LEAVING CERTIFICATE BIOLOGY HIGHER LEVEL EXAM PAPER SOLUTIONS

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LEAVING CERTIFICATE BIOLOGY HIGHER LEVEL EXAM PAPER SOLUTIONS Sample Paper 3 Section A Question 1 a) A-Lag Phase, B-Log Phase, C- Stationary Phase, D- Decline Phase, E- Survival Phase. 5(2) b) Rapid Growth due to an abundance of resources such as oxygen, food, moisture or lack of competion. (2) c) In the stationary phase there is no increase in numbers, as the number of deaths = number of new bacteria produced.

• constant temperature during an experiment
• lower surface
• specific defence role of white blood cells
• rate of heart beat
• general body movement
• white blood cells
• large amounts
• body
• protein

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• Général
• Protein
• DeFence
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• Température

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• Publié par: phawyir
• Nombre de lectures: 17
• Langue: English

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M A T H E M A T I C S I N B I O L O G Y V I E W P O I N T Introductory Science and Mathematics Education for 21st-Century Biologists 1,3 2,3 William Bialekand David Botstein*

Galileo wrote that “the book of nature is written in the language of mathematics”; his quantitative approach to understanding the natural world arguably marks the beginning of modern science. Nearly 400 years later,the fragmented teaching of science in our universities still leaves biology outside the quantitative and mathe- matical culture that has come to define the physical sciences and engineering. This strikes us as particularly inopportune at a time when opportunities for quantitative thinking about biological systems are exploding. We propose that a way out of this dilemma is a unified introductory science curriculum that fully incorporates math- ematics and quantitative thinking.

Dramatic advances in biological understand ing, coupled with equally dramatic advances in experimental techniques and computation al analyses, are transforming the science of biology. The emergence of new frontiers of research in functional genomics, molecular evolution, intracellular and dynamic imaging, systems neuroscience, complex diseases, and the systemlevel integration of signal transduction and regulatory mechanisms re quire an everlarger fraction of biologists to confront deeply quantitative issues that con nect to ideas from the more mathematical sciences. At the same time, increasing num bers of physical scientists and engineers are recognizing that exciting frontiers of their own disciplines lie in the study of biological phenomena. Characteristic of this new intellec tual landscape is the need for strong interaction across traditional disciplinary boundaries. Biology curricula at our colleges and universities have not kept pace with these developments (1). Even though most biology students take several years of prerequisite courses in mathematics and the physical sci ences, these students have too little education and experience in quantitative thinking and computation to prepare them to participate in the new world of quantitative biology. At the same time, advanced physical science stu dents who become interested in biological phenomena can find it surprisingly difficult to master the complex and apparently uncon nected information that is the working knowl edge of every biologist. These barriers to communication between disciplines become significant early, such that advanced under graduates in the different disciplines already

1 2 Department of Physics,Department of Molecular 3 Biology, Lewis-SiglerInstitute for Integrative Genomics, Princeton University, Princeton, NJ 08544, USA. *To whom correspondence should be addressed. E- mail: [e-mail]

speak noticeably different languages. Effec tive solutions to this problem will require collaboration between university faculty in biology and traditionally mathematical sci ences. We believe that the needs of biology should provide a stimulus to reexamine the teaching of all science.

Quantitative Courses as Prerequisites During the last century, the educational path leading to professional degrees in the biolog ical and biomedical sciences (i.e., Ph.D., Sc.D., or M.D.) in the United States became rather standard. Undergraduates interested in biology and medicine begin their studies with a set of “prerequisite” courses, typically one or two semesters each of mathematics and physics and two to four semesters of chem istry. For most biologists and physicians, this early college experience, most of it preceding serious enagagement with biology itself, is the end of their education in mathematics and the physical sciences. For reasons of history, this prerequisite mathematics, physics, and chemistry educa tion is delivered by departments as a service to students who take them because it is re quired for a degree in biology or for entry into medical school. Many of the students taking these courses have no real enthusiasm for mathematics, physics, or chemistry per se and perceive these courses simply as obsta cles to be overcome on the way to a career in biology or medicine. Not surprisingly, the faculty who teach these service courses are ill prepared to make connections between what is presented in the prerequisites and what is exciting in the biological sciences. Almost without exception, larger universities teach students hoping to major in mathematics, physics, chemistry, or engineering separately from those hoping to be biologists or physi cians. The difference in sophistication (and difficulty) of the quantitative content of these separate tracks can be startling.

These traditions have resulted in a deep bifurcation in culture and quantitative com petence among the scientific disciplines. On one branch are mathematics, the physical sci ences, and engineering. Scientists educated along this branch achieve a high level of quantitative expertise: They generally have some mastery over and comfort with not only multivariate calculus and differential equa tions, but also linear algebra, Fourier analy sis, probability, and statistics. All scientists in these areas are expected to be able to program as well as to use computers themselves. Projects of any size, whether theoretical or experimental, require custom software, for example, to acquire and analyze data and to carry out simulations. Beyond textbook knowledge of mathematical and computational methods, quantitative thinking is the daily es sence of the science to which this educational path leads, and this is expressed in a rich inter play of theory, experiment, and computation. On the other branch are biology and med icine. With significant exceptions (e.g., pop ulation genetics, structural biology, and some areas of neuroscience), biologists today rare ly achieve mathematical competence beyond elementary calculus and maybe a few statis tical formulae. Although everybody uses a computer, biologists rarely use anything but standard commercial software. Virtually all biologists today must use some sophisticated programs (e.g., sequence comparison at the National Center for Biotechnology Informa tion’s Web site), yet distressingly few aca demic biologists feel comfortable teaching the underlying principles to their students, and fewer are able to program even a rudi mentary software implementation of such an algorithm themselves. Most biologists re quire consultations with biostatisticians in or der to do anything but the simplest statistics, and all too often mathematical or statistical analysis in published biological papers is in adequate or omitted entirely. The cultures of students following the two paths, not surprisingly, are also different. Whereas the students (and their teachers) on the physical science branch are focused on principles and reasoning as the goal of their education, students (and teachers) on the biologymedicine branch find themselves focused more on mastering huge arrays of facts. Although this characterization is partly a stereotype and good teaching can help

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M A T H E M A T I C S I N B I O L O G Y bridge these cultures, undergraduates areidea that mathematics describes the naturalwhen done well, should allow students to strongly influenced by these ideas. world is something that is taught in the physcontinue their education in any area of sci ics department. Understanding how to reasonence. Scientists educated in this way, regard Toward a New Level of Understanding in the language of mathematical symbols isless of their ultimate professional specialty, The reader may well ask whether the bifurcationessential, but one must go further to appreciwould share a common scientific language, of scientific cultures is really a problem, especially ate that these symbols actually stand for thefacilitating both crossdisciplinary under in view of the muchheralded success of the biovariables of the natural world, that these varistanding and collaboration. logical sciences over the last half century, of ables can be measured quantitatively in theThere are many challenges in designing which the sequencing of the human and otherfield or in the laboratory, and hence thatsuch a program. Clearly it cannot and should genomes is emblematic. After all, this success was abstract mathematical relations among symnot be the sum of everything in introductory achieved by scientists in different disciplines bols can become concrete relations among courses in mathematics, physics, chemistry, working together, each mostly educated along onethe results of experiments. There is an enorcomputer science, and biology, including the or the other of the educational branches described mous challenge in raising a generation of history of each idea. It must be reasonable in above. Why not continue as before?scientists who are equally at home with thislength yet provide a serious and useful intro Our answer is that the basic nature and quantitative mode of thought and with the duction to all of these disciplines in context goals of biological research are changing funcomplexities of real organisms.with each other. The primary challenge in damentally. In the past, biological processes Progress requires unflinching honesty designing an integrated curriculum, therefore, and the underlying genes, proteins, otherabout the depth of the problem. Forty yearsis to identify each of the individual intellec molecules, and environmental factors were of ago, Snow wrote eloquently of the difficulties tual concepts, methods, and facts that are necessity studied one by one in relative isoraised by the emergence of two cultures, onefundamental and generalizable, independent lation. In contrast, today we are already no scientific and one humanistic. Today we have of their history. Whereas advanced courses in longer satisfied with studies or answers thattwo cultures within science itself, one maththe individual disciplines can reinforce mate do not place each of these in a larger context. ematical and the other not. If biology is to rial treated briefly in an introductory course, We now know that there are tens of thouassimilate into the world of quantitative scithe firstyear science curriculum offers a spe sands of genes encoded in the genomes and ence, biologists and nonbiologists alike willcial opportunity to convey the intellectual that simple perturbations, such as a change inneed a different kind of education than wepoint of view and the quantitative attitude nutrition or a heat shock, alter the expression provide today (2). towardthe natural world that is embodied by of thousands of them. Similarly, in the pastGalileo’s dictum. An Integrated Introductory regulatory systems were of necessity studied Any attempt to create a multidisci Quantitative Science Curriculum in a limited way, resulting in largely intuitive,plinary curriculum leads to difficult ques onebit explanations (e.g., genes are turnedWhat is to be done? The answers may not tions about what will be left out. Seldom on or off, proteins are inhibited or not); todaybe the same for all students. We proposeemphasized, however, are the opportunities we cannot and should not be satisfied withhere an approach aimed specifically at stu for synergy. Teaching mathematical meth explanation of phenomena that are not fullydents interested in a research career in theods in the context of the natural science quantitative. We know from experience thatbiological sciences, whether in academia, problems that motivate their development boxes and arrows or even more formal wiringindustry, or medicine. For them, we advois an obvious example and already happens diagrams are not sufficient to specify thecate an integrated introductory curriculum in most physics curricula; for example, in function of a network. These architecturalin which mathematics, the physical sciencan integrated curriculum, calculus would be descriptions must be completed by models ofes, and biology are introduced together. taught together with basic physics. Making the underlying dynamics. New goals are inInstead of separate prerequisite courses inthe most of these opportunities cannot help sight, namely robust mathematical modelsmathematics, physics, chemistry, and com but facilitate both the teaching and learning and computer simulations that faithfully preputation, the fundamental ideas of each ofof all the relevant disciplines. Thermody dict behavior of entire biological systems.these disciplines should be introduced at a namics, kinetic theory, and the rudiments One might even hold out hope for the discovhigh level of sophistication in context withof statistical physics appear in different ery of theoretical principles that transcend relevant biological problems. Indeed, we guises in introductory physics and chemis detailed models and unify our understandingthink that the choices made in such a curtry courses, and even introductory biology of seemingly different systems. Many of riculum should be motivated in no small courses make reference to binding con these ideas were articulated 20 years ago inpart by connections with biology. The emstants and chemical potential. Most intro the context of neuroscience; with the emer phasis on integration is particularly impor ductory physics courses include some gence of much wider possibilities for systemtant at the introductory (i.e., first year orapproach to“modern physics,”and intro level analysis, they have migrated into many two of college) level, because a large part ductory chemistry courses provide at least diverse areas of biology.of the goal is to show the students how eachthe outlines of quantum theory to describe In order to participate fully in the research discipline contributes to understanding the electrons, orbitals, and chemical bonding. of the future, it will be essential for scientistsphenomena of life, how these phenomenaIn these cases, unification of the curricula to be conversant not only with the language illustrate and reinforce our quantitative un would convey a clearer picture both of the of biology but also with the languages ofderstanding of phenomena in the inanimateunderlying principles and the diversity of mathematics, computation, and the physical world, and how the boundaries between their applications. sciences. It is important to recognize that thedisciplines are becoming arbitrary and ir More subtly, but perhaps most crucially, problem cannot be solved by specifying min relevant. Integration will allow students to there are commonalities of the mathematical imal mathematical expertise for future biololearn the languages of the different disci structures that summarize our understanding gists and assigning our colleagues in theplines in context.of seemingly disparate topics. Classical me mathematics department the task of inculcatThe goal should be students with a mas chanics presents a model of the world’s dy ing this expertise in our students. Althoughtery of a broad set of skills and the confidencenamics based (in the introductory account) on physics students, for example, often taketo approach biological phenomena quantita simple differential equations, but chemical many mathematics courses, the fundamentaltively. Such an integrated science curriculum,kinetics and even the dynamics of popula www.sciencemag.org SCIENCE VOL303 6FEBRUARY 2004 789

M A T H E M A T I C S I N B I O L O G Y tions provide models of the same general introductory course practical access to con form. Although the different systems haveceptual tools that are much more sophisti important special features (e.g., the conservacated than those currently taught in the tion laws), surely we would like to commu standard firstyear mathematics courses. nicate the more general idea that dynamics Although real mastery over these ideas will are described by differential equations andrequire continuing reinforcement through encourage students to discover the applicabilout the undergraduate curriculum (as is cur ity of this approach to the dynamics of more rently done for physical science students), a complex biological systems through well unified introduction can empower the stu designed laboratory exercises. In a similardents to explore ideas far beyond what is spirit, statistical physics and kinetic theorycurrently accessible to them. provide probabilistic models of the world, but A final and, in the context of biology, Mendelian genetics is also a probabilisticpossibly the most important synergy derives model and an understanding of probability isfrom the judicious use of nonstandard exam at the heart of all practical data analysis. ples for basic principles and methods of phys Today, not only can we integrate subjects ics and chemistry. For example, it makes that share common mathematical structures,sense, in modern times, to introduce students we can also integrate these abstract structuresto the idea of molecular motion and thermo with their practical implementation through dynamics in solution rather than focusing computation. If the students are taught to only on the world of ideal gases. With afford program and to use simple algorithms and ifable modern instrumentation, students can they learn to use highlevel languages (e.g.,observe and record Brownian motion in a Matlab or Mathematica), they can visualize microscope, for example, and satisfy them and verify for themselves the mathematicalselves quantitatively how this motion derives ideas and thereby become comfortable withfrom invisible molecules bouncing around in those they find less intuitive or more abstract. the solution and even how many such mole In statistics, for example, it is possible to cules there must be. This handson approach begin by applying simulation and bootstraphas the advantage that the phenomena (and of algorithms (e.g., for findingPcourse the underlying principles) are directlyvalues). By starting in this way, students will more easily and obviously relevant to research in biology. come to appreciate parametric methods and In a similar vein, much of basic combinato closedform solutions and learn to understandrics, probability theory, and statistics can be and to use them appropriately.presented in tandem with basic genetics, re We believe that integrating mathemat sulting a substantial saving in overall time ics, computation, and the scientific contextwhen compared with separate courses in dif for these ideas will allow students in anferent departments. Again, the concurrent use

of computation will provide students with tools that will serve them well in all of their scientific careers thereafter. Our proposal for an integrated introduc tory education for quantitatively oriented bi ologists really is an experiment in a more general problem: science education in the modern world. This is a problem whose so lution will require collaborations among scientists who now reside in quite different departments and cultures; enthusiastic as we are, we also are cognizant of the difficulties that will no doubt arise. On the other hand, the necessary collaborations among the fac ulty from several disciplines may well set a wonderful example for students. To conclude, we believe there is a great opportunity to construct a unified, mathemat ically sophisticated introduction to physics and chemistry, which draws on examples from biology wherever possible. Such a course would provide a coherent introduction to quantitative thinking about the natural world, and invite all students, including biol ogists of the future, to partake of the grand tradition, which flows from Galileo’s vision.

References and Notes 1. Committee on Undergraduate Biology Education to Prepare Research Scientists for the 21st Century, Board on Life Sciences, Division of Earth and Life Sciences, National Research Council,BIO 2010: Transforming Undergraduate Education for Future Re- search Biologists(National Academies Press, Wash- ington, DC, 2003). 2. C.P. Snow,The Two Cultures and the Scientific Rev- olution(Cambridge Univ. Press, New York, 1959).

V I E W P O I N T Uses and Abuses of Mathematics in Biology Robert M. May

In the physical sciences,mathematical theory and experimental investigationthe particulate nature of inheritance were have always marched together. Mathematics has been less intrusive in the lifecontemporary with Darwin, and his pub sciences,possibly because they have until recently been largely descriptive,lished work accessible to Darwin. Fisher lacking the invariance principles and fundamental natural constants of physics.and others have suggested that Fleeming Increasingly in recent decades,however,mathematics has become pervasive inJenkin’s fundamental and intractable ob biology,taking many different forms: statistics in experimental design; patternjections toThe Origin of Speciescould seeking in bioinformatics; models in evolution,ecology,and epidemiology; andhave been resolved by Darwin or one of his much else. I offer an opinionated overview of such uses—and abuses.colleagues, if only they had grasped the mathematical significance of Mendel’s Darwin once wrote“have solved one of DarwinI have deeply regretted’results (s major prob1). But half a century elapsed that I did not proceed far enough at least tolems. In his day, it was thought that inbefore Hardy and Weinberg (HW) re understand something of the great leadingheritance“blended”maternal and paternalsolved the difficulties by proving that par principles of mathematics; for men thuscharacteristics. However, as pointed out toticulate inheritance preserved variation endowed seem to have an extra sense.”Darwin by the engineer Fleeming Jenkinwithin populations (2). With the benefit of hindsight, we can seeand others, with blending inheritance it isToday, the HW Law stands as a kind of how much an“extra sense”Newtonvirtually impossible to preserve the naturalcould indeed’s First Law (bodies remain in their variation within populations that is bothstate of rest or uniform motion in a straight observed and essential to his theory of howline, except insofar as acted upon by external Zoology Department, Oxford University, Oxford OX1 3PS, UK. evolution works. Mendel’forces) for evolution: Gene frequencies in as observations on 790 VOL 3036 FEBRUARY 2004SCIENCE www.sciencemag.org