Hierarchical clustering of the correlation patterns: new method of domain identification in proteins.

New method of identification of dynamical domains in proteins - Hierarchical Clustering of the Correlation Patterns (HCCP) is proposed. HCCP allows to identify the domains using single three-dimensional structure of the studied proteins and does not require any adjustable parameters that can influence the results. The method is based on hierarchical clustering performed on the matrices of correlation patterns, which are obtained by the transformation of ordinary pairwise correlation matrices. This approach allows to extract additional information from the correlation matrices, which increases reliability of domain identification. It is shown that HCCP is insensitive to small variations of the pairwise correlation matrices. Particularly it produces identical results if the data obtained for the same protein crystallized with different spatial positions of domains are used for analysis. HCCP can utilize correlation matrices obtained by any method such as normal mode or essential dynamics analysis, Gaussian network or anisotropic network models, etc. These features make HCCP an attractive method for domain identification in proteins.

Hierarchy of motions and quasi-particles in a simplified model of potassium channel selectivity filter.

We develop a simplified model of themultiply occupied Kcsa-like selectivityfilter based on the best availablestructural data. The existence of hierarchyof motions in the selectivity filter isshown. Fast fluctuations of the ion-iondistances may be considered adiabaticallydecoupled from the slow diffusive motion ofthe ions' center of masses. The latter canbe considered as a quasi-particle, called aquasi-ion, moving in an effectivepotential. In the Kcsa-like selectivityfilter occupied by three ions the effectivepotential allows free barrier-lessdiffusional motion of the quasi-ions. Theconcept of the quasi-ions performing iontranslocation through the channel may bevital in explaining barrier-less `knock-on' conduction postulated for real channels.

Self-regulation phenomena in bacterial reaction centers. I. General theory.

A model for light-induced charge separation in a donor-acceptor system of the reaction center of photosynthetic bacteria is described. This description is predicated on a self-regulation of the flow of photo-activated electrons due to self-consistent, slow structural rearrangements of the macromolecule. Effects of the interaction between the separated charges and the slow structural modes of the biomolecule may accumulate during multiple, sequential charge transfer events. This accumulation produces non-linear dynamic effects on system function, providing a regulation of the charge separation efficiency. For a biomolecule with a finite number of different charge-transfer states, the quasi-stationary populations of these states with a localized electron on different cofactors may deviate from a Lagmuir law dependence with actinic light intensity. Such deviations are predicted by the model to be due to light-induced structural changes. The theory of self-regulation developed here assumes that light-induced changes in the effective adiabatic potential occur along a slow structural coordinate. In this model, a "light-adapted" conformational state appears when bifurcation produces a new minimum in the adiabatic potential. In this state, the lifetime of the charge-separated state may be quite different from that of the "dark-adapted" conformation. The results predicted by this theory agree with previously obtained experimental results on photosynthetic reaction centers.

Effects of mutual influence of photoinduced electron transitions and slow structural rearrangements in bacterial photosynthetic reaction centers.

We describe the phenomenon of light-induced structural transformations in the reaction centers (RC) of photosynthetic bacteria which makes self-regulation of the RC charge separation efficiency possible. The nature of the effect is that the light-driven electron transfer (ET) between the RC redox-cofactors causes structural changes in the protein-cofactors system and this in turn affects the ET kinetics. If the electron-conformation interaction is strong enough, then such self-regulation gives birth to a new RC conformational state of enhanced charge separation efficiency. We show experimental results of stationary and kinetic absorbance change characteristics under different photoexcitation conditions, indicating structural rearrangements on a rather long (minutes) time scale, mainly within the secondary acceptor binding pocket. To simplify the description, in constructing a theory of structure-function reorganization in the RC we employ the adiabatic approach. Final expressions enable us to make qualitative comparison with experimentally observed kinetics of the fast and slow stages of 'free' and 'structurally controlled' electron relaxation, respectively.

Ion regulation of the kinetics of potential-dependent potassium channels.

We apply a theoretical approach developed earlier. The interaction ofions that permeate a channel with slowly relaxing charged channel-forminggroups (ion-conformational interaction - ICI) is addressed by thisapproach. One can describe the ion concentration influence (ion regulation)on channel functioning in this manner. A patch-clamp method in a'whole-cell' configuration is used to study the ICI. For this purpose theinfluence of an external concentration of potassium ions on thepotential-dependent potassium current (I(A)) in the externalmembrane of GH(3) cells was studied. The increase of[K(+) (out)] from 5 mM to 100 mM causes anon-monotonous shift of current-voltage dependencies. The dependence of bothan activation time constant tgr(n) and a steady-state activation(n(∞)) on [K(+)](out) have a minimum andmaximum respectively. The analysis of the results suggests that the observedeffects are caused by ICI. A physical model is developed to describe thedependence of the potassium channel kinetics on the external concentrationof the ions and the membrane potential. The 'deformation' of the closedstate of the gate and the corresponding energy shifts cause the observednon-monotonous dependencies due to ICI. Thus, the general theoreticalapproach has an experimental confirmation and is applied to concreteexamples. Formulas for concentrational dependencies of the channel kineticsare given for practical uses.

Mathematical model of pacemaker activity in bursting neurons of snail, Helix pomatia.

On the basis of experimental data we have developed a mathematical model of pacemaker activity in bursting neurons of snail Helix pomatia which includes a minimal model of membrane potential oscillation, spike-generating mechanism, voltage- and time-dependent inward calcium current, intracellular calcium ions, [Ca2+]in, their fast buffering and accumulation, stationary voltage-dependent [Ca2+]in-inhibited calcium current. A resulting model of bursting pacemaker activity reproduces all experimental phenomena which were mimicked on the minimal model for membrane potential oscillation including (a) the effect of polarizing current on bursting activity, (b) an increase of input resistance during depolarizing phase, (c) induced hyperpolarization, etc. This model demonstrates adaptation of bursting activity to both the polarizing current and changes in the stationary sodium or potassium conductances. The model also reproduces the behavior of the transmembrane ionic current at membrane potentials clamped in different phases of slow-wave development; the calculated current-voltage relationships of the model neuronal membrane using a slow ramp potential clamp demonstrate hysteresis properties. Relationships between the model of bursting activity and the properties if intact bursting neurons are discussed.