Bettina Keller

Markov models of molecular kinetics: Generation and validation

Markov state models of molecular kinetics (MSMs), in which the long-time statistical dynamics of a molecule is approximated by a Markov chain on a discrete partition of configuration space, have seen widespread use in recent years. This approach has many appealing characteristics compared to straightforward molecular dynamics simulation and analysis, including the potential to mitigate the sampling problem by extracting long-time kinetic information from short trajectories and the ability to straightforwardly calculate expectation values and statistical uncertainties of various stationary and dynamical molecular observables. In this paper, we summarize the current state of the art in generation and validation of MSMs and give some important new results. We describe an upper bound for the approximation error made by modeling molecular dynamics with a MSM and we show that this error can be made arbitrarily small with surprisingly little effort. In contrast to previous practice, it becomes clear that the best MSM is not obtained by the most metastable discretization, but the MSM can be much improved if non-metastable states are introduced near the transition states. Moreover, we show that it is not necessary to resolve all slow processes by the state space partitioning, but individual dynamical processes of interest can be resolved separately. We also present an efficient estimator for reversible transition matrices and a robust test to validate that a MSM reproduces the kinetics of the molecular dynamics data.

Macrolide-based transgene control in mammalian cells and mice

Heterologous mammalian gene regulation systems for adjustable expression of multiple transgenes are necessary for advanced human gene therapy and tissue engineering, and for sophisticated in vivo gene-function analyses, drug discovery, and biopharmaceutical manufacturing. The antibiotic-dependent interaction between the repressor (E) and operator (ETR) derived from an Escherichia coli erythromycin-resistance regulon was used to design repressible (EOFF) and inducible (EON) mammalian gene regulation systems (E.REX) responsive to clinically licensed macrolide antibiotics (erythromycin, clarithromycin, and roxithromycin). The EOFF system consists of a chimeric erythromycin-dependent transactivator (ET), constructed by fusing the prokaryotic repressor E to a eukaryotic transactivation domain that binds and activates transcription from ETR-containing synthetic eukaryotic promoters (PETR). Addition of macrolide antibiotic results in repression of transgene expression. The EON system is based on E binding to artificial ETR-derived operators cloned adjacent to constitutive promoters, resulting in repression of transgene expression. In the presence of macrolides, gene expression is induced. Control of transgene expression in primary cells, cell lines, and microencapsulated human cells transplanted into mice was demonstrated using the E.REX (EOFF and EON) systems. The macrolide-responsive E.REX technology was functionally compatible with the streptogramin (PIP)–regulated and tetracycline (TET)–regulated expression systems, and therefore may be combined for multiregulated multigene therapeutic interventions in mammalian cells and tissues.

A synthetic mammalian gene circuit reveals antituberculosis compounds

Synthetic biology provides insight into natural gene-network dynamics and enables assembly of engineered transcription circuitries for production of difficult-to-access therapeutic molecules. In Mycobacterium tuberculosis EthR binds to a specific operator (OethR) thereby repressing ethA and preventing EthA-catalyzed conversion of the prodrug ethionamide, which increases the resistance of the pathogen to this last-line-of-defense treatment. We have designed a synthetic mammalian gene circuit that senses the EthR–OethR interaction in human cells and produces a quantitative reporter gene expression readout. Challenging of the synthetic network with compounds of a rationally designed chemical library revealed 2-phenylethyl-butyrate as a nontoxic substance that abolished EthRs repressor function inside human cells, in mice, and within M. tuberculosis where it triggered derepression of ethA and increased the sensitivity of this pathogen to ethionamide. The discovery of antituberculosis compounds by using synthetic mammalian gene circuits may establish a new line of defense against multidrug-resistant M. tuberculosis.

A synthetic time-delay circuit in mammalian cells and mice

Time-delay circuitries in which a transcription factor processes independent input parameters can modulate NF-κB activation, manage quorum-sensing cross-talk, and control the circadian clock. We have constructed a synthetic mammalian gene network that processes four different input signals to control either immediate or time-delayed transcription of specific target genes. BirA-mediated ligation of biotin to a biotinylation signal-containing VP16 transactivation domain triggers heterodimerization of chimeric VP16 to a streptavidin-linked tetracycline repressor (TetR). At increasing biotin concentrations up to 20 nM, TetR-specific promoters are gradually activated (off to on, input signal 1), are maximally induced at concentrations between 20 nM and 10 μM, and are adjustably shut off at biotin levels exceeding 10 μM (on to off, input signal 2). These specific expression characteristics with a discrete biotin concentration window emulate a biotin-triggered bandpass filter. Removal of biotin from the culture environment (input signal 3) results in time-delayed transgene expression until the intracellular biotinylated VP16 pool is degraded. Because the TetR component of the chimeric transactivator retains its tetracycline responsiveness, addition of this antibiotic (input signal 4) overrides biotin control and immediately shuts off target gene expression. Biotin-responsive immediate, bandpass filter, and time-delay transcription characteristics were predicted by a computational model and have been validated in standard cultivation settings or biopharmaceutical manufacturing scenarios using trangenic CHO-K1 cell derivatives and have been confirmed in mice. Synthetic gene circuitries provide insight into structure–function correlations of native signaling networks and foster advances in gene therapy and biopharmaceutical manufacturing.

Gas-inducible transgene expression in mammalian cells and mice

We describe the design and detailed characterization of a gas-inducible transgene control system functional in different mammalian cells, mice and prototype biopharmaceutical manufacturing. The acetaldehyde-inducible AlcR-PalcA transactivator-promoter interaction of the Aspergillus nidulans ethanol-catabolizing regulon was engineered for gas-adjustable transgene expression in mammalian cells. Fungal AlcR retained its transactivation characteristics in a variety of mammalian cell lines and reversibly adjusted transgene transcription from chimeric mammalian promoters (PAIR) containing PalcA-derived operators in a gaseous acetaldehyde-dependent manner. Mice implanted with microencapsulated cells engineered for acetaldehyde-inducible regulation (AIR) of the human glycoprotein secreted placental alkaline phosphatase showed adjustable serum phosphatase levels after exposure to different gaseous acetaldehyde concentrations. AIR-controlled interferon-β production in transgenic CHO-K1-derived serum-free suspension cultures could be modulated by fine-tuning inflow and outflow of acetaldehyde-containing gas during standard bioreactor operation. AIR technology could serve as a tool for therapeutic transgene dosing as well as biopharmaceutical manufacturing.

Variational Approach to Molecular Kinetics

The eigenvalues and eigenvectors of the molecular dynamics propagator (or transfer operator) contain the essential information about the molecular thermodynamics and kinetics. This includes the stationary distribution, the metastable states, and state-to-state transition rates. Here, we present a variational approach for computing these dominant eigenvalues and eigenvectors. This approach is analogous to the variational approach used for computing stationary states in quantum mechanics. A corresponding method of linear variation is formulated. It is shown that the matrices needed for the linear variation method are correlation matrices that can be estimated from simple MD simulations for a given basis set. The method proposed here is thus to first define a basis set able to capture the relevant conformational transitions, then compute the respective correlation matrices, and then to compute their dominant eigenvalues and eigenvectors, thus obtaining the key ingredients of the slow kinetics.

Comparing geometric and kinetic cluster algorithms for molecular simulation data

The identification of metastable states of a molecule plays an important role in the interpretation of molecular simulation data because the free-energy surface, the relative populations in this landscape, and ultimately also the dynamics of the molecule under study can be described in terms of these states. We compare the results of three different geometric cluster algorithms (neighbor algorithm, K-medoids algorithm, and common-nearest-neighbor algorithm) among each other and to the results of a kinetic cluster algorithm. First, we demonstrate the characteristics of each of the geometric cluster algorithms using five two-dimensional data sets. Second, we analyze the molecular dynamics data of a beta-heptapeptide in methanol--a molecule that exhibits a distinct folded state, a structurally diverse unfolded state, and a fast folding/unfolding equilibrium--using both geometric and kinetic cluster algorithms. We find that geometric clustering strongly depends on the algorithm used and that the density based common-nearest-neighbor algorithm is the most robust of the three geometric cluster algorithms with respect to variations in the input parameters and the distance metric. When comparing the geometric cluster results to the metastable states of the beta-heptapeptide as identified by kinetic clustering, we find that in most cases the folded state is identified correctly but the overlap of geometric clusters with further metastable states is often at best approximate.

Novel promoter/transactivator configurations for macrolide‐ and streptogramin‐responsive transgene expression in mammalian cells

The recently developed heterologous macrolide‐ (E.REX system) and streptogramin‐ (PIP system) responsive gene regulation systems show significant differences in their regulation performance in diverse cell lines.

Complex RNA folding kinetics revealed by single-molecule FRET and hidden Markov models.

We have developed a hidden Markov model and optimization procedure for photon-based single-molecule FRET data, which takes into account the trace-dependent background intensities. This analysis technique reveals an unprecedented amount of detail in the folding kinetics of the Diels–Alderase ribozyme. We find a multitude of extended (low-FRET) and compact (high-FRET) states. Five states were consistently and independently identified in two FRET constructs and at three Mg2+ concentrations. Structures generally tend to become more compact upon addition of Mg2+. Some compact structures are observed to significantly depend on Mg2+ concentration, suggesting a tertiary fold stabilized by Mg2+ ions. One compact structure was observed to be Mg2+-independent, consistent with stabilization by tertiary Watson–Crick base pairing found in the folded Diels–Alderase structure. A hierarchy of time scales was discovered, including dynamics of 10 ms or faster, likely due to tertiary structure fluctuations, and slow dynamics on the seconds time scale, presumably associated with significant changes in secondary structure. The folding pathways proceed through a series of intermediate secondary structures. There exist both compact pathways and more complex ones, which display tertiary unfolding, then secondary refolding, and, subsequently, again tertiary refolding.

Dynamic properties of force fields

Molecular-dynamics simulations are increasingly used to study dynamic properties of biological systems. With this development, the ability of force fields to successfully predict relaxation timescales and the associated conformational exchange processes moves into focus. We assess to what extent the dynamic properties of model peptides (Ac-A-NHMe, Ac-V-NHMe, AVAVA, A10) differ when simulated with different force fields (AMBER ff99SB-ILDN, AMBER ff03, OPLS-AA/L, CHARMM27, and GROMOS43a1). The dynamic properties are extracted using Markov state models. For single-residue models (Ac-A-NHMe, Ac-V-NHMe), the slow conformational exchange processes are similar in all force fields, but the associated relaxation timescales differ by up to an order of magnitude. For the peptide systems, not only the relaxation timescales, but also the conformational exchange processes differ considerably across force fields. This finding calls the significance of dynamic interpretations of molecular-dynamics simulations into question.