Kinetic vs. energetic discrimination in biological copying

We study stochastic copying schemes in which discrimination between a right and a wrong match is achieved via different kinetic barriers or different binding energies of the two matches. We demonstrate that, in single-step reactions, the two discrimination mechanisms are strictly alternative and can not be mixed to further reduce the error fraction. Close to the lowest error limit, kinetic discrimination results in a diverging copying velocity and dissipation per copied bit. On the opposite, energetic discrimination reaches its lowest error limit in an adiabatic regime where dissipation and velocity vanish. By analyzing experimentally measured kinetic rates of two DNA polymerases, T7 and Pol{\gamma}, we argue that one of them operates in the kinetic and the other in the energetic regime. Finally, we show how the two mechanisms can be combined in copying schemes implementing error correction through a proofreading pathwayComment: 18 pages, 10 figures, main text+supplementary information. Accepted for publication in Phys. Rev. Let

The free energy cost of reducing noise while maintaining a high sensitivity

Living systems need to be highly responsive, and also to keep fluctuations low. These goals are incompatible in equilibrium systems due to the Fluctuation Dissipation Theorem (FDT). Here, we show that biological sensory systems, driven far from equilibrium by free energy consumption, can reduce their intrinsic fluctuations while maintaining high responsiveness. By developing a continuum theory of the E. coli chemotaxis pathway, we demonstrate that adaptation can be understood as a non-equilibrium phase transition controlled by free energy dissipation, and it is characterized by a breaking of the FDT. We show that the maximum response at short time is enhanced by free energy dissipation. At the same time, the low frequency fluctuations and the adaptation error decrease with the free energy dissipation algebraically and exponentially, respectively

Thermodynamics of Error Correction

Information processing at the molecular scale is limited by thermal fluctuations. This can cause undesired consequences in copying information since thermal noise can lead to errors that can compromise the functionality of the copy. For example, a high error rate during DNA duplication can lead to cell death. Given the importance of accurate copying at the molecular scale, it is fundamental to understand its thermodynamic features. In this paper, we derive a universal expression for the copy error as a function of entropy production and {\cred work dissipated by the system during wrong incorporations}. Its derivation is based on the second law of thermodynamics, hence its validity is independent of the details of the molecular machinery, be it any polymerase or artificial copying device. Using this expression, we find that information can be copied in three different regimes. In two of them, work is dissipated to either increase or decrease the error. In the third regime, the protocol extracts work while correcting errors, reminiscent of a Maxwell demon. As a case study, we apply our framework to study a copy protocol assisted by kinetic proofreading, and show that it can operate in any of these three regimes. We finally show that, for any effective proofreading scheme, error reduction is limited by the chemical driving of the proofreading reaction.Comment: 9 pages, 5 figure

Protocols for copying and proofreading in template-assisted polymerization

We discuss how information encoded in a template polymer can be stochastically copied into a copy polymer. We consider four different stochastic copy protocols of increasing complexity, inspired by building blocks of the mRNA translation pathway. In the rst protocol, monomer incorporation occurs in a single stochastic transition. We then move to a more elaborate protocol in which an intermediate step can be used for error correction. Finally, we discuss the operating regimes of two kinetic proofreading protocols: one in which proofreading acts from the nal copying step, and one in which it acts from an intermediate step. We review known results for these models and, in some cases, extend them to analyze all possible combinations of energetic and kinetic discrimination. We show that, in each of these protocols, only a limited number of these combinations leads to an improvement of the overall copying accuracyPeer ReviewedPostprint (published version

Dynamic curvature regulation accounts for the symmetric and asymmetric beats of Chlamydomonas flagella

Axonemal dyneins are the molecular motors responsible for the beating of cilia and flagella. These motors generate sliding forces between adjacent microtubule doublets within the axoneme, the motile cytoskeletal structure inside the flagellum. To create regular, oscillatory beating patterns, the activities of the axonemal dyneins must be coordinated both spatially and temporally. It is thought that coordination is mediated by stresses or strains that build up within the moving axoneme, but it is not known which components of stress or strain are involved, nor how they feed back on the dyneins. To answer this question, we used isolated, reactivate axonemes of the unicellular alga Chlamydomonas as a model system. We derived a theory for beat regulation in a two-dimensional model of the axoneme. We then tested the theory by measuring the beat waveforms of wild type axonemes, which have asymmetric beats, and mutant axonemes, in which the beat is nearly symmetric, using high-precision spatial and temporal imaging. We found that regulation by sliding forces fails to account for the measured beat, due to the short lengths of Chlamydomonas cilia. We found that regulation by normal forces (which tend to separate adjacent doublets) cannot satisfactorily account for the symmetric waveforms of the mbo2 mutants. This is due to the model's failure to produce reciprocal inhibition across the axes of the symmetrically beating axonemes. Finally, we show that regulation by curvature accords with the measurements. Unexpectedly, we found that the phase of the curvature feedback indicates that the dyneins are regulated by the dynamic (i.e. time-varying) component of axonemal curvature, but not by the static one. We conclude that a high-pass filtered curvature signal is a good candidate for the signal that feeds back to coordinate motor activity in the axoneme

Thermodynamic costs of information processing in sensory adaption

Biological sensory systems react to changes in their surroundings. They are characterized by fast response and slow adaptation to varying environmental cues. Insofar as sensory adaptive systems map environmental changes to changes of their internal degrees of freedom, they can be regarded as computational devices manipulating information. Landauer established that information is ultimately physical, and its manipulation subject to the entropic and energetic bounds of thermodynamics. Thus the fundamental costs of biological sensory adaptation can be elucidated by tracking how the information the system has about its environment is altered. These bounds are particularly relevant for small organisms, which unlike everyday computers operate at very low energies. In this paper, we establish a general framework for the thermodynamics of information processing in sensing. With it, we quantify how during sensory adaptation information about the past is erased, while information about the present is gathered. This process produces entropy larger than the amount of old information erased and has an energetic cost bounded by the amount of new information written to memory. We apply these principles to the E. coli's chemotaxis pathway during binary ligand concentration changes. In this regime, we quantify the amount of information stored by each methyl group and show that receptors consume energy in the range of the information-theoretic minimum. Our work provides a basis for further inquiries into more complex phenomena, such as gradient sensing and frequency response.Comment: 17 pages, 6 figure

Contribution of increasing plasma membrane to the energetic cost of early zebrafish embryogenesis

© The Author(s), 2020. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Rodenfels, J., Sartori, P., Golfier, S., Nagendra, K., Neugebauer, K. M., & Howard, J. Contribution of increasing plasma membrane to the energetic cost of early zebrafish embryogenesis. Molecular Biology of the Cell, 31(7), (2020): 520-526, doi:10.1091/mbc.E19-09-0529.How do early embryos allocate the resources stored in the sperm and egg? Recently, we established isothermal calorimetry to measure heat dissipation by living zebra­fish embryos and to estimate the energetics of specific developmental events. During the reductive cleavage divisions, the rate of heat dissipation increases from ∼60 nJ · s−1 at the two-cell stage to ∼90 nJ · s−1 at the 1024-cell stage. Here we ask which cellular process(es) drive this increasing energetic cost. We present evidence that the cost is due to the increase in the total surface area of all the cells of the embryo. First, embryo volume stays constant during the cleavage stage, indicating that the increase is not due to growth. Second, the heat increase is blocked by nocodazole, which inhibits DNA replication, mitosis, and cell division; this suggests some aspect of cell proliferation contributes to these costs. Third, the heat increases in proportion to the total cell surface area rather than total cell number. Fourth, the heat increase falls within the range of the estimated costs of maintaining and assembling plasma membranes and associated proteins. Thus, the increase in total plasma membrane associated with cell proliferation is likely to contribute appreciably to the total energy budget of the embryo.The analysis of these data was initiated in the 2019 Physical Biology of the Cell course at the Marine Biological Laboratory in Woods Hole, MA. We acknowledge the support and feedback from the course directors and participants. This work was supported by funding from EMBO Long-Term Fellowship ALTF 754–2015 (to J.R.), the Eric and Wendy Schmidt Membership in Biology at the Institute for Advanced Study (to P.S.), National Institutes of Health (NIH) R21 HD094013 (to K.M.N.), and NIH R01 GM110386 (to J.H.). Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the NIH

Geometry of environment-to-phenotype mapping: Unifying adaptation strategies in varying environments

Biological organisms exhibit diverse strategies for adapting to varying environments. For example, a population of organisms may express the same phenotype in all environments (`unvarying strategy'), or follow environmental cues and express alternative phenotypes to match the environment (`tracking strategy'), or diversify into coexisting phenotypes to cope with environmental uncertainty (`bet-hedging strategy'). We introduce a general framework for studying how organisms respond to environmental variations, which models an adaptation strategy by an abstract mapping from environmental cues to phenotypic traits. Depending on the accuracy of environmental cues and the strength of natural selection, we find different adaptation strategies represented by mappings that maximize the longterm growth rate of a population. The previously studied strategies emerge as special cases of our model: the tracking strategy is favorable when environmental cues are accurate, whereas when cues are noisy, organisms can either use an unvarying strategy or, remarkably, use the uninformative cue as a source of randomness to bet-hedge. Our model of the environment-to-phenotype mapping is based on a network with hidden units; the performance of the strategies is shown to rely on having a high-dimensional internal representation, which can even be random.Comment: 12 pages, plus supplemental figure