Applied Numerics in System Biology
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Applied numerics in system biology Max von Kleist Vitaly Belik Vikram Sunkara About me 2004 MS Physics, Biophysics, Moscow Lomonosov University 2000-2001 HU Berlin 2008 Dr. rer. nat. Georg-August-Universität Göttingen 2010-2012 MIT, Cambridge, MA 2004-2013 MPI for Dynamics and Selforganisation, Göttingen 2014-2016 TU Berlin since 2016 Professor (Juniorprofessor) FU Berlin AG System Modeling, Institut für veterinary Epidemiology and Biostatistics [email protected] Research focus Spreading processes on networks (epidemiology, opinion formation) Human and animal mobility Combining biological and metadata Data science (sensor data for health applications) Host-parasite-environment interactions, hormone dynamics Epidemics V Belik, T Geisel, D Brockmann Physical Review X 1 (1), 011001 Underlying network (A) (B) (C) V Belik, T Geisel, D Brockmann Physical Review X 1 (1), 011001 Human mobility 4 II II II I IIIII I II IIIIV I II III IV 40% 6 30% 3/5 4/83 4/5408 4/10 Survey Phone 20% (ID) Model p 10% 0% 1 2345 6 7 8 9 10 11 12 13 14 15 16 17 Motif ID FIG. 3. Possible daily mobility patterns are limited, since up to 90% of the identified daily mobility networks can be described with only 17CM different Schneider, motifs. The probability V Belik,p(ID) T Couronné, to find one of the Z 17 Smoreda, motifs in the surveys MC (cyan González - Paris, blue - Chicago), the phone data (orange - Paris), and the model (light green - Paris, dark green - Chicago) is presented. The motifs are grouped according toJournal their size separated of The by Royal dashed lines Society and for each Interface group the fraction 10 (84), of observed 20130246 and feasible motifs Nf are shown. Most of the motifs can also be classified with four rules: I) The motif of size N consists of a tour with only one stop and another tour with N 2stops.II)ThemotifofsizeN consists of only a single tour with N stops. III) The motif of size N consists of two tours with− one stop and another tour with N 3stops.IV)ThemotifofsizeN consists of a tour with two stops and another tour with N 3 stops. Despite the fact that− the number of workers is significantly different in both cities, the rank and the probability to− find a specific motif exhibit similar behavior. than one. In fact, this is observed for motifs created ac- While the time spent for working and staying at home is cording to rule II) and III). relatively flat distributed with some characteristic dura- In general, motifs may not be unique, if a person can re- tions of 3.5h, 8.6h, and 14h, respectively, the probability peat a tour several times within a day. However, the rep- of an activity at another place decreases with its dura- etition of tours is uncommon, thus an edge corresponds tion. The staying time distribution has no characteristic to exactly one trip. In the survey data, the observed mo- duration, suggesting that the location change follows an tifs without multiple trips are su⇥cient to reproduce over underlying ’bursty’ behavior - the location changes are 95% of the travel behavior correctly and we observe that not distributed evenly over time, but in groups inter- tours T (x)withx>1 are performed only once during a spersed with periods of inactivity. To support this obser- day (for details see SI). vation, we study the time between two similar activities, These observations imply that each person has a char- shown in Fig. 5B. While the time based on home and acteristic daily motif although the visited locations can work are governed by the daily routines, the time between change. Thus a user has a personal number of preferred other locations shows in fact that in the trip selection re- places on a daily basis, which are more likely visited in a lated to flexible activities ’bursts’ exist. This temporal specific sequence given by its motif. inter-event dynamics has been reported in specific human activities such as web browsing, printing patterns, email, and phone communication [31, 39–42], but it has not been II. PERTURBATION-BASED MODEL incorporated in models of human mobility. Inspired by these observations, we developed a perturbation-based model, to reproduce not only the observed daily motifs, It is surprising that nearly the entire population can be but also their frequency of occurrence. described with a few unique daily motifs. To understand In the following the model for a non-working (NW) agent this observation, we study the time spent at certain lo- is explained and the additional, minor features for work- cations as well as the time between the starting time of ing (W) agents are described in the SI. Accounting for an activity and the next activity of the same kind. the difference of the home and other locations, the model From both surveys the frequency of staying at a place for assumes a fixed activity at home and any number of flex- a particular time period is extracted for three groups of ible activities elsewhere (shopping, recreation, etc.). The activities, home, work, and other, as shown in Fig. 5A. Animal trade network Animation by T Selhorst H Lentz et al., Trade communities and their spatial patterns in the German pork production network, Preventive veterinary medicine, 98, 176 (2011) Swine trade network 4000 nodes with edges occurring more than 50 times ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms10331 Metabolism, Pancreatic kidney Liver Liver Myocardial Arteriosclerosis Vascular Arterial Heart inborn diseases diseases cirrhosis cirrhosis, ischemia diseases occlusive diseases errors biliary diseases Hydrochlorothiazide Allopurinol Torasemide Enoxaparin Bivalirudin Niacin Papaverine Bentiromide Losartan Colchicine Epoprostenol Pentoxifylline Tolvaptan Tirofiban Eptifibatide Streptokinase Biotin Enalapril Furosemide Ethacrynic Irbesartan Spironolactone acid Perindopril Isosorbide Dofetilide mononitrate Flecainide Mexiletine Sulfinpyrazone Lidocaine Vitamin A Coronary Verapamil Cardiomyopathy, Malabsorption Liraglutide Varicose Procainamide disease dilated syndromes veins Sodium Isosorbide Amiodarone Disopyramide Glimepiride Dinitrate Chlorpropamide Tolbutamide tetradecyl Moricizine sulfate Sotalol Insulin aspart Diabetes Amrinone mellitus, Sitagliptin Fenofibrate Propafenone Arrhythmias, Propranolol Diabetes Miglitol Insulin lispro type 2 Atorvastatin Lovastatin Quinidine cardiac mellitus, Ibutilide Acebutolol type 1 Nateglinide Tolazamide Digoxin Diabetes Coronary DronedaroneDiltiazem Gliclazide Pioglitazone Cardiovascular mellitus artery Isoproterenol Gastroenteritis Hyperinsulinism Glyburide Rosiglitazone Simvastatin diseases disease Diazoxide Loperamide Metformin Acarbose Pravastatin Lung Probucol Orlistat Mycobacterium Bone diseases infections diseases Zoledronate Joint Bacterial Insulin Rifabutin Colorectal diseases Budesonide infections resistance Inflammatory neoplasms CalcitriolPamidronate bowel Tetracycline Ciprofloxacin Cilastatin Levofloxacin diseases Intestinal Ketoprofen Floxuridine Cholecalciferol neoplasms Keratosis Naproxen Leflunomide Indomethacin Ibuprofen Salicyclic acid Neuroendocrine Erlotinib Bone Chloroquine Thyroid Diclofenac tumors Octreotide diseases, Auranofin Colitis Mycophenolic metabolic diseases Etodolac Tazarotene Mesalazine Sunitinib Calcidiol Liothyronine Triamcinolone Gastrointestinal Psoriasis Acitretin neoplasms Sulfasalazine Pilocarpine Adenocarcinoma Sulindac Celecoxib Hydroxyurea Endocrine Head and neck system Arthritis, Hypopigmentation Arthritis rheumatoid neoplasms diseases Crohn's Leukaemia,Teniposide Cyclosporine Monobenzone disease lymphoid Arsenic Hydrocortisone Hydroxychloroquine Leukaemia, Progesterone trioxide Colitis, Daunorubicin myeloid, Gefitinib ulcerative Leukaemia acute Imatinib Theophylline Dexamethasone Nicotine Cromoglicic Tiotropium acid Olsalazine Lupus Sarcoma Oxtriphylline Mercaptopurine Dacarbazine Aminophylline Salbutamol erythematosus, Alitretinoin Skin Balsalazide systemic Cytarabine Arformoterol Methotrexate Docetaxel diseases Vincristine Nedocromil Asthma Calcipotriol Haematological Doxorubicin Zafirlukast Azathioprine diseases Isoetharine Lymphoma Atropine Pimecrolimus Bleomycin Ephedrine Prednisolone Fluticasone Dyphylline Neoplasms propionate Montelukast Fluocinonide Ketotifen Prednisone Zileuton Cladribine Epirubicin Pseudoephedrine Vinblastine Eye Capecitabine diseases Collagen Rheumatic Macular diseases diseases Kidney Breast degeneration Hypersensitivity neoplasms neoplasms Letrozole Chlorpheniramine Mitoxantrone Lomustine Autoimmune Tamoxifen Megestrol Multiple Fludarabine Pegaptanib Diphenhydramine diseases sclerosis Carmustine Medroxyprogesterone Promethazine Plerixafor Fluoxymesterone Vinorelbine Baclofen Estradiol HistamineCyproheptadine Methylprednisolone Spinal Bicalutamide Conjugated Dexrazoxane Tizanidine estrogens Phosphate Fingolimod cord Flutamide Methyltestosterone Parkinsonian Dantrolene Aminoglutethimide diseases Chlorotrianisene disorders Trihexyphenidyl Quetiapine Diethylstilbestrol Citalopram Motor Ropinirole Risperidone Amyotrophic Prostatic neuron Leuprolide neoplasms Blood disease lateral Goserelin coagulation Levodopa Biperiden sclerosis Estramustine Aneamia, Finasteride disorders Amantadine Dementia hemolytic Phytonadione Zhong at al. 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