Krishnendu Pal

Bio: Krishnendu Pal is an academic researcher from Indian Association for the Cultivation of Science. The author has contributed to research in topics: Antiresonance & Potassium channel blocker. The author has an hindex of 4, co-authored 11 publications receiving 30 citations. Previous affiliations of Krishnendu Pal include S.N. Bose National Centre for Basic Sciences & Bose Corporation.

Dynamical characterization of inactivation path in voltage-gated Na(+) ion channel by non-equilibrium response spectroscopy.

Abstract: Inactivation path of voltage gated sodium channel has been studied here under various voltage protocols as it is the main governing factor for the periodic occurrence and shape of the action potential. These voltage protocols actually serve as non-equilibrium response spectroscopic tools to study the ion channel in non-equilibrium environment. In contrast to a lot of effort in finding the crystal structure based molecular mechanism of closed-state(CSI) and open-state inactivation(OSI); here our approach is to understand the dynamical characterization of inactivation. The kinetic flux as well as energetic contribution of the closed and open- state inactivation path is compared here for voltage protocols, namely constant, pulsed and oscillating. The non-equilibrium thermodynamic quantities used in response to these voltage protocols serve as improved characterization tools for theoretical understanding which not only agrees with the previously known kinetic measurements but also predict the energeti...

Probing kinetic drug binding mechanism in voltage-gated sodium ion channel: open state versus inactive state blockers

Abstract: The kinetics and nonequilibrium thermodynamics of open state and inactive state drug binding mechanisms have been studied here using different voltage protocols in sodium ion channel. We have found that for constant voltage protocol, open state block is more efficient in blocking ionic current than inactive state block. Kinetic effect comes through peak current for mexiletine as an open state blocker and in the tail part for lidocaine as an inactive state blocker. Although the inactivation of sodium channel is a free energy driven process, however, the two different kinds of drug affect the inactivation process in a different way as seen from thermodynamic analysis. In presence of open state drug block, the process initially for a long time remains entropy driven and then becomes free energy driven. However in presence of inactive state block, the process remains entirely entropy driven until the equilibrium is attained. For oscillating voltage protocol, the inactive state blocking is more efficient in damping the oscillation of ionic current. From the pulse train analysis it is found that inactive state blocking is less effective in restoring normal repolarisation and blocks peak ionic current. Pulse train protocol also shows that all the inactive states behave differently as one inactive state responds instantly to the test pulse in an opposite manner from the other two states.

Spatiotemporal antiresonance in coupled reaction-diffusion systems.

Abstract: We present a theoretical study of the spatiotemporal antiresonance in a system of two diffusively coupled chemical reactions, one of which is driven by an external periodic forcing. Although antiresonance is well known in various physical systems, the phenomenon in coupled chemical reactions has largely been overlooked. Based on the linearized dynamics around the steady state of the two-component coupled reaction-diffusion systems we have derived the general analytical expressions for the amplitude-frequency response functions of the driven and undriven components of the system. Our theoretical analysis is well corroborated by detailed numerical simulations on coupled Gray-Scott reaction-diffusion systems exhibiting antiresonance dip in the amplitude-frequency response curve as a result of destructive interference between the coupling and the periodic external forcing imparting differential stability of the two subsystems. This leads to the emergence of spatiotemporal patterns in an undriven subsystem, while the driven one settles down to a homogeneously stable steady state.

Non-Equilibrium Thermodynamics

Abstract: In the preceding chapters with few exceptions we studied systems at equilibrium. This means that the systems do not change or evolve over time.

The Fourth Element.

Abstract: This tutorial clarifies the axiomatic definition of (v(α); i(β)) circuit elements via a lookup table dubbed an A-pad, of admissible (v; i) signals measured via Gedanken probing circuits. The (v(α); i(β)) elements are ordered via a complexity metric. Under this metric, the memristor emerges naturally as the fourth element, characterized by a state-dependent Ohm's law. A logical generalization to memristive devices reveals a common fingerprint consisting of a dense continuum of pinched hysteresis loops whose area decreases with the frequency ω and tends to a straight line as ω ~ ∞, for all bipolar periodic signals and for all initial conditions. This common fingerprint suggests that the term memristor be used hence-forth as a moniker for memristive devices.

Memristor, Hodgkin-Huxley, and Edge of Chaos.

Abstract: From a pedagogical point of view, the memristor is defined in this tutorial as any 2-terminal device obeying a state-dependent Ohm’s law. This tutorial also shows that from an experimental point of view, the memristor can be defined as any 2-terminal device that exhibits the fingerprints of “pinched” hysteresis loops in the v–i plane. It also shows that memristors endowed with a continuum of equilibrium states can be used as non-volatile analog memories. This tutorial shows that memristors span a much broader vista of complex phenomena and potential applications in many fields, including neurobiology. In particular, this tutorial presents toy memristors that can mimic the classic habituation and LTP learning phenomena. It also shows that sodium and potassium ion-channel memristors are the key to generating the action potential in the Hodgkin-Huxley equations, and that they are the key to resolving several unresolved anomalies associated with the Hodgkin-Huxley equations. This tutorial ends with an amazing new result derived from the new principle of local activity, which uncovers a minuscule life-enabling Goldilocks zone, dubbed the edge of chaos, where complex phenomena, including creativity and intelligence, may emerge. From an information processing perspective, this tutorial shows that synapses are locally-passive memristors, and that neurons are made of locally-active memristors.

Brains Are Made of Memristors.

Abstract: This exposition shows that the potassium ion-channels and the sodium ion-channels that are distributed over the entire length of the axons of our neurons are in fact locally-active memristors. In particular, they exhibit all of the fingerprints of memristors, including the characteristic pinched hysteresis Lissajous figures in the voltage-current plane, whose loop areas shrink as the frequency of the periodic excitation signal increases. Moreover, the pinched hysteresis loops for the potassium ion-channel memristor, and the sodium ion-channel memristor, from the Hodgkin-Huxley axon circuit model are unique for each periodic excitation signal. An in-depth circuit-theoretic analysis and characterizations of these two classic biological memristors are presented via their small-signal memristive equivalent circuits, their frequency response, and their Nyquist plots. Just as the Hodgkin-Huxley circuit model has stood the test of time, its constituent potassium ion-channel and sodium ion-channel memristors are destined to be classic examples of locally-active memristors in future textbooks on circuit theory and bio-physics.