Conductances Of Membrane Currents Research Articles

Cyclodextrin-Scaffolded Alamethicin with Remarkably Efficient Membrane Permeabilizing Properties and Membrane Current Conductance

Bacterial resistance to classical antibiotics is a serious medical problem, which continues to grow. Small antimicrobial peptides represent a potential solution and are increasingly being developed as novel therapeutic agents. Many of these peptides owe their antibacterial activity to the formation of trans-membrane ion-channels resulting in cell lysis. However, to further develop the field of peptide antibiotics, a thorough understanding of their mechanism of action is needed. Alamethicin belongs to a class of peptides called peptaibols and represents one of these antimicrobial peptides. To examine the dynamics of assembly and to facilitate a thorough structural evaluation of the alamethicin ion-channels, we have applied click chemistry for the synthesis of templated alamethicin multimers covalently attached to cyclodextrin-scaffolds. Using oriented circular dichroism, calcein release assays, and single-channel current measurements, the α-helices of the templated multimers were demonstrated to insert into lipid bilayers forming highly efficient and remarkably stable ion-channels.

Improving visualization and analysis of relationships between neuronal model parameters in discrete parameter spaces

We explore relationships between parameters in a 12-dimensional parameter space of a 2-compartment conductance-based model of the AB (anterior burster) neuron in the lobster stomatogastric ganglion (STG). The parameter space was created by systematically varying maximal conductances of membrane currents from a hand-tuned AB model [1] to determine ranges and variation steps that could potentially produce physiologically realistic behavior. This parameter space preparation contained between 3 to 5 discrete values for each of the 12 maximal conductances. Every parameter set representing an individual model neuron was simulated and classified as functional if it produced biologically realistic activity matching the behavior of the real AB neuron under several selection criteria [2]. Interactions between pairs of parameters in such a grid-based space can be visualized by 3D bar-plots, in which color, representing the third dimension, depicts the frequency of “good” models for each of the possible combinations of values for that pair. One can attempt to identify relationships between parameters (which, in turn, may point to a possible co-regulation of the corresponding ionic currents) by searching for “ridges” of high frequency (i.e., “hot” colors) in such plots. However, due to the limited number of parameter values, identification of such interactions in the plot, as well as any numerical analysis to follow, can be difficult. In order to deal with this limitation, and at the same time to transform the data into more of a scatter-plot-like form (which is more suitable for numerical analyses such as regression modeling or curve-fitting), random jitter is often added to the discrete values to prevent mark overlapping [3]. Although this procedure may improve the visibility of relationships between parameters under some circumstances, in extreme situations, due to its randomness, it may actually obscure interactions otherwise present in the data. Therefore, we propose two methods for increasing the clarity and interpretability of such relationships in sparse parameter spaces. The overarching idea for these methods is that the information contained in the data can be used to amplify the visualization of the relationships in the corresponding displays. We extend the random jitter technique, by utilizing the “gravity effect” and the “jump effect,” so that areas of higher density affect the results of the jitter procedure. Rather than having the original parameter values vary purely randomly within the jitter limits, the procedures, while still random, incorporate a “bias” towards the areas of higher co-occurrence. In the gravity-based approach, for each combination of the parameter values, a set of vectors proportional to the frequencies of the neighboring combinations is calculated. Then, a resultant vector is computed to “pull” the jittered points along its direction. In the jump-based approach, the jittered data points “jump” towards one of the neighboring combinations, or stay within the original jitter area, based on a probability proportional to the frequency of each of the combinations involved. In both cases, if there is a relationship present in the data, it will be enhanced, making it easier to discern and analyze. On the other hand, if there is no relationship between a given pair of parameters, the plot will be equivalent to the regular jitter. Importantly, these techniques significantly augment our previous visualization approaches [4], by allowing identification of relationships that are non-linear. For instance, the relationship between the soma delayed-rectifier potassium, IKd, and the transient calcium, ICaT, currents, which in our previous work was assumed to be linear, based on the current results, might actually have an exponential character.

Classifying functional and non-functional model neurons using the theory of rough sets

We explored a 12-dimensional parameter space of a 2-compartment model of the AB (anterior burster) neuron, which is one of the two cells that form the pacemaker kernel in the pyloric network in the lobster stomatogastric ganglion (STG). The computational exploration started with a hand-tuned AB model [1] and systematically varied maximal conductances of membrane currents to determine ranges and variation steps that could potentially produce physiologically realistic behavior. We varied the conductances for the following currents in the model: fast sodium INa and delayed-rectifier potassium IKd in the axon compartment, and delayed-rectifier IKd, calcium-dependent IKCa, transient potassium IA, transient ICaT and persistent ICaS calcium, persistent sodium INaP, and hyperpolarization-activated inward Ih in the some/neurite (S/N) compartment. To model the descending modulatory inputs, a voltage-gated inward current (such as the one activated by the neuropeptide proctolin) Iproc was added to the S/N compartment. Both compartments also contained the leak current IL. Every parameter set representing an individual model neuron was simulated and analyzed in terms of its period, burst duration, spike and slow wave amplitude, number of spikes per burst, spike frequency, and after-hyperpolarization potential, as well as the model’s responses to neuromodulator deprivation and current injections. All of the above characteristics had to be within limits determined in physiological experiments performed on the AB cell, in order for a model to be classified as functional [2]. In addition to several other data mining and visualization techniques we have previously employed to analyze the parameter space of the “good” models [3], we propose to utilize the theory of rough sets (RS) to investigate the role and importance of the parameters in differentiating between the functional and non-functional models. One of the most useful aspects of the RS theory in these kinds of classification tasks is the concept of a reduct—the smallest possible subset of attributes (i.e., maximal conductances in our model) that preserves the classification accuracy of the full set of attributes [4]. There are usually several such reducts for a given problem, and by extracting the so-called core of the reducts (i.e., the attributes that all the discovered reducts have in common), one can estimate the relative importance of the attributes. For instance, based on the 10 reducts computed from our dataset, we can state that soma CaT, NaP, Kd, KCa, and Proc, are absolutely necessary for differentiation between the functional and non-functional models (they were included in all 10 reducts), the axon Na current is very important (utilized in 9 out of 10 reducts), while the leak currents (both in the soma and the axon) seem to be the least important (they were present in 6 and 7 of the reducts, respectively). Furthermore, based on reducts, one can easily generate IF-THEN rules that not only describe how the model’s proper behavior depends on its parameters, but also how those parameters (i.e., ionic currents) “cooperate” with one another to assure such activity. For example, one of the most trustworthy rules we discovered (confidence of 78%) describes the following relationship: IF soma NaP∈[2.7μS÷6.4μS) AND soma KCa∈[3,000μS÷6,000μS) AND axon Na∈[300μS÷450μS) THEN “functional AB model,” where the values in parentheses represent the ranges for the corresponding maximum membrane conductances.