Quantifying Amide-Aromatic Interactions at Molecular and Atomic Levels: Experimentally Determined Enthalpic and Entropic Contributions to Interactions of Amide sp2O, N, C and sp3C Unified Atoms with Naphthalene sp2C Atoms in Water.

In addition to amide hydrogen bonds and the hydrophobic effect, interactions involving π-bonded sp2 atoms of amides, aromatics, and other groups occur in protein self-assembly processes including folding, oligomerization, and condensate formation. These interactions also occur in aqueous solutions of amide and aromatic compounds, where they can be quantified. Previous analysis of thermodynamic coefficients quantifying net-favorable interactions of amide compounds with other amides and aromatics revealed that interactions of amide sp2O with amide sp2N unified atoms (presumably C═O···H-N hydrogen bonds) and amide/aromatic sp2C (lone pair π, n-π*) are particularly favorable. Sp3C-sp3C (hydrophobic), sp3C-sp2C (hydrophobic, CH-π), sp2C-sp2C (hydrophobic, π-π), and sp3C-sp2N interactions are favorable, sp2C-sp2N interactions are neutral, while sp2O-sp2O and sp2N-sp2N self-interactions and sp2O-sp3C interactions are unfavorable. Here, from determinations of favorable effects of 14 amides on naphthalene solubility at 10, 25, and 45 °C, we dissect amide-aromatic interaction free energies into enthalpic and entropic contributions and find these vary systematically with amide composition. Analysis of these results yields enthalpic and entropic contributions to intrinsic strengths of interactions of amide sp2O, sp2N, sp2C, and sp3C unified atoms with aromatic sp2C atoms. For each interaction, enthalpic and entropic contributions have the same sign and are much larger in magnitude than the interaction free energy itself. The amide sp2O-aromatic sp2C interaction is enthalpy-driven and entropically unfavorable, consistent with direct chemical interaction (e.g., lone pair-π), while amide sp3C- and sp2C-aromatic sp2C interactions are entropy-driven and enthalpically unfavorable, consistent with hydrophobic effects. These findings are relevant for interactions involving π-bonded sp2 atoms in protein processes.

Quantifying Amide-Aromatic Interactions at Molecular and Atomic Levels: Experimentally-determined Enthalpic and Entropic Contributions to Interactions of Amide sp 2 O, N, C and sp 3 C Unified Atoms with Naphthalene sp 2 C Atoms in Water.

In addition to amide hydrogen bonds and the hydrophobic effect, interactions involving π-bonded sp 2 atoms of amides, aromatics and other groups occur in protein self-assembly processes including folding, oligomerization and condensate formation. These interactions also occur in aqueous solutions of amide and aromatic compounds, where they can be quantified. Previous analysis of thermodynamic coefficients quantifying net-favorable interactions of amide compounds with other amides and aromatics revealed that interactions of amide sp 2 O with amide sp 2 N unified atoms (presumably C=O···H-N hydrogen bonds) and amide/aromatic sp 2 C (lone pair-π, n-π * ) are particularly favorable. Sp 3 C-sp 3 C (hydrophobic), sp 3 C-sp 2 C (hydrophobic, CH-π), sp 2 C-sp 2 C (hydrophobic, π-π) and sp 3 C-sp 2 N interactions are favorable, sp 2 C-sp 2 N interactions are neutral, while sp 2 O-sp 2 O and sp 2 N-sp 2 N self-interactions and sp 2 O-sp 3 C interactions are unfavorable. Here, from determinations of favorable effects of fourteen amides on naphthalene solubility at 10, 25 and 45 °C, we dissect amide-aromatic interaction free energies into enthalpic and entropic contributions and find these vary systematically with amide composition. Analysis of these results yields enthalpic and entropic contributions to intrinsic strengths of interactions of amide sp 2 O, sp 2 N, sp 2 C and sp 3 C unified atoms with aromatic sp 2 C atoms. For each interaction, enthalpic and entropic contributions have the same sign and are much larger in magnitude than the interaction free energy itself. The amide sp 2 O-aromatic sp 2 C interaction is enthalpy-driven and entropically unfavorable, consistent with direct chemical interaction (e.g. lone pair-π) while amide sp 3 C- and sp 2 C-aromatic sp 2 C interactions are entropy-driven and enthalpically unfavorable, consistent with hydrophobic effects. These findings are relevant for interactions involving π-bonded sp 2 atoms in protein processes.

How Glutamate Promotes Liquid-liquid Phase Separation and DNA Binding Cooperativity of E. coli SSB Protein.

E. coli single-stranded-DNA binding protein (EcSSB) displays nearest-neighbor (NN) and non-nearest-neighbor (NNN)) cooperativity in binding ssDNA during genome maintenance. NNN cooperativity requires the intrinsically-disordered linkers (IDL) of the C-terminal tails. Potassium glutamate (KGlu), the primary E. coli salt, promotes NNN-cooperativity, while KCl inhibits it. We find that KGlu promotes compaction of a single polymeric SSB-coated ssDNA beyond what occurs in KCl, indicating a link of compaction to NNN-cooperativity. EcSSB also undergoes liquid-liquid phase separation (LLPS), inhibited by ssDNA binding. We find that LLPS, like NNN-cooperativity, is promoted by increasing [KGlu] in the physiological range, while increasing [KCl] and/or deletion of the IDL eliminate LLPS, indicating similar interactions in both processes. From quantitative determinations of interactions of KGlu and KCl with protein model compounds, we deduce that the opposing effects of KGlu and KCl on SSB LLPS and cooperativity arise from their opposite interactions with amide groups. KGlu interacts unfavorably with the backbone (especially Gly) and side chain amide groups of the IDL, promoting amide-amide interactions in LLPS and NNN-cooperativity. By contrast, KCl interacts favorably with these amide groups and therefore inhibits LLPS and NNN-cooperativity. These results highlight the importance of salt interactions in regulating the propensity of proteins to undergo LLPS.

Temperature effects on RNA polymerase initiation kinetics reveal which open complex initiates and that bubble collapse is stepwise.

Transcription initiation is highly regulated by promoter sequence, transcription factors, and ligands. All known transcription inhibitors, an important class of antibiotics, act in initiation. To understand regulation and inhibition, the biophysical mechanisms of formation and stabilization of the "open" promoter complex (OC), of synthesis of a short RNA-DNA hybrid upon nucleotide addition, and of escape of RNA polymerase (RNAP) from the promoter must be understood. We previously found that RNAP forms three different OC with λPR promoter DNA. The 37 °C RNAP-λPR OC (RPO) is very stable. At lower temperatures, RPO is less stable and in equilibrium with an intermediate OC (I3). Here, we report step-by-step rapid quench-flow kinetic data for initiation and growth of the RNA-DNA hybrid at 25 and 37 °C that yield rate constants for each step of productive nucleotide addition. Analyzed together, with previously published data at 19 °C, our results reveal that I3 and not RPO is the productive initiation complex at all temperatures. From the strong variations of rate constants and activation energies and entropies for individual steps of hybrid extension, we deduce that contacts of RNAP with the bubble strands are disrupted stepwise as the hybrid grows and translocates. Stepwise disruption of RNAP-strand contacts is accompanied by stepwise bubble collapse, base stacking, and duplex formation, as the hybrid extends to a 9-mer prior to disruption of upstream DNA-RNAP contacts and escape of RNAP from the promoter.

Experimentally determined strengths of favorable and unfavorable interactions of amide atoms involved in protein self-assembly in water.

Folding and other protein self-assembly processes are driven by favorable interactions between O, N, and C unified atoms of the polypeptide backbone and side chains. These processes are perturbed by solutes that interact with these atoms differently than water does. Amide NH···O=C hydrogen bonding and various π-system interactions have been better characterized structurally or by simulations than experimentally in water, and unfavorable interactions are relatively uncharacterized. To address this situation, we previously quantified interactions of alkyl ureas with amide and aromatic compounds, relative to interactions with water. Analysis yielded strengths of interaction of each alkylurea with unit areas of different hybridization states of unified O, N, and C atoms of amide and aromatic compounds. Here, by osmometry, we quantify interactions of 10 pairs of amides selected to complete this dataset. An analysis yields intrinsic strengths of six favorable and four unfavorable atom-atom interactions, expressed per unit area of each atom and relative to interactions with water. The most favorable interactions are sp2O-sp2C (lone pair-π, presumably n-π*), sp2C-sp2C (π-π and/or hydrophobic), sp2O-sp2N (hydrogen bonding) and sp3C-sp2C (CH-π and/or hydrophobic). Interactions of sp3C with itself (hydrophobic) and with sp2N are modestly favorable, while sp2N interactions with sp2N and with amide/aromatic sp2C are modestly unfavorable. Amide sp2O-sp2O interactions and sp2O-sp3C interactions are more unfavorable, indicating the preference of amide sp2O to interact with water. These intrinsic interaction strengths are used to predict interactions of amides with proteins and chemical effects of amides (including urea, N-ethylpyrrolidone [NEP], and polyvinylpyrrolidone [PVP]) on protein stability.

Fluorescence-Detected Conformational Changes in Duplex DNA in Open Complex Formation by Escherichia coli RNA Polymerase: Upstream Wrapping and Downstream Bending Precede Clamp Opening and Insertion of the Downstream Duplex.

FRET (fluorescence resonance energy transfer) between far-upstream (-100) and downstream (+14) cyanine dyes (Cy3, Cy5) showed extensive bending and wrapping of λPR promoter DNA on Escherichia coli RNA polymerase (RNAP) in closed and open complexes (CC and OC, respectively). Here we determine the kinetics and mechanism of DNA bending and wrapping by FRET and of formation of RNAP contacts with -100 and +14 DNA by single-dye protein-induced fluorescence enhancement (PIFE). FRET and PIFE kinetics exhibit two phases: rapidly reversible steps forming a CC ensemble ({CC}) of four intermediates [initial (RPC), early (I1E), mid (I1M), and late (I1L)], followed by conversion of {CC} to OC via I1L. FRET and PIFE are first observed for I1E, not RPc. FRET and PIFE together reveal large-scale bending and wrapping of upstream and downstream DNA as RPC advances to I1E, decreasing the Cy3-Cy5 distance to ∼75 Å and making RNAP-DNA contacts at -100 and +14. We propose that far-upstream DNA wraps on the upper ß'-clamp while downstream DNA contacts the top of the ß-pincer in I1E. Converting I1E to I1M (∼1 s time scale) reduces FRET efficiency with little change in -100 or +14 PIFE, interpreted as clamp opening that moves far-upstream DNA (on ß') away from downstream DNA (on ß) to increase the Cy3-Cy5 distance by ∼14 Å. FRET increases greatly in converting I1M to I1L, indicating bending of downstream duplex DNA into the clamp and clamp closing to reduce the Cy3-Cy5 distance by ∼21 Å. In the subsequent rate-determining DNA-opening step, in which the clamp may also open, I1L is converted to the initial unstable OC (I2). Implications for facilitation of CC-to-OC isomerization by upstream DNA and upstream binding, DNA-bending transcription activators are discussed.

RNA Polymerase: Step-by-Step Kinetics and Mechanism of Transcription Initiation.

To determine the step-by-step kinetics and mechanism of transcription initiation and escape by E. coli RNA polymerase from the λPR promoter, we quantify the accumulation and decay of transient short RNA intermediates on the pathway to promoter escape and full-length (FL) RNA synthesis over a wide range of NTP concentrations by rapid-quench mixing and phosphorimager analysis of gel separations. Experiments are performed at 19 °C, where almost all short RNAs detected are intermediates in FL-RNA synthesis by productive complexes or end-products in nonproductive (stalled) initiation complexes and not from abortive initiation. Analysis of productive-initiation kinetic data yields composite second-order rate constants for all steps of NTP binding and hybrid extension up to the escape point (11-mer). The largest of these rate constants is for incorporation of UTP into the dinucleotide pppApU in a step which does not involve DNA opening or translocation. Subsequent steps, each of which begins with reversible translocation and DNA opening, are slower with rate constants that vary more than 10-fold, interpreted as effects of translocation stress on the translocation equilibrium constant. Rate constants for synthesis of 4- and 5-mer, 7-mer to 9-mer, and 11-mer are particularly small, indicating that RNAP-promoter interactions are disrupted in these steps. These reductions in rate constants are consistent with the previously determined ∼9 kcal cost of escape from λPR. Structural modeling and previous results indicate that the three groups of small rate constants correspond to sequential disruption of in-cleft, -10, and -35 interactions. Parallels to escape by T7 RNAP are discussed.

Quantifying Interactions of Nucleobase Atoms with Model Compounds for the Peptide Backbone and Glutamine and Asparagine Side Chains in Water.

Alkylureas display hydrocarbon and amide groups, the primary functional groups of proteins. To obtain the thermodynamic information that is needed to analyze interactions of amides and proteins with nucleobases and nucleic acids, we quantify preferential interactions of alkylureas with nucleobases differing in the amount and composition of water-accessible surface area (ASA) by solubility assays. Using an established additive ASA-based analysis, we interpret these thermodynamic results to determine interactions of each alkylurea with five types of nucleobase unified atoms (carbonyl sp2O, amino sp3N, ring sp2N, methyl sp3C, and ring sp2C). All alkylureas interact favorably with nucleobase sp2C and sp3C atoms; these interactions become more favorable with an increasing level of alkylation of urea. Interactions with nucleobase sp2O are most favorable for urea, less favorable for methylurea and ethylurea, and unfavorable for dialkylated ureas. Contributions to overall alkylurea-nucleobase interactions from interactions with each nucleobase atom type are proportional to the ASA of that atom type with proportionality constant (interaction strength) α, as observed previously for urea. Trends in α-values for interactions of alkylureas with nucleobase atom types parallel those for corresponding amide compound atom types, offset because nucleobase α-values are more favorable. Comparisons between ethylated and methylated ureas show interactions of amide compound sp3C with nucleobase sp2C, sp3C, sp2N, and sp3N atoms are favorable while amide sp3C-nucleobase sp2O interactions are unfavorable. Strongly favorable interactions of urea with nucleobase sp2O but weakly favorable interactions with nucleobase sp3N indicate that amide sp2N-nucleobase sp2O and nucleobase sp3N-amide sp2O hydrogen bonding (NH···O═C) interactions are favorable while amide sp2N-nucleobase sp3N interactions are unfavorable. These favorable amide-nucleobase hydrogen bonding interactions are prevalent in specific protein-nucleotide complexes.

The mechanism and high-free-energy transition state of lac repressor-lac operator interaction.

Significant, otherwise-unavailable information about mechanisms and transition states (TS) of protein folding and binding is obtained from solute effects on rate constants. Here we characterize TS for lac repressor(R)-lac operator(O) binding by analyzing effects of RO-stabilizing and RO-destabilizing solutes on association (ka) and dissociation (kd) rate constants. RO-destabilizing solutes (urea, KCl) reduce ka comparably (urea) or more than (KCl) they increase kd, demonstrating that they destabilize TS relative to reactants and RO, and that TS exhibits most of the Coulombic interactions between R and O. Strikingly, three solutes which stabilize RO by favoring burial/dehydration of amide oxygens and anionic phosphate oxygens all reduce kd without affecting ka significantly. The lack of stabilization of TS by these solutes indicates that O phosphates remain hydrated in TS and that TS preferentially buries aromatic carbons and amide nitrogens while leaving amide oxygens exposed. In our proposed mechanism, DNA-binding-domains (DBD) of R insert in major grooves of O pre-TS, forming most Coulombic interactions of RO and burying aromatic carbons. Nucleation of hinge helices creates TS, burying sidechain amide nitrogens. Post-TS, hinge helices assemble and the DBD-hinge helix-O-DNA module docks on core repressor, partially dehydrating phosphate oxygens and tightening all interfaces to form RO.

Experimental Atom-by-Atom Dissection of Amide-Amide and Amide-Hydrocarbon Interactions in H2O.

Quantitative information about amide interactions in water is needed to understand their contributions to protein folding and amide effects on aqueous processes and to compare with computer simulations. Here we quantify interactions of urea, alkylated ureas, and other amides by osmometry and amide-aromatic hydrocarbon interactions by solubility. Analysis of these data yields strengths of interaction of ureas and naphthalene with amide sp2O, amide sp2N, aliphatic sp3C, and amide and aromatic sp2C unified atoms in water. Interactions of amide sp2O with urea and naphthalene are favorable, while amide sp2O-alkylurea interactions are unfavorable, becoming more unfavorable with increasing alkylation. Hence, amide sp2O-amide sp2N interactions (proposed n-σ* hydrogen bond) and amide sp2O-aromatic sp2C (proposed n-π*) interactions are favorable in water, while amide sp2O-sp3C interactions are unfavorable. Interactions of all ureas with sp3C and amide sp2N are favorable and increase in strength with increasing alkylation, indicating favorable sp3C-amide sp2N and sp3C-sp3C interactions. Naphthalene results show that aromatic sp2C-amide sp2N interactions in water are unfavorable while sp2C-sp3C interactions are favorable. These results allow interactions of amide and hydrocarbon moieties and effects of urea and alkylureas on aqueous processes to be predicted or interpreted in terms of structural information. We predict strengths of favorable urea-benzene and N-methylacetamide interactions from experimental information to compare with simulations and indicate how amounts of hydrocarbon and amide surfaces buried in protein folding and other biopolymer processes and transition states can be determined from analysis of urea and diethylurea effects on equilibrium and rate constants.

Basis of Protein Stabilization by K Glutamate: Unfavorable Interactions with Carbon, Oxygen Groups.

Potassium glutamate (KGlu) is the primary Escherichia coli cytoplasmic salt. After sudden osmotic upshift, cytoplasmic KGlu concentration increases, initially because of water efflux and subsequently by K+ transport and Glu- synthesis, allowing water uptake and resumption of growth at high osmolality. In vitro, KGlu ranks with Hofmeister salts KF and K2SO4 in driving protein folding and assembly. Replacement of KCl by KGlu stabilizes protein-nucleic acid complexes. To interpret and predict KGlu effects on protein processes, preferential interactions of KGlu with 15 model compounds displaying six protein functional groups-sp3 (aliphatic) C; sp2 (aromatic, amide, carboxylate) C; amide and anionic (carboxylate) O; and amide and cationic N-were determined by osmometry or solubility assays. Analysis of these data yields interaction potentials (α-values) quantifying non-Coulombic chemical interactions of KGlu with unit area of these six groups. Interactions of KGlu with the 15 model compounds predicted from these six α-values agree well with experimental data. KGlu interactions with all carbon groups and with anionic (carboxylate) and amide oxygen are unfavorable, while KGlu interactions with cationic and amide nitrogen are favorable. These α-values, together with surface area information, provide quantitative predictions of why KGlu is an effective E. coli cytoplasmic osmolyte (because of the dominant effect of unfavorable interactions of KGlu with anionic and amide oxygens and hydrocarbon groups on the water-accessible surface of cytoplasmic biopolymers) and why KGlu is a strong stabilizer of folded proteins (because of the dominant effect of unfavorable interactions of KGlu with hydrocarbon groups and amide oxygens exposed in unfolding).

Contributions of Coulombic and Hofmeister Effects to the Osmotic Activation of Escherichia coli Transporter ProP.

Osmosensing transporters mediate osmolyte accumulation to forestall cellular dehydration as the extracellular osmolality increases. ProP is a bacterial osmolyte-H(+) symporter, a major facilitator superfamily member, and a paradigm for osmosensing. ProP activity is a sigmoid function of the osmolality. It is determined by the osmolality, not the magnitude or direction of the osmotic shift, in cells and salt-loaded proteoliposomes. The activation threshold varies directly with the proportion of anionic phospholipid in cells and proteoliposomes. The osmosensory mechanism was probed by varying the salt composition and concentration outside and inside proteoliposomes. Data analysis was based on the hypothesis that the fraction of maximal transporter activity at a particular luminal salt concentration reflects the proportion of ProP molecules in an active conformation. ProP attained the same activity at the same osmolality when diverse, membrane-impermeant salts were added to the external medium. Contributions of Coulombic and/or Hofmeister salt effects to ProP activation were examined by varying the luminal salt cation (K(+) and Na(+)) and anion (chloride, phosphate, and sulfate) composition and then systematically increasing the luminal salt concentration by increasing the external osmolality. ProP activity increased with the sixth power of the univalent cation concentration, independent of the type of anion. This indicates that salt activation of ProP is a Coulombic, cation effect resulting from salt cation accumulation and not site-specific cation binding. Possible origins of this Coulombic effect include folding or assembly of anionic cytoplasmic ProP domains, an increase in local membrane surface charge density, and/or the juxtaposition of anionic protein and membrane surfaces during activation.

Chemical Interactions of Polyethylene Glycols (PEGs) and Glycerol with Protein Functional Groups: Applications to Effects of PEG and Glycerol on Protein Processes.

In this work, we obtain the data needed to predict chemical interactions of polyethylene glycols (PEGs) and glycerol with proteins and related organic compounds and thereby interpret or predict chemical effects of PEGs on protein processes. To accomplish this, we determine interactions of glycerol and tetraEG with >30 model compounds displaying the major C, N, and O functional groups of proteins. Analysis of these data yields coefficients (α values) that quantify interactions of glycerol, tetraEG, and PEG end (-CH2OH) and interior (-CH2OCH2-) groups with these groups, relative to interactions with water. TetraEG (strongly) and glycerol (weakly) interact favorably with aromatic C, amide N, and cationic N, but unfavorably with amide O, carboxylate O, and salt ions. Strongly unfavorable O and salt anion interactions help make both small and large PEGs effective protein precipitants. Interactions of tetraEG and PEG interior groups with aliphatic C are quite favorable, while interactions of glycerol and PEG end groups with aliphatic C are not. Hence, tetraEG and PEG300 favor unfolding of the DNA-binding domain of lac repressor (lacDBD), while glycerol and di- and monoethylene glycol are stabilizers. Favorable interactions with aromatic and aliphatic C explain why PEG400 greatly increases the solubility of aromatic hydrocarbons and steroids. PEG400-steroid interactions are unusually favorable, presumably because of simultaneous interactions of multiple PEG interior groups with the fused ring system of the steroid. Using α values reported here, chemical contributions to PEG m-values can be predicted or interpreted in terms of changes in water-accessible surface area (ΔASA) and separated from excluded volume effects.

Separating chemical and excluded volume interactions of polyethylene glycols with native proteins: Comparison with PEG effects on DNA helix formation.

Small and large PEGs greatly increase chemical potentials of globular proteins (µ2), thereby favoring precipitation, crystallization, and protein-protein interactions that reduce water-accessible protein surface and/or protein-PEG excluded volume. To determine individual contributions of PEG-protein chemical and excluded volume interactions to µ2 as functions of PEG molality m3 , we analyze published chemical potential increments µ23 = dµ2/dm3 quantifying unfavorable interactions of PEG (PEG200-PEG6000) with BSA and lysozyme. For both proteins, µ23 increases approximately linearly with the number of PEG residues (N3). A 1 molal increase in concentration of PEG -CH2 OCH2 - groups, for any chain-length PEG, increases µBSA by ∼2.7 kcal/mol and µlysozyme by ∼1.0 kcal/mol. These values are similar to predicted chemical interactions of PEG -CH2 OCH2 - groups with these protein components (BSA ∼3.3 kcal/mol, lysozyme ∼0.7 kcal/mol), dominated by unfavorable interactions with amide and carboxylate oxygens and counterions. While these chemical effects should be dominant for small PEGs, larger PEGS are expected to exhibit unfavorable excluded volume interactions and reduced chemical interactions because of shielding of PEG residues in PEG flexible coils. We deduce that these excluded volume and chemical shielding contributions largely compensate, explaining why the dependence of µ23 on N3 is similar for both small and large PEGs.

Coulombic free energy and salt ion association per phosphate of all-atom models of DNA oligomer: dependence on oligomer size.

We investigate how the coulombic Gibbs free energy and salt ion association per phosphate charge of DNA oligomers vary with oligomer size (i.e. number of charged residues ∣ZD∣) at 0.15 M univalent salt by non-linear Poisson Boltzmann (NLPB) analysis of all-atom DNA models. Calculations of these quantities ([Formula: see text], [Formula: see text]) are performed for short and long double-stranded (ds) and single-stranded (ss) DNA oligomers, ranging from 4 to 118 phosphates (ds) and from 2 to 59 phosphates (ss). Behaviors of [Formula: see text] and [Formula: see text] as functions of ∣ZD∣ provide a measure of the range of the coulombic end effect and determine the size of an oligomer at which an interior region with the properties (per charge) of the infinite-length polyelectrolyte first appears. This size (10-11 phosphates at each end for ds DNA and 6-9 for ss DNA at 0.15 M salt) is in close agreement with values obtained previously by Monte Carlo and NLPB calculations for cylindrical models of polyions, and by analysis of binding of oligocations to DNA oligomers. Differences in [Formula: see text] and in [Formula: see text] between ss and ds DNA are used to predict effects of oligomeric size and salt concentration on duplex stability in the vicinity of 0.15 M salt. Results of all-atom calculations are compared with results of less structurally detailed models and with experimental data.

Conditional ambiguity of one-dimensional crystal structures determined from a minimum of diffraction intensity data.

When the number of intensities greatly exceeds the number of unknown atomic coordinates, the problem of obtaining a crystal structure from the intensities is overdetermined and, for a sufficiently small structure, a chemically meaningful solution can be found by direct methods. A difficulty in determining a structure has been historically attributed to the non-uniqueness of such a structure owing to multiple, or homometric, structures that yield the same set of intensities. The number of homometric structures has not been rigorously analyzed owing to the complexity of this problem. By using the method of elementary symmetric polynomials with a new origin definition, one-dimensional crystal structures of a small number of identical atoms (N < 5), determined from a minimum (N - 1) of the lowest-resolution intensities, are enumerated. It is demonstrated that such a structure is unique for N ≤ 3. Interestingly, for N = 4, the structure can be determined either uniquely or twofold ambiguously, depending on the intensity values. These results suggest that, even for larger structures, a minimum set of (or not many more) accurately measured intensities can yield a unique structure.

Protein diffusion in the periplasm of E. coli under osmotic stress.

The physical and mechanical properties of the cell envelope of Escherichia coli are poorly understood. We use fluorescence recovery after photobleaching to measure diffusion of periplasmic green fluorescent protein and probe the fluidity of the periplasm as a function of external osmotic conditions. For cells adapted to growth in complete medium at 0.14-1.02 Osm, the mean diffusion coefficient increases from 3.4 µm² s⁻¹ to 6.6 µm² s⁻¹ and the distribution of D(peri) broadens as growth osmolality increases. This is consistent with a net gain of water by the periplasm, decreasing its biopolymer volume fraction. This supports a model in which the turgor pressure drops primarily across the thin peptidoglycan layer while the cell actively maintains osmotic balance between periplasm and cytoplasm, thus avoiding a substantial pressure differential across the cytoplasmic membrane. After sudden hyperosmotic shock (plasmolysis), the cytoplasm loses water as the periplasm gains water. Accordingly, increases threefold. The fluorescence recovery after photobleaching is complete and homogeneous in all cases, but in minimal medium, the periplasm is evidently thicker at the cell tips. For the relevant geometries, Brownian dynamics simulations in model cytoplasmic and periplasmic volumes provide analytical formulae for extraction of accurate diffusion coefficients from readily measurable quantities.

Coulombic free energy of polymeric nucleic acid: low- and high-salt analytical approximations for the cylindrical Poisson-Boltzmann model.

An accurate analytical expression for the Coulombic free energy of DNA as a function of salt concentration ([salt]) is essential in applications to nucleic acid (NA) processes. The cylindrical model of DNA and the nonlinear Poisson-Boltzmann (NLPB) equation for ions in solution are among the simplest approaches capable of describing Coulombic interactions of NA and salt ions and of providing analytical expressions for thermodynamic quantities. Three approximations for Coulombic free energy G(u,infinity)(coul) of a polymeric nucleic acid are derived and compared with the numerical solution in a wide experimental range of 1:1 [salt] from 0.01 to 2 M. Two are obtained from the two asymptotic solutions of the cylindrical NLPB equation in the high-[salt] and low-[salt] limits: these are sufficient to determine G(u,infinity)(coul) of double-stranded (ds) DNA with 1% and of single-stranded (ss) DNA with 3% accuracy at any [salt]. The third approximation is experimentally motivated Taylor series up to the quadratic term in ln[salt] in the vicinity of the reference [salt] 0.15 M. This expression with three numerical coefficients (Coulombic free energy and its first and second derivatives at 0.15 M) predicts dependence of G(u,infinity)(coul) on [salt] within 2% of the numerical solution from 0.01 to 1 M for ss (a = 7 A, b = 3.4 A) and ds (a = 10 A, b = 1.7 A) DNA. Comparison of cylindrical free energy with that calculated for the all-atom structural model of linear B-DNA shows that the cylindrical model is completely sufficient above 0.01 M of 1:1 [salt]. The choice of two cylindrical parameters, the distance of closest approach of ion to cylinder axis (radius) a and the average axial charge separation b, is discussed in application to all-atom numerical calculations and analysis of experiment. Further development of analytical expression for Coulombic free energy with thermodynamic approaches accounting for ionic correlations and specific effects is suggested.

Exact and user-friendly kinetic analysis of the two-step rapid equilibrium Michaelis-Menten mechanism.

Most enzyme kinetic experiments are carried out under pseudo-first-order conditions, that is, when one of the reactant species (the enzyme or the substrate) is in a large excess of the other species. More accurate kinetic information about the system can be gained without the restrictions of the pseudo-first-order conditions. We present a practical and general method of analysis of the common two-step rapid equilibrium Michaelis-Menten mechanism. The formalism is exact in that it does not involve any other approximations such as the steady-state, limitations on the reactant concentrations or on reaction times. We apply this method to the global analysis of kinetic progress curves for bovine alkaline phosphatase assays carried out under both pseudo-first-order and pseudo-second-order conditions.