We consider a model of a stepping molecular motor consisting of two connected heads. Directional motion of the stepper takes place along a one-dimensional track. Each head is subject to a periodic potential without spatial reflection symmetry. When the potential for one head is switched on, it is switched off for the other head. Additionally, the system is subject to the influence of symmetric, white Lévy noise that mimics the action of external random forcing. The stepper exhibits motion with a preferred direction which is examined by analyzing the median of the displacement of a midpoint between the positions of the two heads. We study the modified dynamics of the stepper by numerical simulations. We find flux reversals as noise parameters are changed. Speed and direction appear to very sensitively depend on characteristics of the noise.

Drugs carry a proarrhythmic risk, which gets even greater when they are used in combination. In vitro assessment of the proarrhythmic potential of drugs is limited to one compound and thus neglects the potential of drug-drug interactions, including those involving active metabolites. Here we present the results of an in vitro study of potential drug-drug interactions at the level of the hERG channel for the combination of up to three compounds: loratadine, desloratadine and ketoconazole. Experiments were performed at room temperature on an automated patch-clamp device CytoPatch 2, with the use of heterogeneously, stably transfected HEK cells. Single drugs, pairs and triplets were used. The results provided as the inhibition of the I current for pairs were compared against the calculated theoretical interaction. Models applied to calculate the combined effect of inhibitory actions of simultaneously given drugs include: (1) simple additive model with a maximal inhibition limit of 1 (all channels blocked in 100%); (2) Bliss independence; and (3) Loewe additivity. The observed IC values for loratadine, desloratadine and ketoconazole were 5.15, 1.95 and 0.74 μm respectively. For the combination of drugs tested in pairs, the effect was concentration dependent. In lower concentrations, the synergistic effect was observed, while for the highest tested concentrations it was subadditive. To triple the effect, it was subadditive regardless of concentrations. The square root of sum of squares of differences between the observed and predicted total inhibition was calculated to assess the theoretical interaction models. For most of the drugs, the allotopic model offered the best fit.

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.

We study a generic model of coupled oscillators. In the model there is competition between phase synchronization and diffusive effects. For a model with a finite number of states we derive how a phase transition occurs when the coupling parameter is varied. The phase transition is characterized by a symmetry breaking and a discontinuity in the first derivative of the order parameter. We quantitatively account for how the synchronized pulse is a low-entropy structure that facilitates the production of more entropy by the system as a whole. For a model with many states we apply a continuum approximation and derive a potential Burgers' equation for a propagating pulse. No phase transition occurs in that case. However, positive entropy production by diffusive effects still exceeds negative entropy production by the shock formation.