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Summer 2008 Sylabus Biophysics II Cell Biophysics English: RM224, 15:15-18:30 Lecture notes with the according references will be published in the www. 1. 2. 3. 4. 5. 6. Basic Cell Biology Membrane Biophysics Active and Passive Physics of the Cytoskeleton Intracellular Transport Neurophysics Photosynthesis Membrane Biophysics Textbooks •Life - As a Matter of Fat. The Emerging Science of Lipidomics von O. G. Mouritsen von Springer, Berlin (Gebundene Ausgabe - Januar 2005) • Cevc, G. and Marsh, D. 1987. Phospholipid bilayers. Physical principles and models. Wiley-Interscience, New York. •Intermolecular and Surface Forces (Academic, London, 1992) J Israelachvili •de Gennes, P.G. and Prost, J (1993). The Physics of Liquid Crystals. Oxford: Clarendon Press. ISBN 0-19-852024-7. Entropie S = Entropie W = Zahl von Zuständen (Konfigurationen) die einen thermodynamischen System mit Energie E zugänglich sind Freie Energie F = U – TS U: internal energy Entropische Abstoßung thermisch fluktuierender Membranen Literatur: Reinhard Lipowsky, The conformation of membranes, Nature, Vol. 349, p. 475 (7 Febr 1991) Entropische Kräfte: Eine entropische Kraft ist nicht durch fundamentale mikroskopische Kräfte bestimmt sonder durch den thermodynamischen Gesamtzustand des Systems. Entropische Käfte treten auf wenn sich das System „wehrt“ gegen einen Entropieverlust. Es ist charakteristisch für diese Kräfte, dass sie mit der Temoeratur zu nehmen. Van der Waals Potential Die anziehende Van der Waals Wechselwirkung resultiert auf molekularer Ebene aus dem Einfluss gegenseitig induzierter Dipolmomente. Die aufwändige Herleitung erfolgt üblicherweise über die Lifshitz-Theorie. Der allgemeine Fall der Wechsel-wirkung zweier Schichtsysteme über eine Grenzschicht wurde von Parsegian und Ninham hergeleitet. Darauf beruht die ausführliche Betrachtung von Fenzl für den Fall der Wechselwirkung zwischen zwei Membranen. Betrachte eine thermisch fluktuierende Zellmembran, die sich nahe an einer anderen Oberfläche befindet. Membranfluktuationen, die eine Wellenlänge Lmax überschreiten sind durch die einschränkende Oberfläche nicht mehr möglich. Der Verlust and Entropie S = Sbound – Sfree kann abgeschätzt werden über den Verlust der Anzahl von möglichen Moden. Anzahl der nicht mehr möglichen Moden proportional zu : => Fluktuationsabstoßungskraft pro Flächenelement: Adhäsionsübergang T < Tu Die Fluktuations-Wechselwirkung spielt vor allem für den thermisch induzierten Adhäsionsübergang eine Rolle. T > Tu Kritische Entbindungstemperatur Tu Sterische Stabilisierung von Kolloiden •Kolloide sind mit einer Polymerschicht überzogen. •Überlapp führt zu einer entropischenAbstoßung (Verkleinerung des Konfigurationsraums der Polymere). •Gleichgewicht zwischen van-der-WaalsKräfte und entropischerAbstoßung. Hydrationskräfte Aus Messungen der lamellaren Periode d in multilamellaren Vesikeln bei verschiedenen osmotischen Drücken wurde die Existenz einer kurzreichweitigen repulsiven Wechselwirkung postuliert. Der hydrophile Charakter der Phospholipide führt zu einer Absenkung der freien Energie, wenn die hydrophilen Kopfgruppen mit Wasser umgeben sind. Die Ausbildung einer endlichen Wasserschicht zwischen den Membranen wird begünstigt. Dies führt zu dem Auftreten der so genannten Hydrationswechselwirkung. Sie wird durch den empirischen Ansatz mit H0 typischerweise in der Größenordnung von wenigen kBT Å-2 und lh = 2Å beschrieben. Die theoretische Beschreibung der Wechselwirkung wird noch immer kontrovers diskutiert. Der empirische Ansatz ist jedoch gut bestätigt. 3. Active and Passive Physics of the Cytoskeleton 3.1 Fundamental Polymer Physics Literatur: • M. Doi and S. F. Edwards, The Theory of Polymer Dynamics, Oxford Press • M. Doi, Introduction to Polymer Physics, Oxford Press Polymer A polymer is a large molecule (macromolecule) composed of repeating structural units connected by covalent chemical bonds. The word is derived from the Greek, πολυ, poly, "many"; and μέρος, meros, "part". Well known examples of polymers include plastics, DNA and proteins. A simple example is polypropylene. While "polymer" in popular usage suggests "plastic", the term actually refers to a large class of natural and synthetic materials with a variety of properties and purposes. Natural polymer materials such as shellac and amber have been in use for centuries. Biopolymers such as proteins and nucleic acids play crucial roles in biological processes. A variety of other natural polymers exist, such as cellulose, which is the main constituent of wood and paper. Some common synthetic polymers are Bakelite, neoprene, nylon, PVC (polyvinyl chloride), polystyrene, polyacrylonitrile and PVB (polyvinyl butyral). Polymers are studied in the fields of polymer chemistry, polymer physics, and polymer science. Polypropylene Starting in 1811 Henri Braconnot did pioneering work in derivative cellulose compounds, perhaps the earliest important work in polymer science. The term polymer was coined in 1833 by Jöns Jakob Berzelius. The development of vulcanization later in the nineteenth century improved the durability of the natural polymer rubber, signifying the first popularized semi-synthetic polymer. In 1907, Leo Baekeland created the first completely synthetic polymer, Bakelite, by reacting phenol and formaldehyde at precisely controlled temperature and pressure. Bakelite was then publicly introduced in 1909. Polyethylene Polyethylene or polythene (IUPAC name poly(ethene)) is a thermoplastic commodity heavily used in consumer products (notably the plastic shopping bag). Over 60 million tons of the material are produced worldwide every year. Freely rotating chain Polymer backbone displays no bending stiffness flexible polymer chain Ideal chain An ideal chain (or freely-jointed chain) is the simplest model to describe a polymer. It only assumes a polymer as a random walk and neglects any kind of interactions among monomers. Although it is simple, its generality gives us some insights about the physics of polymers. In this model, monomers are rigid rods of a fixed length l, and their orientation is completely independent of the orientations and positions of neighbouring monomers, to the extent that two monomers can co-exist at the same place. N monomers form the polymer, whose total unfolded length is: , where N is the number of monomers. In this very simple approach where no interactions between monomers are considered, the energy of the polymer is taken to be independent of its shape, which means that at ,thermodynamic equilibrium, all of its shape configurations are equally likely to occur as the polymer fluctuates in time, according to the Maxwell-Boltzmann distribution. Let us call the total end to end vector of an ideal chain and the vectors corresponding to individual monomers. Those random vectors have components in the three directions of space. Most of the expressions given in this article assume that the number of monomers N is large, so that the central limit theorem applies. The central limit theorem (CLT) states that the sum of a large number of independent and identically-distributed random variables will be approximately normally distributed (i.e., following a Gaussian distribution, or bell-shaped curve) if the random variables have a finite variance. The figure below shows a sketch of a (short) ideal chain. Since are independent, it follows from the Central limit theorem that is distributed according to a normal distribution (or gaussian distribution): precisely, in 3D, Rx,Ry, and Rz are distributed according to a normal distribution of mean 0 and of variance: Polymer size: Real Chains Solvent and temperature effect where Rg is the radius of gyration of the polymer, N is the number of bond segments (N, which is the degree of polymerization) of the chain.For good solvent, ν = 3 / 5; for bad solvent, ν = 1 / 3. Therefore polymer in good solvent has larger size and behaves like a fractal object. In bad solvent it behaves like a solid sphere. In the so called θ solvent, ν = 1 / 2, which is the result of simple random walk. The chain behaves as if an ideal chain. The quality of solvent depends also on temperature. For a flexible polymer, low temperature may correspond to poor quality and high temperature makes the same solvent good. At a particular temperature called theta (θ) temperature, the solvent behaves as if an ideal chain. Excluded volume interaction The simplest formulation of excluded volume is the , a random walk that cannot repeat its previous path. A path of this walk of N steps in three dimensions represents a conformation of a polymer with excluded volume interaction. Because of the self-avoiding nature, the number of possible conformation is significantly reduced. The radius of gyration is generally larger than that of ideal chain. Entropic elasticity of an ideal chain If the two free ends of an ideal chain are attached to some kind of micro-manipulation device, then the device experiences a force exerted by the polymer. The ideal chain's energy is constant, and thus its time-average, the internal energy, is also constant, which means that this force necessarily stems from a purely entropic effect. This entropic force is very similar to the pressure experienced by the walls of a box containing an ideal gas. The internal energy of an ideal gas depends only on its temperature, and not on the volume of its containing box, so it is not an energy effect that tends to increase the volume of the box like gas pressure does. This implies that the pressure of an ideal gas has a purely entropic origin. What is the microscopic origin of such an entropic force or pressure? The most general answer is that the effect of thermal fluctuations tends to bring a thermodynamic system toward a macroscopic state that corresponds to a maximum in the number of microscopic states (or micro-states) that are compatible with this macroscopic state. In other words, thermal fluctuations tend to bring a system toward its macroscopic state of maximum entropy. is proportional to . Homework 7 • Finde Beispiele für die entropische Abstoßung durch thermodynamische Fluktuationen! • Was versteht man unter Depletion Forces?