Error correction during DNA replication

DNA polymerase (DNAP) is a dual-purpose enzyme that plays two opposite roles in two different situations during DNA replication. It plays its normal role as a {\it polymerase} catalyzing the elongation of a new DNA molecule by adding a monomer. However, it can switch to the role of an {\it exonuclease} and shorten the same DNA by cleavage of the last incorporated monomer from the nascent DNA. Just as misincorporated nucleotides can escape exonuclease causing replication error, correct nucleotide may get sacrificed unnecessarily by erroneous cleavage. The interplay of polymerase and exonuclease activities of a DNAP is explored here by developing a minimal stochastic kinetic model of DNA replication. Exact analytical expressions are derived for a few key statistical distributions; these characterize the temporal patterns in the mechanical stepping and the chemical (cleavage) reaction. The Michaelis-Menten-like analytical expression derived for the average rates of these two processes not only demonstrate the effects of their coupling, but are also utilized to measure the extent of {\it replication error} and {\it erroneous cleavage}.Comment: Accepted for publication in Physical Review E (8 pages, including 6 figures

Template-directed biopolymerization: tape-copying Turing machines

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 and their collective behavior from the perspective of statistical physics, emphasizing their common features in spite of the crucial differences in their biological functions. We also draw attention of the physics community to another class of modular machines that carry out a different type of template-directed polymerization. We hope this review will inspire new kinetic models for these modular machines.Comment: Author-edited final version of a review article published in Biophysical Reviews and Letters [copyright World Scientific Publishing Company]; publisher-edited electronic version available at http://www.worldscientific.com/doi/abs/10.1142/S179304801230008

Quality control by a mobile molecular workshop: quality versus quantity

Ribosome is a molecular machine that moves on a mRNA track while, simultaneously, polymerizing a protein using the mRNA also as the corresponding template. We define, and analytically calculate, two different measures of the efficiency of this machine. However, we arugue that its performance is evaluated better in terms of the translational fidelity and the speed with which it polymerizes a protein. We define both these quantities and calculate these analytically. Fidelity is a measure of the quality of the products while the total quantity of products synthesized in a given interval depends on the speed of polymerization. We show that for synthesizing a large quantity of proteins, it is not necessary to sacrifice the quality. We also explore the effects of the quality control mechanism on the strength of mechano-chemical coupling. We suggest experiments for testing some of the ideas presented here.Comment: Final version published in Physical Review

Investigating Unipolar Switching in Niobium Oxide Resistive Switches: Correlating Quantized Conductance and Mechanism

Memory devices based on resistive switching (RS) have not been fully realised due to lack of understanding of the underlying switching mechanisms. Nature of ion transport responsible for switching and growth of conducting filament in transition metal oxide based RS devices is still in debate. Here, we investigated the mechanism in Niobium oxide based RS devices, which shows unipolar switching with high ON/OFF ratio, good endurance cycles and high retention times. We controlled the boundary conditions between low-conductance insulating and a high-conductance metallic state where conducting filament (CF) can form atomic point contact and exhibit quantized conductance behaviour. Based on the statistics generated from quantized steps data, we demonstrated that the CF is growing atom by atom with the applied voltage sweeps. We also observed stable quantized states, which can be utilized in multistate switching

Distribution of lifetimes of kinetochore-microtubule attachments: interplay of energy landscape, molecular motors and microtubule (de-)polymerization

Before a cell divides into two daughter cells, chromosomes are replicated resulting in two sister chromosomes embracing each other. Each sister chromosome is bound to a separate proteinous structure, called kinetochore (kt), that captures the tip of a filamentous protein, called microtubule (MT). Two oppositely oriented MTs pull the two kts attached to two sister chromosomes thereby pulling the two sisters away from each other. Here we theoretically study an even simpler system, namely an isolated kt coupled to a single MT; this system mimics an {\it in-vitro} experiment where a single kt-MT attachment is reconstituted using purified extracts from budding yeast. Our models not only account for the experimentally observed "catch-bond-like" behavior of the kt-MT coupling, but also make new predictions on the probability distribution of the lifetimes of the attachments. In principle, our new predictions can be tested by analyzing the data collected in the {\it in-vitro} experiments provided the experiment is repeated sufficiently large number of times. Our theory provides a deep insight into the effects of (a) size, (b) energetics, and (c) stochastic kinetics of the kt-MT coupling on the distribution of the lifetimes of these attachments.Comment: This is an author-created, un-copyedited version of an article accepted for publication in "Physical Biology" (IOP). IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from i

An efficient method for multiobjective optimal control and optimal control subject to integral constraints

We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a "budget" remaining to satisfy each constraint; the augmented Hamilton-Jacobi-Bellman PDE is then solved numerically. The efficiency of our approach hinges on the causality in that PDE, i.e., the monotonicity of characteristic curves in one of the newly added dimensions. A semi-Lagrangian "marching" method is used to approximate the discontinuous viscosity solution efficiently. We compare this to a recently introduced "weighted sum" based algorithm for the same problem. We illustrate our method using examples from flight path planning and robotic navigation in the presence of friendly and adversarial observers.Comment: The final version accepted by J. Comp. Math. : 41 pages, 14 figures. Since the previous version: typos fixed, formatting improved, one mistake in bibliography correcte

Controlled inter-state switching between quantized conductance states in resistive devices for multilevel memory

A detailed understanding of quantization conductance (QC), their correlation with resistive switching phenomena and controlled manipulation of quantized states is crucial for realizing atomic-scale multilevel memory elements. Here, we demonstrate highly stable and reproducible quantized conductance states (QC-states) in Al/Niobium oxide/Pt resistive switching devices. Three levels of control over the QC-states, required for multilevel quantized state memories, like, switching ON to different quantized states, switching OFF from quantized states, and controlled inter-state switching among one QC states to another has been demonstrated by imposing limiting conditions of stop-voltage and current compliance. The well defined multiple QC-states along with a working principle for switching among various states show promise for implementation of multilevel memory devices