MBI Publications

MBI Publications for Mathematics (5)

  • D. Chowdhury
    Stochastic mechano-chemical kinetics of molecular motors: a multidisciplinary enterprise from a physicist’s perspective
    pp. 370 (Submitted)

    Abstract

    Amolecularmotor ismade of either a singlemacromolecule or amacromolecular
    complex. Just like their macroscopic counterparts, molecular
    motors €œtransduce€? input energy into mechanical work. All the nanomotors
    considered here operate under isothermal conditions far from equilibrium.
    Moreover, one of the possible mechanisms of energy transduction,
    called Brownian ratchet, does not even have any macroscopic counterpart.
    But, molecular motor is not synonymous with Brownian ratchet; a large
    number of molecular motors execute a noisy power stroke, rather than
    operating as Brownian ratchet. We review not only the structural design
    and stochastic kinetics of individual single motors, but also their coordination,
    cooperation and competition as well as the assembly of multimodule
    motors in various intracellular kinetic processes. Although all
    the motors considered here execute mechanical movements, efficiency and
    power output are not necessarily good measures of performance of some
    motors. Among the intracellular nano-motors, we consider the porters,
    sliders and rowers, pistons and hooks, exporters, importers, packers and
    movers as well as those that also synthesize, manipulate and degrade
    €œmacromolecules of life€?. We review mostly the quantitative models for
    the kinetics of these motors. We also describe several of those motordriven
    intracellular stochastic processes for which quantitative models are
    yet to be developed. In part I, we discuss mainly the methodology and
    the generic models of various important classes of molecular motors. In
    part II, we review many specific examples emphasizing the unity of the
    basic mechanisms as well as diversity of operations arising from the differences
    in their detailed structure and kinetics. Multi-disciplinary research
    is presented here from the perspective of physicists.
  • K. Rejniak
    A single-cell approach in modelling the dynamics of tumour microregions
    Mathematical Biosciences and EngineeringVol. 2 No. 3 (2005) pp. 643-655

    Abstract

  • A. Sharma and D. Chowdhury
    Error correction during DNA replication
    Physical Review EVol. 86 No. 011913 (2012)

    Abstract

    DNA polymerase (DNAP) is a dual-purpose enzyme that plays two opposite roles in two different situations
    during DNA replication. It plays its a normal role as a polymerase catalyzing the elongation of a new DNA
    molecule by adding a monomer. However, it can switch to the role of an 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 a replication error, the 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 replication error and erroneous cleavage.
  • V. Krivan and R. Cressman
    Competition in di-and tri-trophic food web modules
    Journal of Theoretical BiologyVol. 343 (2013) pp. 127-137

    Abstract

    Competition in di-and tri-trophic food web modules with many competing species is studied.The food web modules considered are apparent competition between n species sharing a single predator and a diamond-like food web with a single resource,a single top predator and many competing middle species.The predators have either fixed preferences for their prey,or they switch between available prey in away that maximizes their fitness. Dependence of these food web dynamics on environmental carrying capacity and food web connectance is studied.The results predict that optimal flexible for aging strongly weakens apparent competition and promotes species coexistence. Food web robustness (defined here as the proportion of surviving species) does not decrease with increased connectance in these food-webs. Moreover, it is shown that flexible prey switching leads to the same population equilibria as in corresponding food webs with highly specialized predators. The results show that flexible for aging behavior by predators can have very strong impact on species richness, as well as the response of communities to changes in resource enrichment and food web connectance when compared to the same food-web topology with inflexible top predators. Several results on global stability using Lyapunov functions areprovided.
  • V. Krivan
    Behavioral refuges and predator-prey coexistence
    Journal of Theoretical BiologyVol. 339 (2014) pp. 112-121

    Abstract

    The effects of a behavioral refuge caused either by the predator optimal foraging or prey adaptive antipredator behavior on the Gause predator-prey model are studied. It is shown that both of these mechanisms promote predator-prey coexistence either at an equilibrium, or along a limit cycle. Adaptive prey refuge use leads to hysteresis in prey antipredator behavior which allows predator-prey coexistence along a limit cycle. Similarly, optimal predator foraging leads to sigmoidal functional responses with a potential to stabilize predator-prey population dynamics at an equilibrium, or along a limit cycle.

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