(In)validity of the constant field and constant currents assumptions in theories of ion transport.

Constant electric fields and constant ion currents are often considered in theories of ion transport. Therefore, it is important to understand the validity of these helpful concepts. The constant field assumption requires that the charge density of permeant ions and flexible polar groups is virtually voltage independent. We present analytic relations that indicate the conditions under which the constant field approximation applies. Barrier models are frequently fitted to experimental current-voltage curves to describe ion transport. These models are based on three fundamental characteristics: a constant electric field, negligible concerted motions of ions inside the channel (an ion can enter only an empty site), and concentration-independent energy profiles. An analysis of those fundamental assumptions of barrier models shows that those approximations require large barriers because the electrostatic interaction is strong and has a long range. In the constant currents assumption, the current of each permeating ion species is considered to be constant throughout the channel; thus ion pairing is explicitly ignored. In inhomogeneous steady-state systems, the association rate constant determines the strength of ion pairing. Among permeable ions, however, the ion association rate constants are not small, according to modern diffusion-limited reaction rate theories. A mathematical formulation of a constant currents condition indicates that ion pairing very likely has an effect but does not dominate ion transport.

Electrostatics of a simple membrane model using Green's functions formalism.

The electrostatics of a simple membrane model picturing a lipid bilayer as a low dielectric constant slab immersed in a homogeneous medium of high dielectric constant (water) can be accurately computed using the exact Green's functions obtainable for this geometry. We present an extensive discussion of the analysis and numerical aspects of the problem and apply the formalism and algorithms developed to the computation of the energy profiles of a test charge (e.g., ion) across the bilayer and a molecular model of the acetylcholine receptor channel embedded in it. The Green's function approach is a very convenient tool for the computer simulation of ionic transport across membrane channels and other membrane problems where a good and computationally efficient first-order treatment of dielectric polarization effects is crucial.

Ionic interactions and the global conformations of the hammerhead ribozyme.

Here we investigate the global conformation of the hammerhead ribozyme. Electrophoretic studies demonstrate that the structure is folded in response to the concentration and type of ions present. Folding based on colinear alignment of arms II and III is suggested, with a variable angle subtended by the remaining helix I. In the probable active conformation, a small angle is subtended between helices I and II. Using uranyl photocleavage, an ion binding site has been detected in the long single-stranded region. The folded conformation could generate a preactivation of the scissile bond to permit in-line attack of the 2'-hydroxyl group, with a bound metal ion playing an integral role in the chemistry.

Quantal analysis of excitatory postsynaptic currents at the hippocampal mossy fiber-CA3 pyramidal cell synapse.

Unitary excitatory postsynaptic current (EPSC) amplitude histograms obtained from synapses between mossy fibers (MF) and CA3 pyramidal cells in hippocampus were analyzed with the aim of deriving the mean peak current of quantal events, its coefficient of variation CVq, the number of release sites NS, and the release probability PR. Unitary EPSC histograms with multiple peaks were fitted satisfactorily under the assumption that quantal events have a slightly skewed amplitude distribution and that the release mechanism is described by models with either binomial (standard), nonuniform, or nonstationary statistics. The average peak current of the quantal event derived from these fits reflected the opening of between 15 and 65 glutamate receptor (GluR) channels of the AMPAR subtype. The variability in the amplitude of quantal events is characterized by a CVq of 25% to 30%. The best fits to multiple peak EPSC histograms are obtained if it is assumed that the number of release sites contained within a single MF-bouton is between 8 and 21, a value comparable to the published number of morphologically measured presynpatic active zones and postsynaptic densities (PSDs) of individual MF-CA3 synapses. This suggests that at the MF-CA3 synapse each presynaptic zone and its associated PSD act as independent units, contributing one quantal event to unitary EPSCs. Simulations of unitary EPSC distributions, based on measurements of PSD size could, however, indicate that the interpretation of multipeak EPSC amplitude distributions at MF-CA3 synapses in terms of fluctuating release probabilities might be an over-simplification, and that postsynaptic factors may contribute significantly to fluctuations of unitary EPSC amplitudes.

DNA curvature does not require bifurcated hydrogen bonds or pyrimidine methyl groups.

Short tracts of the homopolymer dA.dT confer intrinsic curvature on the axis of the DNA double helix. This phenomenon is assumed to be a consequence of such tracts adopting a stable B'-DNA conformation that is distinct from B-form structure normally assumed by other DNA sequences. The more stable B' structure of dA.dT tracts has been attributed to several possible stabilizing factors: (1) optimal base stacking interactions consequent upon the high propeller twist, (2) bifurcated hydrogen bonds between adjacent dA.dT base-pairs, (3) stacking interactions involving the dT methyl groups, and finally (4) a putative spine of ordered water molecules in the minor groove. DNA oligodeoxynucleotides have been synthesized that enable these hypotheses to be tested; of particular interest is the combination of effects due to bifurcation (2) and methylation of the pyrimidines nucleotides (3). The data indicate that neither bifurcated hydrogen bonds nor pyrimidine methyl groups nor both are essential for DNA curvature. The data further suggest that the influence of the minor groove spine of hydration on the B'-formation is small. The experiments favor the hypothesis that base stacking interactions are the dominant force in stabilizing the B'-form structure.

Modeling DNA structures: molecular mechanics and molecular dynamics.

Model building studies may be used to supplement structurally low resolution experimental data with detailed three-dimensional hypothetical atomic models. Because of the strong relation between structure and function in biological molecules such models may give a consistent, integral view of a wealth of experimental data. In most cases such models will predict the outcome of certain experiments. The outcome of these experiments will often either confirm the model may be used for further refinement or even demand a major revision of the model. Coordinates obtained from X-ray fiber diffraction data or in special cases single-crystal data may provide the elements for DNA or RNA model building. Local and nonlocal optimization may be used to refine these structures and to evaluate their statistical significance as estimated by a chosen force field. Appreciable progress using nonlocal optimization procedures can only be expected if the dimensionality of the problem can be reduced sufficiently to the relevant degrees of freedom. Taking advantage of structural symmetries may critically improve the convergence while refining the target molecule or its building blocks. Monte Carlo and molecular dynamics methods allow one to calculate averaged quantities. In addition, molecular dynamics provides time evolutions of certain averages. During the simulation of certain physical properties of molecules a huge amount of data will be generated. They will provide many answers, but these answers may not always apply to the original question. So what type of questions will be reliably answered by a force field? Relatively safe answers concern the local geometry of the molecules. If a conformation leads to strong distortions of bond distances or angles or to close van der Waals contacts, this conformation can safely be rejected. Optimizing such unfavorable structures energetically may lead to structures showing how to avoid such distortions. More difficult are energetical questions: which of two conformers is more stable, or what is the free energy of the substrate in the active site? One cannot always be sure that the force field provides the correct answer. Therefore, one should pose only those questions which can be checked experimentally. Because of the many possible answers, the experiment may benefit by starting with a choice proposed by the simulation. The application of this procedure to curved DNA and the DNA four-way junction was successful.

Modeling DNA structures.

For a molecule of biological importance, one expects a strong correlation between the three-dimensional structure and its biological function(s). Molecular simulations allow the prediction of physical properties of macromolecules. Many of these properties are closely related to the molecular structure. Model-building studies may thus supplement structurally low-resolution experimental data with detailed three-dimensional hypothetical atomic models. Such studies may give a consistent integral view of a wealth of experimental data. In most cases, such models will predict the outcome of certain experiments. Their actual results will often either confirm the model, be used for further refinement, or demand a major revision. Empirical force-fields provide a large amount of physicochemical knowledge concerning structural and other physical properties about various classes of molecules. They give reasonable bond distances and angles and prevent short van der Waals contacts. Difficulties arise for the prediction of large-scale structural elements. These are not only determined by short-range interactions, but also result from long-range electrostatic, hydration, and hydrophobic forces. In the case of the ionically driven DNA B-Z transition, the point of transition as a function of ionic strength and size can be correctly predicted (33). More must be done for a better understanding of the hydration forces (6). What type of questions will be reliably answered by a force-field? Relatively safe answers concern the local geometry of the molecules. If a conformation leads to strong distortions of bond distances or angles or to close van der Waals contacts, it can safely be rejected. Optimizing such unfavorable structures energetically may lead to structures showing how to avoid such distortions. More difficult are energetic questions: Which of two conformers is more stable, or what is the free energy of the substrate in the active site (63)? One cannot always be sure that the force-field provides the correct answers. Therefore, one should concentrate on questions that can be checked experimentally. The application of such concepts to model curved DNA (19, 60) and the DNA four-way junction (61) provides promising results. To explore the knowledge contained in the force-fields, several methods have been proposed. Taking advantage of structural symmetries may improve critically the convergence, while refining the target molecule or its building blocks. A numerically stable derivative for the torsion potential has been proposed. The optimization method of conjugated gradients (see Section II,B) is a powerful tool to find the way downhill toward a local minimum. To surmount barriers and escape local minima requires nonlocal optimization procedures.(ABSTRACT TRUNCATED AT 400 WORDS)

Model for the interaction of DNA junctions and resolving enzymes.

Four-way DNA junctions are thought to be important intermediates in a number of recombination processes. Resolution of these junctions occurs by cleavage of two strands of DNA to generate two duplex molecules. The interaction between DNA junctions and resolving enzymes appears to be largely structure-specific, reflecting a molecular recognition on a significant scale. We propose a working model for this interaction that takes account of the present state of knowledge of the structure of the DNA junction, and the substrate requirements of the enzymes. We note that three different enzymes introduce cleavages at phosphodiester bonds that are presented on one side of the molecule, suggesting that the enzymes selectively interact with this face of the junction. By forcing a junction of constant sequence to adopt one or other of the two possible antiparallel isomers, we show that the junction is cleaved in such a way as to suggest a constant mode of interaction with the protein that is dependent on structure rather than sequence. We propose that the feature that is recognized is a mutual inclination of two DNA helices at approximately 120 degrees. We show that a number of DNA substrates that contain similar inclined helices, such as a three-way junction, bulged duplexes and a duplex that is curved because of repeated runs of oligoadenine sequences, are each cleaved by phage T4 endonuclease VII. This mode of DNA-protein interaction could be significant in either recombination or DNA repair processes.

Rings of anionic amino acids as structural determinants of ion selectivity in the acetylcholine receptor channel.

To gain an insight into the molecular basis of the weak but significant selectivity among alkali metal cations of the nicotinic acetylcholine receptor (AChR) channel, we have determined single-channel conductance and permeability ratios for alkali metal cations on specifically mutated Torpedo californica AChR channels expressed in Xenopus oocytes. The mutations involved charged and polar side chains in the three anionic rings (extracellular, intermediate and cytoplasmic ring) which have previously been found to determine the rate of K+ transport through the AChR channel. The results obtained reveal that mutations in the intermediate ring exert much stronger effects on ion selectivity than do mutations in the extracellular and the cytoplasmic ring. The experimental results, together with simulations of the channel's energy profile, suggest that the amino acid residues forming the intermediate ring come into close contact with permeating cations and possibly represent part of the physical correlate of the postulated selectivity filter in the AChR channel.

The stereochemistry of a four-way DNA junction: a theoretical study.

The stereochemical conformation of the four-way helical junction in DNA (the Holliday junction; the postulated central intermediate of genetic recombination) has been analysed, using molecular mechanical computer modelling. A version of the AMBER program package was employed, that had been modified to include the influence of counterions and a global optimisation procedure. Starting from an extended planar structure, the conformation was varied in order to minimise the energy, and we discuss three structures obtained by this procedure. One structure is closely related to a square-planar cross, in which there is no stacking interaction between the four double helical stems. This structure is probably closely similar to that observed experimentally in the absence of cations. The remaining two structures are based on related, yet distinct, conformations, in which there is pairwise coaxial stacking of neighbouring stems. In these structures, the four DNA stems adopt the form of two quasi-continuous helices, in which base stacking is very similar to that found in standard B-DNA geometry. The two stacked helices so formed are not aligned parallel to each other, but subtend an angle of approximately 60 degrees. The strands that exchange between one stacked helix and the other are disposed about the smaller angle of the cross (i.e. 60 degrees rather than 120 degrees), generating an approximately antiparallel alignment of DNA sequences. This structure is precisely the stacked X-structure proposed on the basis of experimental data. The calculations indicate distortions from standard B-DNA conformation that are required to adopt the stacked X-structure; a widening of the minor groove at the junction, and reorientation of the central phosphate groups of the exchanging strands. An important feature of the stacked X-structure is that it presents two structurally distinct sides. These may be recognised differently by enzymes, providing a rationalisation for the points of cleavage by Holliday resolvases.

Fluorescence energy transfer shows that the four-way DNA junction is a right-handed cross of antiparallel molecules.

The four-way junction between DNA helices is the central intermediate in recombination, and the manner of its interaction with resolvase enzymes can determine the genetic outcome of the process. A knowledge of its structure is a prerequisite to understanding the interaction with proteins, and there has been recent progress. Here we use fluorescence energy transfer to determine the relative distances between the ends of a small DNA junction, and hence the path of the strands. Our results are consistent with the geometry of an 'X'. The interconnected helices are juxtaposed so that the continuous strands of each helix generate an antiparallel alignment, and the two interchanged strands do not cross at the centre. The acute angle of the X structure is defined by a right-handed rotation of the helical axes about the axis perpendicular to the X plane, as viewed from the centre of the X.

The structure of the Holliday junction, and its resolution.

The Holliday (four-way) junction is a critical intermediate in homologous genetic recombination. We have studied the structure of a series of four-way junctions, constructed by hybridization of four 80 nucleotide synthetic oligonucleotides. These molecules migrate anomalously slowly in gel electrophoresis. Each arm of any junction could be selectively shortened by cleavage at a unique restriction site, and we have studied the relative gel mobilities of species in which two arms were cleaved. The pattern of fragments observed argues strongly for a structure with two-fold symmetry, based on an X shape, the long arms of which are made from pairwise colinear association of helical arms. The choice of partners is governed by the base sequence at the junction, allowing a potential isomerization between equivalent structural forms. Resolvase enzymes can distinguish between these structures, and the resolution products are determined by the structure adopted, i.e., by the sequence at the junction. In the absence of cations, the helical arms of the junction are fully extended in a square configuration, and unstacking results in junction thymines becoming reactive to osmium tetroxide.

Parallel stranded DNA.

A series of four hairpin deoxyoligonucleotides was synthesized with a four-nucleotide central loop (either C or G) flanked by the complementary sequences d(T)10 and d(A)10. Two of the molecules contain either a 3'-p-3' or 5'-p-5' linkage in the loop, so that the strands in the stem have the same, that is, parallel (ps) polarity. The pair of reference oligonucleotides have normal phosphodiester linkages throughout and antiparallel (aps) stem regions. All the molecules adopt a duplex helical structure in that (i) the electrophoretic mobilities in polyacrylamide gels of the ps and aps oligomers are similar. (ii) The ps hairpins are substrates for T4 polynucleotide kinase, T4 DNA ligase, and Escherichia coli exonuclease III. (iii) Salt-dependent thermal transitions are observed for all hairpins, but the ps molecules denature 10 degrees C lower than the corresponding aps oligomers. (iv) The ultraviolet absorption and circular dichroism spectra are indicative of a base-paired duplex in the stems of the ps hairpins but differ systematically from those of the aps counterparts. (v) The bis-benzimidazole drug Hoechst-33258, which binds in the minor groove of B-DNA, exhibits very little fluorescence in the presence of the ps hairpins but a normal, enhanced emission with the aps oligonucleotides. In contrast, the intercalator ethidium bromide forms a strongly fluorescent complex with all hairpins, the intensity of which is even higher for the ps species. (vi) The pattern of chemical methylation is the same for both the ps and aps hairpins. The combined results are consistent with the prediction from force field analysis of a parallel stranded right-handed helical form of d(A)n.d(T)n with a secondary structure involving reverse Watson-Crick base pairs and a stability not significantly different from that of the B-DNA double helix. Models of the various hairpins optimized with force field calculations are described.

The influence of exocyclic substituents of purine bases on DNA curvature.

Complementary oligonucleotides with 5' overhanging deoxyguanosine or deoxycytidine stretches, respectively, of the general form 5'-d(GGGCAARAAC).5'-d(CCCGTTYTTG), where R represents the bases adenine (A), hypoxanthine (base of inosine nucleoside, I), purine (R), 2-aminopurine (n2R), or 2,6-diaminopurine (n2,6(2)R) and where Y represents the pyrimidine bases thymine (T) or cytosine (C), have been chemically synthesized. After hybridization of complementary fragments, they were ligated to form multimers and analyzed by polyacrylamide gel electrophoresis. Anomalous gel migration was observed for the sequences 5'-d(AARAA) when the R.Y base pair was dA.dT, dI.dC, or dR.dT. All of these base pairs lack at least the amino group at position 2 of the purine base. The degree of anomalous gel migration was also related to the substituent at position 6 of the purine base. An amino group at position 6 was more effective than a carbonyl or a hydrogen in inducing anomalous gel migration. Additionally, the fragments 5'-d(GGGCAIAIAC).5'-d(CCCGTCTCTG), 5'-d(GGGCAIIIAC).5'-d(CCCGTCCCTG), and 5'-d(GGGCIIAIIC).5'-d(CCCGCCTCCG) were prepared in which increasing numbers of dA.dT base pairs are replaced by dI.dC base pairs. The degree of gel-migration anomaly of these sequences correlates with the number of dA.dT base pairs left in the five-base purine block. The data support the hypothesis that within the deoxyadenosine tracts, the base pairs fold into the minor groove at position 2 of the base to balance for the NH2 groups at position 6. This hypothesis explains the formation of a B'-form DNA structure for the deoxyadenosine tracts as well as DNA curvature.

Molecular mechanics calculations of dA12.dT12 and of the curved molecule d(GCTCGAAAAA)4.d(TTTTTCGAGC)4.

Using the AMBER software package (Weiner and Kollman 1981) substantially modified for electrostatic contributions, the structural energies of the double-stranded oligonucleotides dA12.dT12 and d(GCTCGAAAAA)4.d(TTTTTCGAGC)4 were minimized. Using various starting structures for the molecule dA12.dT12, one final structure is obtained which possesses the experimentally determined properties of poly(dA).poly(dT). This structure is an A-form-B-form-hybrid structure similar to that of Arnott et al. (1983). The dA-strand is similar to an A-form while the dT-strand is similar to normal B-form. This structure and separately optimized B-form sequence stretches were used to construct the double-stranded fragment d(GCTCGAAAAA)4 which again was optimized. This sequence, when imbedded in a DNA fragment as contiguous repeats, shows a gel migration anomaly which has been interpreted as stable curvature of the DNA (Diekmann 1986). The calculated structure of this sequence indeed has a curved helix axis and is discussed as a model for curved DNA. A theoretical formalism is presented which allows one to calculate the structural parameters of any nucleic acid double helix in two different geometrical representations. This formalism is used to determine the parameters of the base-pair orientations of the curved structure in terms of wedge as well as cylindrical parameters. In the structural model presented here, the curvature of the helix axis results from an alternation of two different DNA structures in which the base-pairs possess different angles with the helix axis ('cylinder tilt'). Resulting from geometric restraints, a negative cylinder tilt angle correlates strongly with the closing of the minor groove ('wedge roll'). The blocks with different structure are not exactly coincident with the dA5-blocks and the B-DNA stretches. Within the dA5 block, base-pair tilt and wedge roll adopt large values which proceed into the 3' flanking B-DNA sequence by about one base-pair. These properties of the structure calculated here are discussed in terms of different models explaining DNA curvature.