Running projects

Financed by ECMath

  • CH11

    Sensing with Nanopores

    Dr. Jürgen Fuhrmann / Dr. Clemens Guhlke

    Project heads: Dr. Jürgen Fuhrmann / Dr. Clemens Guhlke
    Project members: -
    Duration: -
    Status: running
    Located at: Weierstraß-Institut

    Description

    Sensing with nanopores is a promising new technology to analyze macromolecules like DNA strands by low cost/high speed measurements. The sensing device is constructed based on a nanopore embedded into a membrane which separates two electrodes. The system is filled with an electrolyte containing macromolecules to be analyzed. An electric potential is applied to the electrodes and induces an ionic current through the pore. Sensing is based on the observation that this ionic current is influenced by the geometrical configurations of the pore and of the macromolecules positioned within the pore. Under controlled movement of the macromolecule through the pore a characteristic time dependent current signal is generated, which is correlated to the structure of the pore and the macromolecule. Therefore nanopores can be used to count and even to characterize macromolecules in an electrolytic solution. n order to achieve a better understanding of the of phenomena that control the passing time of the analytes (macromolecules) through the nanopore, and to derive a relation between characteristic properties of the macromolecule and the generated current, the project will focus on three groups of tasks: Development of an appropriate nanopore model in the context of non-equilibrium thermodynamics, which accounts for the geometrical properties of pore and analyte, the charged boundary layers, ion diffusion and fluid flow. Combination and analysis of novel numerical discretization schemes, like pressure robust methods for fluid flow and novel finite volume discretization approaches for the PNP system in order to provide physically meaningful numerical models of the double layer structure and its impact on the fluid flow. Use of asymptotic analysis to derive reduced models, which include the relevant features of the complete thermodynamic model in different regimes.

    https://www.wias-berlin.de/projects/ECMath-CH11/
  • CH12

    Advanced Magnetic Resonance Imaging: Fingerprinting and Geometric Quantification

    Prof. Dr. Michael Hintermüller

    Project heads: Prof. Dr. Michael Hintermüller
    Project members: Dr. Guozhi Dong
    Duration: -
    Status: running
    Located at: Humboldt Universität Berlin

    Description

    Very recently, magnetic resonance fingerprinting (MRF) has been introduced as a highly promising MRI acquisition scheme which allows for the simultaneous quantification of the tissue parameters (e.g. T1, T2 and others) using a single acquisition process. In MRF, the tissue of interest is excited through a random sequence of pulses without needing to wait for the system to return to equilibrium between pulses. After each pulse, a subset of the signal's Fourier coefficients is collected, as in classical MRI, and a reconstruction of the net magnetization image is performed. These reconstructions suffer from the presence of artifacts since the Fourier coefficients are not fully sampled. The formed sequence of image elements is then compared to a family of predicted sequences (dictionary of fingerprints) each of which corresponds to a specific combination of values of the tissue parameters. This dictionary is computed beforehand by solving the Bloch equations. The idea is that, provided the dictionary is rich enough, every material element (voxel) can be then mapped to its parameter values. While first very promising results have been obtained in biomedical engineering, many aspects of MRF remain widely open and require a proper mathematization for optimizing and robustifying the procedure. The aim of this project is, thus, to provide a quantitative mathematical model for the MRF process, leading to a variational image reconstruction problem subject to dynamical constraints describing magnetization and an embedded reconstruction scheme. This model will be subject to a detailed mathematical analysis and its efficient numerical solution.

    http://wias-berlin.de/people/papafitsoros/MRF/
  • CH13

    Empirical Bayes methods for patient-specific prediction and control of pharmacological interventions

    Dr. Rainald Ehrig / Prof. Dr. Susanna Röblitz

    Project heads: Dr. Rainald Ehrig / Prof. Dr. Susanna Röblitz
    Project members: Dr Ilja Klebanov
    Duration: -
    Status: running
    Located at: Konrad-Zuse-Zentrum für Informationstechnik Berlin

    Description

    One of the main goals of mathematical modeling related to medical applications is to obtain patient-specific parametrizations and model predictions. In clinical practice, however, the number of available measurements for single patients is usually limited due to time and cost restrictions. This hampers the process of making patient-specific predictions about the outcome of a treatment. On the other hand, data are often available for many patients, in particular if extensive clinical studies have been performed. Empirical Bayes methods can provide a solution to this controversy. Instead of applying Bayes’ rule to each measurement separately, these methods usually boil down to combining all measurements in order to construct an informative prior as a first step and then using this prior for the Bayesian inference of the individual parametrizations in a second step. We want to demonstrate the applicability and benefit of this approach on a high-dimensional model system for predicting patient-specific treatment success rates related to in vitro fertilization in reproductive medicine.

    http://www.zib.de/projects/empirical-bayes-methods-patient-specific-prediction-and-control-pharmacological-interventions
  • CH14

    Understanding cell trajectories with sparse similarity learning

    Prof. Dr. Tim Conrad / Prof. Dr. Gitta Kutyniok / Prof. Dr. Christof Schütte

    Project heads: Prof. Dr. Tim Conrad / Prof. Dr. Gitta Kutyniok / Prof. Dr. Christof Schütte
    Project members: -
    Duration: -
    Status: running
    Located at: Freie Universität Berlin / Technische Universität Berlin / Konrad-Zuse-Zentrum für Informationstechnik Berlin

    Description

    In living organisms, biological cells transition from one state to another. This happens during normal cell development (e.g. aging) or is triggered by events, such as diseases. The time-ordered set of state changes is called a trajectory. Identifying these cell trajectories is a crucial part in bio-medical research to understand changes on a gene and molecular level. It allows to derive biological insights such as disease mechanisms and can lead to new biomedical discoveries and to advances in health-care. With the advent of single cell experiments such as Drop-Seq or inDrop, individual gene expression profiles of thousands of cells can be measured in a single experiment. These large data-sets allow to determine a cell's state based on its gene activity (cell expression profiles, CEPs), which can be expressed as a large feature vector representing its location in some large state space. The main problem with these experiments is that the actual time-information is lost, and needs to be recovered. The state-of-the art solution is to introduce the concept of pseudo-time in which the cells are ordered by CEP similarity. To find robust and biological meaningful trajectories based on CEPs, two main tasks have to be performed: (1) A CEP-based metric has to be learned to define pair-wise distances between CEPs. (2) Given this metric, similar CEP groups and transition paths between those groups should be identified and analysed.

  • CH15

    Analysis of Empirical Shape Trajectories

    Hon Prof. Hans-Christian Hege / Prof. Tim Sullivan / Dr. Christoph von Tycowicz

    Project heads: Hon Prof. Hans-Christian Hege / Prof. Tim Sullivan / Dr. Christoph von Tycowicz
    Project members: -
    Duration: -
    Status: running
    Located at: Freie Universität Berlin

    Description

    The reconstruction of discretized geometric shapes from empirical data, especially from image data, is important for many applications in medicine, biology, materials science, and other fields. During the last years, a number of techniques for performing such geometrical reconstructions and for conducting shape analysis have been developed. An important mathematical concept in this context are shape spaces. These are high-dimensional quotient manifolds with Riemannian structure, whose points represent geometrical shapes. Using suitable metrics and probability density functions on such manifolds, distances between shapes or statistical shape priors (for utilization in reconstruction tasks) can be defined. A frequently encountered situation is that instead of a set of discrete shapes a series of shapes is given, varying with some parameter (e.g. time). The corresponding mathematical object is a trajectory in shape space. For many analysis questions it is helpful to consider the shape trajectories as such (instead of individual shapes) - often together with co-varying parameters. The focus of this project is to develop new mathematical methods for the analysis, processing and reconstruction of empirically defined shape trajectories. By treating the trajectories as curves in shape space, we plan to exploit the rich geometric structure inherent to these spaces. In consequence, we expect the derived schemes to benefit from a compact encoding of constraints and a superior consistency as compared to their Euclidean counterparts. To develop new mathematical methods for the analysis, processing and reconstruction of empirically defined shape trajectories exploiting the rich geometric structure of shape space.

    http://www.zib.de/projects/analysis-empirical-shape-trajectories
  • CH16

    Reliable joint simulations for orthopaedic decision making in hip surgery

    Prof. Dr. Ralf Kornhuber / Dr.-Ing. Stefan Zachow

    Project heads: Prof. Dr. Ralf Kornhuber / Dr.-Ing. Stefan Zachow
    Project members: Dr. Jonathan Youett
    Duration: -
    Status: running
    Located at: Freie Universität Berlin

    Description

    This project aims at estimating the unknown parameters of a physics-based joint model together with a systematic sensitivity analysis, to ensure the reliability of a computer-assisted surgery planning tool developed in previous Matheon projects. The estimation shall be carried out using a Bayesian approach in combination with reduced basis methods to achieve feasible computing times. This calibration of the model will be accompanied by a clinical validation based on real patient data, in cooperation with the Orthopaedic Research Center of the university hospital Stavanger.

    http://www.mi.fu-berlin.de/en/math/groups/ag-numerik/projects/A-CH1/index.html
  • CH17

    Hybrid reaction-diffusion / Markov-state model of systems with many interacting molecules

    Prof. Dr. Frank Noé / Prof. Dr. Christof Schütte

    Project heads: Prof. Dr. Frank Noé / Prof. Dr. Christof Schütte
    Project members: -
    Duration: -
    Status: running
    Located at: Freie Universität Berlin

    Description

    While simulations of detailed molecular structure, e.g. using atomistic or coarse- grained MD simulation is able to describe the evolution of molecular systems at length/timescales of nanometers/milliseconds, we require a way to bridge from the molecular scale to large-scale/long-time evolutions of molecular superstructures such as actin networks on the scale of micrometers/hours. Such time- and lengthscales while still maintaining some structural, and importantly single-molecule resolution, can be covered by particle-based reaction-diffusion simulations. Molecular kinetic models of small parts of the overall machinery (single molecules and small complexes) can be parametrized with high-throughput MD simulations, enhanced sampling simu- lations, possibly by incorporating constraints from experimental data. In order to ex- plore the long-range and long-time behavior of mixtures and superstructures of many molecules, we set out ot develop a rigorous and computationally efficient coupling be- tween molecular kinetics models and particle-based reaction-diffusion dynamics (Fig. 1).

  • CH18

    Boundary-Sensitive Hodge Decompositions

    Prof. Dr. Konrad Polthier

    Project heads: Prof. Dr. Konrad Polthier
    Project members: -
    Duration: 01.06.2017 - 31.12.2018
    Status: running
    Located at: Freie Universität Berlin

    Description

    Based on novel results for smooth and discrete Hodge-type decompositions on manifolds with boundary, this project aims to incorporate discrete boundary-sensitive Hodge decompositions as a central tool for the analysis of blood flow and parameterization of blood vessels. These decompositions provide the following two substantial improvements over existing methods: first, they are able to distinguish harmonic blood flow arising from boundary in- and out ow from harmonic circulations induced by the interior topology of the geometry. Second, they guarantee a theoretically-sound linkage of certain fields with controlled boundary behaviour to cohomological quantities of the geometry, which is the essential and still missing ingredient for the creation of periods to ensure global matching of parameter lines in modern parameterization techniques.

    http://www.mi.fu-berlin.de/en/math/groups/ag-geom/projects/ch18/index.html
  • CH19

    Estimating Dynamics of Macromolecular Systems by Low Rank Approximation Techn

    Priv.-Doz. Dr. Konstantin Fackeldey / Prof. Dr. Frank Noé / Prof. Dr. Reinhold Schneider / Hao Wu

    Project heads: Priv.-Doz. Dr. Konstantin Fackeldey / Prof. Dr. Frank Noé / Prof. Dr. Reinhold Schneider / Hao Wu
    Project members: -
    Duration: 01.06.2017 - 31.12.2018
    Status: running
    Located at: Freie Universität Berlin / Technische Universität Berlin

    Description

    The dynamics of a molecular system can be described by the propagation of probabilities. The project aims at estimating coarse grained models of probability densities for molecular dynamics (MD) by nonlinear projections from a high dimensional space onto a low dimensional space. Molecular processes such as protein kinetics from all-atom simulations and the like suffer from the high dimensionality of the underlying space. To overcome this, projections from the high dimensional space onto a low dimensional space have been introduced, such that the system can be described on a coarser scale by using less degrees of freedom. In the present project we apply low rank tensor approximations, to tackle the curse of dimensions. We will use Observable Operator models (OOM) to estimate the dynamics using data from short time simulation.

  • CH20

    Stochasticity driving robust pattern formation in brain wiring

    Dr. Max von Kleist / Dr. Martin Weiser

    Project heads: Dr. Max von Kleist / Dr. Martin Weiser
    Project members: -
    Duration: -
    Status: running
    Located at: Freie Universität Berlin

    Description

    During brain development, synaptic connection patterns are formed in an extremely robust manner. As the interconnection patterns are much too complex to be encoded directly in the genome, they must emerge from simpler rules. In this project we investigate mechanistic stochastic models of axon growth and filopodial dynamics, checking whether their simulation leads to connection patterns and dynamics as observed in vivo, and with the same robustness.

    http://www.zib.de/projects/BrainWiring
  • CH21

    Data-Driven Modelling of Cellular Processes and beyond

    Prof. Dr. Tim Conrad / Dr. Stefan Klus / Prof. Dr. Christof Schütte

    Project heads: Prof. Dr. Tim Conrad / Dr. Stefan Klus / Prof. Dr. Christof Schütte
    Project members: Wei Zhang
    Duration: 01.06.2017 - 31.12.2018
    Status: running
    Located at: Konrad-Zuse-Zentrum für Informationstechnik Berlin

    Description

    Cellular processes are governed by diffusion, transport, and interactions of its constituents. For many processes the spatial inhomogeneity of cells is of secondary importance; modelling such processes means finding appropriate kinetic models of the underlying cellular reaction networks (CRNs). The availability of such models is key to many areas of the life sciences ranging from computational biology to system medicine and is essential for understanding the fundamentals of cellular behavior, its malfunction under external stress and its restoration by regenerative interventions.

  • MI-CH1

    Robust Optimization of Load Balancing in the Operating Theatre

    Dr. Guillaume Sagnol

    Project heads: Dr. Guillaume Sagnol
    Project members: -
    Duration: 01.06.2017 - 31.12.2018
    Status: running
    Located at: Technische Universität Berlin

    Description

    The operating theater (OT) is one of the most expensive hospital resources, and its management is a very complex task, which involves combinatorial aspects in an uncertain environment (surgical durations, emergency cases, availability of recovery beds). This project is concerned with the tactical (middle-term) planning of the OT, which aims at maximizing the utilization of resources in the OT, balancing the workload over the different operating sessions, and ensuring an equitable access and treatment duration to all patients.





Financed by others

  • CH-TU25

    Weak convergence of numerical methods for stochastic partial differential equations with applications to neurosciences

    Dr. Raphael Kruse

    Project heads: Dr. Raphael Kruse
    Project members: -
    Duration: 01.05.2014 - 30.04.2020
    Status: running
    Located at: Technische Universität Berlin

    Description

    In this project we develop and investigate novel numerical methods for the discretization of stochastic partial differential equations arising, for instance, in neuroscience. Our numerical methods are based on the Galerkin finite element method combined with suitable time stepping schemes such as the backward Euler method or backward difference formulas.

    http://www.math.tu-berlin.de/fachgebiete_ag_modnumdiff/diffeqs/v_menue/fg_differentialgleichungen/nwg_uq0/v_menue/research_projects/weak_convergence_of_numerical_methods_for_spdes_with_applications_to_neurosciences/
  • CH-AP2

    Genealogies and inference for populations with highly skewed offspring distributions under further evolutionary forces

    Prof. Dr. Jochen Blath

    Project heads: Prof. Dr. Jochen Blath
    Project members: -
    Duration: 01.10.2012 - 30.06.2018
    Status: running
    Located at: Technische Universität Berlin

    Description

    Multiple merger coalescent modeling and analysis has up to now been mainly focused on neutral, haploid, single-locus set-ups. The central aim of this project is to develop the stochastic models, theoretical results and inference methods required to effectively describe and analyse the observed patterns of genetic variation in sequence data in real populations with skewed offspring distributions under the influence of further evolutionary forces, especially recombination, selection and population structure; in other words, the systematic development of the basics of a `mathematical population genetics for highly variableoffspring distributions'. Given recent progress in DNA sequencing technology, and insight in the limitations of inference methods based single locus set-ups, particular emphasis will be put on realistic diploid multi-locus models and the corresponding statistical machinery for data analysis.

    http://www.dfg-spp1590.de/abstracts.php#5
  • CH-AP7

    Efficient calculation of slow and stationary scales in molecular dynamics

    Prof. Dr. Frank Noé

    Project heads: Prof. Dr. Frank Noé
    Project members: -
    Duration: -
    Status: running
    Located at: Freie Universität Berlin

    Description

    Molecular dynamics (MD) simulation is a technique that may aid in the understanding of fundamental processes in biology and chemistry, and has important technological applications in pharmacy, biotechnology, and nanotechnology. Many complex molecular processes are of multi-scale nature in that they have timescales spanning the range 10−15 s to 1 s, often with no pronounced gap that would permit efficient coarse-grained time integration. Molecular dynamics is a Markov process in a high-dimensional state space. The dom- inant timescales and their associated transitions between metastable (long-lived) states are given by the eigenvalues and eigenfunctions of the transfer operator of the Markov process. These dominant eigenvalues and eigenfunctions therefore need to be approxi- mated. The introduction of Markov state models (MSMs) to molecular simulation in the past few years has been a breakthrough in providing the ability to perform such an approx- imation. An MSM consists of a discretization of the molecular state space into sets, often found by geometric clustering of available simulation data, and a matrix of tran- sition probabilities between them, estimated from the same simulation data. This is an estimation of a set discretization of the transfer operator. Despite their success, MSMs currently suffer from two fundamental problems: 1. Discretization Problem: When the initial discretization for the MSM, based on geometric distances in the data, is poor, the results will be spurious, resulting in numerical unreliability. When the user is interested in approximating a sizable number (e.g. 10 − 100) of slow processes with high accuracy, the common practice to use data-driven geometric clustering methods may not be a viable approach. 2. Sampling Problem: MSMs contain only information of states that have been visited and transitions that have occurred in the simulation data. While the slowest events may occur on timescales of seconds, affordable simulation lengths are on the order of microseconds. Thus, MSM construction suffers from a severe sampling problem. Both problems are coupled, and we now set out to develop a concise mathematical and algorithmic framework to address them.

  • CH-AP8

    Probing scales in equilibrated systems by optimal nonequilibrium forcing

    Prof. Dr. Carsten Hartmann / Prof. Dr. Christof Schütte / PD Dr. Marcus Weber

    Project heads: Prof. Dr. Carsten Hartmann / Prof. Dr. Christof Schütte / PD Dr. Marcus Weber
    Project members: -
    Duration: 01.10.2014 - 30.06.2018
    Status: running
    Located at: Freie Universität Berlin

  • CH-AP9

    Origin of the scaling cascades in protein dynamics

    Prof. Dr. Carsten Hartmann

    Project heads: Prof. Dr. Carsten Hartmann
    Project members: -
    Duration: 01.10.2014 - 30.06.2018
    Status: running
    Located at: Freie Universität Berlin

    Description

    The molecular dynamics of proteins and peptides is a hierarchical process which in­volves characteristic time scales ranging from 10-12 seconds to 100 seconds. Although the physical models of the local intramolecular interactions are relatively well devel­oped, and molecular dynamics simulations have proven successful in recovering the dynamics of large-scale biomolecular systems, a mathematical understanding of how local interactions in the molecular root model give rise to a cascade of processes on different time scales is still lacking.
    In this project we will investigate how these scaling cascades arise from the physical models of molecular dynamics and develop mathematical tools for their analysis. Our root model is a diffusion in a high-dimensional potential energy landscape that mod­els the local interactions between atoms or groups of atoms. The local interactions in the molecular force .eld (i.e., the gradient of the potential energy) then induce long-range effects and may give rise to the observed long time scales on the order of seconds. Yet the predictability of molecular dynamics with respect to variations in the physical parameters (e.g., force .eld parameters) or boundary conditions (e.g., temperature) is re­markably poor, the reason being the nonlinearity, the large dimensionality of the models and noise present in the systems, which altogether promote large-scale effects induced by small noise or slow collective motions of atoms or groups of atoms.
    For molecular systems with reversible dynamics, the relevant so-called implied time scales are related to the dominant eigenvalues of the underlying Markov generator. These eigenvalues can be estimated from molecular dynamics simulations and serve as approximations of experimentally measurable quantities. In molecular dynamics simu­lations it is possible to selectively tune the strength of a speci.c physical interaction (e.g., strength of long-range forces between different amino acids) or boundary conditions (e.g., temperature or pH), rendering them an ideal tool for analyzing the connection between root model and observed time scales. To investigate how the cascades of time scales arise in molecular dynamics we will extend numerical continuation methods for dynamical systems to stochastic molecular systems in order to study the changes in the implied time scales under variation of force .eld parameters or boundary conditions. We will compare analytical results to results from numerical simulations (classical and ab-initio molecular dynamics) and to results from infrared (IR) spectroscopy. Despite its popularity in the protein folding community, implied time scales are only one possible way to quantify molecular dynamics time scales. For instance, the exponen­tial convergence rate towards the thermodynamic equilibrium state is closely linked to experimentally measurable quantities. A second focus of the project is therefore to com­pare quantities which represent these relaxation time scales. To this end we will extend the numerical continuation approach to other observables, such as entropy production rates that, in certain cases, can be related to the shape of the molecular potential or Han­kel singular values that characterize the response of the system to the environmental noise and can be related to the typical residence time of a conformation.
    The understanding how scaling cascades in protein dynamics originate from the known hierarchy of physical interactions will be crucial for the development of multi-scale models, which consistently capture time scales on any desired level of coarseness. Moreover it will yield insight into biological phenomena such as allosteric regulation mechanisms or pathological misfolding events caused by single-point mutations.

    http://sfb1114.imp.fu-berlin.de/research/index.php?option=com_projectlog&view=project&id=9
  • CH-AP10

    Multiscale modeling and simulation for spatiotemporal master equations

    Prof. Dr. Frank Noé / Prof. Dr. Christof Schütte

    Project heads: Prof. Dr. Frank Noé / Prof. Dr. Christof Schütte
    Project members: -
    Duration: 01.10.2014 - 30.06.2018
    Status: running
    Located at: Freie Universität Berlin

    Description

    Accurate modeling of reaction kinetics is important for understanding the functionality of biological cells and the design of chemical reactors. Depending on the particle con­centrations and on the relation between particle mobility and reaction rate constants, different mathematical models are appropriate. In the limit of slow diffusion and small concentrations, both discrete particle numbers and spatial inhomogeneities must be taken into account. The most detailed root model consists of particle-based reaction-diffusion dynamics (PBRD), where all individual par­ticles are explicitly resolved in time and space, and particle positions are propagated by some equation of motion, and reaction events may occur only when reactive species are adjacent.
    For rapid diffusion or large concentrations, the model may be coarse-grained in dif­ferent ways. Rapid diffusion leads to mixing and implies that spatial resolution is not needed below a certain lengthscale. This permits the system to be modeled via a spa­tiotemporal chemical Master equation (STCME), i.e. a coupled set of chemical Master equations acting on spatial subvolumes. The STCME becomes a chemical Master equa­tion (CME) when diffusion is so fast that the entire system is well-mixed. When particle concentrations are large, populations may be described by concentrations rather than by discrete numbers, leading to a PDE or ODE formulation.

    Many biological processes call for detailed models (PBRD, ST-CME or CME), but these models are extremely costly to solve. Ef.cient mathematical and computational methods are needed in order to approximate the solutions of these models with some guaranteed accuracy level. An approach to optimal or ef.cient switching between different models is, as yet, missing.
    In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD <-> ST-CME <-> CME) coupled to population scaling (CME <-> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD <-> CME <-> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.

    http://sfb1114.imp.fu-berlin.de/research/index.php?option=com_projectlog&view=project&id=12
  • CH-AP12

    pcCells - physicochemical principles of cellular information processing

    Prof. Dr. Frank Noé

    Project heads: Prof. Dr. Frank Noé
    Project members: -
    Duration: 01.01.2013 - 31.12.2017
    Status: running
    Located at: Freie Universität Berlin

    Description

    Biological cells are able to perform complex signal transduction tasks quickly, energy-efficiently and yet in a robust and noise-tolerant manner. These signal transduction tasks rely on intracellular information processing mechanisms in which chemical signals are sent, transmitted and received and the state of the overall machinery is stored in chemical or conformational switches. The physicochemical principles of information processing in cells is still not well understood, owing to fundamental restrictions in resolution in experiments and in sampling of molecular dynamics simulations. Here, we will develop new simulation methods based on adaptive molecular dynamics and Markov models. These methods, together with new statistical mechanical theories and single-molecule experimental analyses will be employed to investigate the molecular basis of intracellular signal processing mechanisms. Central to our proposal is the hypothesis that intracellular signal processing relies on spatiotemporal order of molecules arising from dynamical sorting. This hypothesis will be tested using examples of protein-ligand and protein-protein sorting in neuronal signalling. The proposed project is highly multidisciplinary, involving physical chemistry, computer science, mathematics and biology.

    http://compmolbio.biocomputing-berlin.de/index.php/projects/80-erc
  • CH-AP14

    Conformational dynamics of biomolecules: Reconciling simulation and experimental data

    Prof. Dr. Frank Noé

    Project heads: Prof. Dr. Frank Noé
    Project members: -
    Duration: 01.01.2012 - 31.12.2018
    Status: running
    Located at: Freie Universität Berlin

    Description

    We develop methods for constructing kinetic models of biomolecular conformation dynamics from single-molecule experimental data, or by reconciling kinetic experimental data and molecular dynamics simulation data. In the present funding period we aim at developing an approach to directly compute MSMs from single-molecule experiments, with the following main objectives:
    1. Estimate conformation dynamics (eigenvalues, eigenvectors of the underlying Markovian dynamics) directly from single-molecule trajectories.
    2. Quantify the estimation errors of 1.
    3. Applications to optical tweezer data (collaboration with Susan Marqusee).
    4. Use 1. to compute improved Markov state models; Applications to simulation data.
    5. Provide publicly available software implementation.


    http://compmolbio.biocomputing-berlin.de/index.php/projects/91-dfg825-2-2
  • CH-AP16

    Projection theory of transfer operators

    Prof. Dr. Christof Schütte / PD Dr. Marcus Weber

    Project heads: Prof. Dr. Christof Schütte / PD Dr. Marcus Weber
    Project members: -
    Duration: 01.01.2014 - 31.12.2017
    Status: running
    Located at: Konrad-Zuse-Zentrum für Informationstechnik Berlin

    Description

    The main object is analysing sufficent ways to compute a galerkin approximation of the transfer operator. This includes to study the theoretical properties of a galerkin approximation of specific systems and to development algorithms which guarantee those properties for the numerical approximation. Furthermore, one is interested in making this computation as cheap as possible.

    http://www.zib.de/projects/projection-theory-transfer-operators
  • CH-AP19

    Meth4SysPharm: Modeling methods for systems pharmacology and application to HIV-1

    Dr. Max von Kleist

    Project heads: Dr. Max von Kleist
    Project members: -
    Duration: 01.03.2014 - 01.03.2019
    Status: running
    Located at: Freie Universität Berlin

    Description

    'Systems pharmacology' denotes the application of systems biology approaches to research questions arising in pharmacology. The aim is to understand the interaction of drugs with com- plex biological networks and to use this knowledge to develop- and improve medical therapy. Within the proposed project we will address unsolved mathematical challenges arising from this novel, interdisciplinary approach. We will integrate knowledge and data from three subtopics in order to study the mechanisms of drug resistance development in HIV-1, as a model system. In close cooperation with experts from the respective fields, the systems' response to drug interference, in terms of 'evolutionary dynamics' will be assessed alongside with the temporal resolution of drug interference ('drug action and pharmacokinetics') and their implications for the 'optimal use of therapy'. The proposed research program is expected to provide methodologi- cal advance that allows projecting these interrelations into measurable clinical outcomes, while addressing a relevant medical problem at the same time.

    http://page.mi.fu-berlin.de/vkleist/CurrentProjects.htm
  • CH-AP20

    Integrative mathematical modeling of physiological- and molecular factors of osteoarthritis of the knee

    Dr. Max von Kleist

    Project heads: Dr. Max von Kleist
    Project members: -
    Duration: 01.03.2014 - 01.03.2018
    Status: running
    Located at: Freie Universität Berlin

    Description

    Osteoarthritis of the knee (OAK) is a complex multi-factorial condition that is characterised by a lack of hyaline cartilage self repair 1, inflammation & pain 2. As for many other multi-factorial conditions, computational models may be useful tools of direct clinical relevance that allow studying the interaction of putative factors. Within this subproject, we want to develop a comprehensive computational model of cartilage homeostasis that will help us to understand and to evaluate the onset and progression of OAK. While the underlying mechanisms of OAK remain unknown, several factors have been previously associated with osteoarthritis and studied in isolation, such as cell density-dependent extracellular matrix (EM) generation 3,4, EM metabolism 5, the effect of nutrient gradients 5,6 and the influence of (mechano-) growth factors 7.

    Our research group has a broad expertise in interdisciplinary research in biomedicine 8,11 with a particular focus on mechanistic mathematical modelling 8,9 including in vitro to in vivo extrapolation, as well as the analysis of complex clinical samples 10. Within this consortium, we aspire to combine biochemical data from PrevOP subprojects SP1-3 (inflammation, cartilage self-repair & pain) and OVERLOAD projects SP5, 7-8 (fluid transport, mechano-sensitive signalling, cartilage self-repair), to successively develop mathematical models of cartilage homeostasis. Particularly, integration of results from OVERLOAD SP5 may allow to couple image-derived clinical data to metabolic events in the cartilage. The developed comprehensive model of OAK will further our understanding of the disease and the interplay of the mentioned factors, provide insights into disease mechanisms and strategies for its prevention (like, e.g. physical training). The aim of the project is thus to provide a translational framework between in vitro bio-molecular studies, ex vivo analysis, animal models and human patients with OAK (clinical projects in PrevOP/OVERLOAD).

    http://overload-prevop.charite.de/verbund/m_v_kleist_cschuette/
  • CH-AP24

    Free Boundary Problems and Level Set Methods

    Prof. Dr. Michael Hintermüller

    Project heads: Prof. Dr. Michael Hintermüller
    Project members: -
    Duration: 01.05.2011 - 31.03.2018
    Status: running
    Located at: Humboldt Universität Berlin

    Description

    Project part FREELEVEL will focus on two research streams: (i) shape and topological sensitivity-based solvers in tomography and (ii) the extension of spatially adapted regularization to more general image restoration problems, e.g., involving blind deconvolution, and non-convex regularization. Concerning tomography problems, a level-set-based algorithm relying on shape and extended topological sensitivities will be realized for FDOT and MIT, respectively. For MIT, first a reduced model leading to an elliptic PDE-system will be studied and, in a next step, the full Maxwell system will be taken into account. For numerical efficiency purposes, a shape-aware adaptive finite element method will be intertwined with the level-set solver (partly with FEMBEM). In the area of image restoration, we are motivated by optical diffusion tomography problems for detecting objects located behind turbid media and by convolution identification in dual-MR techniques (MRI). We formulate these problems in terms of blind deconvolution, preferably with non-convex regularization with respect to the image. The resulting problems will be studied and solved numerically. With respect to the latter - split Bregman - iteratively re-weighted total variation and semismooth Newton solvers will be investigated. Further, motivated by sparse magnetic resonance imaging, problems in compressed sensing with convex (OPTIM) and non-convex relaxation (MRI) of the 0-norm will be treated. The latter is interesting as there is evidence that non-convex regularization goes along with a possible reduction in acquired data. Further, FREELEVEL will focus on topics supporting other projects, such as piecewise polynomial Mumford-Shah based image segmentation using topological sensitivities (INVERSE).

    Within the SFB, FREELEVEL acts as a center of expertise for shape and topological sensitivity-based level-set solvers for tomography problems. Moreover, FREELEVEL contributes expertise and software in image restoration to the SFB through various cooperations with practitioners (MRI) as well as the applied mathematics group within the SFB (OPTIM, INVERSE).

    http://math.uni-graz.at/mobis/freelevel.html