Shreyas Bhaban

Design of a constant force clamp and estimation of molecular motor motion using modern control approach

Since its inception, optical traps have become an important tool for single molecule investigation because of its precise ability to manipulate microparticles and probe systems with a force resolution of the order of fN. Its use as a constant force clamp is of particular importance in the study of molecular motors and DNA. The highly nonlinear nature (specially the presence of hysteresis) of the force-extension relationships in such biomolecules is traditionally modelled as a linear Hookean spring for small force perturbations. For these linear models to hold, high disturbance rejection bandwidths are required so that the perturbations from the regulated values remain small. The absence of systematic design and performance quantification in the current literature is addressed by designing an optimized PI and a H∞ controller, that significantly improve the force regulation and its bandwidth. A major application of constant force clamps is in step detection of biomolecules, where due to the presence of thermal noise, one has to extract the stepping data via postprocessing. In this paper, a real time step-detection scheme, currently lacking in literature, is achieved via a mixed objective H2/H∞ synthesis. In the design, the H∞ norm for force regulation and stepping estimation error is minimized while keeping the H2 norm of the thermal noise on the stepping estimate is kept bounded.Since its inception, optical traps have become an important tool for single molecule investigation because of its precise ability to manipulate microparticles and probe systems with a force resolution of the order of fN. Its use as a constant force clamp is of particular importance in the study of molecular motors and DNA. The highly nonlinear nature (specially the presence of hysteresis) of the force-extension relationships in such biomolecules is traditionally modelled as a linear Hookean spring for small force perturbations. For these linear models to hold, high disturbance rejection bandwidths are required so that the perturbations from the regulated values remain small. The absence of systematic design and performance quantification in the current literature is addressed by designing an optimized PI and a H∞ controller, that significantly improve the force regulation and its bandwidth. A major application of constant force clamps is in step detection of biomolecules, where due to the presence of thermal noise, one has to extract the stepping data via postprocessing. In this paper, a real time step-detection scheme, currently lacking in literature, is achieved via a mixed objective H2/H∞ synthesis. In the design, the H∞ norm for force regulation and stepping estimation error is minimized while keeping the H2 norm of the thermal noise on the stepping estimate is kept bounded.

Memory erasure using time-multiplexed potentials

We study the thermodynamics of a Brownian particle under the influence of a time-multiplexed harmonic potential of finite width. The memory storage mechanism and the erasure protocol based on time-multiplexed potentials are utilized to experimentally realize erasure with work performed close to Landauers bound. We quantify the work performed on the system with respect to the duty ratio of time multiplexing, which also provides a handle for approaching reversible erasures. A Langevin dynamics based simulation model is developed for the proposed memory bit and the erasure protocol, which guides the experimental realization. The study also provides insight into transport on the microscale.

Interrogating Emergent Transport Properties for Molecular Motor Ensembles: A Semi-analytical Approach

Intracellular transport is an essential function in eucaryotic cells, facilitated by motor proteins—proteins converting chemical energy into kinetic energy. It is understood that motor proteins work in teams enabling unidirectional and bidirectional transport of intracellular cargo over long distances. Disruptions of the underlying transport mechanisms, often caused by mutations that alter single motor characteristics, are known to cause neurodegenerative diseases. For example, phosphorylation of kinesin motor domain at the serine residue is implicated in Huntington’s disease, with a recent study of phosphorylated and phosphomimetic serine residues indicating lowered single motor stalling forces. In this article we report the effects of mutations of this nature on transport properties of cargo carried by multiple wild-type and mutant motors. Results indicate that mutants with altered stall forces might determine the average velocity and run-length even when they are outnumbered by wild type motors in the ensemble. It is shown that mutants gain a competitive advantage and lead to an increase in the expected run-length when the load on the cargo is in the vicinity of the mutant’s stalling force or a multiple of its stalling force. A separate contribution of this article is the development of a semi-analytic method to analyze transport of cargo by multiple motors of multiple types. The technique determines transition rates between various relative configurations of motors carrying the cargo using the transition rates between various absolute configurations. This enables a computation of biologically relevant quantities like average velocity and run-length without resorting to Monte Carlo simulations. It can also be used to introduce alterations of various single motor parameters to model a mutation and to deduce effects of such alterations on the transport of a common cargo by multiple motors. Our method is easily implementable and we provide a software package for general use.

Analysis of Heat Dissipation and Reliability in Information Erasure: A Gaussian Mixture Approach

This article analyzes the effect of imperfections in physically realizable memory. Motivated by the realization of a bit as a Brownian particle within a double well potential, we investigate the energetics of an erasure protocol under a Gaussian mixture model. We obtain sharp quantitative entropy bounds that not only give rigorous justification for heuristics utilized in prior works, but also provide a guide toward the minimal scale at which an erasure protocol can be performed. We also compare the results obtained with the mean escape times from double wells to ensure reliability of the memory. The article quantifies the effect of overlap of two Gaussians on the the loss of interpretability of the state of a one bit memory, the required heat dissipated in partially successful erasures and reliability of information stored in a memory bit.

Steady state dynamics of molecular motors reveals load dependent cooperativity

Intracellular transport of cargoes inside eukaryotic cells is primarily carried out by bio-mechanical machines called molecular motors. These motors facilitate the directed transfer of intracellular cargo to desired locations inside the cell. In vivo modes of transport often involve multiple agents, possibly of different types, teaming up to carry a common cargo. We analyze the stochastic dynamics of such cargos and prove that the probability distribution of various motor-motor configurations in an ensemble reaches a unique steady state. Existence of such a unique steady state indicates a degree of robustness of the system of multiple motors sharing a cargo. Analysis of the steady state distribution for an ensemble of two kinesin motors for varying load forces reveals a degree of cooperativity between the motors, where configurations that have the two motors clustered together are favored for moderate loads. We further show that when subjected to high forces, such as those encountered due to obstacles along the path of travel, motors preferably adopt a configuration that facilitates high probability of regaining motion once the obstacle is removed. Simulation results of the steady state distribution of a two motor ensemble for low, moderate and high load forces are presented, which corroborate analytical studies.

Noise induced transport at microscale enabled by optical fields

Transport at the micro scale is an essential aspect for many emerging areas including manufacturing systems at the nanoscale. Transfer of beads decorated with cargo under the influence of optical fields provide an attractive means of such transport. Physical models that describe beads in optical fields under the influence of thermal noise are available which yield a qualitative understanding of the bead motion; however, it is difficult to arrive at models that provide quantitative agreement. The first contribution of the article is the determination of a model of a bead under a static field realized by optical forces where the model can be used to predict the motion of the bead under a time-varying optical potential with high fidelity. Close agreement between model based Monte Carlo simulations and experimental observations is seen. The other contribution is a strategy for directed transport of micron-sized particles that utilizes the proposed models to arrive at conclusions which are experimentally verified and easy to implement. The effectiveness of this transport mechanism is justified based on splitting probability computations. Applications to transport of cargo across multiple locations and transport of multiple cargo are experimentally demonstrated.