Multispecies activity screening of microcin J25 mutants yields antimicrobials with increased specificity toward pathogenic Salmonella species relative to human commensal Escherichia coli.

Modern large-scale agricultural practices that incorporate high density farming with subtherapeutic antibiotic dosing are considered a major contributor to the rise of antibiotic-resistant bacterial infections of humans with species of Salmonella being a leading agriculture-based bacterial infection. Microcin J25, a potent and highly stable antimicrobial peptide active against Enterobacteriaceae, is a candidate antimicrobial against multiple Salmonella species. Emerging evidence supports the hypothesis that the composition of the microbiota of the gastrointestinal tract prevents a variety of diseases by preventing infectious agents from proliferating. Reducing clearance of off-target bacteria may decrease susceptibility to secondary infection. Of the Enterobacteriaceae susceptible to microcin J25, Escherichia coli are the most abundant within the human gut. To explore the modulation of specificity, a collection of 207 mutants encompassing 12 positions in both the ring and loop of microcin J25 was built and tested for activity against Salmonella and E. coli strains. As has been found previously, mutational tolerance of ring residues was lower than loop residues, with 22% and 51% of mutations, respectively, retaining activity toward at least one target within the target organism test panel. The multitarget screening elucidated increased mutational tolerance at position G2, G3, and G14 than previously identified in panels composed of single targets. Multiple mutations conferred differential response between the different targets. Examination of specificity differences between mutants found that 30% showed significant improvements to specificity toward any of the targets. Generation and testing of a combinatorial library designed from the point-mutant study revealed that microcin J25I13T reduces off-target activity toward commensal human-derived E. coli isolates by 81% relative to Salmonella enterica serovar Enteritidis. These in vitro specificity improvements are likely to improve in vivo treatment efficacy by reducing clearance of commensal bacteria in the gastrointestinal tract of hosts.

On Differences between Deterministic and Stochastic Models of Chemical Reactions: Schlögl Solved with ZI-Closure.

Deterministic and stochastic models of chemical reaction kinetics can give starkly different results when the deterministic model exhibits more than one stable solution. For example, in the stochastic Schlögl model, the bimodal stationary probability distribution collapses to a unimodal distribution when the system size increases, even for kinetic constant values that result in two distinct stable solutions in the deterministic Schlögl model. Using zero-information (ZI) closure scheme, an algorithm for solving chemical master equations, we compute stationary probability distributions for varying system sizes of the Schlögl model. With ZI-closure, system sizes can be studied that have been previously unattainable by stochastic simulation algorithms. We observe and quantify paradoxical discrepancies between stochastic and deterministic models and explain this behavior by postulating that the entropy of non-equilibrium steady states (NESS) is maximum.

Solving Stochastic Reaction Networks with Maximum Entropy Lagrange Multipliers.

The time evolution of stochastic reaction networks can be modeled with the chemical master equation of the probability distribution. Alternatively, the numerical problem can be reformulated in terms of probability moment equations. Herein we present a new alternative method for numerically solving the time evolution of stochastic reaction networks. Based on the assumption that the entropy of the reaction network is maximum, Lagrange multipliers are introduced. The proposed method derives equations that model the time derivatives of these Lagrange multipliers. We present detailed steps to transform moment equations to Lagrange multiplier equations. In order to demonstrate the method, we present examples of non-linear stochastic reaction networks of varying degrees of complexity, including multistable and oscillatory systems. We find that the new approach is as accurate and significantly more efficient than Gillespie's original exact algorithm for systems with small number of interacting species. This work is a step towards solving stochastic reaction networks accurately and efficiently.

Interactions of a class IIb bacteriocin with a model lipid bilayer, investigated through molecular dynamics simulations.

The emergence of antibiotic resistant microorganisms poses an alarming threat to global health. Antimicrobial peptides (AMPs) are considered a possible effective alternative to conventional antibiotic therapies. An understanding of the mechanism of action of AMPs is needed in order to better control and optimize their bactericidal activity. Plantaricin EF is a heterodimeric AMP, consisting of two peptides Plantaricin E (PlnE) and Plantaricin F (PlnF). We studied the behavior of these peptides on the surface of a model lipid bilayer. We identified the residues that facilitate peptide-peptide interactions. We also identified residues that mediate interactions of the dimer with the membrane. PlnE interacts with the membrane through amino acids at both its termini, while only the N terminus of PlnF approaches the membrane. By comparing the activity of single-site mutants of the two-peptide bacteriocin and the simulations of the bacteriocin on the surface of a model lipid bilayer, structure activity relationships are proposed. These studies allow us to generate hypotheses that relate biophysical interactions observed in simulations with the experimentally measured activity. We find that single-site amino acid substitutions result in markedly stronger antimicrobial activity when they strengthen the interactions between the two peptides, while, concomitantly, they weaken peptide-membrane association. This effect is more pronounced in the case of the PlnE mutant (G20A), which interacts the strongest with PlnF and the weakest with the membrane while displaying the highest activity.

Characterization of Class IIa Bacteriocin Resistance in Enterococcus faecium.

Vancomycin-resistant enterococci, particularly resistant Enterococcus faecium, pose an escalating threat in nosocomial environments because of their innate resistance to many antibiotics, including vancomycin, a treatment of last resort. Many class IIa bacteriocins strongly target these enterococci and may offer a potential alternative for the management of this pathogen. However, E. faecium's resistance to these peptides remains relatively uncharacterized. Here, we explored the development of resistance of E. faecium to a cocktail of three class IIa bacteriocins: enterocin A, enterocin P, and hiracin JM79. We started by quantifying the frequency of resistance to these peptides in four clinical isolates of E. faecium We then investigated the levels of resistance of E. faecium 6E6 mutants as well as their fitness in different carbon sources. In order to elucidate the mechanism of resistance of E. faecium to class IIa bacteriocins, we completed whole-genome sequencing of resistant mutants and performed reverse transcription-quantitative PCR (qRT-PCR) of a suspected target mannose phosphotransferase (ManPTS). We then verified this ManPTS's role in bacteriocin susceptibility by showing that expression of the ManPTS in Lactococcus lactis results in susceptibility to the peptide cocktail. Based on the evidence found from these studies, we conclude that, in accord with other studies in E. faecalis and Listeria monocytogenes, resistance to class IIa bacteriocins in E. faecium 6E6 is likely caused by the disruption of a particular ManPTS, which we believe we have identified.

Rare loss-of-function mutation in complement component C3 provides insight into molecular and pathophysiological determinants of complement activity.

The plasma protein C3 is a central element in the activation and effector functions of the complement system. A hereditary dysfunction of C3 that prevents complement activation via the alternative pathway (AP) was described previously in a Swedish family, but its genetic cause and molecular consequences have remained elusive. In this study, we provide these missing links by pinpointing the dysfunction to a point mutation in the ß-chain of C3 (c.1180T > C; p.Met(373)Thr). In the patient's plasma, AP activity was completely abolished and could only be reconstituted with the addition of normal C3. The M373T mutation was localized to the macroglobulin domain 4 of C3, which contains a binding site for the complement inhibitor compstatin and is considered critical for the interaction of C3 with the AP C3 convertase. Structural analyses suggested that the mutation disturbs the integrity of macroglobulin domain 4 and induces conformational changes that propagate into adjacent regions. Indeed, C3 M373T showed an altered binding pattern for compstatin and surface-bound C3b, and the presence of Thr(373) in either the C3 substrate or convertase-affiliated C3b impaired C3 activation and opsonization. In contrast to known gain-of-function mutations in C3, patients affected by this loss-of-function mutation did not develop familial disease, but rather showed diverse and mostly episodic symptoms. Our study therefore reveals the molecular mechanism of a relevant loss-of-function mutation in C3 and provides insight into the function of the C3 convertase, the differential involvement of C3 activity in clinical conditions, and some potential implications of therapeutic complement inhibition.

Maximum Entropy Prediction of Non-Equilibrium Stationary Distributions for Stochastic Reaction Networks with Oscillatory Dynamics.

Many chemical reaction networks in biological systems present complex oscillatory dynamics. In systems such as regulatory gene networks, cell cycle, and enzymatic processes, the number of molecules involved is often far from the thermodynamic limit. Although stochastic models based on the probabilistic approach of the Chemical Master Equation (CME) have been proposed, studies in the literature have been limited by the challenges of solving the CME and the lack of computational power to perform large-scale stochastic simulations. In this paper, we show that the infinite set of stationary moment equations describing the stochastic Brusselator and Schnakenberg oscillatory reactions networks can be truncated and solved using maximization of the entropy of the distributions. The results from our numerical experiments compare with the distributions obtained from well-established kinetic Monte Carlo methods and suggest that the accuracy of the prediction increases exponentially with the closure order chosen for the system. We conclude that maximum entropy models can be used as an efficient closure scheme alternative for moment equations to predict the non-equilibrium stationary distributions of stochastic chemical reactions with oscillatory dynamics. This prediction is accomplished without any prior knowledge of the system dynamics and without imposing any biased assumptions on the mathematical relations among species involved.

Structure-Function Analysis of the Two-Peptide Bacteriocin Plantaricin EF.

Plantaricin EF is a two-peptide bacteriocin that depends on the complementary action of two different peptides (PlnE and PlnF) to function. The structures of the individual peptides have previously been analyzed by nuclear magnetic resonance spectroscopy ( Fimland, N. et al. ( 2008 ) , Biochim. Biophys. Acta 1784 , 1711 - 1719 ), but the bacteriocin structure and how the two peptides interact have not been determined. All two-peptide bacteriocins identified so far contain GxxxG motifs. These motifs, together with GxxxG-like motifs, are known to mediate helix-helix interactions in membrane proteins. We have mutated all GxxxG and GxxxG-like motifs in PlnE and PlnF in order to determine if any of these motifs are important for antimicrobial activity and thus possibly for interactions between PlnE and PlnF. Moreover, the aromatic amino acids Tyr and Trp in PlnE and PlnF were substituted, and four fusion polypeptides were constructed in order to investigate the relative orientation of PlnE and PlnF in target cell membranes. The results obtained with the fusion polypeptides indicate that PlnE and PlnF interact in an antiparallel manner and that the C-terminus of PlnE and N-terminus of PlnF are on the outer part of target cell membranes and the N-terminus of PlnE and C-terminus of PlnF are on the inner part. The preference for an aromatic residue at position 6 in PlnE suggests a positioning of this residue in or near the membrane interface on the cells inside. Mutations in the GxxxG motifs indicate that the G5xxxG9 motif in PlnE and the S26xxxG30 motif in PlnF are involved in helix-helix interactions. Atomistic molecular dynamics simulation of a structural model consistent with the results confirmed the stability of the structure and its orientation in membranes. The simulation approved the anticipated interactions and revealed additional interactions that further increase the stability of the proposed structure.

Enterocin A mutants identified by saturation mutagenesis enhance potency towards vancomycin-resistant Enterococci.

Vancomycin-resistant Enterococci infections are a significant clinical problem. One proposed solution is to use probiotics, such as lactic acid bacteria, to produce antimicrobial peptides at the site of infection. Enterocin A, a class 2a bacteriocin, exhibits inhibitory activity against E. faecium and E. faecalis, which account for 86% of vancomycin-resistant Enterococci infections. In this study, we aimed to engineer enterocin A mutants with enhanced potency within a lactic acid bacterial production system. Peptide mutants resulting from saturation mutagenesis at sites A24 and T27 were efficiently screened in a 96-well plate assay for inhibition of pathogen growth. Several mutants exhibit increased potency relative to wild-type enterocin A in both liquid- and solid-medium growth assays. In particular, A24P and T27G exhibit enhanced inhibition of multiple strains of E. faecium and E. faecalis, including clinically isolated vancomycin-resistant strains. A24P and T27G enhance killing of E. faecium 8 by 13 ± 3- and 18 ± 4-fold, respectively. The engineered enterocin A/lactic acid bacteria systems offer significant potential to combat antibiotic-resistant infections.

A closure scheme for chemical master equations.

Probability reigns in biology, with random molecular events dictating the fate of individual organisms, and propelling populations of species through evolution. In principle, the master probability equation provides the most complete model of probabilistic behavior in biomolecular networks. In practice, master equations describing complex reaction networks have remained unsolved for over 70 years. This practical challenge is a reason why master equations, for all their potential, have not inspired biological discovery. Herein, we present a closure scheme that solves the master probability equation of networks of chemical or biochemical reactions. We cast the master equation in terms of ordinary differential equations that describe the time evolution of probability distribution moments. We postulate that a finite number of moments capture all of the necessary information, and compute the probability distribution and higher-order moments by maximizing the information entropy of the system. An accurate order closure is selected, and the dynamic evolution of molecular populations is simulated. Comparison with kinetic Monte Carlo simulations, which merely sample the probability distribution, demonstrates this closure scheme is accurate for several small reaction networks. The importance of this result notwithstanding, a most striking finding is that the steady state of stochastic reaction networks can now be readily computed in a single-step calculation, without the need to simulate the evolution of the probability distribution in time.

Chloride-Inducible Expression Vector for Delivery of Antimicrobial Peptides Targeting Antibiotic-Resistant Enterococcus faecium.

Antibiotic-resistant enterococcal infections are a major concern in hospitals where patients with compromised immunity are readily infected. Enterococcus faecium bacteria are of particular interest as these pathogens account for over 80% of vancomycin-resistant enterococcal infections. Antimicrobial peptides (AMPs) produced at the site of infection by engineered bacteria may offer a potential alternative to traditional antibiotics for the treatment of resistant bacteria such as E. faecium. For this mode of delivery to be effective, it is essential to identify a suitable protein expression system that can be used in the desired delivery bacterium. In this study, we describe a promising chloride-inducible promoter and its application in the bacterial delivery of AMPs from Lactococcus lactis to reduce counts of E. faecium bacteria in vitro. Reporter gene studies show that at chloride concentrations found within the human intestines, the chloride-inducible promoter exhibits high levels of protein expression compared to those of the commonly used nisin-inducible promoter. These results indicate that this system is powerful and would not require the exogenous administration of an inducer molecule. In its application for AMP production against E. faecium in vitro, L. lactis producing AMPs under the chloride promoter rapidly decreased E. faecium counts by nearly 10,000-fold. As an extension of this application, we also demonstrate the potential in using this type of delivery system in combination with traditional antibiotics to slow the development of resistance. Collectively, this study shows the promise of using a chloride-inducible promoter for the bacterial delivery of AMPs in the body for the treatment of vancomycin-resistant enterococci (VRE) and other antibiotic-resistant bacteria.

On a theory of stability for nonlinear stochastic chemical reaction networks.

We present elements of a stability theory for small, stochastic, nonlinear chemical reaction networks. Steady state probability distributions are computed with zero-information (ZI) closure, a closure algorithm that solves chemical master equations of small arbitrary nonlinear reactions. Stochastic models can be linearized around the steady state with ZI-closure, and the eigenvalues of the Jacobian matrix can be readily computed. Eigenvalues govern the relaxation of fluctuation autocorrelation functions at steady state. Autocorrelation functions reveal the time scales of phenomena underlying the dynamics of nonlinear reaction networks. In accord with the fluctuation-dissipation theorem, these functions are found to be congruent to response functions to small perturbations. Significant differences are observed in the stability of nonlinear reacting systems between deterministic and stochastic modeling formalisms.

Convergent transcription confers a bistable switch in Enterococcus faecalis conjugation.

Convergent gene pairs with head-to-head configurations are widespread in both eukaryotic and prokaryotic genomes and are speculated to be involved in gene regulation. Here we present a unique mechanism of gene regulation due to convergent transcription from the antagonistic prgX/prgQ operon in Enterococcus faecalis controlling conjugative transfer of the antibiotic resistance plasmid pCF10 from donor cells to recipient cells. Using mathematical modeling and experimentation, we demonstrate that convergent transcription in the prgX/prgQ operon endows the system with the properties of a robust genetic switch through premature termination of elongating transcripts due to collisions between RNA polymerases (RNAPs) transcribing from opposite directions and antisense regulation between complementary counter-transcripts. Evidence is provided for the presence of truncated RNAs resulting from convergent transcription from both the promoters that are capable of sense-antisense interactions. A mathematical model predicts that both RNAP collision and antisense regulation are essential for a robust bistable switch behavior in the control of conjugation initiation by prgX/prgQ operons. Moreover, given that convergent transcription is conserved across species, the mechanism of coupling RNAP collision and antisense interaction is likely to have a significant regulatory role in gene expression.

Investigation of Changes in Tetracycline Repressor Binding upon Mutations in the Tetracycline Operator.

The tetracycline operon is an important gene network component, commonly used in synthetic biology applications because of its switch-like character. At the heart of this system is the highly specific interaction of the tet repressor protein (TetR) with its cognate DNA sequence (tetO). TetR binding on tetO practically stops expression of genes downstream of tetO by excluding RNA polymerase from binding the promoter and initiating transcription. Mutating the tetO sequence alters the strength of TetR-tetO binding and thus provides a tool to synthetic biologists to manipulate gene expression levels. We employ molecular dynamics (MD) simulations coupled with the free energy perturbation method to investigate the binding affinity of TetR to different tetO mutants. We also carry out in vivo tests in Escherichia coli for a series of promoters based on these mutants. We obtain reasonable agreement between experimental green fluorescent protein (GFP) repression levels and binding free energy differences computed from molecular simulations. In all cases, the wild-type tetO sequence yields the strongest TetR binding, which is observed both experimentally, in terms of GFP levels, and in simulation, in terms of free energy changes. Two of the four tetO mutants we tested yield relatively strong binding, whereas the other two mutants tend to be significantly weaker. The clustering and relative ranking of this subset of tetO mutants is generally consistent between our own experimental data, previous experiments with different systems and the free energy changes computed from our simulations. Overall, this work offers insights into an important synthetic biological system and demonstrates the potential, as well as limitations of molecular simulations to quantitatively explain biologically relevant behavior.

SynBioSS designer: a web-based tool for the automated generation of kinetic models for synthetic biological constructs.

Modeling tools can play an important role in synthetic biology the same way modeling helps in other engineering disciplines: simulations can quickly probe mechanisms and provide a clear picture of how different components influence the behavior of the whole. We present a brief review of available tools and present SynBioSS Designer. The Synthetic Biology Software Suite (SynBioSS) is used for the generation, storing, retrieval and quantitative simulation of synthetic biological networks. SynBioSS consists of three distinct components: the Desktop Simulator, the Wiki, and the Designer. SynBioSS Designer takes as input molecular parts involved in gene expression and regulation (e.g. promoters, transcription factors, ribosome binding sites, etc.), and automatically generates complete networks of reactions that represent transcription, translation, regulation, induction and degradation of those parts. Effectively, Designer uses DNA sequences as input and generates networks of biomolecular reactions as output. In this paper we describe how Designer uses universal principles of molecular biology to generate models of any arbitrary synthetic biological system. These models are useful as they explain biological phenotypic complexity in mechanistic terms. In turn, such mechanistic explanations can assist in designing synthetic biological systems. We also discuss, giving practical guidance to users, how Designer interfaces with the Registry of Standard Biological Parts, the de facto compendium of parts used in synthetic biology applications.

Multiscale models of the antimicrobial peptide protegrin-1 on gram-negative bacteria membranes.

Antimicrobial peptides (AMPs) are naturally-occurring molecules that exhibit strong antibiotic properties against numerous infectious bacterial strains. Because of their unique mechanism of action, they have been touted as a potential source for novel antibiotic drugs. We present a summary of computational investigations in our lab aimed at understanding this unique mechanism of action, in particular the development of models that provide a quantitative connection between molecular-level biophysical phenomena and relevant biological effects. Our work is focused on protegrins, a potent class of AMPs that attack bacteria by associating with the bacterial membrane and forming transmembrane pores that facilitate the unrestricted transport of ions. Using fully atomistic molecular dynamics simulations, we have computed the thermodynamics of peptide-membrane association and insertion, as well as peptide aggregation. We also present a multi-scale analysis of the ion transport properties of protegrin pores, ranging from atomistic molecular dynamics simulations to mesoscale continuum models of single-pore electrodiffusion to models of transient ion transport from bacterial cells. Overall, this work provides a quantitative mechanistic description of the mechanism of action of protegrin antimicrobial peptides across multiple length and time scales.

Analytical Derivation of Moment Equations in Stochastic Chemical Kinetics.

The master probability equation captures the dynamic behavior of a variety of stochastic phenomena that can be modeled as Markov processes. Analytical solutions to the master equation are hard to come by though because they require the enumeration of all possible states and the determination of the transition probabilities between any two states. These two tasks quickly become intractable for all but the simplest of systems. Instead of determining how the probability distribution changes in time, we can express the master probability distribution as a function of its moments, and, we can then write transient equations for the probability distribution moments. In 1949, Moyal defined the derivative, or jump, moments of the master probability distribution. These are measures of the rate of change in the probability distribution moment values, i.e. what the impact is of any given transition between states on the moment values. In this paper we present a general scheme for deriving analytical moment equations for any N-dimensional Markov process as a function of the jump moments. Importantly, we propose a scheme to derive analytical expressions for the jump moments for any N-dimensional Markov process. To better illustrate the concepts, we focus on stochastic chemical kinetics models for which we derive analytical relations for jump moments of arbitrary order. Chemical kinetics models are widely used to capture the dynamic behavior of biological systems. The elements in the jump moment expressions are a function of the stoichiometric matrix and the reaction propensities, i.e the probabilistic reaction rates. We use two toy examples, a linear and a non-linear set of reactions, to demonstrate the applicability and limitations of the scheme. Finally, we provide an estimate on the minimum number of moments necessary to obtain statistical significant data that would uniquely determine the dynamics of the underlying stochastic chemical kinetic system. The first two moments only provide limited information, especially when complex, non-linear dynamics are involved.

Poisson-Nernst-Planck models of nonequilibrium ion electrodiffusion through a protegrin transmembrane pore.

Protegrin peptides are potent antimicrobial agents believed to act against a variety of pathogens by forming nonselective transmembrane pores in the bacterial cell membrane. We have employed 3D Poisson-Nernst-Planck (PNP) calculations to determine the steady-state ion conduction characteristics of such pores at applied voltages in the range of -100 to +100 mV in 0.1 M KCl bath solutions. We have tested a variety of pore structures extracted from molecular dynamics (MD) simulations based on an experimentally proposed octomeric pore structure. The computed single-channel conductance values were in the range of 290-680 pS. Better agreement with the experimental range of 40-360 pS was obtained using structures from the last 40 ns of the MD simulation, where conductance values range from 280 to 430 pS. We observed no significant variation of the conductance with applied voltage in any of the structures that we tested, suggesting that the voltage dependence observed experimentally is a result of voltage-dependent channel formation rather than an inherent feature of the open pore structure. We have found the pore to be highly selective for anions, with anionic to cationic current ratios (I(Cl-)/I(K+)) on the order of 10(3). This is consistent with the highly cationic nature of the pore but surprisingly in disagreement with the experimental finding of only slight anionic selectivity. We have additionally tested the sensitivity of our PNP model to several parameters and found the ion diffusion coefficients to have a significant influence on conductance characteristics. The best agreement with experimental data was obtained using a diffusion coefficient for each ion set to 10% of the bulk literature value everywhere inside the channel, a scaling used by several other studies employing PNP calculations. Overall, this work presents a useful link between previous work focused on the structure of protegrin pores and experimental efforts aimed at investigating their conductance characteristics.

Dimerization of protegrin-1 in different environments.

The dimerization of the cationic ß-hairpin antimicrobial peptide protegrin-1 (PG1) is investigated in three different environments: water, the surface of a lipid bilayer membrane, and the core of the membrane. PG1 is known to kill bacteria by forming oligomeric membrane pores, which permeabilize the cells. PG1 dimers are found in two distinct, parallel and antiparallel, conformations, known as important intermediate structural units of the active pore oligomers. What is not clear is the sequence of events from PG1 monomers in solution to pores inside membranes. The step we focus on in this work is the dimerization of PG1. In particular, we are interested in determining where PG1 dimerization is most favorable. We use extensive molecular dynamics simulations to determine the potential of mean force as a function of distance between two PG1 monomers in the aqueous subphase, the surface of model lipid bilayers and the interior of these bilayers. We investigate the two known distinct modes of dimerization that result in either a parallel or an antiparallel ß-sheet orientation. The model bilayer membranes are composed of anionic palmitoyl-oleoyl-phosphatidylglycerol (POPG) and palmitoyl-oleoyl-phosphatidylethanolamine (POPE) in a 1:3 ratio (POPG:POPE). We find the parallel PG1 dimer association to be more favorable than the antiparallel one in water and inside the membrane. However, we observe that the antiparallel PG1 ß-sheet dimer conformation is somewhat more stable than the parallel dimer association at the surface of the membrane. We explore the role of hydrogen bonds and ionic bridges in peptide dimerization in the three environments. Detailed knowledge of how networks of ionic bridges and hydrogen bonds contribute to peptide stability is essential for the purpose of understanding the mechanism of action for membrane-active peptides as well as for designing peptides which can modulate membrane properties. The findings are suggestive of the dominant pathways leading from individual PG1 molecules in solution to functional pores in bacterial membranes.

Path-integral method for predicting relative binding affinities of protein-ligand complexes.

We present a novel approach for computing biomolecular interaction binding affinities based on a simple path integral solution of the Fokker-Planck equation. Computing the free energy of protein-ligand interactions can expedite structure-based drug design. Traditionally, the problem is seen through the lens of statistical thermodynamics. The computations can become, however, prohibitively long for the change in the free energy upon binding to be determined accurately. In this work, we present a different approach based on a stochastic kinetic formalism. Inspired by Feynman's path integral formulation, we extend the theory to classical interacting systems. The ligand is modeled as a Brownian particle subjected to the effective nonbonding interaction potential of the receptor. This allows the calculation of the relative binding affinities of interacting biomolecules in water to be computed as a function of the ligand's diffusivity and the curvature of the potential surface in the vicinity of the binding minimum. The calculation is thus exceedingly rapid. In test cases, the correlation coefficient between actual and computed free energies is >0.93 for accurate data sets.