Immobilization of Candida antarctica lipase B on ILs modified CNTs with different chain lengths: Regulation of substrate tunnel "Leucine gating"

Ionic liquids (ILs) have been widely used as chemical modifiers to modify the carriers and thus improve the efficiency, activity and stability of the enzymes. However, as thousands of ILs have been found up to date, it's a huge work for screening and designing suitable ILs for immobilization of enzymes. Moreover, the mechanism of improving enzymes catalytic performance is still remain ambiguous. Thus, this study investigated the impact of ILs with different chain lengths on the enzymatic properties of Candida antarctica lipase B (CALB). Molecular dynamics simulations were employed to examine the interaction between ILs modified CNTs and CALB, as well as their effects on CALB's structure. The results revealed that ILs with different chain lengths significantly influenced the absorption orientation of CALB. Tunnel analysis identified a key role for Leu278 in regulating the open or closed state of Tunnel 2 during CALB's catalytic cycle. The weak interaction analysis demonstrated that ILs with suitable chain lengths provided spatial freedom and formed strong interactions with CNTs and ILs (vdW and hbond). This led to a conformational flip of Leu278, stabilizing the open state of Tunnel 2 and improving the activity and stability of immobilized CALB. This study provides novel insights into the design of new green modifiers to modulate carrier performance and obtain immobilized enzymes with better performance, and establishes a theoretical basis for the design and selection of modifiers for ILs in future work.

Enzyme immobilization studied through molecular dynamic simulations

In recent years, simulations have been used to great advantage to understand the structural and dynamic aspects of distinct enzyme immobilization strategies, as experimental techniques have limitations in establishing their impact at the molecular level. In this review, we discuss how molecular dynamic simulations have been employed to characterize the surface phenomenon in the enzyme immobilization procedure, in an attempt to decipher its impact on the enzyme features, such as activity and stability. In particular, computational studies on the immobilization of enzymes using i) nanoparticles, ii) self-assembled monolayers, iii) graphene and carbon nanotubes, and iv) other surfaces are covered. Importantly, this thorough literature survey reveals that, while simulations have been primarily performed to rationalize the molecular aspects of the immobilization event, their use to predict adequate protocols that can control its impact on the enzyme properties is, up to date, mostly missing.

Molecular Insights of Cellobiose Dehydrogenase Adsorption on Self-Assembled Monolayers

Cellobiose dehydrogenase (CDH) is capable of direct electron transfer (DET) on electrodes and is a promising redox enzyme for bioelectrochemical applications. Its unique two-domain structure makes the function of CDH adsorbed on the surface of the electrode deeply affected by the external environment, such as ion species, strength, pH, and surface charge density. To date, however, the exact mechanism of how the external environment tailors the structure and dynamics of CDH adsorbed on the electrode surface still remains poorly understood. Here, multiscale simulations were performed to look for insight into the effect of Na⁺ and Ca²⁺ ions on the activation of CDH on oppositely charged self-assembled monolayer (NH₂-SAM and COOH-SAM) surfaces with different surface charge densities (SCDs). Both Na⁺ and Ca²⁺ can promote CDH conformation switch from the open state to the closed state, while the promotion effect of Ca²⁺ is stronger than that of Na⁺ at the same conditions. However, the high ionic strength (IS) of Ca²⁺ renders the cytochrome (CYT) domain of CDH away from the NH₂-SAM with low SCD. In contrast, whatever the IS, the NH₂-SAM surface with high SCD can not only enhance the CYT-surface interaction but also achieve a closed-state conformation due to a similar role of Ca²⁺. Overall, this study gains molecular-level insights into the role of ion species and surface charge in modulating the structure and conformation of CDH on the SAM surface, thereby tailoring its activity.

The evolution mechanism of an FeMo alloy catalyst for growth of single-walled carbon nanotubes

Adding small fractions of Mo to Fe nanoparticles (NPs) can reduce the melting point of FeMo NPs to lower than that of Fe NPs to prolong the lifetime of the alloy catalyst which in turn promotes the quality of catalytically synthesized single-walled carbon nanotubes (SWCNTs). In this study, we reveal the mechanism of the above-mentioned abnormal melting behavior by employing molecular dynamics simulations. Our results indicate that the bond length between the Fe atoms and the number of bonds between the Mo atoms play an important role in reducing the melting point of the FeMo NPs. This study provides useful insight into the evolution mechanism of the alloy catalyst for the growth of SWCNTs.

Modulating the adsorption orientation of methionine-rich laccase by tailoring the surface chemistry of single-walled carbon nanotubes

Achieving fast electron transfer process between oxidoreductase and electrodes is pivotal for the biocathode of enzymatic biofuel cells (EBFCs). However, in-depth understanding of the interplay mechanism between enzymes and electrode materials remains challenging when designing and constructing EBFCs. Herein, atomic-scale insight into the direct electron transfer (DET) behavior of Thermus thermophilus laccase (TtLac) with a special methionine-rich β-hairpin motif adsorbed on the carboxyl-functionalized carbon nanotube (COOH-CNT) and amino-functionalized carbon nanotube (NH₂-CNT) surfaces were disclosed by multi-scale molecular simulations. Simulation results reveal that electrostatic modification is an effective way to tune the DET behavior for TtLac on the modified-CNTs electrode surface. Surprisingly, the positively charged TtLac can be attracted by both negatively charged COOH-CNT and positively charged NH₂-CNT surfaces, yet only the latter is capable to trigger the DET process due to the 'lying-on' adsorption orientation. Specifically, the T1 copper site is near the methionine-rich β-hairpin motif, which is the key binding site for TtLac binding onto the NH₂-CNT surface via electrostatic interaction, π-π stacking and cation-π interaction. Moreover, TtLac on the NH₂-CNT surface undergoes less conformational changes than those on the COOH-CNT surface, which allows the laccase stability and catalytic efficiency to be well preserved. These findings provide a fundamental guidance for future design and fabrication of methionine-rich laccase-based EBFCs with high power output and long lifespan.

Turning the structure of the Aβ42 peptide by different functionalized carbon nanotubes: a molecular dynamics simulation study

Functionalized carbon nanotubes (CNTs) can inhibit the self-assembly of amyloid-beta (Aβ) peptides. Under abnormal conditions, the structure of the Aβ peptides undergoes a fundamental transformation, and this transformation will induce conformational conversions of other polymerized Aβ peptides. Here, we explore the interactions between different functionalized CNTs and Aβ₄₂ peptides by molecular dynamics simulations. Our results show that compared to the original CNTs, the highly functionalized CNTs induce different adsorption patterns of the peptides. This adsorption pattern destroys the α-helix structure and increases the β-turn and random coil content significantly. The hydrogen bonds formed by the peptide and water molecules or CNTs further reveal the reasons for the structural transformation of the peptide. Due to electrostatic interactions and π-π stacking interactions, some amino acids (such as Phe4, Lys16, Phe20, and Lys28) are tightly fixed on the surfaces, and other amino acids move around these amino acids to accelerate the unfolding and denaturation of the peptide. Our research shows that functionalized CNTs have excellent potential to inhibit the abnormal aggregation of Aβ₄₂ peptides. Our research also provides theoretical guidance in the design and synthesis of carbon nanomedicines for protein conformation diseases.

Molecular understanding of acetylcholinesterase adsorption on functionalized carbon nanotubes for enzymatic biosensors

The immobilization of acetylcholinesterase on different nanomaterials has been widely used in the field of amperometric organophosphorus pesticide (OP) biosensors. However, the molecular adsorption mechanism of acetylcholinesterase on a nanomaterial's surface is still unclear. In this work, multiscale simulations were utilized to study the adsorption behavior of acetylcholinesterase from Torpedo californica (TcAChE) on amino-functionalized carbon nanotube (CNT) (NH₂-CNT), carboxyl-functionalized CNT (COOH-CNT) and pristine CNT surfaces. The simulation results show that the active center and enzyme substrate tunnel of TcAChE are both close to and oriented toward the surface when adsorbed on the positively charged NH₂-CNT, which is beneficial to the direct electron transfer (DET) and accessibility of the substrate molecule. Meanwhile, the NH₂-CNT can also reduce the tunnel cost of the enzyme substrate of TcAChE, thereby further accelerating the transfer rate of the substrate from the surface or solution to the active center. However, for the cases of TcAChE adsorbed on COOH-CNT and pristine CNT, the active center and substrate tunnel are far away from the surface and face toward the solution, which is disadvantageous for the DET and transportation of enzyme substrate. These results indicate that NH₂-CNT is more suitable for the immobilization of TcAChE. This work provides a better molecular understanding of the adsorption mechanism of TcAChE on functionalized CNT, and also provides theoretical guidance for the ordered immobilization of TcAChE and the design, development and improvement of TcAChE-OPs biosensors based on functionalized carbon nanomaterials.

Improved Biomedical Properties of Polydopamine-Coated Carbon Nanotubes

Carbon nanotubes (CNTs) due to their outstanding mechanical, thermal, chemical, and optical properties were utilized as a base material and were coated with polydopamine (PDA) (PDA@CNT) via the simple self-polymerization of dopamine (DA). Then, PDA@CNT coatings of up to five layers were examined for potential biomedical applications. The success of multiple coating of CNTs with PDA was confirmed via increased weight loss values with the increased number of PDA coatings of CNTs at 500 °C by thermogravimetric analysis. The surface area of bare CNTs was measured as 263.9 m2/g and decreased to 197.0 m2/g after a 5th coating with PDA. Furthermore, the antioxidant activities of CNT and PDA@CNTs were determined via total flavonoid content (TFC), total phenol content (TPC), and Fe(III)-reducing antioxidant power (FRAP) tests, revealing the increased antioxidant ability of PDA@CNTs with the increasing numbers of PDA coatings. Moreover, a higher inhibition percentage of the activity of the alpha-glucosidase enzyme with 95.1 ± 2.9% inhibition at 6 mg/mL PDA-1st@CNTs concentration was found. The CNT and PDA@CNTs exhibited blood compatibility, less than a 2.5% hemolysis ratio, and more than 85% blood clotting indexes. The minimum inhibition concentration (MIC) of PDA-5th@CNTs against E. coli and S. aureus bacteria was determined as 10 mg/mL.

Understanding the close encounter of heme proteins with carboxylated multiwalled carbon nanotubes: a case study of contradictory stability trend for hemoglobin and myoglobin

Carbon nanotubes (CNTs) are one of the unique and promising nanomaterials that possess plenty of applications, such as biosensors, advanced drug delivery systems and biotechnology. CNTs bind rapidly with proteins, which result in the formation of a protein coating layer known as a "protein corona" around the surface of the nanomaterial. This hinders their applications as a drug carrier and influences the properties of biological macromolecules. The present work focuses on studying the thermal stability and molecular level interactions of two heme proteins, hemoglobin (Hb) and myoglobin (Mb), in the presence of carboxylated functionalized multi-walled CNTs (CA-MWCNTs). Through the current study, the following steps have been taken to distinguish the biocompatibility of the hydrophilic surface CA-MWCNTs for heme proteins via a series of spectroscopic techniques and differential scanning calorimetry (DSC). UV-Visible and steady-state fluorescence spectroscopy were used to reveal changes in the aromatic amino acid residues of heme proteins upon the addition of CA-MWCNTs. Circular dichroism spectroscopy (CD) shows the alteration in the native structure of proteins in the presence of the nanomaterial. A tremendous increase in the size of the protein CA-MWCNTs system is observed in dynamic light scattering (DLS), which clearly manifests the protein corona formation. Unexpectedly, both proteins interact differently with CA-MWCNTs, which is observed in CD spectroscopy and DSC. In the presence of CA-MWCNTs, an increase in the transition temperature (T_m) was observed for Hb, while the T_m value decreases for Mb. Different interactions with proteins at the molecular scale may be the reason for this unexpected behavior. Henceforth, the present results can help in the design of the next-generation drug carrier nanomaterials with the idea of the heme protein corona formation prior to development.

Efficient tyrosinase nano-inhibitor based on carbon dots behaving as a gathering of hydrophobic cores and key chemical group

Small organic molecules have been extensively applied to achieve enzymatic inhibition. Although numerous efforts have been made to deliver efficient inhibitors, small inhibitors applications are hindered by many drawbacks. Moreover, reporters comprising nanoparticle inhibitory activity against enzymes are very scarce in the literature. In this scenario, carbon nanodots (CDs) emerge as promising candidates for efficient enzyme inhibition due to their unique properties. Here, CDs specific molecular characteristics (core composition and chemical surface groups) have been investigated to produce a more potent enzyme inhibition. Mushroom tyrosinase (mTyr) has been adopted as an enzymatic prototype. The CDs revealed a high affinity to mTyr (Ka ≈ 10⁶ M^-1), mainly through hydrophobic forces and followed by slight mTyr structural alteration. CDs competitively inhibit mTyr, with low inhibition constant (K_I = 517.7 ± 17.0 nM), which is up 70 fold smaller then the commercial inhibitor (kojic acid) and the starch nanoparticles previously reported. The results expose that the CDs act as a hydrophobic agglomerate with carboxyl groups on its surface, mimicking characteristics found on small molecule inhibitors (but with superior performance). All these results highlight the CD excellent potential as an efficient low toxic Tyr inhibitor, opening the prospect of using these nanoparticles in the cosmetic and food industries.

Lysozyme Adsorption on Different Functionalized MXenes: A Multiscale Simulation Study

Recently, MXenes, due to their abundant advantages, have been widely applied in energy storage, separation, catalysis, biosensing, et al. In this study, parallel tempering Monte Carlo and molecular dynamics methods were performed to investigate lysozyme adsorption on different functionalized Ti₃C₂T_x (-O, -OH, and -F). The simulation results show that lysozyme can adsorb effectively on Ti₃C₂T_x surfaces, and the order of interaction strength is Ti₃C₂O₂ > Ti₃C₂F₂ > Ti₃C₂(OH)₂. Electrostatics together with van der Waals interactions control protein adsorption. The orientation distributions of lysozyme adsorbed on the Ti₃C₂O₂ and Ti₃C₂F₂ surfaces are more concentrated than that on the Ti₃C₂(OH)₂ surface. During adsorption, the conformation of lysozyme remains stable, suggesting the good biocompatibility of Ti₃C₂T_x. Besides, the distribution of the interfacial water layer on the Ti₃C₂T_x surface has a certain impact on protein adsorption. This study provides theoretical insights for understanding the biocompatibility of 2D Ti₃C₂T_x materials and may help us evaluate the engineering of their surfaces for future biorelated applications.

Simulation Insight into the Synergic Role of Citrate and Polyaspartic Peptide in Biomineralization

Hydroxyapatite (HAP) is one of the most important inorganic components in biological minerals such as bones and teeth. More than 90% of the total citrate is accumulated in human bones and other biomineralized tissues. In addition, mineralizing proteins are enriched in glutamate and aspartate residues, which are important for their mineral-regulating properties. However, how citrate ions (CITs) and/or acidic amino acids regulate the formation of HAP is still unclear. In this work, molecular dynamics simulations were performed to study how CIT regulates the adsorption behavior of polyaspartic acid (PASP) on the HAP surface in the calcium phosphate solution. The simulation results indicate that PASP can be used as an ion chelator to complex Ca²⁺ and can serve as templates for HAP mineralization by templating the distribution of Ca²⁺ on its surface, which are attributed to the -COO^- and α-helix structure. Most importantly, the orientation distributions of PASP in all systems are narrower with the help of CIT, thereby PASP can be adsorbed on the HAP surface stably with a "lying-down" orientation. This indicates that CIT can be used as a bridging agent to bond the acidic peptide to the HAP surface in biomineralization. Thus, the synergic role of CIT and the acidic peptide on the HAP surface were revealed in this work, which can provide new insights into the interfacial phenomena during the biomineralization.

Lysozyme Adsorption on Porous Organic Cages: A Molecular Simulation Study

Recently, porous organic cages (POCs) have emerged as a novel porous material with many merits and are widely utilized in many application fields. In this work, for the first time, molecular dynamics simulations were performed to investigate the mechanism of lysozyme adsorption onto the CC3 crystal, a kind of widely studied POC material. The simulation results show that lysozyme adsorbs onto the surface of CC3 with "top end-on," "back-on," or "side-on" orientations. It is found that the van der Waals interaction is the primary contribution to the binding; the conformation of the lysozyme is well preserved during the adsorption process. This provides some evidence for its biocompatibility and feasibility in biorelated applications. Arginine plays an important role in mediating the adsorption through nonpolar aliphatic chains. More importantly, the distribution and structure of the water layer on the POC surface has a significant impact on adsorption. This study provides insights into the development of POC materials with defined morphologies for the adsorption of biomolecules and may help the rational design of biorelated systems.

Electrostatic Effect of Functional Surfaces on the Activity of Adsorbed Enzymes: Simulations and Experiments

The efficient immobilization of haloalkane dehalogenase (DhaA) on carriers with retaining of its catalytic activity is essential for its application in environmental remediation. In this work, adsorption orientation and conformation of DhaA on different functional surfaces were investigated by computer simulations; meanwhile, the mechanism of varying the catalytic activity was also probed. The corresponding experiments were then carried out to verify the simulation results. (The simulations of DhaA on SAMs provided parallel insights into DhaA adsorption in carriers. Then, the theory-guided experiments were carried out to screen the best surface functional groups for DhaA immobilization.) The electrostatic interaction was considered as the main impact factor for the regulation of enzyme orientation, conformation, and enzyme bioactivity during DhaA adsorption. The synergy of overall conformation, enzyme substrate tunnel structural parameters, and distance between catalytic active sites and surfaces codetermined the catalytic activity of DhaA. Specifically, it was found that the positively charged surface with suitable surface charge density was helpful for the adsorption of DhaA and retaining its conformation and catalytic activity and was favorable for higher enzymatic catalysis efficiency in haloalkane decomposition and environmental remediation. The neutral, negatively charged surfaces and positively charged surfaces with high surface charge density always caused relatively larger DhaA conformation change and decreased catalytic activity. This study develops a strategy using a combination of simulation and experiment, which can be essential for guiding the rational design of the functionalization of carriers for enzyme adsorption, and provides a practical tool to rationally screen functional groups for the optimization of adsorbed enzyme functions on carriers. More importantly, the strategy is general and can be applied to control behaviors of different enzymes on functional carrier materials.

Thermodynamics, Kinetics and Mechanisms of Noncompetitive Allosteric Inhibition of Chymotrypsin by Dihydrolipoic Acid-Coated Gold Nanoclusters

Enzymes are an important class of biomacromolecules which catalyze many metabolic processes in living systems. Nanomaterials can be synthesized with tailored sizes as well as desired surface modifications, thus acting as promising enzyme regulators. Fluorescent gold nanoclusters (AuNCs) are a representative class of ultrasmall nanoparticles (USNPs) with sizes of ∼2 nm, smaller than most of proteins including enzymes. In this work, we chose α-chymotrypsin (ChT) and AuNCs as the model system. Activity assays and inhibition kinetics studies showed that dihydrolipoic acid (DHLA)-coated AuNCs (DHLA-AuNCs) had a high inhibitory potency (IC₅₀ = 3.4 μM) and high inhibitory efficacy (>80%) on ChT activity through noncompetitive inhibition mechanism. In distinct contrast, glutathione (GSH)-coated AuNCs (GSH-AuNCs) had no significant inhibition effects. Fluorescence spectroscopy, agarose gel electrophoresis and circular dichroism (CD) spectroscopy were conducted to explore the underlying mechanisms. A two-step interaction model was proposed. First, both DHLA-AuNCs and GSH-AuNCs might be bound to the positively charged sites of ChT through electrostatic forces. Second, further hydrophobic interactions occurred between three tyrosine residues of ChT and the hydrophobic carbon chain of DHLA, leading to a significant structural change thus to deactivate ChT on the allosteric site. On the contrary, no such interactions occurred with GSH of zwitterionic characteristic, which explained no inhibitory effect of GSH-AuNCs on ChT. To the best of our knowledge, this is the first example of the allosteric inhibition of ChT by nano regulators. These findings provide a fundamental basis for the design and development of nano regulators.

How do proteins 'response' to common carbon nanomaterials?

Carbon nanomaterials are widely produced and applied in biological and environmental fields because of their outstanding physical and chemical properties, which pose a threat to the safety of living organisms and the ecological environment. Therefore, understanding how carbon nanomaterials and their derivatives work on organisms is becoming important. In recent years, more and more researchers have explored the damage of carbon nanomaterials to organisms at the molecular level. This review pays special emphasis on how proteins response to the main carbon nanomaterials (fullerene, carbon nanotubes, graphene and their derivatives). In addition, how to use the interaction between carbon nanomaterials and proteins to do some beneficial things for human and the development of safe nanomaterials is simply discussed. Finally, some suggestions have been made to lay a theoretical foundation for future research.

An investigation into non-covalent functionalization of a single-walled carbon nanotube and a graphene sheet with protein G:A combined experimental and molecular dynamics study

Investigation of non-covalent interaction of hydrophobic surfaces with the protein G (PrG) is necessary due to their frequent utilization in immunosensors and ELISA. It has been confirmed that surfaces, including carbonous-nanostructures (CNS) could orient proteins for a better activation. Herein, PrG interaction with single-walled carbon nanotube (SWCNT) and graphene (Gra) nanostructures was studied by employing experimental and MD simulation techniques. It is confirmed that the PrG could adequately interact with both SWCNT and Gra and therefore fine dispersion for them was achieved in the media. Results indicated that even though SWCNT was loaded with more content of PrG in comparison with the Gra, the adsorption of the PrG on Gra did not induce significant changes in the IgG tendency. Several orientations of the PrG were adopted in the presence of SWCNT or Gra; however, SWCNT could block the PrG-FcR. Moreover, it was confirmed that SWCNT reduced the α-helical structure content in the PrG. Reduction of α-helical structure of the PrG and improper orientation of the PrG-SWCNT could remarkably decrease the PrG tendency to the Fc of the IgG. Importantly, the Gra could appropriately orient the PrG by both exposing the PrG-FcR and also by blocking the fragment of the PrG that had tendency to interact with Fab in IgG.

Hydrogenation-controlled mechanical properties in graphene helicoids: exceptional distribution-dependent behavior

Mechanical properties of pristine GHs along with patterned and randomly hydrogenated GHs have been investigated for various geometries and H-coverages.

The potential impact of carboxylic-functionalized multi-walled carbon nanotubes on trypsin: A Comprehensive spectroscopic and molecular dynamics simulation study

In this study, we report a detailed experimental, binding free energy calculation and molecular dynamics (MD) simulation investigation of the interactions of carboxylic-functionalized multi-walled carbon nanotubes (COOH-f-MWCNTs) with porcine trypsin (pTry). The enzyme exhibits decreased thermostability at 330K in the presence of COOH-f-MWCNTs. Furthermore, the activity of pTry also decreases in the presence of COOH-f-MWCNTs. The restricted diffusion of the substrate to the active site of the enzyme was observed in the experiment. The MD simulation analysis suggested that this could be because of the blocking of the S1 pocket of pTry, which plays a vital role in the substrate selectivity. The intrinsic fluorescence of pTry is quenched with increase in the COOH-f-MWCNTs concentration. Circular dichroism (CD) and UV–visible absorption spectroscopies indicate the ability of COOH-f-MWCNTs to experience conformational change in the native structure of the enzyme. The binding free energy calculations also show that electrostatics, π-cation, and π-π stacking interactions play important roles in the binding of the carboxylated CNTs with pTry. The MD simulation results demonstrated that the carboxylated CNTs adsorb to the enzyme stronger than the CNT without the–COOH groups. Our observations can provide an example of the nanoscale toxicity of COOH-f-MWCNTs for proteins, which is a critical issue for in vivo application of COOH-f-MWCNTs.

Zinc ion-induced conformational changes in new Delphi metallo-β-lactamase 1 probed by molecular dynamics simulations and umbrella sampling

The hydrolysis of a β-lactam core ring caused by new Delphi metallo-β-lactamase 1 (NDM-1) with the help of two zinc cofactors induces significant resistance toward β-lactam antibiotics. Molecular dynamics (MD) simulations and the umbrella sampling method are integrated to study the conformational change mechanism of NDM-1 mediated by zinc ion binding. The statistical analyses of interaction contacts of the antibiotic ampicillin (AMP) with residues based on MD trajectories suggest that two Zn ions are essential for maintaining the binding of AMP with NDM-1. Umbrella sampling simulations further reveal that double-Zn coordination exerts strong restriction on the motions of loop L10 relative to loops L3 and L4. Principal component (PC) analysis also demonstrates that zinc ion binding totally inhibits the motion extent of NDM-1 and changes internal motion modes in NDM-1. We expect that the current study can provide significant dynamical information involving conformational changes of NDM-1 for the development of efficient inhibitors to decrease drug resistance of NDM-1 toward antibiotics.

Hamiltonian replica exchange simulations of glucose oxidase adsorption on charged surfaces

Hamiltonian replica exchange Monte Carlo simulations efficiently identify the lowest-energy orientations of proteins on charged surfaces at variable ionic strengths.