Nicolas rashevsky download pdf mathematical biology

Surface Equilibria of Biological and Organic Colloids. New York. Lenoir, Timothy Lewontin, Richard C. Lillie, Ralph S. Protoplasmic Action and Nervous Action. Cowdry ed , General Cytology. Chicago: University of Chicago Press, pp.

Lotka, Alfred J. Elements of Physical Biology. Baltimore, MD: Williams and Wilkins. Lucas, Keith Maienschein, Jane Marshall, Louise H. McCulloch, Warren S. McNeill, William H. Morgan, Thomas H. Morowitz, Harold J. Waterman and Harold J. Morowitz eds. NY: Blaisdell, pp. Nernst, Walther Neurath, Otto. Pauly, Philip J. Pearson, Karl Pestre, Dominique Physique et physiciens en France Planck, Max Porter, Theodore M.

The Rise of Statistical Thinking Provine, William B. The Origins of Theoretical Population Genetics. Rapoport, Anatol Certainties and Doubts: A Philosophy of Life. Rashevsky, Nicolas a. Rashevsky, Nicolas b. Rashevsky, Nicolas Rashevsky, Nicolas c. Rashevsky, Nicolasa. Rashevsky, Nicolasb. Rashevsky, Nicolas Mathematical Biophysics: Physicomathematical Foundations of Biology.

Advances and Applications of Mathematical Biology. Mathematical Biophysics Revised Edition. Rashevsky, Nicolas ed. Physicomathematical Aspects of Biology. New York and London: Academic Press.

Rashevsky, Nicolas and Rashevsky, Emile Rashevsky, Nicolas and Landahl, Herbert D. Reiner, John M. Philosophy of Science 8 1 : — Richards, Oscar W.

Rosen, Robert n. Snell eds. New York and London: Academic Press, pp. New York: Columbia University Press. Ruse, Michael The Philosophy of Biology. London: Hutchinson University Library. Schrecker, Ellen W. New York: Oxford University Press. Schweber, Silvan S. Simon, Herbert A. As a result, we tell our pre- research and the challenges of academic life tenure people to be careful about what they work on in their research. What attracted you to these fields?

Are undergraduate students at Bates College in- I started undergrad as a biology major, with volved in aspects of your research? Many students write a senior thesis, and some major. Not till graduate school did I first learn math- seek opportunities for summer research. At times, interests. I find it fasci- ples for my collaborator in environmental studies. These collabo- or animal. After earning tenure, I sought new re- rations have pushed forward our research in exciting search directions and geographically-close collabo- ways.

Ecology emerged for many reasons: my in- terests, the wealth of projects in and near Maine, a What are some of the advantages of being in a Bates focus on the environment, and the fact that liberal arts institution? I could approach ecological modeling using differ- Just as mathematical biology spans a whole spec- ential equations methods that were familiar from trum between math and biology, liberal arts institu- epidemiological work.

Being in the middle of offer little guidance for their faculty as to what the spectrum gives us wiggle room in exactly how to kinds of work are valued toward promotion to full intertwine our two main responsibilities of research professor.

Also, our small size means faculty for pre-tenure faculty falls away. The AAUP talked members all get to interact. Meanwhile, fewer women get pro- other things. The moral of that story is: keep trying! Collabo- overcome, but being aware of their existence and rators can be helpful on this, but projects often fall scale is one starting point.

And the interwoven na- between our disciplines in such a way that none of ture of the multiple factors involved suggests an us know, initially, where to submit. What advice would you give to a young and as- Have you ever found the complexity of biological piring mathematical biologist? For a mathematical biologist starting out at a liberal Yes, pretty much all the time. However, I have had arts college, I would emphasize the value of profes- a crucial experience over and over again: asking sional community.

The so seek out local, national, even international com- more I ask these questions—and the more they lead munities. SMB, for example, offers opportunities to to fruitful discussions—the more likely I am to ask volunteer, and has an active education committee more questions! Furthermore, my collaborators ask that is helpful to those of us whose jobs emphasize their own questions, and we all end up learning in undergraduate education. Both math and biological systems are daunting, and we work through it together.

If you have any spare time, what do you do when you are not working? What are the challenges facing women in Most of my non-work time these days is with my academia and how could they be overcome? I These topics are relevant to me both for my own also enjoy my herbs-and-vegetables garden and out- choices and for mentoring others, as I am the se- door activities in Maine.

Snowshoeing season has nior woman in my department. I have read about recently arrived, and that is always a favorite! There is less explicit bias About Meredith L. Greer than in the past, but there remains implicit bias Dr.

Meredith Greer is Associate Professor of Mathe- in academic life, as can be seen in nationwide stud- matics at Bates College. For more info, please visit: ies. The interplay between the Mathematical Biology evolutionary and spatial dynamics result in interest- ing behavior such as accelerating waves and spatial Matthew Chan self-structuring in populations, both commonly ob- The University of Sydney served in invasive species.

Peter Kim terested in the effect on wavespeed and population structure when the population is affected by Allee effects. What specific areas are you interested inves- tigating? For the near future, I hope to continue with the theme of modeling population structure and the evolution of traits.

Peter Kim is also working on. I have also been interested in disease modeling, but have only done things which are on a tangent to this.

The problem of properly synthesizing the trea- sure trove of data out there in the form of Twitter, Wikipedia access logs, Google Flu Trends etc Hopefully in the future there will be a chance for me to try my hand at this area. What do you hope to do after graduation? I am still undecided on this. Both academia and in- dustry are appealing in their own way. It would be great if I could find something that lies in between! What advice will you give to an undergradu- What attracted you to mathematical biology?

Mary Myerscough. I fields. He then supposed that liquid B contained several substances C, D, E, F, that interacted in some way to form substance A, which was insoluble in liquid B. He reasoned that in this system, the interaction of C, D, E, and F to form A would cause the droplets of A already in existence to increase in size.

There is also evidence that Rashevsky had spent some time working with bacteriologist Ralph R. His theory was based on thermodynamic principles: the system needs a minimal free energy, and thus it moves from one state of relatively minimal energy to a lower one.

With further idealizing assumptions, Rashevsky then developed mathematical expressions for the rate of change of the mass M of the drop. Rashevsky examined several hypo- thetical cases, and his goal, essentially, was to devise equations that would allow one to calculate the critical size at which a growing cell would spontaneously divide.

Cell studies during this period were characterized by a diversity of methods and motivations, but experimental studies of the cell largely employed biochemical and physical methods. See also Rashevsky, a, b. General physiologists who focused on cell division expressed the problem in terms of surfaces, interfaces, tensions, osmosis, permeability, colloids, and dynamics.

The early work of physiologist Ralph S. Lillie was typical of this approach. He then performed experiments to test this hypothesis — exposing sea urchin eggs to chemical and physical stimuli such as hypotonic seawater, cyanide in seawater, salt solutions of various con- centrations, and extreme heat.

The change in cell form was seen to accompany a change in the surface tension of the cell membrane, which Lillie reasoned could result from an increase in the permeability of the cell membrane to electrolytes. His method was to form a hypothesis based on previous experimental results, and perform a large number of measurements to test the hypothesis. Lillie , For biographical information on Lillie, see Gerard, Following the presentation of data and calculations on the data, Lillie would draw conclusions about the nature of cell division and the role of chemical stimuli in the process.

To the extent that mathematics entered the picture in these studies, it was mostly to arrange experimental data in quantitative terms. Although he worked within the same conceptual frame- work as Lillie, often citing his work, his method was formal and deductive. Rashevsky was not merely applying mathematical formulae after the accumulation of data, he was using the mathematical method to idealize the cell and re-conceptualize the entities that played a role in its function.

See Keller , pp. Since the midth century, physiologists who studied the process of excitation in nerve focused on the quantitative relations they could observe when they applied an electric current to excitable tissue. Using these measurements, experimental neurophysiologists drew conclusions about the relations between quantitative aspects of nerve conduction.

In addition to this, theories were developed that proposed mecha- nisms underlying the observable electrical impulse that traveled along the nerve. A modern physiological laboratory is scarcely to be distinguished from a physical laboratory, having borrowed its instruments, at least, from the former [sic]. See also Marshall, , ; Kevles and Geison, Forbes and Thatcher, ; Gasser and Erlanger, The relation between the strength or intensity of the current necessary for excitation and its duration became the focus of several physical theories of nerve conduction, which attempted to propose a mechanism that would be consistent with the observable strength— duration relation.

Hoorweg, Keith Lucas, and Louis Lapicque found that when a current was passed through a nerve, the longer the pulse, the smaller the threshold intensity. See e. Hoorweg ; Lapicque and Lapicque, ; Lucas, Hill, ; Blair, a, b; Rashevsky, a. The introduction of the squid giant axon by John Z. They assumed that a critical concentration of ions is necessary for excitation, and arrived at expressions for the strength— duration relation upon stimulation by an electric current. The second group of theories, which included those of Jan L.

Hoorweg, Louis Lapicque, and Henry A. Blair, displayed what Rashevsky called the phenomenological method, that is, they established mathematical equations without attempts at their physical interpretation. He noted that both groups of theories assumed the existence of one type of exciting substance, which had to reach a critical level for excitation to occur. At the outset, however, Rashevsky said nothing about the nature of these substances.

Rashevsky set h at 1, and the concentrations 42 Rashevsky, , a, b, c, a, b. For more on this work in with context of the development of electromechanical machines, see Cordeschi , Chapter 3. Nernst, ; Hill, Hoorweg, ; Lapicque, ; Blair, b. These equations describe the rate of change over time of each ion as proportional to the current applied as a stimulus and the amount of increase i. Rashevsky was not entirely ignorant of empirical work on nerve conduction. In this same paper, he incorporated more of the current experimental work being done on nerve conduction, particularly that of Ralph W.

Gerard, and compared calculated values with those observed by Lapicque. Blair, b, While some investigators were concerned with strictly empirical, phenomenological studies of the nerve impulse and the strength—duration relation, many attempted to work out theories that proposed an underlying mechanism to explain these observations. Mathematics was also not completely foreign to many physiologists at the time.

As the University of Oregon zoologist Oscar W. It was known that the value of this constant could be determined experimentally.

Cole and Curtis, These methods, such as measurement, were exemplars of experimental physics, and it was this aspect of the physical sciences that was admired by physiologists. The main thing is to apply mathematics methodologically 54 Rashevsky, along with Landahl, was also invited to present work on cell perme- ability at the Cold Spring Harbor Symposium on Quantitative Biology Rashevsky and Landahl, Bronk, Afterwards the various complexities of the case have to be taken into account … as second, third, and higher approximations.

This use of abstract conceptions in the beginning is the characteristic of the physico- mathematical method. For Edward U. From these particulars, one must try to infer a general relation structure i.

Pure mathematics is the science of abstract relation structures… It follows that pure mathematics is the chief tool of the theoretical physicist.

Predictive power was something that Rashevsky rarely mentioned in his work. From the late 19th century, theoretical physics and experimental physics generally existed as two separate cultures, that is, theoretical physicists were rarely involved in experi- mental work.

See also Einstein [], p. ABRAHAM university departments, and many theoreticians were involved in ana- lyzing and interpreting experimental results. Thus, in a sense, Rashevsky was only partly accurate in his characterization of the method of the- oretical physics. At the time, there were several areas of biology where math- ematical methods were used in a systematic way: in the biometrics of Karl Pearson,65 in the population genetics of Ronald A.

Fisher, J. It was a technique used to assess present populations, to determine the rate of change in a species and thus provide an aid to prediction. Pearson, Fisher, ; Haldane, ; Wright, Although they made impor- tant contributions to the biological sciences, both Pearson and Fisher were trained in mathematical and physical sciences, and their work arguably formed the basis of modern mathematical statistics.

Viewing the natural world — both organic and inor- ganic — as a system, Lotka used the framework of physical chemistry to treat the kinetics, statics, and dynamics of living systems. Like Rashevsky, he had a dream of discipline building, and also looked at hypothetical situations. Volterra had a background in classical mechanics, and brought a mechanistic ap- proach to his work on predator—prey interactions. His predator—prey equations relied on the kinetic gas theory model.

Volterra based his model on a physical analogy between the collision of gas molecules in a closed container and the interaction of two species. Volterra likened encounters between individuals from two populations to these colli- sions. Thus, the probability of an encounter would be proportional to the product of the number of both species.

Volterra made several sim- plifying assumptions: that the prey is only destroyed by being eaten, and that the predator only eats one prey species. In a sense, Volterra had a similar attitude toward theory as Rashevsky. He would begin with initial hypotheses based on sometimes unrealistic assumptions, repre- sented mathematically. Following this, for Volterra, one would deter- mine how well the mathematical predictions accorded with reality, adjusting the starting hypothesis as needed.

Lotka, , pp. In this sense he was accurate, to the extent that mathematical physics resem- bled applied mathematics and had little contact with experimental work.

More accurately, Rashevsky on the whole was dealing with microscopic phenomena — whereas Lotka and Volterra were dealing with macro- 79 Kingsland, , p. Al- though it might appear that he was casting his own work as superior to theirs, he did see their work and his as constituting two branches of the same discipline: mathematical biology Rashevsky, , p.

As Robert Kohler and Lily Kay have documented, Weaver aimed to foster interdisciplinary ap- proaches in biology. Although Rashevsky continued to publish work in physics journals, by , he had published 12 papers in life sciences journals, thus exposing his work to the biological community.

As the Depression hit, he was forced to leave Westinghouse, but fortunately, had made some initial contacts that would bring him to the University of Chicago. Bitter that he had just spent 2 weeks in Chicago and had made the 83 Kohler, ; Kay, Rashevsky to Bitter, 1 March , Francis O. Rockefeller in to aid education in the U. Thurstone, who was then Chairman of the Depart- ment of Psychology, was instrumental in bringing Rashevsky to the school.

It has been reported that several other Chicago researchers, most likely those he had been in contact with the previous year, also facilitated his transfer: the physiologist Ralph S.

Compton, and the experimental psychologist Karl S. Simon Flexner, physician and Director of the Rockefeller Institute for Medical Research, had written to Weaver in September of , regarding a paper Rashevsky had recently published in the journal Philosophy of Science. Mathematical Foundations of Biology, vol. New York. Rashevsky, N. Mathematical Principles in Biology and Stressing the complexity of biological phenomena,.

Rashevsky argued that the methods of theoretical physics — namely mathematics — were McCormmach, , Vol. Biology BMB. This is an international journal Biophysics, Mathematical Biophysics: Physicomathematical Foundations of Biology. II, 3rd Ed.

Rashevsky, N Rosen, R a. Bulletin of Mathematical Biophysics — Rosen, R b. Engineering and Biology, Georgia June 23, vol. The Feynman Lectures on Physics, Vol.