## Introduction

Pseudomonas aeruginosa is a Gram-negative bacterium capable of colonising a wide variety of different environments and habitats. The cystic fibrosis (CF) lung is one such environment and colonisation by P. aeruginosa is highly prevalent, leading to increased mortality in CF patients1. P. aeruginosa lung infections currently account for the majority of the morbidity and mortality seen in CF patients2 and the chronicity of P. aeruginosa infections is associated with the bacterium’s ability to form a biofilm3. Bacterial biofilms are comprised of colonies of bacterial cells enveloped within an extracellular matrix (ECM)4. The ECM itself encompasses polysaccharide, protein, lipid and nucleic acid constituents, referred to collectively as the matrixome5. Explanted lungs of deceased CF patients reveal that it is the mucoid P. aeruginosa phenotype that is primarily responsible for destruction of the CF lung6. The mucoid phenotype is characterised as exopolysaccharide (EPS) alginate overproducing, where its matrixome is primarily composed of linear, acetylated, anionic alginate7,8,9,10, cross-linked by calcium (Ca2+), an ion significantly elevated in the CF lung11. Recently, we have used quantum chemical Density-Functional Theory (DFT) to construct molecular models, structurally representative of the mucoid P. aeruginosa EPS, that prove Ca2+ can induce highly stable EPS aggregation relative to other biological ions elevated in CF sputum12.

The formation of stable P. aeruginosa cation cross-linked biofilm matrices relies on the quorum sensing signalling pathway. Quorum sensing (QS) is a mechanism where individual bacterial cells perceive the cell density in their local environment and, in turn, coordinate gene expression on a population-wide scale13. It is a mechanism reliant upon the production of cell-to-cell signals, called quorum sensing autoinducer (QSAI) molecules, leading to biofilm matrix proliferation14. When a single bacterium releases a QSAI molecule, it is at too small a concentration to be detected by neighbouring bacterial cells. However, if QSAI molecules are collectively released by enough bacteria, the concentration of these molecules increases past a threshold level, allowing the bacteria to recognise a critical cell mass and activate specific genes15. Specifically, for P. aeruginosa aggregates, QSAI release from approximately 2000 cells is required to initiate QS16. QS, effectively, is the mechanism underlying bacterial cell-to-cell communication and, importantly, is a mechanism active in CF lungs infected with P. aeruginosa17. Confocal laser scanning microscopy has identified the existence of three distinct ECM layers surrounding naturally occurring bacterial sub-populations embedded within biofilm matrices18. The first is a layer surrounding individual bacterial cells, the second a layer separating individual cells (intercellular ECM) and the third a layer separating different sub-populations18. Considered along-side observations that QSAI molecules can partition into the biofilm matrix19, the implication is that the QSAI molecules must pass through ECM material to reach neighbouring bacteria. The type and variety of molecular interactions that facilitate the movement of QSAI’s through the ECM is not understood and these molecules are simply assumed to be freely diffusible20,21.

The vast majority of Gram-negative bacteria utilise acetylated homoserine lactones (HSL) as their primary QSAI molecules15, which are typically specific to the LasR and/or RhlR transcriptional activators22. Specifically, C4-HSL and 3-oxo-C12-HSL are the two primary HSL based QSAI molecules utilised by P. aeruginosa in the CF lung17,23. The transcriptional regulators RhlR and LasR are bound by C4-HSL and 3-oxo-C12-HSL respectively in order to regulate the expression of several genes24,25, and transcriptome analysis has determined that between 6 and 10% of the P. aeruginosa genome is regulated by these systems26. C4-HSL is a QSAI molecule that, most notably, plays a significant role in biofilm (EPS) proliferation, maturation and virulence factor expression in P. aeruginosa biofilms24,27. There also exists a third key QSAI molecule, the Pseudomonas quinolone signal (PQS)28, which is also present in the lungs of infected CF patients29. This signal is found in higher concentrations when bacterial cultures reach the late stationary phase of growth30 and therefore plays a major role in biofilm maintenance. For example, PQS production is able to regulate the autolysis of cells31, assist in iron (Fe3+) sequestration32,33,34 and induce rhamnolipid production35.

3-oxo-C12-HSL is a QSAI molecule most implicated in the initial differentiation to the biofilm mode of life upon deposition within the CF lung, with this molecule’s role becoming negligible once bacteria have established a firm attachment to the substratum14,24,27. Conversely, C4-HSL and PQS (Fig. 1) are two QSAI molecules important for establishing mature biofilms and therefore contributing to biofilm chronicity. They are molecules that will move throughout the EPS and are ideal candidates to study possible modes of interaction with the EPS matrix. The intent of this work is to rationalise which molecular interactions dictate the motion of these molecules through the EPS, beyond the explanation of simple diffusion. The use of in silico theoretical modelling, specifically molecular dynamics and molecular docking, has been used primarily to study the origin of interactions between QS inhibitor molecules and the QS regulatory proteins LasR and RhlR36,37,38. However, there has not been application of any theoretical techniques to study the nature and origin of the interactions, at the atomic-scale, between QSAI molecules and EPS, despite its obvious connection to pharmaceutical design and EPS penetration. Therefore, the purpose of this investigation is to identify the key molecular functionality of QSAI molecules, secreted by mucoid P. aeruginosa in the CF lung, which mediate interactions with the EPS matrix. To this end, finite temperature explicit solvent molecular dynamics (MD) has been employed to identify QSAI-EPS adducts which are representative of those that occur at physiological equilibrium. Combined with DFT, to ensure accurate energy calculations of QSAI-EPS systems, post-simulation thermodynamic stabilities and binding energies of such adducts have been accurately evaluated and molecular functionality pertinent for binding elucidated at the atomic-scale.

## Results

### Exothermic association of four EPS chains about Ca2+ ions

As detailed in the “Materials and methods” section, a DFT procedure was employed to develop an exothermic calcium cross-linked 4-chain EPS network suitable for studying EPS-QSAI interactions. This 4-chain EPS model (either 4-PolyMG or 4-PolyM) was constructed through the fibrillar stacking of smaller Ca2+ cross-linked 2-chain EPS units (either two 2-PolyMG or two 2-PolyM systems).

The formation energies (evaluated according to Eq. (1)) for each stacking arrangement in the 4-PolyMG and 4-PolyM systems are given in Tables S1 and S2 respectively. In both 4-chain systems, all stacking arrangements are thermodynamically stable (all possesses negative formation energies), which shows that, independent of in which orientation the 2-chain systems aggregate, having two 2-chain systems in the vicinity of one another, and/or combining to form a larger 4-chain system, is thermodynamically stable.

The number of ionic bonds established between the adjoining stacks (Tables S1, S2) correlates well with overall thermodynamic stability, with the 4-chain systems that establish the largest and smallest number of ionic bonds corresponding to the most and least thermodynamically stable systems respectively. Furthermore, stacking arrangements that establish an equal number of ionic bonds between adjoining stacks are comparatively as stable, independent of the number of hydrogen bonds also established. This, in turn, highlights that the formation of exothermic 4-chain complexes is driven more through the formation of ionic interactions rather than hydrogen bonding interactions. Previous DFT modelling has highlighted that exothermic association of multiple algal alginate disaccharides about divalent cations is driven through ionic interactions also39 and this work extends this observation to bacterial alginates (the mucoid P. aeruginosa EPS).

The thermodynamic stability of the 4-PolyMG system increases as the number of acetyl groups facing the adjoining stack decreases and the number of ionic bonds between adjoining stacks subsequently increases. Having both acetyl groups facing away from the adjoining stack minimises steric repulsion and facilitates the close association of four chains about Ca2+ ions. Interestingly, it is thermodynamically stable to have two 2-PolyMG chains in the same vicinity without interacting, for example, when both acetyl groups face towards the adjoining stack. Similar observations have been made in MD simulated annealing studies investigating Ca2+ induced association of three copolymeric $$\beta$$-d-mannuronate-$$\alpha$$-l-guluronate decamers, which also identify multi-chain aggregations whereby the third chain lies in the vicinity of a Ca2+ cross-linked 2-chain system without directly binding40. In our models, this is a feature, driven by acetyl steric repulsion, that creates void spaces within the EPS. Structurally, P. aeruginosa biofilms can be described as open systems encompassing cells, extracellular matrix material and void spaces41, where the latter act as channels allowing the flow of water throughout the biofilm42. All stacking arrangements lead to ionic association of four chains in the 4-PolyM system, therefore, the presence of acetylated mannuronate–guluronate blocks in the EPS provides a structural origin for void spaces and water channels in mucoid P. aeruginosa biofilms.

Following subsequent DFT simulations of the 4-PolyM and 4-PolyMG systems, it is clear that the 4-PolyMG* system (Fig. 2) is slightly more thermodynamically stable relative to the 4-PolyM* system (Fig. S4). The stability difference is minor because these 4-chain complexes share highly similar geometrical features. Specifically, the average O-Ca2+, COO-Ca2+, OH-Ca2+, Glycosidic O-Ca2+ and Ring O-Ca2+ bond lengths in the 4-PolyMG* system are highly similar to those observed in the 4-PolyM* system (Table S3). The only ionic contact present in the 4-PolyM* system that isn’t present in the 4-PolyMG* system is the acetyl O-Ca2+ contact. Ionic contacts to acetyl groups, therefore, are a geometric feature that distinguishes multi-chain, exothermic, ionic association of acetylated mannuronate EPS fractions from acetylated mannuronate–guluronate EPS fractions. Acetyl groups are involved in ionic association in the former, but are implicated in increased steric repulsion and preventing ionic association in the latter. The slight difference in stability between these two systems is rationalised when considering the additional ionic contact established between adjoining stacks, the number of calcium ions involved in the formation of ionic bonds between adjoining stacks and their coordination numbers (CN). Higher maximum coordination numbers are observed in the 4-PolyMG* system (CN = 7), which also encompasses an additional ionic bond between the adjoining stacks, compared to the 4-PolyM* system (CN = 6). Furthermore, five Ca2+ ions are involved in establishing ionic bonds between the adjoining stacks in the 4-PolyMG* system, whereas only four are involved in the 4-PolyM* system. Overall, these three factors outline a larger 4-chain intracomplex space in the 4-PolyMG* system, compared to the 4-PolyM* system, making it more stable.

Within the 4-PolyMG* system, the COO-Ca2+ contacts are the ionic bonds that are most stable (shortest of all O-Ca2+ bonds with the largest bond populations; Table S3) and occur most frequently (Fig. 2). Therefore, the COO group is the functional group most implicated in the formation of an exothermic 4-chain complex, correlating well with previous findings in MD simulations of Ca2+ induced algal alginate gelation43,44,45. Ca2+ ions with CN = 7 are coordinated to four different uronate residues, whereas when the CN = 5 or 6, the Ca2+ ions are only bound to three uronate residues. Coordination to four uronate residues per Ca2+ ion is closer to the classical egg-box description of calcium chelation by alginates46. Previous DFT modelling in the group has highlighted that calcium chelation by two bacterial alginate chains deviates from the egg-box model12, so it is interesting to observe egg-box characteristics regained as the number of coordinating bacterial alginate chains increases. Even though coordination to four uronate residues is possible, no Ca2+ ion is bound to more than three EPS chains. The implication of this, is that, 3-chain complexation is possible about a single Ca2+ ion, but 4-chain complexation is not; $$\ge$$ 2 Ca2+ ions are needed to establish 4-chain aggregation. Finally, returning to the discussion on void spaces, fibrillar stacking of two 4-PolyMG* systems, to form an 8-chain system, would recover a stacking arrangement where acetyl groups face towards the adjoining stack—creating a void space. Therefore, this further highlights, in acetylated mannuronate–guluronate EPS fractions, the formation of void spaces is inevitable.

### Physiological EPS structure

The 4-PolyMGMD structure, which corresponds to the structure of the hydrated mucoid P. aeruginosa EPS at physiological temperature, is shown in Fig. 3.

Immediately, it is clear that there is a significant deviation away from the neatly stacked EPS chains obtained from the DFT modelling and the adoption of an entangled V-shaped motif. This motif isn’t unexpected, as it has also been observed in MD simulations of calcium algal alginates40. The creation of a V-shaped cleft, introduces a structural discontinuity into the EPS, which assists in rationalising the complex, discontinuous, EPS structures observed in transmission electron microscopy (TEM) measurements on P. aeruginosa biofilms47. Interestingly, the V-shaped cleft, perhaps, also provides an origin for the large-scale branched/dendritic organisation of P. aeruginosa EPS scaffolds48.

The increased conformational flexibility allows the system to undergo torsional change which maximises the establishment COO-Ca2+ interactions. The frequency of COO-Ca2+ interactions (25 contacts) far exceed the frequency of any other O-Ca2+ contact, with the only other Ca2+ coordinating oxygen functional group being the hydroxyl group (OH-Ca2+; 2 contacts). The OH-Ca2+, glycosidic O-Ca2+ and ring O-Ca2+ interactions, the latter two absent from the 4-PolyMGMD structure, are comparatively as stable in the 4-PolyMG* structure (Table S3) and are eliminated from the 4-PolyMG* structure upon thermal equilibration at 310 K as a result of the EPS chains favouring the establishment of COO-Ca2+ above all other oxygen-Ca2+ interactions. Carboxylate groups being the dominant contributor to the Ca2+ chelation geometry has been observed extensively in finite temperature MD simulations of solvated calcium alginate networks40,43,44,45,49. Combined with the 4-PolyMGMD structure obtained in this work, it is clear how the presence of temperature and solvent reduces the diversity in the geometry of the chelation site within Ca2+ chelate pockets and highlights that the preferred mode of aggregation under physiological conditions is through the carboxylate groups.

The only structural feature retained from the 4-PolyMG* system, is the acetyl groups facing away from the neighbouring stack. Therefore, there has not been a complete (180°) inversion about the chain axes in any of the EPS chains. The acetyl groups prefer to face the solvent environment than face the neighbouring stack which, in turn, reinforces the tendency of the acetyl groups to orient further away from the main EPS chains. Only Ca 2 and Ca 6 (Fig. 3) are bound to three EPS chains—all other calcium ions are involved in coordination to two EPS chains. More calcium ions were bound to three EPS chains in the exothermic 4-PolyMG* structure and, therefore, in the 4-PolyMGMD structure it is clear that the intracomplex space is heavily reduced upon thermal equilibration at physiological temperature. Effectively, the exothermic 4-chain system (4-PolyMG*) has partitioned into two sets of 2-chain systems (2 $$\times$$ 2-PolyMG systems) with only Ca 2 and Ca 6 keeping the bacterial alginate network together. The reduction in the size of the intracomplex space is the reason for the origin of V-shaped cleft. The structural morphology of the 4-PolyMGMD system, correlates well with morphologies of calcium cross-linked mannuronate–guluronate heteropolymers observed in recent large-scale multi-chain implicit solvent MD simulations50. In these simulations, heteropolymers (copolymeric mannuronate–guluronate) have increased chain flexibility relative to homopolymers (polymannuronate) which leads to entanglement upon calcium cross-linking and giving discontinuous, V-shaped, morphologies possessing open clefts after aggregation50.

### QSAI simulations

EPS-C4-HSL and EPS-PQS structures and their formation energies are shown in Figs. 4 and 5 respectively. The PQS molecule binds early and remains bound to the EPS throughout the full time-scale of the trajectory and, therefore, EPS-PQS adducts are displayed at 2 ns intervals for brevity (Fig. 5).

The C4-HSL molecule fails to show any molecular interactions with the EPS. The C4-HSL molecule liberates the cleft and migrates over the EPS interface, but after 6 ns (Fig. 4) becomes separated from the EPS and does not return. In contrast, the PQS molecule forms both an ionic interaction between its ketone oxygen and a single Ca2+ ion and a hydrogen bonding interaction between its hydroxyl group and a single EPS carboxylate group (Fig. 5). Consequently, the PQS molecule forms a thermodynamically stable ionic complex with the EPS. In fact, these interactions are sufficient to keep the PQS molecule tethered in the cleft of the 4-PolyMGMD structure, overcoming hydrophobic repulsion between the hydrocarbon and EPS chains, for the full time-scale of the trajectory. After 8 ns, the ionic ketone O-Ca2+ interaction is lost and is compensated for by a rearrangement in the single hydrogen bonding interaction, which keeps the PQS molecule bound within the cleft. The EPS-PQS adduct at 6 ns, where the hydroxyl hydrogen bond is absent and only the ketone O-Ca2+ remains, is the least thermodynamically stable configuration and, interestingly, is less stable than the EPS-PQS adduct at 10 ns where only the hydroxyl hydrogen bond exists. Fluorescence resonance energy transfer (FRET) investigations of PQS incorporation into lipopolysaccharide (LPS) scaffolds have shown the hydroxyl group to be critically important for PQS–LPS interactions51 and these simulations further call attention to the role of the PQS hydroxyl group in molecular binding. The propensity of the PQS molecule to form ionic and hydrogen bonding interactions with the EPS significantly reduces its mobility and, conversely, the C4-HSL molecule, which forms no such interactions, is notably more mobile.

Despite the C4-HSL molecule sharing similar functional groups to PQS, namely, two ketone functional groups, one located on its “head” group and the other as part of an amide linkage attaching the hydrocarbon tail, neither of these groups form any ionic interactions with the EPS Ca2+ ions. The relative hydrophobicity of C4-HSL is smaller than PQS, the latter of which possesses conjugated aromatic rings and a larger hydrocarbon tail. It is, therefore, no surprise that the C4-HSL molecule partitions more readily into bulk solvent. Biofilms are heavily hydrated systems, with the major matrix component being water52. The C4-HSL molecule has the disposition to readily move into the solvent phase and consequently into void spaces filled with water, in preference to remaining in the EPS vicinity. Now, in this circumstance, its transport is assisted by convection53 and its diffusibility increases as a result of decreased tortuosity54. Along with the absence of any molecular interactions with the EPS, this offers non-local behaviour and gives the molecule the ability to travel further distances throughout the biofilm. By contrast, the PQS molecule shows a preference for remaining in the EPS vicinity for the full time-scale of its trajectory. The PQS ketone and hydroxyl groups are heavily implicated in molecular interactions with the EPS and our simulations would suggest that PQS is, potentially, a short range QSAI signal. In fact, this complements recent secondary ion mass spectroscopy and confocal Raman microscopy studies into spatial distributions of alkyl quinolones in P. aeruginosa biofilms, which also expose PQS as a local QSAI signal55,56. AQNO, an alkyl quinolone structural analogue of PQS, where the ketone and hydroxyl groups are absent, had the larger spatial distribution56, thus, offering a link, reinforced by our simulations, between the PQS ketone and hydroxyl groups and reduced movement throughout the EPS. The localisation of PQS at the boundary between infected and non-infected sub-populations, within bacteriophage-infected P. aeruginosa biofilms, behaves as a warning signal allowing non-infected bacteria in the immediate neighbourhood to avoid danger57. The ability of the PQS molecule to localise and tether to the EPS, when the C4-HSL molecule does not, suggests that this molecule, perhaps, could be selectively retained. Local PQS retention and local signal accumulation by the EPS has survival advantages and, as these simulations outline, the two oxygen bearing functional groups are of paramount importance to facilitate this.

The EPS-C4-HSL and EPS-PQS configurations, which correspond to the minima in the configurational and electrostatic energies are shown, for reference, in Fig. S5. The C4-HSL molecule is well separated from the EPS in this configuration, with the distance from its hydrocarbon tail end to the nearest EPS acetyl and EPS-bound Ca2+ ion being ~ 16 and ~ 19 Å respectively. However, this configuration, although occupying a minima in the configurational and electrostatic energies and being well separated from the EPS, is not the most thermodynamically stable EPS-C4-HSL structure isolated from the simulations. Whilst the C4-HSL molecule can readily partition into the solvent phase, it is more thermodynamically stable for the molecule to remain within the vicinity of EPS, albeit not directly interacting with the EPS through ionic or hydrogen bonds. During the C4-HSL molecule’s migration over the EPS, it does not interfere significantly with the EPS ionic scaffold, with the average Ca2+ coordination numbers, only accounting for EPS oxygen donors, held in the range of 4 to 4.5 throughout the full time-scale of the trajectory. Hence, binding of this molecule is not influenced by the cationic charge distribution in the EPS. Conceivably, therefore, the C4-HSL molecule exploits solely Van der Waals (VdW) interactions with the EPS, which are not able to render the molecule immobile at physiological temperature. This, in turn, offers a thermodynamic rationale for the apparent free movement of this molecule. The EPS-PQS adduct corresponding with the minima in the electrostatic and configurational energies (Fig. S5a), encompasses the same ionic and hydrogen bonding molecular binding modes to the EPS as is observed throughout. Unlike the analogous C4-HSL structure, this adduct also corresponds to the most thermodynamically stable EPS-PQS system, further accentuating this molecule’s significantly larger propensity to bind to the EPS. It is important to note also, in this configuration, that the PQS $$\pi$$ system does not align in a fashion to ensure the Ca2+ is positioned above its respective plane. As such, the inference is that a quadrupole $$\pi$$-cation interaction is not a molecular interaction contributing significantly to the overall stability of the EPS-PQS complex. Indeed, previous DFT estimations of $$\pi$$-cation interactions, across an array of different aromatic systems, have shown that N-heterocyclic aromatics and the presence of electron withdrawing groups, of which both are present in PQS, lower $$\pi$$-cation binding affinities58.

Quorum quenching (QQ) has emerged in recent years as a strategy to limit and/or prevent biofilm proliferation through reducing the concentration of QSAI molecules in the biofilm, through mechanisms such as enzymatic degradation59. QQ fails to have any impact on QSAI molecules encompassed within an aqueous phase where the QSAI molecule’s motion is driven by convection53. Given the immobility of PQS relative to C4-HSL, which can partition into the solvent medium/void spaces, this work proposes PQS as a viable QQ target. In addition, the observed inability of PQS to propagate throughout the exopolysaccharide matrix underscores the requirement for this molecule to be packaged in outer-membrane vesicles (OMVs) if it is to maximise its effectiveness as a (long-range) cell-to-cell signal. Although, not all PQS molecules will be encompassed within OMVs, as it must mediate its own OMV packaging51,60 and, understandably, must exist as the free molecule to execute its virulence functions—the inclusion of PQS within OMVs is not associated with biological activity60.

Finally, the EPS-PQS adducts are generally, considering the full time-scale of the QSAI trajectories, more thermodynamically stable compared to the EPS-C4-HSL systems; the PQS has a higher EPS affinity. Although, in their most stable configurations respectively, the thermodynamic stabilities are comparable. Intriguingly, in their most stable configurations, it is as stable for the C4-HSL to not interact with the EPS as it is for the PQS molecule to interact with the EPS.

## Discussion

This work probed the origin of molecular interactions between quorum sensing autoinducer (QSAI) molecules and the mucoid P. aeruginosa exopolysaccharide (EPS) matrix, with the aim of rationalising which molecular interactions govern molecular motion throughout the EPS matrix. To achieve this, a combined molecular dynamics (MD) and Density-Functional Theory (DFT) approach has been employed to identify, and calculate the thermodynamic stability of, EPS-QSAI binding configurations that occur at physiological temperature in the presence of water.

Initially, DFT modelling assisted in the development of a large 4-chain EPS molecular model. These calculations identified that at least two Ca2+ ions are needed for the aggregation of four EPS chains and that acetylated copolymeric β-d-mannuronate-α-l-guluronate 4-chain structures are able to facilitate tight complexation about Ca2+ ions when the acetyl groups are oppositely displaced. Furthermore, this structure can be distinguished from the less stable acetylated poly-β-d-mannuronate 4-chain analogue through the absence of acetyl contributions to the Ca2+ ion chelation geometry. Stable Ca2+ cross-linked 4-chain EPS systems show regained egg-box characteristics which were lost at a 2-chain level. The DFT molecular model was transformed, using finite temperature explicit solvent MD, to a molecular model more representative of that which is observed at physiological temperature and in the presence of water. This physiological structure possesses a discontinuous, V-shaped, dendritic morphology arising from a severely reduced intracomplex space. This, in turn, is due to a reduction in the diversity of the Ca2+ chelation geometry as a result of carboxylate groups dominating the Ca2+ coordination environment over all other oxygen functionality.

A physiologically representative molecular model, combined with the MD-DFT theoretical approach, for the first time has provided atomic-scale chemical insight into the required functional groups for EPS adsorption. The C4-HSL molecule interacts with the EPS solely through VdW’s interactions, can partition readily into bulk solvent and void spaces and, is unaffected by the cationic charge distribution. It is most thermodynamically stable for the C4-HSL molecule to exist within the vicinity of the EPS and not directly interact which, in turn, offers a thermodynamic rationale for the apparent unperturbed motion of this molecule throughout the biofilm matrix. In contrast, the PQS molecule has the ability to form thermodynamically stable ionic complexes with EPS-bound Ca2+ as well as establishing a hydrogen bond directly to a single EPS chain. The PQS hydroxyl group is focal for mediating binding to the EPS and the PQS molecule is rendered immobile through EPS binding. As such, these simulations support the observation that outer-membrane vesicles are required to maximise the effectiveness of PQS as a (long range) cell-to-cell signal. Indeed, OMVs have been implicated in the transportation of PQS, but not the transportation of C4-HSL60. The MD simulations in this work answer the question, with regards to intermolecular interactions at the atomic-scale, as to why this is the case. With significantly reduced EPS mobility, the PQS molecule is identified as a potential target for quorum quenching (QQ). In fact, enzymatic PQS deactivation, for example, through exogenous supplementation 2,4-dioxygenase, has proved to be a viable strategy for eliminating PQS and PQS related virulence from P. aeruginosa biofilms61,62.

Finally, the model created and deployed in this work represents the major mucoid P. aeruginosa CF lung biofilm matrix component with the correct ionic composition. As such, the molecular interactions between the QSAI’s and the EPS, which occur at physiological equilibrium, captured in these simulations, would occur at greater length scales also. Therefore, these models and simulations provide critical molecular insight into QSAI motion that is equally as applicable when considering QSAI distribution in large complex living biofilms.

## Materials and methods

### Density functional theory (DFT)

Density functional theory (DFT) is a quantum mechanical (computational) approach to accurately predict the energy of a molecular system. Specifically, DFT is grounded on the following principle: that the total energy of a molecular system is a unique functional of the electron density63. The true density-functional, however, is unknown and various approximations to the true functional exist, each one being parameterised and made suitable for a particular chemical system. As such, it is important to ensure that the functional of choice has a proven track record in accurately predicting the energy for the system of interest.

The procedure for a DFT calculation begins with the choice of an appropriate density functional and definition of the electron density. The electron density can be written in terms of the wavefunctions which, in turn, are expanded in a basis of plane waves—defined by use of periodic boundary conditions and Bloch’s Theorem64. Pseudopotentials are employed to replace the highly oscillatory, and strongly localised, core electron wavefunctions with an electron–ion potential, permitting the use of smaller, more computationally tractable, plane wave basis expansions when describing the electron density64,65.

It is important to note that DFT calculations employing semi-local or conventional hybrid density functionals, PBE and B3LYP for example—the popular choice for biomolecular systems—fail to model dispersion interactions. Dispersion interactions, more appropriately, can be defined as the attractive part of the Van der Walls (VdW) interaction potential between atoms and molecules that are not directly bonded. Specifically, these density functionals cannot provide the desired dependence of the dispersion interaction energy on the interatomic distance66 and, consequently, energetic predictions on large molecular systems, made using these functionals, are less accurate. To rectify this issue, an empirical potential of the form $${C}_{6}{R}^{-6}$$ is added to DFT energy, with R being the interatomic distances and $${C}_{6}$$ being the dispersion coefficients67.

### Computational details

All Density Functional Theory (DFT) calculations were performed using the plane-wave Density Functional Theory (DFT) code, CASTEP64. A convergence tested cut-off energy of 900 eV was employed, as well as a Monkhorst–Pack k-point grid of 1 × 1 × 1 to sample the Brillouin zone68. On-the-fly ultrasoft pseudopotentials were used69 alongside the PBE exchange–correlation functional70. Intra- and intermolecular dispersive forces were accounted for by applying the semi-empirical dispersion correction of Tkatchenko and Scheffler71.

All molecular dynamics trajectories were computed using DL_POLY_472. The conversion of all molecular models into DL_POLY input files was performed using DL_FIELD73. Trajectories were computed with the OPLS2005 forcefield74,75 in the canonical (NVT) ensemble, where the RATTLE algorithm76 was used to constrain covalent bonds to hydrogen, meaning the integration time-step could be increased to 2 ps. The temperature was held at 310 K (body temperature) using Langevin thermostatting77. Electrostatics were treated using the Smooth-Particle-Mesh-Ewald method78 and the distance cut-offs for electrostatic and Leonard–Jones interactions were set to 1.2 nm.

### Defining an initial starting structure

An upregulation of the alginate biosynthetic gene cluster (algD) upon colonisation of the CF lung79 offers a mucoid P. aeruginosa CF lung biofilm matrix that is predominantly composed of bacterial alginate—an anionic, calcium cross-linked, acetylated polymer of mannuronate (M) and guluronate (G) structures possessing no contiguous G residues7,8,9,10. Molecular models of thermodynamically stable Ca2+ cross-linked acetylated copolymeric $$\beta$$-d-mannuronate-$$\alpha$$-l-guluronate (2-PolyMG) and Ca2+ cross-linked acetylated poly-$$\beta$$-d-mannuronate (2-PolyM) 2-chain complexes have previously been developed in the group and validated as being structurally representative of the mucoid P. aeruginosa EPS observed in vivo12. These models can be seen in Fig. S1 and were a starting point for the development of a larger-scale 4-chain system.

Two 2-PolyMG and two 2-PolyM systems were stacked on top of one another to create two 4-chain systems, a 4-polyMG and a 4-PolyM system. Stacking the 2-chain complexes on top of on another ensured that a fibrillar morphology was maintained as is observed in X-ray diffraction and SAXS measurements of calcium-alginate gels80,81. For each 4-chain system, the 2-chain complexes were stacked either parallel or antiparallel along the chain axis with the acetyl groups oriented either parallel or antiparallel. For the 4-PolyM system, which has alternating acetyl orientations, this gave four possible stacking arrangements. In the 4-PolyMG system, which has all of its acetyl groups facing the same orientation, two additional stacking arrangements arose corresponding to the antiparallel acetyl groups both facing towards or away from the neighbouring stack. The stacking arrangements for the 4-PolyMG and 4-PolyM systems are shown in Figs. S2 and S3 respectively.

Each stacking arrangement was subject to a geometry optimisation in a simulation cell measuring 42 Å $$\times$$ 29 Å $$\times$$ 45 Å. Due to the large number of different stacking arrangements, an initial screen was performed to identify the most stable stacking arrangement for the 4-PolyMG and 4-PolyM systems. During these screening optimisations, the SCF tolerance was set to $$1\times {10}^{-5}$$ eV Atom−1 and the energy, force and displacement tolerances for the geometry optimisations were set to $$5 \times {10}^{-5} \text{eV Atom}^{-1}$$, $$0.1 \text{eV}$$ Å−1 and $$5 \times {10}^{-3}$$ Å respectively. The thermodynamic stability of each 4-chain stacking arrangement was measured by means of evaluating a formation energy (Eq. (1)).

$${E}_{f}={E}_{\left\{4-chain\right\}}-{2E}_{\left\{2-chain\right\}}.$$
(1)

$${E}_{\left\{4-chain\right\}}$$ is the energy of the optimised 4-PolyMG or 4-polyM stacking arrangement and $${E}_{\left\{2-chain\right\}}$$ is the energy of the initial 2-PolyMG or 2-PolyM system. The formation energies for all stacking arrangements in the 4-PolyMG and 4-PolyM systems are shown in Tables S1 and S2 respectively. While all stacking arrangements were thermodynamically favourable (Eq. (1) returning a negative formation energy), the initial screen highlighted that the most stable arrangement within the 4-PolyMG system involved stacking the chains parallel with the two acetyl groups oriented antiparallel and facing away from adjoining stack. In the 4-PolyM system, the most stable arrangement involved stacking the chains antiparallel with the acetyl groups oriented parallel.

The most stable 4-PolyMG and 4-PolyM stacking arrangements, from here on labelled 4-PolyMG* and 4-PolyM* respectively, were further optimised at finer tolerances to obtain better converged ground-state geometries. For these optimisations the SCF tolerance was set to $$2 \times {10}^{-6}$$ eV Atom−1 and the energy, force and displacement tolerances for the optimisation were set to $$2 \times {10}^{-5} \text{eV Atom}^{-1}$$, $$0.05 \text{eV}$$ Å−1 and $$2 \times {10}^{-3}$$ Å respectively. The re-evaluated formation energies (according to Eq. (1)) are − 6.90 eV for the 4-PolyMG* structure and − 6.38 eV for the 4-PolyM* structure, meaning the association of two 2-PolyMG systems is slightly more exothermic compared to the association of two 2-PolyM systems. The 4-PolyMG* structure, therefore, corresponds to the most thermodynamically stable arrangement of four mucoid P. aeruginosa EPS chains complexed about Ca2+ ions. This structure is shown in Fig. 2 (and for reference the 4-PolyM* structure is shown in Fig. S4).

### From a DFT structure to a physiological structure

The above DFT optimisations were performed at 0 K in vacuo. Therefore, although the above optimisations allowed for the quantification and identification of the most thermodynamically stable arrangement of four mucoid P. aeruginosa EPS chains complexed about Ca2+ ions, they fail to reflect possible conformational changes that could occur at physiological temperature and in the presence of water.

The 4-PolyMG* structure was, therefore, used as an initial (starting) structure for a subsequent MD simulation to obtain a structure more representative of that observed at physiological temperature. This MD simulation was performed over 2 ns under periodic boundary conditions based on a simulation cell measuring 60 Å $$\times$$ 60 Å $$\times$$ 60 Å encompassing the 4-PolyMG* structure and SPC (Simple Point Charge) water. The thermally equilibrated 4-PolyMG* structure, from here on, is labelled as 4-PolyMGMD and can be seen in Fig. 3. This structure corresponds to a complete molecular model of a hydrated mucoid P. aeruginosa exopolysaccharide (EPS) matrix which exists at physiological temperature.

### EPS-QSAI simulations

MD simulations were performed to sample modes of interaction between the 4-PolyMGMD structure and two QSAI molecules, C4-HSL and PQS (Fig. 1). To get structures of these molecules that are representative of the conformations observed at physiological temperature, these two molecules were equilibrated over 1 ns under periodic boundary conditions in a simulation cell measuring 40 Å $$\times$$ 40 Å $$\times$$ 40 Å, solvated with SPC water.

After obtaining thermally equilibrated conformations for the two QSAI molecules, they were individually combined with 4-PolyMGMD structure, positioned (docked) 6 Å away from the base of a V-shaped cleft that opened up during its thermal equilibration at 310 K (see Fig. 3). MD trajectories were computed over 10 ns under periodic boundary conditions in a simulation cell measuring 60 Å $$\times$$ 60 Å $$\times$$ 60 Å solvated with SPC water. This trajectory length was suitable to allow the molecule to sample preferential interaction modes/binding sites. Structures (EPS-molecule adducts) were isolated from the trajectories every 1 ns, as well as at the time-step corresponding to a minima in the configurational and electrostatic energies, for subsequent DFT thermodynamic stability calculations.

### Thermodynamic stability of the EPS-QSAI adducts

If the isolated EPS-QSAI structures were separated by $$\le$$ 6 Å, their thermodynamic stabilities were evaluated by means of evaluating a formation energy (Eq. (2)).

$${E}_{f}={E}_{\left\{matrix-molecule\, adduct\right\}}-\left({E}_{\left\{4-PolyM{G}_{\left\{MD\right\}}\right\}}+{E}_{\left\{molecule\right\}}\right).$$
(2)

$${E}_{\left\{matrix-molecule \,adduct\right\}}$$ is the energy of an isolated EPS-molecule system, $${E}_{\left\{4-PolyM{G}_{\left\{MD\right\}}\right\}}$$ is the energy of the thermally equilibrated 4-PolyMGMD system and $${E}_{\left\{molecule\right\}}$$ is the energy of a thermally equilibrated molecule, either C4-HSL or PQS. The energy of each system (each term in Eq. (2)) was evaluated using 0 K in vacuo DFT single-point energy calculations where the SCF tolerance was set to $$2 \times {10}^{-6}$$ eV Atom−1. Finally, Mulliken bond populations82 were calculated to classify the nature of bonding between the EPS and the molecule in each of the final EPS-molecule adducts.