DOCSLIB.ORG

Noise-Driven Growth Rate Gain in Clonal Cellular Populations

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Noise-Driven Growth Rate Gain in Clonal Cellular Populations Noise-driven growth rate gain in clonal cellular populations Mikihiro Hashimotoa, Takashi Nozoea, Hidenori Nakaokaa, Reiko Okuraa, Sayo Akiyoshia, Kunihiko Kanekoa,b, Edo Kussellc,d, and Yuichi Wakamotoa,b,1 aDepartment of Basic Science, Graduate School of Arts and Sciences, University of Tokyo, Tokyo 153-8902, Japan; bResearch Center for Complex Systems Biology, University of Tokyo, Tokyo 153-8902, Japan; cDepartment of Biology, Center for Genomics and Systems Biology, New York University, New York, NY 10003; and dDepartment of Physics, New York University, New York, NY 10003 Edited by Daniel L. Hartl, Harvard University, Cambridge, MA, and approved February 5, 2016 (received for review October 19, 2015) Cellular populations in both nature and the laboratory are com- equal the mean generation time when no variability of genera- posed of phenotypically heterogeneous individuals that compete tion time exists at the single-cell level. Population growth rate with each other resulting in complex population dynamics. Predicting is determined not only by an average of single cells but also by population growth characteristics based on knowledge of heteroge- the details of heterogeneity within a population. Therefore, un- neous single-cell dynamics remains challenging. By observing groups derstanding how population growth rates and other properties of cells for hundreds of generations at single-cell resolution, we arise from single-cell heterogeneity poses a fundamental chal- reveal that growth noise causes clonal populations of Escherichia coli lenge to single-cell biology. to double faster than the mean doubling time of their constituent A classical study of theoretical and experimental microbiology single cells across a broad set of balanced-growth conditions. We attempted to reveal the discrepancies between mean cellular show that the population-level growth rate gain as well as age struc- generation times and population doubling times in real bacterial turesofpopulationsandofcelllineages in competition are predict- populations (13). Experimental methods and techniques avail- able. Furthermore, we theoretically reveal that the growth rate gain able at that time, however, hampered reliable tests. Recently, the can be linked with the relative entropy of lineage generation time techniques of single-cell time-lapse microscopy have advanced to distributions. Unexpectedly, we find an empirical linear relation a great extent, revealing the heterogeneous and stochastic nature between the means and the variances of generation times across of single-cell dynamics quantitatively (14). With the aid of conditions, which provides a general constraint on maximal growth microfluidic platforms, tracking single cells over many genera- rates. Together, these results demonstrate a fundamental benefit of tions in controlled constant or changing environments has also noise for population growth, and identify a growth law that sets a become feasible, providing insights into the mechanisms of cell “speed limit” for proliferation. size homeostasis and stress responses (3, 6, 7, 9, 15–22). In this study, through microfluidics time-lapse microscopy and growth noise | age-structured population model | cell lineage analysis | single-cell analysis on large-scale, single-cell lineage trees, we growth law | microfluidics reveal that clonal populations of Escherichia coli indeed grow BIOPHYSICS AND with a doubling time that is smaller than the mean doubling time COMPUTATIONAL BIOLOGY ell growth is an important physiological process that under- of their constituent cells under broad, balanced-growth condi- Clies the fitness of organisms. In exponentially growing cell tions. We show that the observed growth rate gains and pop- populations, proliferation is usually quantified using the bulk ulation age structures are predictable from cellular generation population growth rate, which is assumed to represent the av- time distributions based on a simple age-structured population erage growth rate of single cells within a population. In addition, model. Furthermore, we reveal unique features of long single- basic growth laws exist that relate ribosome function and meta- cell lineages within populations in competition, and provide a bolic efficiency, macromolecular composition, and cell size of the culture as a whole to the bulk population growth rate (1–3). Population growth rate is therefore a quantity of primary im- Significance portance that reports cellular physiological states and fitness. However, at the single-cell level, growth-related parameters Differences between individuals exist even in the absence of such as the division time interval and division cell size are het- genetic differences, e.g., in identical twins. Over the last de- erogeneous even in a clonal population growing at a constant cade, experiments have shown that even genetically identical rate (4–9). Such “growth noise” causes concurrently living cells microbes exhibit large cell-to-cell differences. In particular, the to compete within the population for representation among its timing of cell division events is highly variable between single future descendants. For example, if two sibling cells born from bacterial cells. The effect of this variability on long-term the same mother cell had different division intervals, the faster growth and survival of bacteria, however, remains elusive. dividing sibling is likely to have more descendants in the future Here, we present a striking finding showing that a bacterial population compared with its slower dividing sister, despite the population grows faster on average than its constituent cells. fact that progenies of both siblings may proliferate equally well To explain this counterintuitive result, we present a mathe- (Fig. 1). Intrapopulation competition complicates single-cell matical model that precisely predicts our measurements. Fur- thermore, we show an empirical growth law that constrains analysis because any growth-correlated quantities measured over the maximal growth rate of Escherichia coli. the population deviate from intrinsic single-cell properties (10– 12). In the case of the toy model described in Fig. 1, cells are Author contributions: M.H. and Y.W. designed research; M.H., T.N., H.N., R.O., K.K., E.K., assumed to determine their generation times (division interval) and Y.W. performed research; Y.W. contributed new reagents/analytic tools; M.H., R.O., randomly by roll of a dice. The mean of intrinsic cellular gen- S.A., and Y.W. analyzed data; and M.H., E.K., and Y.W. wrote the paper. eration time is thus ð1 + 2 + ⋯ + 6Þ=6 = 3.5 h, but population The authors declare no conflict of interest. doubling time, which is the time required for a population to This article is a PNAS Direct Submission. double the number of cells, is in fact 3.2 h. This counterintuitive 1To whom correspondence should be addressed. Email: [email protected]. result is a direct consequence of growth noise in a population. This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. Indeed, as we will see, the population doubling time can only 1073/pnas.1519412113/-/DCSupplemental. www.pnas.org/cgi/doi/10.1073/pnas.1519412113 PNAS | March 22, 2016 | vol. 113 | no. 12 | 3251–3256 Downloaded by guest on September 28, 2021 A Cellular generation time decorating the surface of a microfabricated glass coverslip with (interdivision time) biotin and membrane with streptavidin (23). The narrow and hr shallow growth channels can harbor 25 ∼ 40 cells at a time. A Mean generation time of cells small fraction of the cells within growth channels are constantly hr removed to the wide and deep flow channels, which maintains B the number of cells in the growth channels nearly constant. In Sibling cell 1 Descendants contrast to the “mother machine” (7), the width of the growth of sibling cell 1 channels is wider than a single-cell width, and both ends are open Expected ratio of descendant cells to flow channels. This configuration introduces competition among cells to remain within the growth channels, which is an important feature of this device for evaluating growth properties Descendants of both single cells and the population. Fresh medium is con- of sibling cell 2 stantly supplied to the cells both from the flows in the flow channels and above the membrane, allowing efficient environ- Sibling cell 2 mental control. Cellular growth rates in this device were indeed stable during the entire period of observation (SI Appendix, Fig. S2). Furthermore, the statistics of cellular growth were indis- Population doubling time tinguishable across different locations within the growth chan- C 4 nels (SI Appendix, Fig. S3), which confirms efficient control of 2 Population hr growth rate environmental conditions around the cells. Using this device, we 0 0 5 10 15 20 observed clonal proliferation processes of E. coli in constant Time, t environments by time-lapse microscopy, obtaining large-scale Fig. 1. Competition within a population caused by growth noise and its consequence to population growth rate. (A) Toy model of cell proliferation. Here, we consider a model of cell proliferation in which all of the cells in a A Cell D population determine their generation time (interdivision time) randomly Flow Flow by throwing a dice to learn the consequences of intrapopulation growth noise. In this setting, cells can take either of the six possible choices of generation time, τ = 1,2, ⋯, 6 h, with the equal probability of 1/6. The mean hτi = generation time is thus g 3.5 h. (B) Example of pedigree tree showing competition between sibling cells. In this tree, two sibling cells were born B Growth channel Flow channel from the common mother cell at t = 0 h, and divided with different gen- Cellulose membrane eration times (sibling cell 1: τs1 = 5 h; and sibling cell 2: τs2 = 2 h). The de- scendant cells from the both sibling cells follow the same rule of cell divisions irrespectively of the ancestral generation time. The difference of generation C time between the sibling cells 1 and 2 was caused just by chance, but the expected number of descendant cells becomes larger for the fast dividing sibling cell.
Load more

Recommended publications
  • Systems of Evidence in the Age of Complexity
    V12I2.PAUL.FINALLAYOUT1.0613.DOC (DO NOT DELETE) 6/19/14 12:56 PM Copyright © 2014 Ave Maria Law Review SYSTEMS OF EVIDENCE IN THE AGE OF COMPLEXITY George L. Paul † The global economy is transforming in unprecedented fashion. Persistent, exponentially advancing technologies1 now rival the invention of the printing press in their importance to society.2 Indeed, respected economists declare that what is happening is the biggest development in the history of economic activity.3 The result? Complex systems will soon define reality and a new civilization is emerging. And what is happening in the legal realm? Our system of evidence now fails to comprehend the emerging complexity that may soon overwhelm us. Accordingly, the rule of law is in jeopardy. † George L. Paul, a graduate of Yale Law School and Dartmouth College, is a trial lawyer of thirty-two years experience. He has written FOUNDATIONS OF DIGITAL EVIDENCE (2008), Information Inflation: Can the Legal System Adapt, and other books and articles about digital evidence issues. 1. See George L. Paul, Transformation, 9 ABA SCITECH LAWYER, Winter/Spring 2013, at 2, available at www.lrrlaw.com/files/uploads/documents/Transformation,%20by%20George%20Paul.pdf (quoting Daniel Burrus’ statements that exponential hard trends are transforming society in a way that is “bigger than the . printing press”). 2. It is widely acknowledged that the invention of the moveable type printing press by Johannes Gutenberg, circa 1450 C.E., was the technology that more than any other helped usher in modernity. Its acceleration of the transmission of information enabled such things as the Renaissance, the Protestant Reformation, and the Scientific Revolution.
    [Show full text]
  • Criticalreading #Wickedproblem
    #CRITICALREADING #WICKEDPROBLEM We have a “wicked problem” . and that is a fantastic, engaging, exciting place to start. Carolyn V. Williams1 I. INTRODUCTION I became interested in the idea of critical reading—“learning to evaluate, draw inferences, and arrive at conclusions based on evidence” in the text2—when I assumed that my students would show up to law school with this skill . and then, through little fault of their own, they did not. I have not been the only legal scholar noticing this fact. During the 1980s and 90s a few legal scholars conducted research and wrote about law students’ reading skills.3 During the 2000s, a few more scholars wrote about how professors can help develop critical reading skills in law students.4 But it has not been until the past few years or so that legal scholars have begun to shine a light on just how deep the problem of law students’ critical reading skills 1 Professor Williams is an Associate Professor of Legal Writing & Assistant Clinical Professor of Law at the University of Arizona, James E. Rogers College of Law. Thank you to Dean Marc Miller for supporting this Article with a summer research grant. Many thanks to the Legal Writing Institute for hosting the 2018 We Write Retreat and the 2018 Writers’ Workshop and to the participants at each for their comments and support of this project. A heartfelt thank you to Mary Beth Beazley, Kenneth Dean Chestek, and Melissa Henke for graciously providing comments on prior drafts of this Article. Thank you to my oldest Generation Z child for demonstrating independence and the desire to fix broken systems so that I know my solution is possible.
    [Show full text]
  • Formulating a Simple Model Structure
    Formulating a simple model structure 401.661 Advanced Construction Technology Moonseo Park Professor, PhD 39동 433 Phone 880-5848, Fax 871-5518 E-mail: [email protected] Department of Architecture College of Engineering Seoul National University 401.661 Advanced Construction Technology 1 Equilibrium § Stock in equilibrium when unchanging *System in equilibrium when all its stocks are unchanging. § Dynamic Equilibrium e.g., # of US senate inflow = outflow § Static Equilibrium *Same contents. e.g., # of Bach cantatas inflow = outflow = 0 401.661 Advanced Construction Technology 2 Integration & Differentiation 401.661 Advanced Construction Technology 3 Calculus without Mathematics Quantity added during interval of length dt . = R (units/time) * dt (time) *R = the net flow during the interval Concrete Mixer Example § Area of each rectangle= Ridt Net Rate (units/time) § Adding all six rectangles = R1 0 dt Approximation of total water added S2 S1 Stock (units) § How to increase accuracy? t1 t2 401.661 Advanced Construction Technology 4 Fundamental Modes § Positive feedback causes exponential growth, while negative feedback causes goal-seeking behavior. Goal State of the System State of the System Time Time + State of the Goal System (Desired + Net State of System) Increase R State of the - System B Rate Discrepancy + + Corrective Action + §Sterman, J., “Business Dynamics”, Mcgraw-Hill, 2000 401.661 Advanced Construction Technology 5 First-Order Systems § A first-order system contains only one stock. § Linear systems are systems, in which the rate equations are linear combinations of the state variables. dS/dt = Net Inflow = a1S1 + a2S2 … + anSn + b1U1 + b2U2 … + bmUm Where the coefficients ai, bj are constants and any exogenous variable are denoted Uj.
    [Show full text]
  • Generation Times of E. Coli Prolong with Increasing Tannin Concentration While the Lag Phase Extends Exponentially
    plants Article Generation Times of E. coli Prolong with Increasing Tannin Concentration while the Lag Phase Extends Exponentially Sara Štumpf 1 , Gregor Hostnik 1, Mateja Primožiˇc 1, Maja Leitgeb 1,2 and Urban Bren 1,3,* 1 Faculty of Chemistry and Chemical Engineering, University of Maribor, Maribor 2000, Slovenia; [email protected] (S.Š.); [email protected] (G.H.); [email protected] (M.P.); [email protected] (M.L.) 2 Faculty of Medicine, University of Maribor, Maribor 2000, Slovenia 3 Faculty of Mathematics, Natural Sciences and Information Technologies, University of Primorska, Koper 6000, Slovenia * Correspondence: [email protected]; Tel.: +386-2-2294-421 Received: 18 November 2020; Accepted: 29 November 2020; Published: 1 December 2020 Abstract: The current study examines the effect of tannins and tannin extracts on the lag phase duration, growth rate, and generation time of Escherichia coli.Effects of castalagin, vescalagin, gallic acid, Colistizer, tannic acid as well as chestnut, mimosa, and quebracho extracts were determined on E. coli’s growth phases using the broth microdilution method and obtained by turbidimetric measurements. E. coli responds to the stress caused by the investigated antimicrobial agents with reduced growth rates, longer generation times, and extended lag phases. Prolongation of the lag phase was relatively small at low tannin concentrations, while it became more pronounced at concentrations above half the MIC. Moreover, for the first time, it was observed that lag time extensions follow a strict exponential relationship with increasing tannin concentrations. This feature is very likely a direct consequence of the tannin complexation of certain essential ions from the growth medium, making them unavailable to E.
    [Show full text]
  • The Relationship Between Local Content, Internet Development and Access Prices
    THE RELATIONSHIP BETWEEN LOCAL CONTENT, INTERNET DEVELOPMENT AND ACCESS PRICES This research is the result of collaboration in 2011 between the Internet Society (ISOC), the Organisation for Economic Co-operation and Development (OECD) and the United Nations Educational, Scientific and Cultural Organization (UNESCO). The first findings of the research were presented at the sixth annual meeting of the Internet Governance Forum (IGF) that was held in Nairobi, Kenya on 27-30 September 2011. The views expressed in this presentation are those of the authors and do not necessarily reflect the opinions of ISOC, the OECD or UNESCO, or their respective membership. FOREWORD This report was prepared by a team from the OECD's Information Economy Unit of the Information, Communications and Consumer Policy Division within the Directorate for Science, Technology and Industry. The contributing authors were Chris Bruegge, Kayoko Ido, Taylor Reynolds, Cristina Serra- Vallejo, Piotr Stryszowski and Rudolf Van Der Berg. The case studies were drafted by Laura Recuero Virto of the OECD Development Centre with editing by Elizabeth Nash and Vanda Legrandgerard. The work benefitted from significant guidance and constructive comments from ISOC and UNESCO. The authors would particularly like to thank Dawit Bekele, Constance Bommelaer, Bill Graham and Michuki Mwangi from ISOC and Jānis Kārkliņš, Boyan Radoykov and Irmgarda Kasinskaite-Buddeberg from UNESCO for their work and guidance on the project. The report relies heavily on data for many of its conclusions and the authors would like to thank Alex Kozak, Betsy Masiello and Derek Slater from Google, Geoff Huston from APNIC, Telegeography (Primetrica, Inc) and Karine Perset from the OECD for data that was used in the report.
    [Show full text]
  • The Following Paper Posted Here Is Not the Official IEEE Published Version
    The following paper posted here is not the official IEEE published version. The final published version of this paper can be found in the Proceedings of the IEEE International Conference on Communication, Volume 3:pp.1490-1494 Copyright © 2004 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Investigation and modeling of traffic issues in immersive audio environments Jeremy McMahon, Michael Rumsewicz Paul Boustead, Farzad Safaei TRC Mathematical Modelling Telecommunications and Information Technology Research University of Adelaide Institute South Australia 5005, AUSTRALIA University of Wollongong jmcmahon, [email protected] New South Wales 2522, AUSTRALIA [email protected], [email protected] Abstract—A growing area of technical importance is that of packets being queued at routers. distributed virtual environments for work and play. For the This is an area that has not undergone significant research audio component of such environments to be useful, great in the literature. Most of the available literature regarding emphasis must be placed on the delivery of high quality audio synchronization in multimedia relates to synchronizing audio scenes in which participants may change their relative positions. with video playout (e.g. [5], [6], [7]) and / or requires a global In this paper we describe and analyze an algorithm focused on maintaining relative synchronization between multiple users of synchronization clock such as GPS (e.g.
    [Show full text]
  • The Limits to Growth: the 30-Year Update
    Donella Meadows Jorgen Randers Dennis Meadows Chelsea Green (United States & Canada) Earthscan (United Kingdom and Commonwealth) Diamond, Inc (Japan) Kossoth Publishing Company (Hungary) Limits to Growth: The 30-Year Update By Donella Meadows, Jorgen Randers & Dennis Meadows Available in both cloth and paperback editions at bookstores everywhere or from the publisher by visiting www.chelseagreen.com, or by calling Chelsea Green. Hardcover • $35.00 • ISBN 1–931498–19–9 Paperback • $22.50 • ISBN 1–931498–58–X Charts • graphs • bibliography • index • 6 x 9 • 368 pages Chelsea Green Publishing Company, White River Junction, VT Tel. 1/800–639–4099. Website www.chelseagreen.com Funding for this Synopsis provided by Jay Harris from his Changing Horizons Fund at the Rockefeller Family Fund. Additional copies of this Synopsis may be purchased by contacting Diana Wright at the Sustainability Institute, 3 Linden Road, Hartland, Vermont, 05048. Tel. 802/436–1277. Website http://sustainer.org/limits/ The Sustainability Institute has created a learning environment on growth, limits and overshoot. Visit their website, above, to follow the emerging evidence that we, as a global society, have overshot physcially sustainable limits. World3–03 CD-ROM (2004) available by calling 800/639–4099. This disk is intended for serious students of the book, Limits to Growth: The 30-Year Update (2004). It permits users to reproduce and examine the details of the 10 scenarios published in the book. The CD can be run on most Macintosh and PC operating systems. With it you will be able to: • Reproduce the three graphs for each of the scenarios as they appear in the book.
    [Show full text]
  • Chapter 04 Lecture
    Chapter 04 Lecture 1 A GLIMPSE OF HISTORY German physician Robert Koch (1843–1910) Studied disease-causing bacteria; Nobel Prize in 1905 Developed methods of cultivating bacteria Worked on methods of solid media to allow single bacteria to grow and form colonies Tried potatoes, but nutrients limiting for many bacteria • Solidifying liquid nutrient media with gelatin helped • Limitations: melting temperature, digestible • In 1882, Fannie Hess, wife of associate, suggested agar, then used to harden jelly INTRODUCTION Prokaryotes found growing in severe conditions Ocean depths, volcanic vents, polar regions all harbor thriving prokaryotic species Many scientists believe that if life exists on other planets, it may resemble these microbes Individual species have limited set of conditions Also require appropriate nutrients Important to grow microbes in culture Medical significance Nutritional, industrial uses 4.1. PRINCIPLES OF BACTERIAL GROWTH Prokaryotic cells divide by binary fission Cell gets longer and One cell divides into two, two DNA replicates. into four, 48, 816, etc… Exponential growth: population DNA is moved into each future daughter doubles each division cell and cross wall forms. Generation time is time it takes to double Varies among species Cell divides into two cells. Environmental conditions Exponential growth has important consequences Cells separate. 10 cells of food-borne pathogen in potato salad at picnic can become 40,000 cells in 4 hours Daughter cells 4.1. PRINCIPLES OF BACTERIAL GROWTH Growth can be calculated n Nt = N0 x 2 Nt = number of cells in population at time t N0 = original number of cells in population n = number of divisions Example: pathogen in potato salad at picnic in sun Assume 10 cells with 20 minute generation time N0 = 10 cells in original population n = 12 (3 divisions per hour for 4 hours) n 12 Nt = N0 x 2 = 10 x 2 Nt = 10 x 4,096 Nt = 40,960 cells of pathogen in 4 hours! 4.1.
    [Show full text]
  • Pannexin 1 Transgenic Mice: Human Diseases and Sleep-Wake Function Revision
    International Journal of Molecular Sciences Article Pannexin 1 Transgenic Mice: Human Diseases and Sleep-Wake Function Revision Nariman Battulin 1,* , Vladimir M. Kovalzon 2,3 , Alexey Korablev 1, Irina Serova 1, Oxana O. Kiryukhina 3,4, Marta G. Pechkova 4, Kirill A. Bogotskoy 4, Olga S. Tarasova 4 and Yuri Panchin 3,5 1 Laboratory of Developmental Genetics, Institute of Cytology and Genetics SB RAS, 630090 Novosibirsk, Russia; [email protected] (A.K.); [email protected] (I.S.) 2 Laboratory of Mammal Behavior and Behavioral Ecology, Severtsov Institute Ecology and Evolution, Russian Academy of Sciences, 119071 Moscow, Russia; [email protected] 3 Laboratory for the Study of Information Processes at the Cellular and Molecular Levels, Institute for Information Transmission Problems, Russian Academy of Sciences, 119333 Moscow, Russia; [email protected] (O.O.K.); [email protected] (Y.P.) 4 Department of Human and Animal Physiology, Faculty of Biology, M.V. Lomonosov Moscow State University, 119234 Moscow, Russia; [email protected] (M.G.P.); [email protected] (K.A.B.); [email protected] (O.S.T.) 5 Department of Mathematical Methods in Biology, Belozersky Institute, M.V. Lomonosov Moscow State University, 119234 Moscow, Russia * Correspondence: [email protected] Abstract: In humans and other vertebrates pannexin protein family was discovered by homology to invertebrate gap junction proteins. Several biological functions were attributed to three vertebrate pannexins members. Six clinically significant independent variants of the PANX1 gene lead to Citation: Battulin, N.; Kovalzon, human infertility and oocyte development defects, and the Arg217His variant was associated with V.M.; Korablev, A.; Serova, I.; pronounced symptoms of primary ovarian failure, severe intellectual disability, sensorineural hearing Kiryukhina, O.O.; Pechkova, M.G.; loss, and kyphosis.
    [Show full text]
  • A Theory for the Age and Generation Time Distribution of a Microbial Population
    Journal of Mathematical Biology 1, 17--36 (1974) by Springer-Verlag 1974 A Theory for the Age and Generation Time Distribution of a Microbial Population J. L. Lebowitz* and S. I. Rubinow, New York Received October 9, 1973 Summary A theory is presented for the time evolution of the joint age and generation time distribution of a microbial population. By means of the solution to the fundamental equation of the theory, the effect of correlations between the generation times of mother and daughter cells may be determined on the transient and steady state growth stages of the population. The relationships among various generation time distributions measured under different experimental circumstances is clarified. 1. Introduction A striking property of microbial populations, even when grown under constant environmental conditions, is the great variability of the generation times of individual members of the population, illustrated in Fig. 1. The cause of this variability remains an important unsolved biological problem. The variability is generally ascribed to intrinsic variable factors associated with cell growth and maturation, culminating in division [1]. Prescott [2] has suggested that the variability stems from variability in the initial state of a newborn cell, where initial state means cell weight, number of mitochondria, microsomes, etc. Variability in the initial state of the chromosome is likewise a fundamental feature of the Cooper-Helmstetter model for chromo- some replication in E. coli [3]. In both of these views, the generation time is determined at birth. * Also Physics Department, Belfer Graduate School of Sciences, Yeshiva University, New York, NY 10019, U.S.A. Journ.
    [Show full text]
  • Causemap: Fast Inference of Causality from Complex Time Series
    CauseMap: fast inference of causality from complex time series M. Cyrus Maher1 and Ryan D. Hernandez2,3,4 1 Department of Epidemiology and Biostatistics, University of California, San Francisco, CA, USA 2 Department of Bioengineering and Therapeutic Sciences, USA 3 Institute for Human Genetics, USA 4 Institute for Quantitative Biosciences (QB3), University of California, San Francisco, CA, USA ABSTRACT Background. Establishing health-related causal relationships is a central pursuit in biomedical research. Yet, the interdependent non-linearity of biological systems renders causal dynamics laborious and at times impractical to disentangle. This pursuit is further impeded by the dearth of time series that are suYciently long to observe and understand recurrent patterns of flux. However, as data generation costs plummet and technologies like wearable devices democratize data collection, we anticipate a coming surge in the availability of biomedically-relevant time series data. Given the life-saving potential of these burgeoning resources, it is critical to invest in the development of open source software tools that are capable of drawing meaningful insight from vast amounts of time series data. Results. Here we present CauseMap, the first open source implementation of convergent cross mapping (CCM), a method for establishing causality from long time series data (&25 observations). Compared to existing time series methods, CCM has the advantage of being model-free and robust to unmeasured confounding that could otherwise induce spurious associations. CCM builds on Takens’ Theorem, a well-established result from dynamical systems theory that requires only mild assumptions. This theorem allows us to reconstruct high dimensional system dy- namics using a time series of only a single variable.
    [Show full text]
  • Demystifying Millennial Students: Fact Or Fiction Leza Madsen Associate Professor Western Washington University, [email protected]
    Western Washington University Western CEDAR Western Libraries Faculty and Staff ubP lications Western Libraries and the Learning Commons 1-7-2007 Demystifying Millennial Students: Fact or Fiction Leza Madsen Associate Professor Western Washington University, [email protected] Hazel Cameron Follow this and additional works at: https://cedar.wwu.edu/library_facpubs Part of the Higher Education Administration Commons, and the Higher Education and Teaching Commons Recommended Citation Demystifying Millennial Students: Fact or Fiction (with Hazel Cameron), Hawaii International Conference on Education, Proceedings (2007) This Article is brought to you for free and open access by the Western Libraries and the Learning Commons at Western CEDAR. It has been accepted for inclusion in Western Libraries Faculty and Staff ubP lications by an authorized administrator of Western CEDAR. For more information, please contact [email protected]. Introduction In order to teach effectively, educators need to understand the generation of students they are trying to reach. This paper will examine the Millennial generation, those individuals born around 1980. We will review the era they grew up in, the population’s characteristics, learning styles, attitudes, values, lifestyles and the implications this knowledge has for educators. We believe that by understanding the Millennials we can design programs, courses and learning environments better suited to these students. We offer some examples of what has worked for us as librarians at Western Washington University and from our review of the literature. Millennials Defined Neil Howe and William Strauss in Millennials Rising (2000), define Millennials as people born from about 1982-2002. The exact starting date for the cohort varies slightly in other articles.
    [Show full text]