ÚSTAV FYZIKÁLNÍ BIOLOGIE JIHOČESKÁ UNIVERZITA V ČESKÝCH BUDĚJOVICÍCH PŘIHLÁŠKA STUDENTSKÉHO PROJEKTU Projekt Název projektu: Estimation of nonlinear dynamics of S. Pombe cells growth via Rényi Entropy Uchazeč Hlavní řešitel Příjmení, jméno, tituly: Náhlík Tomáš, Mgr. E-mail:
[email protected] Tel.: 737 931 802 Studium v doktorském studijním programu zahájeno dne: 30.9.2009 Pracoviště/místo studia Fakulta (VŠ ústav): Ústav fyzikální biologie JU Katedra (ústav, pracoviště): Školitel: Doc. RNDr. Dalibor Štys CSc Vedoucí projektu Příjmení, jméno, tituly: Štys Dalibor, Doc. RNDr. Csc. E-mail:
[email protected] Tel.: Pracoviště Fakulta (VŠ ústav): Ústav fyzikální biologie JU Katedra (ústav, pracoviště): Celkové náklady na řešení projektu Náklady nebo výdaje na pořízení hmotného a nehmotného majetku: Další provozní náklady nebo výdaje: Doplňkové náklady nebo výdaje: Celkem Kč: V ................................. dne .................. Podpis uchazeče:…………………………......
Zdůvodnění návrhu projektu Stav řešení problematiky projektu (max. 2 stránky): Theory of information transmission dates back to Nyquist (1928) and Hartley (1928) who analysed the information transmission by telegraph lines. The most celebrated article is that of Shannon (1948) which is also among the latest which discusses jointly the physical information transmission and the mathematical theory. Shannon introduced the information measure S and due to its analogy (in fact identity) with Boltzmann entropy of thermodynamics (Boltzmann 1866) called it information entropy. Rényi (1957) introduced a more general information measure but in his time the mathematical theory became too complex for the user to see its practical advantage. The classical Shannon scheme of information transmission consists of the Information source, Transmitter, Noise source, Receiver and Destination. The connection between Transmitter and Receiver is called communication channel. Shannon considers the information source to have a certain statistical structure described by probabilities p(i, j) that a given information, for example a letter, j is followed by information i . The information channel has transmission probability P i for information i and we consider that Pj = ∑ Pi p (i, j ) . 1
From this approach Shannon derived properties of the information measure for independent probabilities p i of events i and came to definition of information entropy. n
n
H=K ∑ p i log p i which we use in the form S= ∑ p i log 2 pi . i=1
i=1
The original derivation has been long time forgotten and over shaded by finding of Rényi who showed that the Shannon measure (3) is only a limit case of more general 1 q information measure I q = q− 1 log 2 p i at q 1 . Rényi entropy – or information has been mathematically proven to be the most general information measure (Jizba and Arimitsu 2004). But practical use of generalization made by Rényi was not recognized. The connection between information entropy and space dimensionality summarized by Theiler (1990), based on older derivations of Hentschel and Procaccia. (1983) and Grassberger (1983) Theiler suggests that this connection lies in the appropriate averaging of measure in the particular space. The distance between points in the 3D space is the spatial diagonal in a cube whose outer edges are Cartesian coordinates of points. In microphotography, is each point transformed by the optical path to a set of points. The transformation function is called point spread function. It is a complicated function imaging the point in the original object to a set of points at the camera chip plane. The point spread function is different for each wavelength and for each point in the observed region – focal volume. The dimension of the point spread function may be, to some extent, assessed from theoretical analysis given by Nijboer and Zernike (1949) whose contemporary form is presented by Braat et al. (2008). For the case of phase contrast microscopy demonstrated in this article the construction of point spread function is far more complicated (i.e. Masato et al. 2005). In confocal microscopy the point spread function may be calculated rather precisely for the object in focus, below and above the focus and used productively for the object reconstruction (Braat et al. 2008). All superresolution microscopy techniques focus on
transformation of the point spread function for a single point emitter/reflector placed in the focal point of as lens (Lipson 2003). For this purpose, the information theory based analysis was developed. The problem of “general” optical microscope, which transfers information from any point in the focal volume at multiple wavelengths is much more complicated, perhaps insoluble in classical analytical terms. But it is of high practical importance. For a single image a set of multifractals – cells and their interior – are transmitted by a transmission channel which has a multifractal character to a receiver. Receiver – camera chip – provides discrete resolution. From the view the multifractal statistic (Jizba and Arimitsu 2004) we may assume to observe spectrum of fractal dimensions of the resulting image. In practical terms, we may observe “best resolution” of different types of information observed in the image when different information representation is given. Using standard sample such as nanoparticles, some degree of calibration of the system may be achieved. However, any clear-cut analysis may be done only in case of existence of isolated points, i.e. dilute appearance of individual fluorescence proteins in the cell. The relation to the real case of living cell interior, where there is a mixture of transparent regions with changing refractivity indexes which change dramatically at scale of 10-20 nm is by classical analytical approach insoluble. The problem in such complicated environment is how to define the best resolution at the destination. In another words, we do not have a clear definition of the information source model – the destination. For the development of the method, we replace objective information resolution (in fact in full accordance with Shannon) by operator’s opinion. He or she would decide which is the observable object in the cell interior, how long it lasts, whether it expands or shrinks. References Boltzmann L., 1866. " Uber die Mechanische Bedeutung des Zweiten Hauptsatzes der Wärmetheorie". Wiener Berichte 53: pp. 195-220 Braat J.M., van Haver S., Janssen A.J.E.M. and Dirksen P., 2008 Assessment of optical systems by means of point-spread functions, Progress in Optics, Vol. 51, Ed. E. Wolf, Elsevier, Amsterdam / The Netherlands Grassberg P., 1983. Generalized dimension of strange attractors, Phys Lett. A97, 227-230 Hartley, J.V., 1928. Bell System Technical Journal 7 Hentschel H.G.E. and Procaccia I., 1983, Fractal nature of turbulence as manifested in turbulent diffusion, Phys. Rev. A 27, 1266 – 1269 Jizba P. and Arimitsu T., 2004 The world according to Renyi: Thermodynamics of multifractal systems,Ann. Phys. 312 17 – 595 Lipson S.G., 2003. Why is super-resolution so ineffcient? Micron 34, pp. 309-312 Masato, S., Hiroshi, O., Kimihiro, S., Suezou, N., 2005. Generalizing Effective Point Spread Function and its Application to the Phase-Contrast Microscope, Opt Rev, vol.12; no.2; pp. 105-108 Nijboer, B.R.A. and Zernike, F., 1949, Contribution in La Th´eorie des Images Optiques (Paris : ´Editions de la Revue d'Optique)
Nyquist, H., 1928. Certain topics in telegraph transmission theory. Trans. AIEE 1928, 47, 617-644 Rényi A., 1961. "On measures of information and entropy". Proceedings of the 4th Berkeley Symposium on Mathematics, Statistics and Probability 1960. pp. 547-561. Shannon, C. E., 1948. A mathematical theory of communication. Bell System Technical Journal, vol. 27, pp. 379-423 and 623-656, July and October
Stanovení badatelských cílů, metody a způsob řešení (max. 2 stránky): Experimental determination of Point Spread Function. Develop software for computing Rényi entropy from images. Observing and making photos of S. Pombe cells in phase contrast microscopy, estimation of nonlinear dynamics of S. Pombe cells. Methods of resolving: Calibration of microscope by using latex nanoparticles, experimental determination of Point Spread Function by using nanoparticles, cultivation of HeLa cells and taking microscope photography in phase contrast with different camera setting. Single point information contribution - sensitivity of image entropy to intensity levels which occur in the image infrequently The goal of the analysis is to obtain model of the biological object. In another words the model of biological system is the destination. It is a general agreement that living organisms are among the prominent examples of non-linear dynamics. We should then seek major features predicted by non-linear dynamics, for example limit cycles. We should thus examine the state space in which the limit cycle evolves. In case of infinite resolution, we should be able to determine complete time dynamics of a dynamic region. In most real cases this is not feasible and, in fact, also not necessary. It is sufficient to be able to identify a region, distinguish it from another and quantify its role in the symbolic dynamic of the cell. Such symbolic dynamic information should be parameter of the biological model in analogy to equilibrium thermodynamics. In each case, there is a sub-set of the state space which is much more populated than the rest and this we observe. The internal structure of living cells invokes the idea that individual structures are those regions of attraction and their dynamics reacts the dynamics of these asymptotically stable objects. The system behavior may be analyzed as symbolic trajectory. In the monolayer or a culture, cells represents sub-systems of and the monolayer is a system. In practical terms it means to determine all measurable phenomenological - variables in sufficient time preceeding the change of state to assure that the state change is independent from any preceeding history. By counting number of transitions and state lifetimes we obtain probability distribution functions for transitions between states.
Harmonogram prací: Months
Scheduled tasks Phase contrast microphotography, Point Spread Function, Samples preparation, Entropy Algorithms
May 2010
June 2010
Phase contrast microphotography, Testing and Optimization Algorithms, Statistical verification
July-August 2010
Phase contrast microphotography, Parameterization of Information equations, Color space independence
September - October 2010 November 2010
Phase contrast microphotography, Completing software applications, Graphical User Interface Evaluation of results, Article preparation
Předpokládaný typ vědeckých výsledků projektu Application note in Bioinformatics Journal, software applications Hlavní řešitel (maximálně 30 řádek) MSc. Thesis 2009 Nonlinear physics and chaos theory, University of South Bohemia, Department of Physics BSc. Thesis 2006 File systems, University of South Bohemia, Department of Informatics Since October 2009 I am working in the Institute of Physical Biology JU. I've performed here a number of experiments with nanoparticles and various cells. Experiments consisted of photographing objects and the subsequent processing of the resulting images using the Shannon and Rényi entropy. Vedoucí projektu (maximálně 30 řádek) Vzdělání:Univerzita Karlova Praha, Přírodovědecká fakulta, obor fyzikální chemie RNDr. 1987, CSc. biochemie, Ústav organické chemie a biochemie ČSAV, 1995, doc. přírodovědné inženýrství, FM TU Liberec, 2006 Významná zaměstnání:1987-1995 (včetně základní vojenské služby Ústav organické chemie a biochemie ČSAV, 1992-1995 stipendista a výzkumný inženýr Plant Cell Biology, Lund University, 1995 –2002 Biologická fakulta JU a MBÚ AVČR Třeboň, vědecký pracovník, duben 2002 – doposud ředitel ústavu fyzikální biologie JU Odborné aktivity:Fyzikální chemie živých systémů, biotechnologie, systémová biologie / biologické inženýrství, transfer technologií, soukromě technologie udržitelného rozvoje Vybrané granty v pozici hlavního řešitele:2000 výzkumné centrum Mechanismus, ekofyziologie a biotechnologie fotosyntézy, 2000 Phare CBC „Nové Hrady – Center of Biological Technologies“ 2005 „Dobudování vědeckotechnického parku v Nových Hradech“, prosperita OPPP, 2007 „Biosimilars“, program Trvalá properita společný výzkum se společností Zentiva a.s. Celkem 33 publikací dle ISI Thompson, asi 220 citací
Požadované finanční prostředky Výdaje a náklady na pořízení hmotného a nehmotného majetku (max. 50000Kč) Drobný hmotný a nehmotný majetek: 28057,- Kč Spotřební materiál Náklady na publikace (max. 2000Kč) Požadované finanční prostředky celkem:
Slovní zdůvodnění a rozpis finančních prostředků Drobný hmotný majetek: Camera Olympus E330 – 25 490,- Kč Tento fotoaparát se vyznačuje nízkým šumem, kvalitní senzorem o rozlišení 7,5 MPix a poměrem stran 4:3., podpora nekomprimovaných formátů RAW a TIFF. Fotoaparát bude použit pro nafocení sérií snímků, které budou poté zpracovány pomocí Rényiho entropie. Verbatim 2.5" Portable USB HDD 640GB – 2567,- Kč Externí hdd bude sloužit pro přenos dat mezi fotoaparátem a počítačem a k uložení pořízených dat a programů.
