12 research outputs found
Fluctuating Currents in Stochastic Thermodynamics I. Gauge Invariance of Asymptotic Statistics
Stochastic Thermodynamics uses Markovian jump processes to model random
transitions between observable mesoscopic states. Physical currents are
obtained from anti-symmetric jump observables defined on the edges of the graph
representing the network of states. The asymptotic statistics of such currents
are characterized by scaled cumulants. In the present work, we use the
algebraic and topological structure of Markovian models to prove a gauge
invariance of the scaled cumulant-generating function. Exploiting this
invariance yields an efficient algorithm for practical calculations of
asymptotic averages and correlation integrals. We discuss how our approach
generalizes the Schnakenberg decomposition of the average entropy-production
rate, and how it unifies previous work. The application of our results to
concrete models is presented in an accompanying publication.Comment: PACS numbers: 05.40.-a, 05.70.Ln, 02.50.Ga, 02.10.Ox. An accompanying
pre-print "Fluctuating Currents in Stochastic Thermodynamics II. Energy
Conversion and Nonequilibrium Response in Kinesin Models" by the same authors
is available as arXiv:1504.0364
Dissipation in noisy chemical networks: The role of deficiency
We study the effect of intrinsic noise on the thermodynamic balance of
complex chemical networks subtending cellular metabolism and gene regulation. A
topological network property called deficiency, known to determine the
possibility of complex behavior such as multistability and oscillations, is
shown to also characterize the entropic balance. In particular, only when
deficiency is zero does the average stochastic dissipation rate equal that of
the corresponding deterministic model, where correlations are disregarded. In
fact, dissipation can be reduced by the effect of noise, as occurs in a toy
model of metabolism that we employ to illustrate our findings. This phenomenon
highlights that there is a close interplay between deficiency and the
activation of new dissipative pathways at low molecule numbers.Comment: 10 Pages, 6 figure
Fluctuation Spectra and Coarse Graining in Stochastic Dynamics
Fluctuations in small biological systems can be crucial for their function.
Large-deviation theory characterizes such rare events from the perspective of
stochastic processes. In most cases it is very difficult to directly determine
the large-deviation functions. Circumventing this necessity, I present a method
to quantify the fluctuation spectra for arbitrary Markovian models with finite
state space. Under non-equilibrium conditions, current-like observables are of
special interest. The space of all current-like observables has a natural
decomposition into orthogonal complements. Remarkably, the fluctuation spectrum
of any observable is entirely determined by only one of these components. The
method is applied to study differences of fluctuations in setups sampling the
same dynamics at different resolutions. Coarse graining relates these models
and can be done in a way that preserves expectation values of observables.
However, the effects of the coarse graining on the fluctuations are not
obvious. These differences are explicitly worked out for a simple model system.Comment: Master's thesis, 79 pages, 21 figure
Fluctuating Currents in Stochastic Thermodynamics II. Energy Conversion and Nonequilibrium Response in Kinesin Models
Unlike macroscopic engines, the molecular machinery of living cells is
strongly affected by fluctuations. Stochastic Thermodynamics uses Markovian
jump processes to model the random transitions between the chemical and
configurational states of these biological macromolecules. A recently developed
theoretical framework [Wachtel, Vollmer, Altaner: "Fluctuating Currents in
Stochastic Thermodynamics I. Gauge Invariance of Asymptotic Statistics"]
provides a simple algorithm for the determination of macroscopic currents and
correlation integrals of arbitrary fluctuating currents. Here, we use it to
discuss energy conversion and nonequilibrium response in different models for
the molecular motor kinesin. Methodologically, our results demonstrate the
effectiveness of the algorithm in dealing with parameter-dependent stochastic
models. For the concrete biophysical problem our results reveal two interesting
features in experimentally accessible parameter regions: The validity of a
non-equilibrium Green--Kubo relation at mechanical stalling as well as negative
differential mobility for superstalling forces.Comment: PACS numbers: 05.70.Ln, 05.40.-a, 87.10.Mn, 87.16.Nn. An accompanying
publication "Fluctuating Currents in Stochastic Thermodynamics I. Gauge
Invariance of Asymptotic Statistics" is available at
http://arxiv.org/abs/1407.206
Thermodynamically Consistent Coarse Graining of Biocatalysts beyond Michaelis--Menten
Starting from the detailed catalytic mechanism of a biocatalyst we provide a
coarse-graining procedure which, by construction, is thermodynamically
consistent. This procedure provides stoichiometries, reaction fluxes (rate
laws), and reaction forces (Gibbs energies of reaction) for the coarse-grained
level. It can treat active transporters and molecular machines, and thus
extends the applicability of ideas that originated in enzyme kinetics. Our
results lay the foundations for systematic studies of the thermodynamics of
large-scale biochemical reaction networks. Moreover, we identify the conditions
under which a relation between one-way fluxes and forces holds at the
coarse-grained level as it holds at the detailed level. In doing so, we clarify
the speculations and broad claims made in the literature about such a general
flux--force relation. As a further consequence we show that, in contrast to
common belief, the second law of thermodynamics does not require the currents
and the forces of biochemical reaction networks to be always aligned.Comment: 14 pages, 5 figure
Nonequilibrium Thermodynamics in Biology: From Molecular Motors to Metabolic Pathways
Biological systems need to exchange energy and matter with their environment in order to stay functional or “alive”. This exchange has to obey the laws of thermodynamics: energy cannot be created and exchange comes at the cost of dissipation, which limits the efficiency of biological function. Additionally, subcellular processes that involve only few molecules are stochastic in their dynamics and a consistent theoretical modeling has to account for that.
This dissertation connects recent development in nonequilibrium thermodynamics with approaches taken in biochemical modeling. I start by a short introduction to thermodynamics and statistical mechanics, with a special emphasis on large deviation theory and stochastic thermodynamics. Building on that, I present a general theory for the thermodynamic analysis of networks of chemical reactions that are open to the exchange of matter.
As a particularly insightful concrete example I discuss the mechanochemical energy conversion in stochastic models of a molecular motor protein, and show how a similar analysis can be performed for more general models. Furthermore, I compare the dissipation in stochastically and deterministically modeled open chemical networks, and present a class of chemical networks that displays exact agreement for arbitrary abundance of chemical species and arbitrary distance from thermodynamic equilibrium. My major achievement is a thermodynamically consistent coarse-graining procedure for biocatalysts, which are ubiquitous in molecular cell biology. Finally, I discuss the thermodynamics of unbranched enzymatic chains
Free-energy transduction in chemical reaction networks: From enzymes to metabolism
We provide a rigorous definition of free-energy transduction and its
efficiency in arbitrary -- linear or nonlinear -- open chemical reaction
networks (CRNs) operating at steady state. Our method is based on the knowledge
of the stoichiometric matrix and of the chemostatted species (i.e. the species
maintained at constant concentration by the environment) to identify the
fundamental currents and forces contributing to the entropy production.
Transduction occurs when the current of a stoichiometrically balanced process
is driven against its spontaneous direction (set by its force) thanks to other
processes flowing along their spontaneous direction. In these regimes, open
CRNs operate as thermodynamic machines. After exemplifying these general ideas
using toy models, we analyze central energy metabolism. We relate the
fundamental currents to metabolic pathways and discuss the efficiency with
which they are able to transduce free energy.Comment: 17 pages, 17 figues, (v2: IV.A.3 & IV.C modified, VI expanded
Global Retinoblastoma Presentation and Analysis by National Income Level.
Importance: Early diagnosis of retinoblastoma, the most common intraocular cancer, can save both a child's life and vision. However, anecdotal evidence suggests that many children across the world are diagnosed late. To our knowledge, the clinical presentation of retinoblastoma has never been assessed on a global scale. Objectives: To report the retinoblastoma stage at diagnosis in patients across the world during a single year, to investigate associations between clinical variables and national income level, and to investigate risk factors for advanced disease at diagnosis. Design, Setting, and Participants: A total of 278 retinoblastoma treatment centers were recruited from June 2017 through December 2018 to participate in a cross-sectional analysis of treatment-naive patients with retinoblastoma who were diagnosed in 2017. Main Outcomes and Measures: Age at presentation, proportion of familial history of retinoblastoma, and tumor stage and metastasis. Results: The cohort included 4351 new patients from 153 countries; the median age at diagnosis was 30.5 (interquartile range, 18.3-45.9) months, and 1976 patients (45.4%) were female. Most patients (n = 3685 [84.7%]) were from low- and middle-income countries (LMICs). Globally, the most common indication for referral was leukocoria (n = 2638 [62.8%]), followed by strabismus (n = 429 [10.2%]) and proptosis (n = 309 [7.4%]). Patients from high-income countries (HICs) were diagnosed at a median age of 14.1 months, with 656 of 666 (98.5%) patients having intraocular retinoblastoma and 2 (0.3%) having metastasis. Patients from low-income countries were diagnosed at a median age of 30.5 months, with 256 of 521 (49.1%) having extraocular retinoblastoma and 94 of 498 (18.9%) having metastasis. Lower national income level was associated with older presentation age, higher proportion of locally advanced disease and distant metastasis, and smaller proportion of familial history of retinoblastoma. Advanced disease at diagnosis was more common in LMICs even after adjusting for age (odds ratio for low-income countries vs upper-middle-income countries and HICs, 17.92 [95% CI, 12.94-24.80], and for lower-middle-income countries vs upper-middle-income countries and HICs, 5.74 [95% CI, 4.30-7.68]). Conclusions and Relevance: This study is estimated to have included more than half of all new retinoblastoma cases worldwide in 2017. Children from LMICs, where the main global retinoblastoma burden lies, presented at an older age with more advanced disease and demonstrated a smaller proportion of familial history of retinoblastoma, likely because many do not reach a childbearing age. Given that retinoblastoma is curable, these data are concerning and mandate intervention at national and international levels. Further studies are needed to investigate factors, other than age at presentation, that may be associated with advanced disease in LMICs