MBI Publications for Mathematics (5)
Stochastic mechano-chemical kinetics of molecular motors: a multidisciplinary enterprise from a physicistâ€™s perspectivepp. 370 (Submitted)
AbstractAmolecularmotor ismade of either a singlemacromolecule or amacromolecular
complex. Just like their macroscopic counterparts, molecular
motors â€œtransduceâ€? 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
â€œmacromolecules of lifeâ€?. 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.
A single-cell approach in modelling the dynamics of tumour microregionsMathematical Biosciences and EngineeringVol. 2 No. 3 (2005) pp. 643-655
A. Sharma and D. Chowdhury
Error correction during DNA replicationPhysical Review EVol. 86 No. 011913 (2012)
AbstractDNA 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 modulesJournal of Theoretical BiologyVol. 343 (2013) pp. 127-137
AbstractCompetition 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.
Behavioral refuges and predator-prey coexistenceJournal of Theoretical BiologyVol. 339 (2014) pp. 112-121
AbstractThe 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.