Markus Kollmann

Single-file diffusion of atomic and colloidal systems: asymptotic laws.

We present a general derivation of the non-Fickian behavior for the self-diffusion of identically interacting particle systems with excluded mutual passage. We show that the conditional probability distribution of finding a particle at position x(t) after time t, when the particle was located at x(0) at t=0, follows a Gaussian distribution in the long-time limit, with variance 2W(t) approximately t(1/2) for overdamped systems and with variance 2W(t) approximately t for classical systems. The asymptotic behavior of the mean-squared displacement, W(t), is shown to be independent of the nature of interactions for homogeneous systems in the fluid state. Moreover, the long-time behavior of self-diffusion is determined by short-time and large-scale collective density fluctuations.

Functioning and robustness of a bacterial circadian clock

Cyanobacteria are the simplest known cellular systems that regulate their biological activities in daily cycles. For the cyanobacterium Synechococcus elongatus, it has been shown by in vitro and in vivo experiments that the basic circadian timing process is based on rhythmic phosphorylation of KaiC hexamers. Despite the excellent experimental work, a full systems level understanding of the in vitro clock is still lacking. In this work, we provide a mathematical approach to scan different hypothetical mechanisms for the primary circadian oscillator, starting from experimentally established molecular properties of the clock proteins. Although optimised for highest performance, only one of the in silico‐generated reaction networks was able to reproduce the experimentally found high amplitude and robustness against perturbations. In this reaction network, a negative feedback synchronises the phosphorylation level of the individual hexamers and has indeed been realised in S. elongatus by KaiA sequestration as confirmed by experiments.

Computational processing and error reduction strategies for standardized quantitative data in biological networks

High‐quality quantitative data generated under standardized conditions is critical for understanding dynamic cellular processes. We report strategies for error reduction, and algorithms for automated data processing and for establishing the widely used techniques of immunoprecipitation and immunoblotting as highly precise methods for the quantification of protein levels and modifications. To determine the stoichiometry of cellular components and to ensure comparability of experiments, relative signals are converted to absolute values. A major source for errors in blotting techniques are inhomogeneities of the gel and the transfer procedure leading to correlated errors. These correlations are prevented by randomized gel loading, which significantly reduces standard deviations. Further error reduction is achieved by using housekeeping proteins as normalizers or by adding purified proteins in immunoprecipitations as calibrators in combination with criteria‐based normalization. Additionally, we developed a computational tool for automated normalization, validation and integration of data derived from multiple immunoblots. In this way, large sets of quantitative data for dynamic pathway modeling can be generated, enabling the identification of systems properties and the prediction of targets for efficient intervention.

Thermal robustness of signaling in bacterial chemotaxis

Temperature is a global factor that affects the performance of all intracellular networks. Robustness against temperature variations is thus expected to be an essential network property, particularly in organisms without inherent temperature control. Here, we combine experimental analyses with computational modeling to investigate thermal robustness of signaling in chemotaxis of Escherichia coli, a relatively simple and well-established model for systems biology. We show that steady-state and kinetic pathway parameters that are essential for chemotactic performance are indeed temperature-compensated in the entire physiological range. Thermal robustness of steady-state pathway output is ensured at several levels by mutual compensation of temperature effects on activities of individual pathway components. Moreover, the effect of temperature on adaptation kinetics is counterbalanced by preprogrammed temperature dependence of enzyme synthesis and stability to achieve nearly optimal performance at the growth temperature. Similar compensatory mechanisms are expected to ensure thermal robustness in other systems.

Role of Translational Coupling in Robustness of Bacterial Chemotaxis Pathway

Evolutionary selection for robustness of signaling output in the face of stochastic variations in protein expression may explain the organization of bacterial chemotaxis genes.

Robust Signal Processing in Living Cells

Cellular signaling networks have evolved an astonishing ability to function reliably and with high fidelity in uncertain environments. A crucial prerequisite for the high precision exhibited by many signaling circuits is their ability to keep the concentrations of active signaling compounds within tightly defined bounds, despite strong stochastic fluctuations in copy numbers and other detrimental influences. Based on a simple mathematical formalism, we identify topological organizing principles that facilitate such robust control of intracellular concentrations in the face of multifarious perturbations. Our framework allows us to judge whether a multiple-input-multiple-output reaction network is robust against large perturbations of network parameters and enables the predictive design of perfectly robust synthetic network architectures. Utilizing the Escherichia coli chemotaxis pathway as a hallmark example, we provide experimental evidence that our framework indeed allows us to unravel the topological organization of robust signaling. We demonstrate that the specific organization of the pathway allows the system to maintain global concentration robustness of the diffusible response regulator CheY with respect to several dominant perturbations. Our framework provides a counterpoint to the hypothesis that cellular function relies on an extensive machinery to fine-tune or control intracellular parameters. Rather, we suggest that for a large class of perturbations, there exists an appropriate topology that renders the network output invariant to the respective perturbations.

A sequestration feedback determines dynamics and temperature entrainment of the KaiABC circadian clock.

The circadian rhythm of the cyanobacterium Synechococcus elongatus is controlled by three proteins, KaiA, KaiB, and KaiC. In a test tube, these proteins form complexes of various stoichiometry and the average phosphorylation level of KaiC exhibits robust circadian oscillations in the presence of ATP. Using mathematical modeling, we were able to reproduce quantitatively the experimentally observed phosphorylation dynamics of the KaiABC clockwork in vitro. We thereby identified a highly non‐linear feedback loop through KaiA inactivation as the key synchronization mechanism of KaiC phosphorylation. By using the novel method of native mass spectrometry, we confirm the theoretically predicted complex formation dynamics and show that inactivation of KaiA is a consequence of sequestration by KaiC hexamers and KaiBC complexes. To test further the predictive power of the mathematical model, we reproduced the observed phase synchronization dynamics on entrainment by temperature cycles. Our model gives strong evidence that the underlying entrainment mechanism arises from a temperature‐dependent change in the abundance of KaiAC and KaiBC complexes.

Diffusion of colloids in one-dimensional light channels

Single-file diffusion (SFD), prevalent in many chemical and biological processes, refers to the one-dimensional motion of interacting particles in pores which are so narrow that the mutual passage of particles is excluded. Since the sequence of particles in such a situation remains unaffected over time t, this leads to strong deviations from normal diffusion, e.g. an increase of the particle mean-square-displacement as the square root of t. We present experimental results of the diffusive behaviour of colloidal particles in one-dimensional channels with varying particle density. The channels are realized by means of a scanning optical tweezers. Based on a new analytical approach (Kollmann 2003 Phys. Rev. Lett. 90 180602) for SFD, we can predict quantitatively the long-time, diffusive behaviour from the short time density fluctuations in our systems.

Quantifying Origins of Cell-to-Cell Variations in Gene Expression

A general dynamic description of protein synthesis was employed to quantify different sources of gene expression noise in cellular systems. To test our approach, we use time-resolved expression data of individual human cells and, from this information, predict the stationary cell-to-cell variation in protein levels in a clonal population. For three of the four human genes investigated, the cellular variations in expression level are not due to fluctuations in promoter activity or transcript copy number, but are almost exclusively a consequence of long-term variations of gene regulatory factors or the global cellular state. Moreover, we show that a dynamic description is much more reliable to discriminate extrinsic and intrinsic sources of noise than it is on grounds of cell-cycle averaged descriptions. The excellent agreement between the theoretical predictions and the experimentally measured noise strengths shows that a quantitative description of gene expression noise is indeed possible on the basis of idealized stochastic processes.

Signatures of gene expression noise in cellular systems

Noise in gene expression, either due to inherent stochasticity or to varying interand intracellular environment, can generate significant cell-to-cell variability of protein levels in clonal populations. We present a theoretical framework, based on stochastic processes, to quantify the different sources of gene expression noise taking cell division explicitly into account. Analytical, time-dependent solutions for the noise contributions arising from the major steps involved in protein synthesis are derived. The analysis shows that the induction level of the activator or transcription factor is crucial for the characteristic signature of the dominant source of gene expression noise and thus bridges the gap between seemingly contradictory experimental results. Furthermore, on the basis of experimentally measured cell distributions, our simulations suggest that transcription factor binding and promoter activation can be modelled independently of each other with sufficient accuracy. ∗To whom the correspondence should be addressed. E-mail: juhe@fdm.uni-freiburg.deNoise in gene expression, either due to inherent stochasticity or to varying inter- and intracellular environment, can generate significant cell-to-cell variability of protein levels in clonal populations. To quantify the different sources of gene expression noise, several theoretical studies have been performed using either a quasi-stationary approximation for the emerging master equation or employing a time-dependent description, when cell division is taken explicitly into account. Here, we give an overview of the different origins of gene expression noise which were found experimentally and introduce the basic stochastic modeling approaches. We extend, and apply a time-dependent description of gene expression noise to experimental data. The analysis shows that the induction level of the transcription factor can be employed to discriminate the noise profiles and their characteristic signatures. On the basis of experimentally measured cell distributions, our simulations suggest that transcription factor binding and promoter activation can be modeled independently of each other with sufficient accuracy.