Untitled

Abstract

Motor proteins, sometimes referred to as mechanoenzymes, are a group of proteins that maintain a large part of intracellular motion. Being enzymes, they undergo chemical reactions leading to energy conversion and changes of their conformation. Being mechanodevices, they use the chemical energy to perform mechanical work, leading to the phenomena of motion. Over the past 20 years a series of novel experiments (e.g. single molecule observations) has been performed to gain the deeper knowledge about chemical states of molecular motors as well as their dynamics in the presence or absence of an external force. At the same time, many theoretical models have been proposed, offering various insights into the nano-world dynamics. They can be divided into three main categories: mechanochemical models, ratchet models and molecular dynamics simulations. We demonstrate that by combining those complementary approaches a deeper understanding of the dynamics and chemistry of the motor proteins can be achieved. As a working example, we choose kinesin -a motor protein responsible for directed transport of organelles and vesicles along microtubule tracts.

Stepping molecular motor amid Lévy white noise

“…After 20 years of intensive research in the field of molecular transport, we know a lot about the structure of molecular motors [1], We also know a lot about rates, speeds, step sizes, and load-velocity characteristics [2,4,28,31,69,73], Yet we have only a limited knowledge of how molecular motors work, especially under the action of nonequilibrium, non-Gaussian noises. The ultimate goal of studies like ours is therefore to find and understand relations between motor structure and function.…”

“…The elastic properties of a linker structure in typical molecular motors, like kinesins, have been formerly addressed in experimental studies and molecular dynamics simulations using g rom acs software [68,69], Based on accumulated evidence, it is unlikely that a molecular machine would respond instantaneously to an elongation with an elastic counteraction that resets the linker structure to its equilibrium conformation of length a or shorter (see Fig. 2).…”

“…In case of kinesin it is 30 amino acids long. It is a simple flexible polypeptide polymer and it is responsible for the internal potential in our model [1, [68][69][70], In particular, the equilibrium length a and elasticity constant k can be seen as characteristics of a neck linker polymer. The distance dmm represents that maximum allowable extension of the neck linker.…”

Bogomolny equations in certain generalized baby BPS Skyrme models

“…All the same, the solutions of equations ( 5) and ( 6) are very often trivial. However, we can prevent this by doing a gauge transformation [9][10][11][12][13][14] L =⇒ L + I, (7) where I is a functional such that δI ≡ 0.…”

“…In fact, apart from a few rather restricted methods (completing to a square [1][2][3][4][5][6], the first order formalism [7], on-shell method [8]), there is also a completely general method, which allows for systematic derivation (if possible) of BPS equations. This method, referred to as the concept of strong necessary conditions (CSNCs), was originally proposed and analyzed in [9][10][11][12][13][14], applied for derivation of Bogomolny equations (Bogomolny decomposition) in [15-17, 31, 35], and was very recently further developed by Adam and Santamaria [18], who proposed the socalled first-order Euler-Lagrange (FOEL) formalism.…”