemanDP, de VriesAH.The MARTINI force field: coarse grained model for biomolecular simulations. J Phys Chem B2007; 111:7812-24; PMID:17569554; http://dx. doi.org/10.1021/jp071097f
63. MarrinkSJ, TielemanDP.Perspective on the Martini model. Chem Soc Rev2013; 42:6801-22; PMID:23708257; http://dx.doi.org/10.1039/c3cs60093a
64. PerioleX, MarrinkSJ.The Martini coarse-grained force field. Methods Mol Biol2013; 924:533-65; PMID:23034762; http://dx.doi.org/10.1007/978-1-62703-017-5_20
65. MartinezM, BruceNJ, RomanowskaJ, KokhDB, OzboyaciM, YuX, ÖztürkMA, RichterS, WadeRC. SDA7: A modular and parallel implementation of the simulation of diffusional association software. J Computational Chem2015; 36:1631-1645; PMID:26123630; http://dx. doi.org/10.1002/jcc.23971
66. ErbanR.From molecular dynamics to Brownian dynamics. Proc Math Phys Eng Sci2014; 470:20140036
67. AllenMP, TildesleyDJ. Computer simulation of liquids Oxford Science Publications1986
68. DoyleP, UnderhillP.Brownian Dynamics Simulations of Polymers and Soft Matter. In: Yip S, ed.Handbook of Materials Modeling: Springer Netherlands, 2005:2619-30
69. BalboJ, MereghettiP, HertenDP, WadeRC.The shape of protein crowders is amajor determinant of protein diffusion. Biophys J2013; 104:1576-84; PMID:23561534; http://dx.doi.org/10.1016/j.bpj.2013.02.041
70. MereghettiP, WadeRC.Atomic detail Brownian Dynamics simulations of concentrated protein solutions with a mean field treatment of hydrodynamic interactions. J Phys Chem B2012; 116:8523-33; PMID:22594708; http://dx.doi.org/10.1021/jp212532h
71. Li L, Kumar S, Buck PM, Burns C, Lavoie J, Singh SK, Warne NW, Nichols P, Luksha N, Boardman D. Concentration dependent viscosity of monoclonal antibody solutions: explaining experimental behavior in terms of molecular properties. Pharm Res2014; 31:3161-78; PMID:24906598; http://dx.doi.org/10.1007/ s11095-014-1409-0
72. WarneNW.Development of high concentration protein biopharmaceuticals: the use of platform approaches in formulation development. Eur J Pharm Biopharm2011; 78:208-12; PMID:21406226; http://dx. doi.org/10.1016/j.ejpb.2011.03.004
73. SharmaVK, PatapoffTW, KabakoffB, PaiS, HilarioE, ZhangB, LiC, BorisovO, KelleyRF, ChornyI, et al.In silico selection of therapeutic antibodies for development: viscosity, clearance, and chemical stability. Proc Natl Acad Sci U S A2014; 111:18601-6; PMID:25512516; http://dx.doi.org/10.1073/pnas.1421779112
74. ZurdoJ.Developability assessment as an early de-risking tool for biopharmaceutical development. Pharmaceutical Bioprocessing2013; 1:29-50; http://dx.doi.org/10.4155/pbp.13.3
75. NicholsP, LiL, KumarS, BuckPM, SinghSK, GoswamiS, BalthazorB, ConleyTR, SekD, AllenMJ.Rational design of viscosity reducing mutants of a monoclonal antibody: hydrophobic vs. electrostatic inter-molecular interactions. MAbs2015; 7:212-30; PMID:25559441; http://dx.doi.org/10.4161/19420862.2014.985504
76. RautA, KaloniaD. Viscosity Analysis of Dual Variable Domain Immunoglobulin Protein Solutions: Role of Size, Electroviscous Effect and Protein-Protein Interactions. Pharmaceutical Res2015; 33:1-12; PMID:25168518
77. YadavS, SreedharaA, KanaiS, LiuJ, LienS, LowmanH, KaloniaDS, ShireSJ.Establishing a link between amino acid sequences and selfassociating and viscoelastic behavior of two closely related monoclonal antibodies. Pharm Res2011; 28:1750-64; PMID:21626060; http://dx.doi.org/10.1007/s11095-011-0410-0
78. AgrawalNJ, HelkB, KumarS, ModyN, SathishHA, SamraHS, BuckPM, LiL, TroutBL.Computational tool for the early screening of monoclonal antibodies for their viscosities. MABS2015; 8:1-6; PMID:26399600; http://dx.doi.org/10.1080/19420862.2015.1099773
79. YadavS, LiuJ, ShireSJ, KaloniaDS.Specific interactions in high concentration antibody solutions resulting in high viscosity. J Pharm Sci2010; 99:1152-68; PMID:19705420; http://dx.doi.org/10.1002/jps.21898
80. SchererTM.Cosolute effects on the chemical potential and interactions of an IgG1 monoclonal antibody at high concentrations. J Phys Chem B2013; 117:2254-66; PMID:23330570; http://dx.doi.org/10.1021/jp3091717
81. EsfandiaryR, ParupudiA, Casas-FinetJ, GadreD, SathishH.Mechanism of reversible self-association of a monoclonal antibody: role of electrostatic and hydrophobic interactions. J Pharm Sci2015; 104:577-86; PMID:25407315; http://dx.doi.org/10.1002/jps.24237
82. GuoZ, ChenA, NassarR, HelkB, MuellerC, TangY, GuptaK, KlibanovA.Structure-activity relationship for hydrophobic salts as viscosity- lowering excipients for concentrated solutions of monoclonal antibodies. Pharm Res2012; 29:3102-9; PMID:22692671; http://dx. doi.org/10.1007/s11095-012-0802-9
83. KamerzellTJ, PaceAL, LiM, DanilenkoDM, McDowellM, GokarnYR, WangYJ.Polar solvents decrease the viscosity of high concentration IgG1 solutions through hydrophobic solvation and interaction: formulation and biocompatibility considerations. J Pharm Sci2013; 102:1182-93; PMID:23359242; http://dx.doi.org/10.1002/jps.23453
84. HeF, WoodsC, LitowskiJ, RoschenL, GadgilH, RazinkovV, KerwinB.Effect of Sugar Molecules on the Viscosity of High Concentration Monoclonal Antibody Solutions. Pharmaceutical Res2011; 28:1552-60; PMID:21573867; http://dx.doi.org/10.1007/s11095-011-0388-7
85. WangS, ZhangN, HuT, DaiWG, FengX, ZhangX, QianF.Viscosity- Lowering Effect of Amino Acids and Salts on Highly Concentrated Solutions of two IgG1 Monoclonal Antibodies. Mol Pharmaceutics2015; 12(12):4478-87; PMID:26528726; http://dx.doi.org/10.1021/acs. molpharmaceut.5b00643
86. InoueN, TakaiE, ArakawaT, ShirakiK.Arginine and lysine reduce the high viscosity of serum albumin solutions for pharmaceutical injection. J Biosci Bioengineering2014; 117:539-43; PMID:24268865; http://dx.doi.org/10.1016/j.jbiosc.2013.10.016
87. InoueN, TakaiE, ArakawaT, ShirakiK.Specific Decrease in Solution Viscosity of Antibodies by Arginine for Therapeutic Formulations. Mol Pharmaceutics2014; 11:1889-96; PMID:24689736; http://dx.doi.org/10.1021/mp5000218
88. SchneiderCP, ShuklaD, TroutBL.Arginine and the Hofmeister Series: The Role of Ion–Ion Interactions in Protein Aggregation Suppression. The J Phy Chem B2011; 115:7447-58; PMID:21568311; http://dx.doi.org/10.1021/jp111920y
89. BowenMN, LiuJ, PatelAR.Compositions and methods useful for reducing the viscosity of protein-containing formulations. United States, 2013The patent publication number is WO2011/139718 A1.
90. KangD, JadinL, NekoroskiT, DrakeF, ZepedaM.Recombinant human hyaluronidase PH20 (rHuPH20) facilitates subcutaneous infusions of large volumes of immunoglobulin in a swine model. Drug Deliv and Transl Res2012; 2:254-64; http://dx.doi.org/10.1007/s13346-012-0065-3
91. WynneC, HarveyV, SchwabeC, WaakaD, McIntyreC, BittnerB. Comparison of Subcutaneous and Intravenous Administration of Trastuzumab: A Phase I/Ib Trial in Healthy Male Volunteers and Patients With HER2-Positive Breast Cancer. J Clin Pharmacol2013; 53:192-201; PMID:23436264; http://dx.doi.org/10.1177/0091270012436560
92. BergHC. Random walks in biology Princeton University Press, 1983