@book{PupkaBartlKelleretal.1999, author = {Pupka, Reiner and Bartl, Peter and Keller, Vera and Kupries, Mario and Reichel, Ingrid and Schmidt, Maren and Tiede, Gabriele}, title = {Abschlußbericht zum Verbundprojekt "Rechnergest{\"u}tzte Modellierung und Steuerung der Vorgangsbearbeitung in verteilten Verwaltungs- und Organisationssystemen"}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Informatik}, volume = {1999, 01}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Informatik}, publisher = {Univ.}, address = {Potsdam}, issn = {0946-7580}, pages = {120, [21] Bl. : graph. Darst.}, year = {1999}, language = {de} } @article{PotenteLeveilleBourretYousefietal.2022, author = {Potente, Giacomo and L{\´e}veill{\´e}-Bourret, {\´E}tienne and Yousefi, Narjes and Choudhury, Rimjhim Roy and Keller, Barbara and Diop, Seydina Issa and Duijsings, Dani{\"e}l and Pirovano, Walter and Lenhard, Michael and Sz{\"o}v{\´e}nyi, P{\´e}ter and Conti, Elena}, title = {Comparative genomics elucidates the origin of a supergene controlling floral heteromorphism}, series = {Molecular biology and evolution : MBE}, volume = {39}, journal = {Molecular biology and evolution : MBE}, number = {2}, publisher = {Oxford Univ. Press}, address = {Oxford}, issn = {0737-4038}, doi = {10.1093/molbev/msac035}, pages = {16}, year = {2022}, abstract = {Supergenes are nonrecombining genomic regions ensuring the coinheritance of multiple, coadapted genes. Despite the importance of supergenes in adaptation, little is known on how they originate. A classic example of supergene is the S locus controlling heterostyly, a floral heteromorphism occurring in 28 angiosperm families. In Primula, heterostyly is characterized by the cooccurrence of two complementary, self-incompatible floral morphs and is controlled by five genes clustered in the hemizygous, ca. 300-kb S locus. Here, we present the first chromosome-scale genome assembly of any heterostylous species, that of Primula veris (cowslip). By leveraging the high contiguity of the P. veris assembly and comparative genomic analyses, we demonstrated that the S-locus evolved via multiple, asynchronous gene duplications and independent gene translocations. Furthermore, we discovered a new whole-genome duplication in Ericales that is specific to the Primula lineage. We also propose a mechanism for the origin of S-locus hemizygosity via nonhomologous recombination involving the newly discovered two pairs of CFB genes flanking the S locus. Finally, we detected only weak signatures of degeneration in the S locus, as predicted for hemizygous supergenes. The present study provides a useful resource for future research addressing key questions on the evolution of supergenes in general and the S locus in particular: How do supergenes arise? What is the role of genome architecture in the evolution of complex adaptations? Is the molecular architecture of heterostyly supergenes across angiosperms similar to that of Primula?}, language = {en} } @article{KellerValleriani2012, author = {Keller, Peter and Valleriani, Angelo}, title = {Single-molecule stochastic times in a reversible bimolecular reaction}, series = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr}, volume = {137}, journal = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr}, number = {8}, publisher = {American Institute of Physics}, address = {Melville}, issn = {0021-9606}, doi = {10.1063/1.4747337}, pages = {7}, year = {2012}, abstract = {In this work, we consider the reversible reaction between reactants of species A and B to form the product C. We consider this reaction as a prototype of many pseudobiomolecular reactions in biology, such as for instance molecular motors. We derive the exact probability density for the stochastic waiting time that a molecule of species A needs until the reaction with a molecule of species B takes place. We perform this computation taking fully into account the stochastic fluctuations in the number of molecules of species B. We show that at low numbers of participating molecules, the exact probability density differs from the exponential density derived by assuming the law of mass action. Finally, we discuss the condition of detailed balance in the exact stochastic and in the approximate treatment.}, language = {en} } @article{KellerRoellyValleriani2015, author = {Keller, Peter and Roelly, Sylvie and Valleriani, Angelo}, title = {On time duality for Markov Chains}, series = {Stochastic models}, volume = {31}, journal = {Stochastic models}, number = {1}, publisher = {Taylor \& Francis Group}, address = {Philadelphia}, issn = {1532-6349}, doi = {10.1080/15326349.2014.969736}, pages = {98 -- 118}, year = {2015}, abstract = {For an irreducible continuous time Markov chain, we derive the distribution of the first passage time from a given state i to another given state j and the reversed passage time from j to i, each under the condition of no return to the starting point. When these two distributions are identical, we say that i and j are in time duality. We introduce a new condition called permuted balance that generalizes the concept of reversibility and provides sufficient criteria, based on the structure of the transition graph of the Markov chain. Illustrative examples are provided.}, language = {en} } @article{KellerRoellyValleriani2015, author = {Keller, Peter and Roelly, Sylvie and Valleriani, Angelo}, title = {A Quasi Random Walk to Model a Biological Transport Process}, series = {Methodology and computing in applied probability}, volume = {17}, journal = {Methodology and computing in applied probability}, number = {1}, publisher = {Springer}, address = {Dordrecht}, issn = {1387-5841}, doi = {10.1007/s11009-013-9372-5}, pages = {125 -- 137}, year = {2015}, abstract = {Transport molecules play a crucial role for cell viability. Amongst others, linear motors transport cargos along rope-like structures from one location of the cell to another in a stochastic fashion. Thereby each step of the motor, either forwards or backwards, bridges a fixed distance and requires several biochemical transformations, which are modeled as internal states of the motor. While moving along the rope, the motor can also detach and the walk is interrupted. We give here a mathematical formalization of such dynamics as a random process which is an extension of Random Walks, to which we add an absorbing state to model the detachment of the motor from the rope. We derive particular properties of such processes that have not been available before. Our results include description of the maximal distance reached from the starting point and the position from which detachment takes place. Finally, we apply our theoretical results to a concrete established model of the transport molecule Kinesin V.}, language = {en} } @unpublished{KellerRoellyValleriani2013, author = {Keller, Peter and Roelly, Sylvie and Valleriani, Angelo}, title = {A quasi-random-walk to model a biological transport process}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-63582}, year = {2013}, abstract = {Transport Molecules play a crucial role for cell viability. Amongst others, linear motors transport cargos along rope-like structures from one location of the cell to another in a stochastic fashion. Thereby each step of the motor, either forwards or backwards, bridges a fixed distance. While moving along the rope the motor can also detach and is lost. We give here a mathematical formalization of such dynamics as a random process which is an extension of Random Walks, to which we add an absorbing state to model the detachment of the motor from the rope. We derive particular properties of such processes that have not been available before. Our results include description of the maximal distance reached from the starting point and the position from which detachment takes place. Finally, we apply our theoretical results to a concrete established model of the transport molecule Kinesin V.}, language = {en} } @unpublished{KellerRoellyValleriani2012, author = {Keller, Peter and Roelly, Sylvie and Valleriani, Angelo}, title = {On time duality for quasi-birth-and-death processes}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-56973}, year = {2012}, abstract = {We say that (weak/strong) time duality holds for continuous time quasi-birth-and-death-processes if, starting from a fixed level, the first hitting time of the next upper level and the first hitting time of the next lower level have the same distribution. We present here a criterion for time duality in the case where transitions from one level to another have to pass through a given single state, the so-called bottleneck property. We also prove that a weaker form of reversibility called balanced under permutation is sufficient for the time duality to hold. We then discuss the general case.}, language = {en} } @book{KellerRoellyValleriana2011, author = {Keller, Peter and Roelly, Sylvie and Valleriana, Angelo}, title = {On Time Duality for Markov Chains with Asborbing Boundardies}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Mathematische Statistik un}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Mathematische Statistik un}, publisher = {Univ.}, address = {Potsdam}, issn = {1613-3307}, pages = {18 S.}, year = {2011}, language = {en} } @phdthesis{Keller2012, author = {Keller, Peter}, title = {Mathematical modeling of molecular motors}, address = {Potsdam}, pages = {116 S.}, year = {2012}, language = {en} } @unpublished{Keller2013, author = {Keller, Peter}, title = {Mathematical modeling of molecular motors}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-63045}, year = {2013}, abstract = {Amongst the many complex processes taking place in living cells, transport of cargoes across the cytosceleton is fundamental to cell viability and activity. To move cargoes between the different cell parts, cells employ Molecular Motors. The motors operate by transporting cargoes along the so-called cellular micro-tubules, namely rope-like structures that connect, for instance, the cell-nucleus and outer membrane. We introduce a new Markov Chain, the killed Quasi-Random-Walk, for such transport molecules and derive properties like the maximal run length and time. Furthermore we introduce permuted balance, which is a more flexible extension of the ordinary reversibility and introduce the notion of Time Duality, which compares certain passage times pathwise. We give a number of sufficient conditions for Time Duality based on the geometry of the transition graph. Both notions are closely related to properties of the killed Quasi-Random-Walk.}, language = {en} }