Entropy facilitated active transport

Optimal transport of active particles induced by substrate concentration oscillations

We show the existence of a stochastic resonant regime in the transport of active colloidal particles under confinement. The periodic addition of substrate to the system causes the spectral amplification to exhibit a maximum for an optimal noise level value. The consequence of this is that particles can travel longer distances with lower fuel consumption. The stochastic resonance phenomenon found allows the identification of optimal scenarios for the transport of active particles, enabling them to reach regions that are otherwise difficult to access, and may therefore find applications in transport in cell membranes and tissues for medical treatments and soil remediation.

Structural and energetic analysis of metastable intermediate states in the E1P-E2P transition of Ca2+-ATPase

Ion pumps (or P-type ATPases) are membrane proteins, which transport ions through biological membranes against a concentration gradient, a function essential for many biological processes, such as muscle contraction, neurotransmission, and metabolism. Molecular mechanisms underlying active ion transport by ion pumps have been investigated by biochemical experiments and high-resolution structure analyses. Here, the transition of sarcoplasmic reticulum Ca²⁺-ATPase upon dissociation of Ca²⁺ is investigated using atomistic molecular dynamics simulations. We find intermediate structures along the pathway are stabilized by transient interactions between A- and P-domains as well as lipid molecules in the transmembrane helices.

Sarcoplasmic reticulum (SR) Ca²⁺-ATPase transports two Ca²⁺ ions from the cytoplasm to the SR lumen against a large concentration gradient. X-ray crystallography has revealed the atomic structures of the protein before and after the dissociation of Ca²⁺, while biochemical studies have suggested the existence of intermediate states in the transition between E1P⋅ADP⋅2Ca²⁺ and E2P. Here, we explore the pathway and free energy profile of the transition using atomistic molecular dynamics simulations with the mean-force string method and umbrella sampling. The simulations suggest that a series of structural changes accompany the ordered dissociation of ADP, the A-domain rotation, and the rearrangement of the transmembrane (TM) helices. The luminal gate then opens to release Ca²⁺ ions toward the SR lumen. Intermediate structures on the pathway are stabilized by transient sidechain interactions between the A- and P-domains. Lipid molecules between TM helices play a key role in the stabilization. Free energy profiles of the transition assuming different protonation states suggest rapid exchanges between Ca²⁺ ions and protons when the Ca²⁺ ions are released toward the SR lumen.

Computational Model for Membrane Transporters. Potential Implications for Cancer

To explain the increased transport of nutrients and metabolites and to control the movement of drug molecules through the transporters to the cancer cells, it is important to understand the exact mechanism of their structure and activity, as well as their biological and physical characteristics. We propose a computational model that reproduces the functionality of membrane transporters by quantifying the flow of substrates through the cell membrane. The model identifies the force induced by conformational changes of the transporter due to hydrolysis of ATP, in ABC transporters, or by an electrochemical gradient of ions, in secondary transporters. The transport rate is computed by averaging the velocity generated by the force along the paths followed by the substrates. The results obtained are in accordance with the experiments. The model provides an overall framework for analyzing the membrane transport proteins that regulate the flows of ions, nutrients and other molecules across the cell membranes, and their activities.

Resonance-driven ion transport and selectivity in prokaryotic ion channels

Ion channels exhibit a remarkably high accuracy in selecting uniquely its associated type of ion. The mechanisms behind ion selectivity are not well understood. Current explanations build mainly on molecular biology and bioinformatics. Here we propose a simple physical model for ion selectivity based on the driven damped harmonic oscillator (DDHO). The driving force for this oscillator is provided by self-organizing harmonic turbulent structures in the dehydrating ionic flow through the ion channel, namely, oscillating pressure waves in one dimension, and toroidal vortices in two and three dimensions. Density fluctuations caused by these turbulences efficiently transmit their energy to aqua ions that resonate with the driving frequency. Consequently, these release their hydration shell and exit the ion channel as free ions. Existing modeling frameworks do not express the required complex spatiotemporal dynamics, hence we introduce a macroscopic continuum model for ionic dehydration and transport, based on the hydrodynamics of a dissipative ionic flow through an ion channel, subject to electrostatic and amphiphilic interactions. This model combines three classical physical fields: Navier-Stokes equations from hydrodynamics, Gauss's law from Maxwell theory, and the convection-diffusion equation from continuum physics. Numerical experiments with mixtures of chemical species of ions in various degrees of hydration indeed reveal the emergence of strong oscillations in the ionic flow that are instrumental in the efficient dehydration and cause a strong ionic jet into the cell. As such, they provide a powerful engine for the DDHO mechanism. Theoretical predictions of the modeling framework match significantly with empirical patch-clamp data. The DDHO standard response curve defines a unique resonance frequency that depends on the mass and charge of the ion. In this way, the driving oscillations act as a selection mechanism that filters out one specific ion. Application of the DDHO model to real ion data shows that this mechanism indeed clearly distinguishes between chemical species and between aqua and bare ions with a large Mahalanobis distance and high oscillator quality. The DDHO framework helps to understand how SNP mutations can cause severe genetic pathologies as they destroy the geometry of the channel and so alter the resonance peaks of the required ion type.

Self-assembling outside equilibrium: emergence of structures mediated by dissipation

Self-assembly under non-equilibrium conditions may give rise to the formation of structures not available at equilibrium.

The role of entropic potential in voltage activation and K+ transport through Kv 1.2 channels

We analyze the entropic effects of inner pore geometry changes of Kv 1.2 channel during membrane depolarization and their implications for the rate of transmembrane transport of potassium ions. We base this on the idea that spatial confinements within the channel pore give rise to entropic barriers which can both effectively affect the stability of open macroconformation and influence channel's ability to conduct the potassium ions through the membrane. First, we calculate the differences in entropy between voltage-activated and resting states of the channel. As a template, we take a set of structures of channel pore in an open state at different membrane potentials generated in our previous research. The obtained results indicate that tendency to occupy open states at membrane depolarization is entropy facilitated. Second, we describe the differences in rates of K⁺ transport through the channel pore at different voltages based on the results of appropriate random walk simulations in entropic and electric potentials. The simulated single channel currents (I) suggest that the geometry changes during membrane depolarization are an important factor contributing to the observed flow of potassium ions through the channel. Nevertheless, the charge distribution within the channel pore (especially at the extracellular entrance) seems most prominent for the observed I/I_max relation at a qualitative level at analyzed voltages.