Showing papers by "Udo Seifert published in 2015"
TL;DR: It is shown quite generally that, in a steady state, the dispersion of observables, like the number of consumed or produced molecules or thenumber of steps of a motor, is constrained by the thermodynamic cost of generating it.
Abstract: Biomolecular systems like molecular motors or pumps, transcription and translation machinery, and other enzymatic reactions, can be described as Markov processes on a suitable network. We show quite generally that, in a steady state, the dispersion of observables, like the number of consumed or produced molecules or the number of steps of a motor, is constrained by the thermodynamic cost of generating it. An uncertainty $\ensuremath{\epsilon}$ requires at least a cost of $2{k}_{B}T/{\ensuremath{\epsilon}}^{2}$ independent of the time required to generate the output.
718 citations
TL;DR: In this paper, the power and efficiency of miniaturized heat engines are related, which paves the way for studies of even smaller systems that experience quantum effects, such as quantum teleportation.
Abstract: Heat engines translate thermal energy into useful mechanical work. New results show how the power and efficiency of miniaturized heat engines are related, which paves the way for studies of even smaller systems that experience quantum effects.
170 citations
TL;DR: It is shown that the bound on the Fano factor that depends on the thermodynamic affinity driving the transformation from substrate to product constrains the number of intermediate states of an enzymatic cycle can be extended to arbitrary multicyclic networks.
Abstract: The Fano factor, an observable quantifying fluctuations of product generation by a single enzyme, can reveal information about the underlying reaction scheme. A lower bound on this Fano factor that depends on the thermodynamic affinity driving the transformation from substrate to product constrains the number of intermediate states of an enzymatic cycle. So far, this bound has been proven only for a unicyclic network of states. We show that the bound can be extended to arbitrary multicyclic networks, with the Fano factor constraining the largest value of the effective length, which is the ratio between the number of states and the number of products, among all cycles.
92 citations
TL;DR: In this paper, a general framework for analyzing the thermodynamics of small systems that are driven by both a periodic temperature variation and some external parameter modulating their energy is introduced, in particular, periodic micro and nano-heat engines.
Abstract: We introduce a general framework for analyzing the thermodynamics of small systems that are driven by both a periodic temperature variation and some external parameter modulating their energy. This set-up covers, in particular, periodic micro and nano-heat engines. In a first step, we show how to express total entropy production by properly identified time-independent affinities and currents without making a linear response assumption. In linear response, kinetic coefficients akin to Onsager coefficients can be identified. Specializing to a Fokker-Planck type dynamics, we show that these coefficients can be expressed as a sum of an adiabatic contribution and one reminiscent of a Green-Kubo expression that contains deviations from adiabaticity. Furthermore, we show that the generalized kinetic coefficients fulfill an Onsager-Casimir type symmetry tracing back to microscopic reversibility. This symmetry allows for non-identical off-diagonal coefficients if the driving protocols are not symmetric under time-reversal. We then derive a novel constraint on the kinetic coefficients that is sharper than the second law and provides an efficiency-dependent bound on power. As one consequence, we can prove that the power vanishes at least linearly when approaching Carnot efficiency. We illustrate our general framework by explicitly working out the paradigmatic case of a Brownian heat engine realized by a colloidal particle in a time-dependent harmonic trap subject to a periodic temperature profile. This case study reveals inter alia that our new general bound on power is asymptotically tight.
80 citations
TL;DR: In this paper, a modified fluctuation-dissipation theorem is used to characterize slow relaxation to equilibrium in systems exhibiting slow relaxation in terms of an effective temperature arising from a modified FL.
Abstract: Systems exhibiting slow relaxation to equilibrium are often characterized in terms of an effective temperature arising from a modified fluctuation–dissipation theorem. Single-molecule experiments provide direct evidence for the validity of this idea.
78 citations
TL;DR: This work analyzes the effect of how a nonzero affinity driving receptors out of equilibrium affects sensitivity in a paradigmatic model of chemotaxis and establishes an intriguing analogy between sensing with nonequilibrium receptors and kinetic proofreading.
Abstract: For a paradigmatic model of chemotaxis, we analyze the effect of how a nonzero affinity driving receptors out of equilibrium affects sensitivity. This affinity arises whenever changes in receptor activity involve adenosine triphosphate hydrolysis. The sensitivity integrated over a ligand concentration range is shown to be enhanced by the affinity, providing a measure of how much energy consumption improves sensing. With this integrated sensitivity we can establish an intriguing analogy between sensing with nonequilibrium receptors and kinetic proofreading: the increase in integrated sensitivity is equivalent to the decrease of the error in kinetic proofreading. The influence of the occupancy of the receptor on the phosphorylation and dephosphorylation reaction rates is shown to be crucial for the relation between integrated sensitivity and affinity. This influence can even lead to a regime where a nonzero affinity decreases the integrated sensitivity, which corresponds to anti-proofreading.
58 citations
TL;DR: In this paper, the authors show that the optimal observable typically does not commute with the Hamiltonian and hence would not be available in a classical two-level system, and they extend this bound to a large class of feedback-driven quantum engines operating periodically and in finite time.
Abstract: A genuine feature of projective quantum measurements is that they inevitably alter the mean energy of the observed system if the measured quantity does not commute with the Hamiltonian. Compared to the classical case, Jacobs proved that this additional energetic cost leads to a stronger bound on the work extractable after a single measurement from a system initially in thermal equilibrium [Phys. Rev. A 80, 012322 (2009)]. Here, we extend this bound to a large class of feedback-driven quantum engines operating periodically and in finite time. The bound thus implies a natural definition for the efficiency of information to work conversion in such devices. For a simple model consisting of a laser-driven two-level system, we maximize the efficiency with respect to the observable whose measurement is used to control the feedback operations. We find that the optimal observable typically does not commute with the Hamiltonian and hence would not be available in a classical two level system. This result reveals that periodic feedback engines operating in the quantum realm can exploit quantum coherences to enhance efficiency.
56 citations
TL;DR: For thermoelectric power generation in a multiterminal geometry, strong numerical evidence for a universal bound as a function of the magnetic-field induced asymmetry of the nondiagonal Onsager coefficients is presented.
Abstract: For thermoelectric power generation in a multiterminal geometry, strong numerical evidence for a universal bound as a function of the magnetic-field induced asymmetry of the nondiagonal Onsager coefficients is presented. This bound implies, inter alia, that the power vanishes at least linearly when the maximal efficiency is approached. In particular, this result rules out that Carnot efficiency can be reached at finite power, which an analysis based on the second law only would, in principle, allow.
54 citations
TL;DR: A novel technique—dynamic optical displacement spectroscopy (DODS) is introduced, to measure stochastic displacements of membranes with unprecedented combined spatiotemporal resolution of 20 nm and 10 μs, and is used to explore the fluctuations in human red blood cells, which showed an ATP-induced enhancement of non-Gaussian behaviour.
Abstract: Stochastic displacements or fluctuations of biological membranes are increasingly recognized as an important aspect of many physiological processes, but hitherto their precise quantification in living cells was limited due to a lack of tools to accurately record them. Here we introduce a novel technique--dynamic optical displacement spectroscopy (DODS), to measure stochastic displacements of membranes with unprecedented combined spatiotemporal resolution of 20 nm and 10 μs. The technique was validated by measuring bending fluctuations of model membranes. DODS was then used to explore the fluctuations in human red blood cells, which showed an ATP-induced enhancement of non-Gaussian behaviour. Plasma membrane fluctuations of human macrophages were quantified to this accuracy for the first time. Stimulation with a cytokine enhanced non-Gaussian contributions to these fluctuations. Simplicity of implementation, and high accuracy make DODS a promising tool for comprehensive understanding of stochastic membrane processes.
54 citations
TL;DR: In this paper, the authors show that the optimal observable typically does not commute with the Hamiltonian and hence would not be available in a classical two-level system, and they extend this bound to a large class of feedback-driven quantum engines operating periodically and in finite time.
Abstract: A genuine feature of projective quantum measurements is that they inevitably alter the mean energy of the observed system if the measured quantity does not commute with the Hamiltonian. Compared to the classical case, Jacobs proved that this additional energetic cost leads to a stronger bound on the work extractable after a single measurement from a system initially in thermal equilibrium (2009 Phys. Rev. A 80 012322). Here, we extend this bound to a large class of feedback-driven quantum engines operating periodically and in finite time. The bound thus implies a natural definition for the efficiency of information to work conversion in such devices. For a simple model consisting of a laser-driven two-level system, we maximize the efficiency with respect to the observable whose measurement is used to control the feedback operations. We find that the optimal observable typically does not commute with the Hamiltonian and hence would not be available in a classical two level system. This result reveals that periodic feedback engines operating in the quantum realm can exploit quantum coherences to enhance efficiency.
50 citations
TL;DR: A coarse-graining method is presented that maps a model comprising two coupled degrees of freedom which represent motor and probe particle to such an effective one-particle model by eliminating the dynamics of the probe particle in a thermodynamically and dynamically consistent way.
Abstract: Many single-molecule experiments for molecular motors comprise not only the motor but also large probe particles coupled to it. The theoretical analysis of these assays, however, often takes into account only the degrees of freedom representing the motor. We present a coarse-graining method that maps a model comprising two coupled degrees of freedom which represent motor and probe particle to such an effective one-particle model by eliminating the dynamics of the probe particle in a thermodynamically and dynamically consistent way. The coarse-grained rates obey a local detailed balance condition and reproduce the net currents. Moreover, the average entropy production as well as the thermodynamic efficiency is invariant under this coarse-graining procedure. Our analysis reveals that only by assuming unrealistically fast probe particles, the coarse-grained transition rates coincide with the transition rates of the traditionally used one-particle motor models. Additionally, we find that for multicyclic motors the stall force can depend on the probe size. We apply this coarse-graining method to specific case studies of the ${\text{F}}_{1}$-ATPase and the kinesin motor.
TL;DR: This study demonstrates the utility of optical stretching, which is easily combined with microfluidic delivery, for the future serial, high-throughput study of the mechanical and thermodynamic properties of phospholipid vesicles.
Abstract: Phospholipid vesicles are common model systems for cell membranes. Important aspects of the membrane function relate to its mechanical properties. Here we have investigated the deformation behaviour of phospholipid vesicles in a dual-beam laser trap, also called an optical stretcher. This study explicitly makes use of the inherent heating present in such traps to investigate the dependence of vesicle deformation on temperature. By using lasers with different wavelengths, optically induced mechanical stresses and temperature increase can be tuned fairly independently with a single setup. The phase transition temperature of vesicles can be clearly identified by an increase in deformation. In the case of no heating effects, a minimal model for drop deformation in an optical stretcher and a more specific model for vesicle deformation that takes explicitly into account the angular dependence of the optical stress are presented to account for the experimental results. Elastic constants are extracted from the fitting procedures, which agree with literature data. This study demonstrates the utility of optical stretching, which is easily combined with microfluidic delivery, for the future serial, high-throughput study of the mechanical and thermodynamic properties of phospholipid vesicles.
TL;DR: Lower and upper bounds on the skewness and kurtosis associated with the cycle completion time of unicyclic enzymatic reaction schemes are obtained and it is demonstrated that evaluating these higher order moments with single molecule data can lead to information about the enzyme scheme that is not contained in the randomness parameter.
Abstract: We obtain lower and upper bounds on the skewness and kurtosis associated with the cycle completion time of unicyclic enzymatic reaction schemes. Analogous to a well-known lower bound on the randomness parameter, the lower bounds on skewness and kurtosis are related to the number of intermediate states in the underlying chemical reaction network. Our results demonstrate that evaluating these higher order moments with single molecule data can lead to information about the enzymatic scheme that is not contained in the randomness parameter.
TL;DR: In this paper, an effective Monte Carlo scheme was proposed to simulate the nucleation and growth of adhesion domains within a system of the size of a cell for tens of seconds without loss of accuracy.
Abstract: Macromolecular complexation leading to coupling of two or more cellular membranes is a crucial step in a number of biological functions of the cell. While other mechanisms may also play a role, adhesion always involves the fluctuations of deformable membranes, the diffusion of proteins and the molecular binding and unbinding. Because these stochastic processes couple over a multitude of time and length scales, theoretical modeling of membrane adhesion has been a major challenge. Here we present an effective Monte Carlo scheme within which the effects of the membrane are integrated into local rates for molecular recognition. The latter step in the Monte Carlo approach enables us to simulate the nucleation and growth of adhesion domains within a system of the size of a cell for tens of seconds without loss of accuracy, as shown by comparison to 106 times more expensive Langevin simulations. To perform this validation, the Langevin approach was augmented to simulate diffusion of proteins explicitly, together with reaction kinetics and membrane dynamics. We use the Monte Carlo scheme to gain deeper insight to the experimentally observed radial growth of micron sized adhesion domains, and connect the effective rate with which the domain is growing to the underlying microscopic events. We thus demonstrate that our technique yields detailed information about protein transport and complexation in membranes, which is a fundamental step toward understanding even more complex membrane interactions in the cellular context.
TL;DR: It is shown that a rich phase diagram emerges from the competition between binding, cooperativity, molecular crowding and membrane spreading, which may shed light on the structuring of adhesions in the contact zones between two living cells.
TL;DR: It is shown that, inter alia, monitoring the time spent in the phosphorylated state of the protein leads to a finite uncertainty only if there is dissipation, whereas the uncertainty obtained from the activity of the transitions of the internal protein can reach the Berg-Purcell limit even in equilibrium.
Abstract: We derive expressions for the dispersion for two classes of random variables in Markov processes. Random variables such as current and activity pertain to the first class, which is composed of random variables that change whenever a jump in the stochastic trajectory occurs. The second class corresponds to the time the trajectory spends in a state (or cluster of states). While the expression for the first class follows straightforwardly from known results in the literature, we show that a similar formalism can be used to derive an expression for the second class. As an application, we use this formalism to analyze a cellular two-component network estimating an external ligand concentration. The uncertainty related to this external concentration is calculated by monitoring different random variables related to an internal protein. We show that, inter alia, monitoring the time spent in the phosphorylated state of the protein leads to a finite uncertainty only if there is dissipation, whereas the uncertainty obtained from the activity of the transitions of the internal protein can reach the Berg-Purcell limit even in equilibrium.
TL;DR: An effective Monte Carlo scheme within which the effects of the membrane are integrated into local rates for molecular recognition is presented, which yields detailed information about protein transport and complexation in membranes, a fundamental step toward understanding even more complex membrane interactions in the cellular context.
Abstract: Macromolecular complexation leading to coupling of two or more cellular membranes is a crucial step in a number of biological functions of the cell. While other mechanisms may also play a role, adhesion always involves the fluctuations of deformable membranes, the diffusion of proteins and the molecular binding and unbinding. Because these stochastic processes couple over a multitude of time and length scales, theoretical modeling of membrane adhesion has been a major challenge. Here we present an effective Monte Carlo scheme within which the effects of the membrane are integrated into local rates for molecular recognition. The latter step in the Monte Carlo approach enables us to simulate the nucleation and growth of adhesion domains within a system of the size of a cell for tens of seconds without loss of accuracy, as shown by comparison to $10^6$ times more expensive Langevin simulations. To perform this validation, the Langevin approach was augmented to simulate diffusion of proteins explicitly, together with reaction kinetics and membrane dynamics. We use the Monte Carlo scheme to gain deeper insight to the experimentally observed radial growth of micron sized adhesion domains, and connect the effective rate with which the domain is growing to the underlying microscopic events. We thus demonstrate that our technique yields detailed information about protein transport and complexation in membranes, which is a fundamental step toward understanding even more complex membrane interactions in the cellular context.
TL;DR: In this paper, the effect of nonzero affinity driving receptors out of equilibrium affects sensitivity, and an intriguing analogy between sensing with nonequilibrium receptors and kinetic proofreading is established, showing that the increase in integrated sensitivity is equivalent to the decrease of the error in KP.
Abstract: For a paradigmatic model of chemotaxis, we analyze the effect how a nonzero affinity driving receptors out of equilibrium affects sensitivity. This affinity arises whenever changes in receptor activity involve ATP hydrolysis. The sensitivity integrated over a ligand concentration range is shown to be enhanced by the affinity, providing a measure of how much energy consumption improves sensing. With this integrated sensitivity we can establish an intriguing analogy between sensing with nonequilibrium receptors and kinetic proofreading: the increase in integrated sensitivity is equivalent to the decrease of the error in kinetic proofreading. The influence of the occupancy of the receptor on the phosphorylation and dephosphorylation reaction rates is shown to be crucial for the relation between integrated sensitivity and affinity. This influence can even lead to a regime where a nonzero affinity decreases the integrated sensitivity, which corresponds to anti-proofreading.