Genome-wide mapping of human DNA replication by optical replication mapping supports a stochastic model of eukaryotic replication.

The heterogeneous nature of eukaryotic replication kinetics and the low efficiency of individual initiation sites make mapping the location and timing of replication initiation in human cells difficult. To address this challenge, we have developed optical replication mapping (ORM), a high-throughput single-molecule approach, and used it to map early-initiation events in human cells. The single-molecule nature of our data and a total of >2,500-fold coverage of the human genome on 27 million fibers averaging ∼300 kb in length allow us to identify initiation sites and their firing probability with high confidence. We find that the distribution of human replication initiation is consistent with inefficient, stochastic activation of heterogeneously distributed potential initiation complexes enriched in accessible chromatin. These observations are consistent with stochastic models of initiation-timing regulation and suggest that stochastic regulation of replication kinetics is a fundamental feature of eukaryotic replication, conserved from yeast to humans.

Exponentially faster cooling in a colloidal system.

As the temperature of a cooling object decreases as it relaxes to thermal equilibrium, it is intuitively assumed that a hot object should take longer to cool than a warm one. Yet, some 2,300 years ago, Aristotle observed that "to cool hot water quickly, begin by putting it in the sun"1,2. In the 1960s, this counterintuitive phenomenon was rediscovered as the statement that "hot water can freeze faster than cold water" and has become known as the Mpemba effect3; it has since been the subject of much experimental investigation4-8 and some controversy8,9. Although many specific mechanisms have been proposed6,7,10-16, no general consensus exists as to the underlying cause. Here we demonstrate the Mpemba effect in a controlled setting-the thermal quench of a colloidal system immersed in water, which serves as a heat bath. Our results are reproducible and agree quantitatively with calculations based on a recently proposed theoretical framework17. By carefully choosing parameters, we observe cooling that is exponentially faster than that observed using typical parameters, in accord with the recently predicted strong Mpemba effect18. Our experiments outline the generic conditions needed to accelerate heat removal and relaxation to thermal equilibrium and support the idea that the Mpemba effect is not simply a scientific curiosity concerning how water freezes into ice-one of the many anomalous features of water19-but rather the prototype for a wide range of anomalous relaxation phenomena of broad technological importance.

Anomalous heating in a colloidal system.

We report anomalous heating in a colloidal system, an experimental observation of the inverse Mpemba effect, where for two initial temperatures lower than the temperature of the thermal bath, the colder of the two systems heats up faster when coupled to the same thermal bath. For an overdamped, Brownian colloidal particle moving in a tilted double-well potential, we find a nonmonotonic dependence of the heating times on the initial temperature of the system. Entropic effects make the inverse Mpemba effect generically weaker-harder to observe-than the usual Mpemba effect (anomalous cooling). We also observe a strong version of anomalous heating, where a cold system heats up exponentially faster than systems prepared under slightly different conditions.

Maximizing power and velocity of an information engine.

Information-driven engines that rectify thermal fluctuations are a modern realization of the Maxwell-demon thought experiment. We introduce a simple design based on a heavy colloidal particle, held by an optical trap and immersed in water. Using a carefully designed feedback loop, our experimental realization of an "information ratchet" takes advantage of favorable "up" fluctuations to lift a weight against gravity, storing potential energy without doing external work. By optimizing the ratchet design for performance via a simple theory, we find that the rate of work storage and velocity of directed motion are limited only by the physical parameters of the engine: the size of the particle, stiffness of the ratchet spring, friction produced by the motion, and temperature of the surrounding medium. Notably, because performance saturates with increasing frequency of observations, the measurement process is not a limiting factor. The extracted power and velocity are at least an order of magnitude higher than in previously reported engines.

Information Engine in a Nonequilibrium Bath.

Information engines can convert thermal fluctuations of a bath at temperature T into work at rates of order k_{B}T per relaxation time of the system. We show experimentally that such engines, when in contact with a bath that is out of equilibrium, can extract much more work. We place a heavy, micron-scale bead in a harmonic potential that ratchets up to capture favorable fluctuations. Adding a fluctuating electric field increases work extraction up to ten times, limited only by the strength of the applied field. Our results connect Maxwell's demon with energy harvesting and demonstrate that information engines in nonequilibrium baths can greatly outperform conventional engines.

Bayesian Information Engine that Optimally Exploits Noisy Measurements.

We have experimentally realized an information engine consisting of an optically trapped, heavy bead in water. The device raises the trap center after a favorable "up" thermal fluctuation, thereby increasing the bead's average gravitational potential energy. In the presence of measurement noise, poor feedback decisions degrade its performance; below a critical signal-to-noise ratio, the engine shows a phase transition and cannot store any gravitational energy. However, using Bayesian estimates of the bead's position to make feedback decisions can extract gravitational energy at all measurement noise strengths and has maximum performance benefit at the critical signal-to-noise ratio.

Finite-Time Landauer Principle.

We study the thermodynamic cost associated with the erasure of one bit of information over a finite amount of time. We present a general framework for minimizing the average work required when full control of a system's microstates is possible. In addition to exact numerical results, we find simple bounds proportional to the variance of the microscopic distribution associated with the state of the bit. In the short-time limit, we get a closed expression for the minimum average amount of work needed to erase a bit. The average work associated with the optimal protocol can be up to a factor of 4 smaller relative to protocols constrained to end in local equilibrium. Assessing prior experimental and numerical results based on heuristic protocols, we find that our bounds often dissipate an order of magnitude less energy.

Direct measurement of weakly nonequilibrium system entropy is consistent with Gibbs-Shannon form.

Stochastic thermodynamics extends classical thermodynamics to small systems in contact with one or more heat baths. It can account for the effects of thermal fluctuations and describe systems far from thermodynamic equilibrium. A basic assumption is that the expression for Shannon entropy is the appropriate description for the entropy of a nonequilibrium system in such a setting. Here we measure experimentally this function in a system that is in local but not global equilibrium. Our system is a micron-scale colloidal particle in water, in a virtual double-well potential created by a feedback trap. We measure the work to erase a fraction of a bit of information and show that it is bounded by the Shannon entropy for a two-state system. Further, by measuring directly the reversibility of slow protocols, we can distinguish unambiguously between protocols that can and cannot reach the expected thermodynamic bounds.

Replication timing is regulated by the number of MCMs loaded at origins.

Replication timing is a crucial aspect of genome regulation that is strongly correlated with chromatin structure, gene expression, DNA repair, and genome evolution. Replication timing is determined by the timing of replication origin firing, which involves activation of MCM helicase complexes loaded at replication origins. Nonetheless, how the timing of such origin firing is regulated remains mysterious. Here, we show that the number of MCMs loaded at origins regulates replication timing. We show for the first time in vivo that multiple MCMs are loaded at origins. Because early origins have more MCMs loaded, they are, on average, more likely to fire early in S phase. Our results provide a mechanistic explanation for the observed heterogeneity in origin firing and help to explain how defined replication timing profiles emerge from stochastic origin firing. These results establish a framework in which further mechanistic studies on replication timing, such as the strong effect of heterochromatin, can be pursued.

Erasure without Work in an Asymmetric Double-Well Potential.

According to Landauer's principle, erasing a memory requires an average work of at least kTln2 per bit. Recent experiments have confirmed this prediction for a one-bit memory represented by a symmetric double-well potential. Here, we present an experimental study of erasure for a memory encoded in an asymmetric double-well potential. Using a feedback trap, we find that the average work to erase can be less than kTln2. Surprisingly, erasure protocols that differ subtly give measurably different values for the asymptotic work, a result we explain by showing that one protocol is symmetric with the respect to time reversal, while the other is not. The differences between the protocols help clarify the distinctions between thermodynamic and logical reversibility.

Replication timing and its emergence from stochastic processes.

The temporal organization of DNA replication has puzzled cell biologists since before the mechanism of replication was understood. The realization that replication timing correlates with important features, such as transcription, chromatin structure and genome evolution, and is misregulated in cancer and aging has only deepened the fascination. Many ideas about replication timing have been proposed, but most have been short on mechanistic detail. However, recent work has begun to elucidate basic principles of replication timing. In particular, mathematical modeling of replication kinetics in several systems has shown that the reproducible replication timing patterns seen in population studies can be explained by stochastic origin firing at the single-cell level. This work suggests that replication timing need not be controlled by a hierarchical mechanism that imposes replication timing from a central regulator, but instead results from simple rules that affect individual origins.

Regulation of DNA replication within the immunoglobulin heavy-chain locus during B cell commitment.

The temporal order of replication of mammalian chromosomes appears to be linked to their functional organization, but the process that establishes and modifies this order during cell differentiation remains largely unknown. Here, we studied how the replication of the Igh locus initiates, progresses, and terminates in bone marrow pro-B cells undergoing B cell commitment. We show that many aspects of DNA replication can be quantitatively explained by a mechanism involving the stochastic firing of origins (across the S phase and the Igh locus) and extensive variations in their firing rate (along the locus). The firing rate of origins shows a high degree of coordination across Igh domains that span tens to hundreds of kilobases, a phenomenon not observed in simple eukaryotes. Differences in domain sizes and firing rates determine the temporal order of replication. During B cell commitment, the expression of the B-cell-specific factor Pax5 sharply alters the temporal order of replication by modifying the rate of origin firing within various Igh domains (particularly those containing Pax5 binding sites). We propose that, within the Igh C(H)-3'RR domain, Pax5 is responsible for both establishing and maintaining high rates of origin firing, mostly by controlling events downstream of the assembly of pre-replication complexes.

High-precision test of Landauer's principle in a feedback trap.

We confirm Landauer's 1961 hypothesis that reducing the number of possible macroscopic states in a system by a factor of 2 requires work of at least kTln2. Our experiment uses a colloidal particle in a time-dependent, virtual potential created by a feedback trap to implement Landauer's erasure operation. In a control experiment, similar manipulations that do not reduce the number of system states can be done reversibly. Erasing information thus requires work. In individual cycles, the work to erase can be below the Landauer limit, consistent with the Jarzynski equality.

Conductive probe AFM study of Pt-thiol and Au-thiol contacts in metal-molecule-metal systems.

The charge transport mechanism between 1,8-octanedithiol (ODT, C(8)H(16)S(2)H(2)) and platinum and gold electrodes is studied by breaking bonds between single ODT molecules and atomic metal junctions using conductive probe atomic force microscopy. Histograms of conductance values show peaks that are obscured by background processes that differ from the metal-molecule-metal conduction path of interest. We introduce a new method to reduce greatly such backgrounds by dividing by a 1-octanethiol (OMT, C(8)H(17)SH) reference histogram, without data selection. The method reveals three series of conductance values for both platinum and gold contacts, which we associate with geometrically different configurations between thiol and metal atoms. The ordering of conductance values, Pt-ODT-Pt > Pt-ODT-Au> Au-ODT-Au, is consistent with a relative dependence on both the number of electron channels and the density of states.

Inferring potential landscapes from noisy trajectories of particles within an optical feedback trap.

While particle trajectories encode information on their governing potentials, potentials can be challenging to robustly extract from trajectories. Measurement errors may corrupt a particle's position, and sparse sampling of the potential limits data in higher energy regions such as barriers. We develop a Bayesian method to infer potentials from trajectories corrupted by Markovian measurement noise without assuming prior functional form on the potentials. As an alternative to Gaussian process priors over potentials, we introduce structured kernel interpolation to the Natural Sciences which allows us to extend our analysis to large datasets. Structured-Kernel-Interpolation Priors for Potential Energy Reconstruction (SKIPPER) is validated on 1D and 2D experimental trajectories for particles in a feedback trap.

Modeling genome-wide replication kinetics reveals a mechanism for regulation of replication timing.

Microarrays are powerful tools to probe genome-wide replication kinetics. The rich data sets that result contain more information than has been extracted by current methods of analysis. In this paper, we present an analytical model that incorporates probabilistic initiation of origins and passive replication. Using the model, we performed least-squares fits to a set of recently published time course microarray data on Saccharomyces cerevisiae. We extracted the distribution of firing times for each origin and found that the later an origin fires on average, the greater the variation in firing times. To explain this trend, we propose a model where earlier-firing origins have more initiator complexes loaded and a more accessible chromatin environment. The model demonstrates how initiation can be stochastic and yet occur at defined times during S phase, without an explicit timing program. Furthermore, we hypothesize that the initiators in this model correspond to loaded minichromosome maintenance complexes. This model is the first to suggest a detailed, testable, biochemically plausible mechanism for the regulation of replication timing in eukaryotes.

Reconciling stochastic origin firing with defined replication timing.

Eukaryotic chromosomes replicate with defined timing patterns. However, the mechanism that regulates the timing of replication is unknown. In particular, there is an apparent conflict between population experiments, which show defined average replication times, and single-molecule experiments, which show that origins fire stochastically. Here, we provide a simple simulation that demonstrates that stochastic origin firing can produce defined average patterns of replication firing if two criteria are met. The first is that origins must have different relative firing probabilities, with origins that have relatively high firing probability being likely to fire in early S phase and origins with relatively low firing probability being unlikely to fire in early S phase. The second is that the firing probability of all origins must increase during S phase to ensure that origins with relatively low firing probability, which are unlikely to fire in early S phase, become likely to fire in late S phase. In addition, we propose biochemically plausible mechanisms for these criteria and point out how stochastic and defined origin firing can be experimentally distinguished in population experiments.

Maximal fluctuation exploitation in Gaussian information engines.

Understanding the connections between information and thermodynamics has been among the most visible applications of stochastic thermodynamics. While recent theoretical advances have established that the second law of thermodynamics sets limits on information-to-energy conversion, it is currently unclear to what extent real systems can achieve the predicted theoretical limits. Using a simple model of an information engine that has recently been experimentally implemented, we explore the limits of information-to-energy conversion when an information engine's benefit is limited to output energy that can be stored. We find that restricting the engine's output in this way can limit its ability to convert information to energy. Nevertheless, a feedback control that inputs work can allow the engine to store energy at the highest achievable rate. These results sharpen our theoretical understanding of the limits of real systems that convert information to energy.