Sejtstruktúrák dinamikájának statisztikus fizikai modellezése = Statistical physical modeling of the dynamics of subcellular structures

- A kinezin nevű motorfehérje két fejét néhány jól meghatározott állapottal jellemezve, a két fejet összekötő neck-linkereket pedig szemiflexibilis polimerláncként leírva, termodinamikailag konzisztens módon felépítettük a dimerikus kinezin molekula telje | - By characterizing the two heads of kinesin with a few well defined kinetic states and considering the two neck linkers (which connect the two heads) as semiflexible polymeric chains, we have constructed a complete kinetic model of the dimeric kinesin i

Sejtbiológiai folyamatok vizsgálata statisztikus fizikai módszerekkel = Studies of biological processes of the cell using the methods of statistical physics

- Elméleti számítások és numerikus szimulációk segítségével megmagyaráztuk a DNS molekuláknak a sejtmag nanopórusain való áthaladásának mechanizmusát [1]. Kidolgoztunk egy olyan módszert, amely lehetővé teszi a polimerdinamikai szimulációk jelentős felgyorsítását a monomerek közötti kötések hosszának és hajlítási merevségének renormálásával. - Megmutattuk, hogy 2-dimenziós random potenciálban a "racsni effektus" (amely a molekuláris motorok működésének az alapja) nagyléptékű mintázatok kialakulásához vezet [6]. - Fehérjék adszorpciójára megalkottunk egy modellt, amely segítségével a zürichi ETH-ban végzett fehérjekicserélődéses kísérleteket értelmeztük [2]. A dinamikus erőspektroszkópia pontosabb elméleti leírását adtuk arra az esetre, amikor egy adhéziós kötés elszakítása során a rendszer több, egymást követő energiagáton megy keresztül [3]. - Optikai csipesz segítségével megmértük az erő-megnyúlás görbét membrán nanocsövek kialakulásakor. Azt tapasztaltuk, majd elméleti számításokkal is alátámasztottuk, hogy az erő nem-monoton módon változik, a maximuma lineárisan függ a húzási terület sugarától, és elsőrendű átalakulást mutat [5]. Kvantitatív leírását adtuk egy membrán veszikulumból kihúzott két nanocső összeolvadásának. Az eredmények új mérési módszert kínálnak a biológiai membránok rugalmas paramétereinek meghatározására [4]. Megmutattuk továbbá, hogy ha görbületre érzékeny fehérjék találhatók a membránban, akkor létezik egy kritikus fehérjekoncentráció, amely felett stabil nanocső nem jöhet létre, a membrán húzása során pedig újabb és újabb hólyagocskák válnak le [7]. | - With the help of theoretical calculations and numerical simulations we explained the mechanism of DNA translocation through the nanopores of the cell nucleus [1]. We also developed a method for speeding up the polymer dynamics simulations by renormalizing the bond length and the bending rigidity. - We showed that in 2-dimensional random potentials the "ratchet effect" (which is the basic mechanism of the operation of molecular motors) leads to the appearance of large-scale patterns [6]. - For protein adsorption we constructed a model, with which we could interpret the protein exchange experiments performed at the ETH Zürich [2]. We gave a refined theoretical description of the dynamic force spectroscopy in case the system overcomes several energy barriers during the rupture of an adhesion bond [3]. - Using optical tweezers we measured the force-extension curves during the formation of membrane nanotubes. We found and explained theoretically that the force changes non-monotonically, its maximal value depends linearly on the radius of the pulling area, and undergoes a first order transition [5]. We gave a quantitative description of the coalescence of two membrane nanotubes pulled from a single vesicle. Our results provide a new method for the determination of the elastic properties of biological membranes [4]. We also showed that if the membrane contains curvature sensitive proteins, then there exists a critical protein concentration, above which no stable tube can form and the pulling of the membrane leads to vesiculation [7]

Élőlények kollektív viselkedésének statisztikus fizikája = Statistical physics of the collective behaviour of organisms

Experiments: We have carried out quantitative experiments on the collective motion of cells as a function of their density. A sharp transition could be observed from the random motility in sparse cultures to the flocking of dense islands of cells. Using ultra light GPS devices developed by us, we have determined the existing hierarchical relations within a flock of 10 homing pigeons. Modelling: From the simulations of our new model of flocking we concluded that the information exchange between particles was maximal at the critical point, in which the interplay of such factors as the level of noise, the tendency to follow the direction and the acceleration of others results in large fluctuations. Analysis: We have proposed a novel link-density based approach to finding overlapping communities in large networks. The algorithm used for the implementation of this technique is very efficient for most real networks, and provides full statistics quickly. Correspondingly, we have developed a by now popular, user-friendly, freely downloadable software for finding overlapping communities. Extending our method to the time-dependent regime, we found that large groups in evolving networks persist for longer if they are capable of dynamically altering their membership, thus, an ability to change the group composition results in better adaptability. We also showed that knowledge of the time commitment of members to a given community can be used for estimating the community's lifetime. Experiments: We have carried out quantitative experiments on the collective motion of cells as a function of their density. A sharp transition could be observed from the random motility in sparse cultures to the flocking of dense islands of cells. Using ultra light GPS devices developed by us, we have determined the existing hierarchical relations within a flock of 10 homing pigeons. Modelling: From the simulations of our new model of flocking we concluded that the information exchange between particles was maximal at the critical point, in which the interplay of such factors as the level of noise, the tendency to follow the direction and the acceleration of others results in large fluctuations. Analysis: We have proposed a novel link-density based approach to finding overlapping communities in large networks. The algorithm used for the implementation of this technique is very efficient for most real networks, and provides full statistics quickly. Correspondingly, we have developed a by now popular, user-friendly, freely downloadable software for finding overlapping communities. Extending our method to the time-dependent regime, we found that large groups in evolving networks persist for longer if they are capable of dynamically altering their membership, thus, an ability to change the group composition results in better adaptability. We also showed that knowledge of the time commitment of members to a given community can be used for estimating the community's lifetime

Effective temperature of mutations.

Biological macromolecules experience two seemingly very different types of noise acting on different time scales: (i) point mutations corresponding to changes in molecular sequence and (ii) thermal fluctuations. Examining the secondary structures of a large number of microRNA precursor sequences and model lattice proteins, we show that the effects of single point mutations are statistically indistinguishable from those of an increase in temperature by a few tens of kelvins. The existence of such an effective mutational temperature establishes a quantitative connection between robustness to genetic (mutational) and environmental (thermal) perturbations

Komplex Hálózatok Moduláris Szerkezete = Modular Structure of Complex Networks

Kidolgoztunk egy módszert, mely lehetővé teszi időben változó hálózatokban a csoportok nyomon követését. A csoportok időfejlődését nagyméretű társaskapcsolat hálózatokban vizsgáltuk és több érdekes összefüggést találtunk a csoportok mérete, időbeli változékonysága és fennmaradási valószínűsége között. Kiterjesztettük a klikk perkolációs módszert irányított- és súlyozott hálózatokra. Ezek segítségével számos nagyméretű valós hálózatot vizsgáltunk. Az irányított csoportosulások viselkedése két nagy osztályba sorolta a vizsgált rendszereket, a súlyozott hálózatoknál pedig érdekes élsúlyok korrelációkat fedtünk fel. A mikroRNS-ek és az általuk gátolt mRNS-ek hálózatát vizsgálva a klikk perkolációs módszer segítségével mikroRNS funkciós csoportokat sikerült beazonosítani, és a sejten belüli jelátviteli hálózatokban gyógyszer célpont fehérjék előrejelzéséhez fejlesztettünk bioinformatikai módszereket. A hálózati hierarchiához kapcsolódóan címkézett hálózatok statisztikai tulajdonságait vizsgálatuk olyan rendszerekben, ahol a címkék maguk is hierarchikusan szerveződnek. Eredményeink szerint a tanulmányozott hálózatok érdekes önhasonlóságot mutatnak a címke indukált részgráfokra történő leszűkítés esetén. A hierarchia tanulmányozásához kapcsolódóan kifejlesztettünk egy önhasonló, hierarchikus multifraktál élbekötési mértéken alapuló véletlen gráf generáló módszert. Megmutattuk, hogy ennek segítségével nagyon sokféle eltérő véletlen hálózat generálható le. | We developed a method enabling the tracking of communities in time evolving networks. We studied the statistical properties of community evolution in large social networks, and revealed interesting non trivial relations between the size, stationarity and survival probability of communities. We extended the clique percolation method for handling directed- and weighted networks, and analyzed numerous real networks with these new algorithms. The behavior of the directed communities classified the examined systems into two major groups, whereas the studies of the weighted networks revealed interesting link weight correlations. We located functional units with the help of the clique percolation method in the network of microRNAs and their regulated mRNAs, and developed bioinformatical tools for signal transduction networks, helping the prediction of drug target proteins. Relating to the field of network hierarchy, we studied the statistical features of tagged networks where the tags were hierarchically organized. According to our results, the examined networks showed an interesting self similarity when restricted to the tag-induced sub-graphs. Relating to the studies of hierarchy, we developed a random graph generator based on self-similar, hierarchical multifractal link probability measure. We have shown, that this method is capable of generating random networks with very diverse properties

Topological phase transitions of random networks

To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables us to establish an equivalence between the equilibrium rewiring problem we consider and the dynamics of a lattice gas on the edge-dual graph of a fully connected network. By assigning energies to the different network topologies and defining the appropriate order parameters, we find a rich variety of topological phase transitions, defined as singular changes in the essential feature(s) of the global connectivity as a function of a parameter playing the role of the temperature. In the ``critical point'' scale-free networks can be recovered.Comment: 4 pages, 3 figures, submitted, corrected and added reference

Characterization of the dissolution of water microdroplets in oil

Water in oil emulsions have a wide range of applications from chemical technology to microfluidics, where the stability of water droplets is of paramount importance. Here using an accessible and easily reproducible experimental setup we describe and characterize the dissolution of water in oil, which renders nanoliter-sized droplets unstable, resulting in their shrinkage and disappearance in a time scale of hours. This process has applicability in creating miniature reactors for crystallization. We test multiple oils and their combinations with surfactants exhibiting widely different rates of dissolution. We derived simple analytical equations to determine the product of the diffusion coefficient and the relative saturation density of water in oil from the measured dissolution data. By measuring the moisture content of mineral and silicone oils with Karl Fischer titration before and after saturating them with water, we calculated the diffusion coefficient of water in these two oilsComment: 8 pages 6 figures 3 supplementary video

Reverse engineering of linking preferences from network restructuring

We provide a method to deduce the preferences governing the restructuring dynamics of a network from the observed rewiring of the edges. Our approach is applicable for systems in which the preferences can be formulated in terms of a single-vertex energy function with f(k) being the contribution of a node of degree k to the total energy, and the dynamics obeys the detailed balance. The method is first tested by Monte-Carlo simulations of restructuring graphs with known energies, then it is used to study variations of real network systems ranging from the co-authorship network of scientific publications to the asset graphs of the New York Stock Exchange. The empirical energies obtained from the restructuring can be described by a universal function f(k) -k ln(k), which is consistent with and justifies the validity of the preferential attachment rule proposed for growing networks.Comment: 7 pages, 6 figures, submitted to PR