Due to large fluctuations in cellular environments, transfer of information in biological processes without regulation is inherently error-prone. The mechanistic details of error-reducing mechanisms in biological copying processes have been a subject of active research; however, how error reduction of a process is balanced with its thermodynamic cost and dynamical properties remain largely unexplored. Here, we study the error reducing strategies in light of the recently discovered thermodynamic uncertainty relation (TUR) that sets a physical bound to the cost-precision trade-off relevant in general dissipative processes. We found that the two representative copying processes, DNA replication by the exonuclease-deficient T7 DNA polymerase and mRNA translation by the \textit{E. coli} ribosome, reduce the error rates to biologically acceptable levels while also optimizing the processes close to the physical limit dictated by TUR.
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 ve…
Templated copying is the central operation by which biology produces complex molecules. Cells copy sequence information from DNA to RNA and on into proteins, which are the molecules responsible for the function and regulation of cellular systems. In the templated copying process the template catalyses the formation of a second molecule carrying the same sequence. Traditionally, people have ignored the separation of the template and copy at the end of the process, but separation is necessary and fundamentally changes the thermodynamics of the process. In general, creating an accurate polymer co…
Living cells use readout molecules to record the state of receptor proteins, similar to measurements or copies in typical computational devices. But is this analogy rigorous? Can cells be optimally efficient, and if not, why? We show that, as in computation, a canonical biochemical readout network generates correlations; extracting no work from these correlations sets a lower bound on dissipation. For general input, the biochemical network cannot reach this bound, even with arbitrarily slow reactions or weak thermodynamic driving. It faces an accuracy-dissipation trade-off that is qualitativel…
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 incorpo…
We review the trade-offs between speed, fluctuations, and thermodynamic cost involved with biological processes in nonequilibrium states, and discuss how optimal these processes are in light of the universal bound set by the thermodynamic uncertainty relation (TUR). The values of the uncertainty product $\mathcal{Q}$ of TUR, which can be used as a measure of the precision of enzymatic processes realized for a given thermodynamic cost, are suboptimal when the substrate concentration $[S]$ is at the Michaelis constant ($K_\text{M}$), and some of the key biological processes are found to work aro…
In this work we to develop a general statistical mechanic formalism to study systems restricted to surfaces of revolution, these are a very well model to study the termodinamical properties of microbiological systems and macromolecules lies on biological membranes such as cellular well.
DNA, RNA and proteins are among the most important macromolecules in a living cell. These molecules are polymerized by molecular machines. These natural nano-machines polymerize such macromolecules, adding one monomer at a time, using another linear polymer as the corresponding template. The machine utilizes input chemical energy to move along the template which also serves as a track for the movements of the machine. In the Alan Turing year 2012, it is worth pointing out that these machines are "tape-copying Turing machines". We review the operational mechanisms of the polymerizer machines an…
Life is a complex biological phenomenon represented by numerous chemical, physical and biological processes performed by a biothermodynamic system/cell/organism. Both living organisms and inanimate objects are subject to aging, a biological and physicochemical process characterized by changes in biological and thermodynamic state. Thus, the same physical laws govern processes in both animate and inanimate matter. All life processes lead to change of an organism's state. The change of biological and thermodynamic state of an organism in time underlies all of three kinds of aging (chronological,…
Based on a thermodynamic analysis of the kinetic model for the protein phosphorylation-dephosphorylation cycle, we study the ATP (or GTP) energy utilization of this ubiquitous biological signal transduction process. It is shown that the free energy from hydrolysis inside cells, $ΔG$ (phosphorylation potential), controls the amplification and sensitivity of the switch-like cellular module; the response coefficient of the sensitivity amplification approaches the optimal 1 and the Hill coefficient increases with increasing $ΔG$. We discover that zero-order ultrasensitivity is mathematically equiv…
Understanding the thermodynamics of the duplication process is a fundamental step towards a comprehensive physical theory of biological systems. However, the immense complexity of real cells obscures the fundamental tensions between energy gradients and entropic contributions that underlie duplication. The study of synthetic, feasible systems reproducing part of the key ingredients of living entities but overcoming major sources of biological complexity is of great relevance to deepen the comprehension of the fundamental thermodynamic processes underlying life and its prevalence. In this paper…
The nanoscopic isothermal machines are not only energy but also information transducers. We show that the generalized fluctuation theorem with information creation and entropy reduction can be fulfilled for the enzymatic molecular machines with the stochastic dynamics, which offers a choice of the work performance in a variety of ways. A model of such dynamics, specified by a critical complex network, is investigated. The main conclusion of the study is that the processing of free energy has to be distinguished from the processing of organization, which we identify with an adequately defined t…
Directional motion of nanoscale motors and driven particles in an isothermal environment costs a finite amount of energy despite zero work as decreed by the 2nd law, but quantifying this general limit remains difficult. Here we derive a universal equality linking directional fidelity of an arbitrary nanoscale object to the least possible energy driving it. The fidelity-energy equality depends on the environmental temperature alone; any lower energy would violate the 2nd law in a thought experiment. Real experimental proof for the equality comes from force-induced motion of biological nanomotor…
The most important thermodynamic work performed by life today is the dissipation of the solar photon flux into heat through organic pigments in water. From this thermodynamic perspective, biological evolution is thus just the dispersal of organic pigments and water throughout Earth's surface, while adjusting the gases of Earth's atmosphere to allow the most intense part of the solar spectrum to penetrate the atmosphere and reach the surface to be intercepted by these pigments. The covalent bonding of atoms in organic pigments provides excited levels compatible with the energies of these photon…
Recent advances in nonequilibrium statistical physics have provided unprecedented insight into the thermodynamics of dynamic processes. The author recently used these advances to extend Landauer's semi-formal reasoning concerning the thermodynamics of bit erasure, to derive the minimal free energy required to implement an arbitrary computation. Here, I extend this analysis, deriving the minimal free energy required by an organism to run a given (stochastic) map $π$ from its sensor inputs to its actuator outputs. I use this result to calculate the input-output map $π$ of an organism that optima…
Local imperfect feedback control in non-equilibrium biophysical systems enabled by thermodynamic constraints
The University of Chicago（芝加哥大学）；The Chicago Center for Theoretical Chemistry（芝加哥理论化学中心）；Department of Chemistry, The University of Chicago（芝加哥大学化学系）；The James Franck Institute（詹姆斯·弗兰克研究所）
Membrane tubulation is a ubiquitous process that occurs both at the plasma membrane and on the membranes of intracellular organelles. These tubulation events are known to be mediated by forces applied on the membrane either due to motor proteins, by polymerization of the cytoskeleton, or due to the interactions between membrane proteins binding onto the membrane. The numerous experimental observations of tube formation have been amply supported by mathematical modeling of the associated membrane mechanics and have provided insights into the force-displacement relationships of membrane tubes. R…
Membrane based nanocalorimeters have been developed for ac calorimetry experiments. It has allowed highly sensitive measurements of heat capacity from solid state physics to complex systems like polymers and proteins. In this article we review what has been developed in ac calorimetry toward the measurement of very small systems. Firstly, at low temperature ac calorimetry using silicon membrane permits the measurement of superconducting sample having geometry down to the nanometer scale. New phase transitions have been found in these nanosystems illustrated by heat capacity jumps versus the ap…
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 th…
A fundamental question in biology is how cell populations evolve into different subtypes based on homogeneous processes at the single cell level. Here we show that population bimodality can emerge even when biological processes are homogenous at the cell level and the environment is kept constant. Our model is based on the stochastic partitioning of a cell component with an optimal copy number. We show that the existence of unimodal or bimodal distributions depends on the variance of partition errors and the growth rate tolerance around the optimal copy number. In particular, our theory provid…
Cell division is an essential biological process, and regulation of cell division is of relevance for many important fields of biology and medicine. Introducing exogenous substances, such as nanoparticles, into the nucleus, has been experimentally studied to regulate the division of cells. Herein we considered this phenomenon from a general view of energetics. Through analyzing the thermodynamics during the cell division process, we investigated the optimal symmetry for cell division and the effect of nanoparticles on the energy barriers. The presence of nanoparticles inside cell nucleus might…
Most proteins must remain soluble in the cytosol in order to perform their biological functions. To protect against undesired protein aggregation, living cells maintain a population of molecular chaperones that ensure the solubility of the proteome. Here we report simulations of a lattice model of interacting proteins to understand how low concentrations of passive molecular chaperones, such as small heat-shock proteins, suppress thermodynamic instabilities in protein solutions. Given fixed concentrations of chaperones and client proteins, the solubility of the proteome can be increased by tun…
The capacity to integrate information is a prominent feature of biological and cognitive systems. Integrated Information Theory (IIT) provides a mathematical approach to quantify the level of integration in a system, yet its computational cost generally precludes its applications beyond relatively small models. In consequence, it is not yet well understood how integration scales up with the size of a system or with different temporal scales of activity, nor how a system maintains its integration as its interacts with its environment. Here, we show for the first time how measures of information…
The high accuracy exhibited by biological information transcription processes is due to kinetic proofreading, i.e., by a mechanism which reduces the error rate of the information-handling process by driving it out of equilibrium. We provide a consistent thermodynamic description of enzyme-assisted assembly processes involving competing substrates, in a Master Equation framework. We introduce and evaluate a measure of the efficiency based on rigorous non-equilibrium inequalities. The performance of several proofreading models are thus analyzed and the related time, dissipation and efficiency vs…
Photosynthesis has been a long-standing research interest due to its fundamental importance. Recently, studies on photosynthesis processes also have inspired attention from a thermodynamical aspect when considering photosynthetic apparatuses as biological quantum heat engines. Quantum coherence is shown to play a crucial role in enhancing the performance of these quantum heat engines. Based on the experimentally reported structure, we propose a quantum heat engine model with a non-Markovian vibrational mode. We show that one can obtain a performance enhancement easily for a wide range of param…
The biological cell exhibits a fantastic range of behaviors, but ultimately these are governed by a handful of physical and chemical principles. Here we explore simple theory, known for decades and based on the simple thermodynamics of mixtures of ideal gases, which illuminates several key functions performed within the cell. Our focus is the free-energy-driven import and export of molecules, such as nutrients and other vital compounds, via transporter proteins. Complementary to a thermodynamic picture is a description of transporters via "mass-action" chemical kinetics, which lends further in…
Even in the steady-state, the number of biomolecules in living cells fluctuates dynamically; and the frequency spectrum of this chemical fluctuation carries valuable information about the mechanism and the dynamics of the intracellular reactions creating these biomolecules. Although recent advances in single-cell experimental techniques enable the direct monitoring of the time-traces of the biological noise in each cell, the development of the theoretical tools needed to extract the information encoded in the stochastic dynamics of intracellular chemical fluctuation is still in its adolescence…
For more than 100 years, humanity (both specialists and enthusiastic laics) has been searching for extraterrestrial life hoping we are not alone. The first step in the quest for extraterrestrial life is to define what and where exactly to look for. Thus, the basic definition of living matter is a conditio sine qua non for the quest. The diversity of species on Earth is so large that our quest for extraterrestrial life cannot be limited to forms and shapes present and known to us from our environment. However, there are two formal conditions that must be fulfilled in order for something to be a…
Biological molecular machines are bifunctional enzymes that catalyze two processes: one donating free energy and the other accepting it. Recent studies show that most protein enzymes have rich stochastic dynamics of transitions between the multitude of conformation substates that make up their native state. This dynamics often manifests itself in fluctuating rates of the catalyzed processes and the presence of short-term memory. For such stochastic dynamics, after dividing the free energy into operational and organizational energy, we proved the generalized fluctuation theorem, which leads to …
