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PubMed2004

Raman spectroscopic characterization of secondary structure in natively unfolded proteins: alpha-synuclein.

The application of Raman spectroscopy to characterize natively unfolded proteins has been underdeveloped, even though it has significant technical advantages. We propose that a simple three-component band fitting of the amide I region can assist in the conformational characterization of the ensemble of structures present in natively unfolded proteins. The Raman spectra of alpha-synuclein, a prototypical natively unfolded protein, were obtained in the presence and absence of methanol, sodium dodecyl sulfate (SDS), and hexafluoro-2-propanol (HFIP). Consistent with previous CD studies, the secondary structure becomes largely alpha-helical in HFIP and SDS and predominantly beta-sheet in 25% methanol in water. In SDS, an increase in alpha-helical conformation is indicated by the predominant Raman amide I marker band at 1654 cm(-1) and the typical double minimum in the CD spectrum. In 25% HFIP the amide I Raman marker band appears at 1653 cm(-1) with a peak width at half-height of approximately 33 cm(-1), and in 25% methanol the amide I Raman band shifts to 1667 cm(-1) with a peak width at half-height of approximately 26 cm(-1). These well-characterized structural states provide the unequivocal assignment of amide I marker bands in the Raman spectrum of alpha-synuclein and by extrapolation to other natively unfolded proteins. The Raman spectrum of monomeric alpha-synuclein in aqueous solution suggests that the peptide bonds are distributed in both the alpha-helical and extended beta-regions of Ramachandran space. A higher frequency feature of the alpha-synuclein Raman amide I band resembles the Raman amide I band of ionized polyglutamate and polylysine, peptides which adopt a polyproline II helical conformation. Thus, a three-component band fitting is used to characterize the Raman amide I band of alpha-synuclein, phosvitin, alpha-casein, beta-casein, and the non-A beta component (NAC) of Alzheimer's plaque. These analyses demonstrate the ability of Raman spectroscopy to characterize the ensemble of secondary structures present in natively unfolded proteins.

Amides↗

PubMed2003

Spectroscopic studies of structural changes in two beta-sheet-forming peptides show an ensemble of structures that unfold noncooperatively.

A characterization of the conformation and stability of model peptide systems that form beta-sheets in aqueous solutions is considerably important in gaining insights into the mechanism of beta-sheet formation in proteins. We have characterized the conformation and equilibrium folding and unfolding of two 20-residue peptides whose NMR spectra suggest a three-stranded beta-sheet topology in aqueous solution: Betanova [Kortemme, T., Ramirez-Alvarado, M., and Serrano, L. (1998) Science 281, 253-256] and (D)P(D)P with d-Pro-Gly segments at the turns [Schenck, H. L., and Gellman, S. H. (1998) J. Am. Chem. Soc. 120, 4869-4870]. Both circular dichroism (CD) and infrared measurements indicate only 20-26% beta-sheet-like structure at 5 degrees C for Betanova and 42-59% beta-sheet for (D)P(D)P. For both peptides, the CD and infrared spectra change nearly linearly with increasing temperatures (or urea concentrations) and lack a sigmoidal signature characteristic of cooperative unfolding. Fluorescence resonance energy transfer (FRET) measurements between donor and acceptor molecules attached to the two ends confirm that Betanova is largely unstructured even at 10 degrees C; the average end-to-end distance estimated from FRET is closer to that of a random coil than a structured beta-sheet. In (D)P(D)P, the FRET results indicate a more compact structure that remains compact even at high temperatures (approximately 80 degrees C) or high urea concentrations (approximately 8 M). These results indicate that both these peptides access an ensemble of conformations at all temperatures or denaturant concentrations, with no significant free energy barrier separating the "folded" and "unfolded" conformations.

Circular Dichroism↗

PubMed2005

Random walks, diffusion limited aggregation in a wedge, and average conformal maps.

We investigate diffusion-limited aggregation (DLA) in a wedge geometry. Arneodo and collaborators have suggested that the ensemble average of DLA cluster density should be close to the noise-free selected Saffman-Taylor finger. We show that a different, but related, ensemble average, that of the conformal maps associated with random clusters, yields a nontrivial shape which is also not far from the Saffman-Taylor finger. However, we have previously demonstrated that the same average of DLA in a channel geometry is not the Saffman-Taylor finger. This casts doubt on the idea that the average of noisy diffusion-limited growth is governed by a simple transcription of noise-free results.

Cluster Analysis↗

PubMed2000

Fluctuations between stabilizing and destabilizing electrostatic contributions of ion pairs in conformers of the c-Myc-Max leucine zipper.

In solution proteins often exhibit backbone and side-chain flexibility. Yet electrostatic interactions in proteins are sensitive to motions. Hence, here we study the contribution of ion pairs toward protein stability in a range of conformers which sample the conformational space in solution. Specifically, we focus on the electrostatic contributions of ion pairs to the stability of each of the conformers in the NMR ensemble of the c-Myc-Max leucine zipper and to their average energy minimized structure. We compute the electrostatic contributions of inter- and intra-helical ion pairs and of an ion pair network. We find that the electrostatic contributions vary considerably among the 40 NMR conformers. Each ion pair, and the network, fluctuates between being stabilizing and being destabilizing. This fluctation reflects the variability in the location of the ion pairing residues and in the geometric orientation of these residues, both with respect to each other and with respect to other charged groups in the rest of the protein. Ion pair interactions in the c-Myc-Max leucine zipper in solution depend on the protein conformer which is analyzed. Hence, the overall stabilizing (or destabilizing) contribution of an ion pair is conformer population-dependent. This study indicates that free energy calculations performed using the continuum electrostatics methodology are sensitive to protein conformational details.

Basic Helix-Loop-Helix Leucine Zipper Transcriptio↗

PubMed1992

PCILO quantum-mechanical relaxed conformational energy map of methyl 4-thio-alpha-maltoside in solution.

A theoretical study is presented of the conformational properties of methyl 4-thio-alpha-maltoside. Quantum-chemical PCILO (perturbed configuration interaction with localized orbitals) energy minimization with evaluation of the solvent effect has been used to calculate semi-rigid and relaxed (phi, psi) conformational-energy surfaces in 1,4-dioxane, methanol, dimethyl sulfoxide, and water. The inclusion of molecular flexibility in the conformational analysis of this disaccharide derivative was found to have a significant effect upon the allowed conformational space of the molecule. Calculations revealed the existence of 15 stable conformers having different internal geometries. The relative abundance of these conformers is strongly influenced by solvent. The locations of the global minima and "virtual" conformations vary with solvent and the flexibility of methyl 4-thio-alpha-maltoside significantly decreases from 1,4-dioxane to water. It was found that the conformational properties of methyl 4-thio-alpha-maltoside differ from those of the corresponding 4-oxygenated analogue, methyl alpha-maltoside. The calculated solution behaviour is supported by very good agreement between the theoretical values mean value of 3JC-4,H-1' = 2.67 and mean value of 3JC-1',H-4 = 5.24 Hz calculated as ensemble averages over all conformers on the relaxed map and the experimental values of 2.95 and 5.15 Hz in water solution.

Carbohydrate Conformation↗

PubMed1999

Probing the binding behavior and conformational states of globular proteins in reversed-phase high-performance liquid chromatography.

Reversed-phase high-performance liquid chromatography (RP-HPLC) is a widely used technique for the separation of proteins under low pH aquo-organic solvent gradient elution conditions, typically carried out at ambient temperatures. These conditions can however induce conformational effects with proteins as evident from changes in their biological or immunological activities. By monitoring the influence of temperature on the retention and band-broadening characteristics of proteins, the role of conformational processes in these lipophilic environments can be examined. These processes can then be interpreted in terms of a two-state model involving a native (N) and a fully unfolded species (U) or more complex folding/unfolding models. In the present study, the gradient elution RP-HPLC behavior of sperm whale myoglobin (SWMYO) and hen egg white lysozyme (HEWL) has been investigated at temperatures between 5 and 85 degrees C with n-octadecyl (C18)- and n-butyl (C4)-silica reversed-phase sorbents. The interaction of these proteins with these reversed-phase sorbents has also been examined in terms of the contributions that the heme prosthetic group of SWMYO and the disulfide bonds in HEWL make to the stabilization of the native conformation of these proteins in these hydrophobic environments. The observed interconversions of multiple peak zones of SWMYO and HEWL in the presence of C18 and C4 ligands have been subsequently analyzed in terms of the unfolding processes that these proteins can undergo at low pH and at elevated temperatures. The ability of hydrocarbonaceous ligands to trap ensemblies of partially unfolded conformational intermediates of proteins in these perturbing environments has been examined. Pseudo-first-order rate constants have been derived for these processes from analysis of the dependencies on time of the concentration of the different protein species at specified temperatures. The relationship of these processes to the conformational transitions that these proteins can undergo via molten globule-like intermediates (i.e., compact denatured states with a significant amount of residual secondary structure) in solution has also been examined. This study thus further documents an experimental strategy to assess the folding/unfolding behavior of globular proteins in the presence of hydrophobic surfaces and aquo-organic solvents, whereby the system parameters can potentially affect the preservation of native conformations, and thus the function, of the protein under these conditions.

Animals↗

PubMed1995

Studies of the bound conformations of methyl alpha-lactoside and methyl beta-allolactoside to ricin B chain using transferred NOE experiments in the laboratory and rotating frames, assisted by molecular mechanics and dynamics calculations.

The conformation in solution of methyl beta-galactopyranosyl-(1-->4)-alpha-glucopyranoside (methyl alpha-lactoside) and methyl beta-galactopyranosyl-(1-->6)-beta-glucopyranoside (methyl beta-allolactoside) has been studied through NMR spectroscopy and molecular mechanics calculations. NOE measurements both in the laboratory and rotating frames, have been interpreted in terms of an ensemble average distribution of conformers. Molecular mechanics calculations have been performed to estimate the probability distribution of conformers from the steric energy maps. The experimental results indicate that methyl alpha-lactoside spends about 90% of its time in a broad low-energy region close to the global minimum, while methyl beta-allolactoside presents much higher flexibility. The conformational changes that occur when both disaccharides are bound to the ricin B chain in aqueous solution have been studied using transferred NOE experiments at several protein/ligand ratios. The observed data indicate that the protein causes a conformational variation in the torsion angles of methyl alpha-lactoside changing towards smaller angle values (phi/psi approximately -20/-20), although the recognized conformer is still within the lowest energy region. In particular, the torsional changes separate Gal H1 from Glc H3 and Glc H6 protons, with a noticeable decrease in the intensities of the corresponding NOE cross-peaks, which were clearly observed for the free disaccharide. On the other hand, different conformations around the phi, psi, and omega glycosidic bonds of methyl beta-allolactoside are recognized by the lectin. In fact, for the methyl-beta-allolactoside-ricin-B complex, only the NOESY cross-peaks corresponding to the protons of the galactose residue are negative, as expected for a molecule in the slow motion regime. In contrast, the corresponding cross peaks for the glucose residue were about zero, as expected for a molecule whose motion is practically independent of the protein. However, for the methyl-alpha-lactoside-ricin-B complex, all the NOESY cross-peaks for both the galactose and glucose moieties were clearly negative. From the NMR experimental point of view, it is demonstrated that the comparison of longitudinal and transversal transferred NOEs allows one to clearly differentiate direct enhancements from spin diffusion effects, which are of major concern when analysing NOE spectra of macromolecules.(ABSTRACT TRUNCATED AT 250 WORDS)

Magnetic Resonance Spectroscopy↗

PubMed1997

The role of PII conformations in the calculation of peptide fractional helix content.

Changes in the temperature, pH, ionic strength, or denaturant concentration of aqueous solutions of the monomeric non-alpha-helical peptide acetylYEAAAKEAPAKEAAAKAamide generate changes in its dichroic spectrum characteristic for a conformational transition. This transition has the characteristic features of a residue PII/unstructured conformational equilibrium in which PII denotes an extended left-handed helical conformation and unstructured denotes all the remaining conformations in a random coil ensemble. Replacement of the proline residue facilitates population of residues in an alpha-helical conformation. However, the ellipticity values for these non-proline peptides merge with the ellipticity of the proline peptide as the population of residues in the alpha-helix conformation is diminished. This convergence suggests that all residues in a host/guest peptide series of the same length share a common PII/unstructured conformational equilibrium in a given solvent. We propose that the fractional helix content of peptides within such a series may be estimated by using a two-state calculation in which the ellipticity for the non-alpha-helix conformations is provided by a peptide having a central proline guest residue.

Amino Acid Sequence↗

PubMed2002

Towards a consistent modeling of protein thermodynamic and kinetic cooperativity: how applicable is the transition state picture to folding and unfolding?

To what extent do general features of folding/unfolding kinetics of small globular proteins follow from their thermodynamic properties? To address this question, we investigate a new simplified protein chain model that embodies a cooperative interplay between local conformational preferences and hydrophobic burial. The present four-helix-bundle 55mer model exhibits protein-like calorimetric two-state cooperativity. It rationalizes native-state hydrogen exchange observations. Our analysis indicates that a coherent, self-consistent physical account of both the thermodynamic and kinetic properties of the model leads naturally to the concept of a native state ensemble that encompasses considerable conformational fluctuations. Such a multiple-conformation native state is seen to involve conformational states similar to those revealed by native-state hydrogen exchange. Many of these conformational states are predicted to lie below native baselines commonly used in interpreting calorimetric data. Folding and unfolding kinetics are studied under a range of intrachain interaction strengths as in experimental chevron plots. Kinetically determined transition midpoints match well with their thermodynamic counterparts. Kinetic relaxations are found to be essentially single-exponential over an extended range of model interaction strengths. This includes the entire unfolding regime and a significant part of a folding regime with a chevron rollover, as has been observed for real proteins that fold with non-two-state kinetics. The transition state picture of protein folding and unfolding is evaluated by comparing thermodynamic free energy profiles with actual kinetic rates. These analyses suggest that some chevron rollovers may arise from an internal frictional effect that increasingly impedes chain motions with more native conditions, rather than being caused by discrete deadtime folding intermediates or shifts of the transition state peak as previously posited.

Calorimetry↗

PubMed1999

New strategy for the conformational analysis of carbohydrates based on NOE and 13C NMR coupling constants. Application to the flexible polysaccharide of Streptococcus mitis J22.

For complex oligosaccharides, which are relatively rigid with modest excursions from a single minimum energy conformation, it is straightforward to build conformational models from NOE data. Other oligosaccharides are more flexible with transitions between distinct minima separated by substantial energy barriers. We show that modeling based on scalar coupling data is superior to NOE-based modeling for the latter case. Long range 13C-13C and 13C-1H coupling constants measured for the heptasaccharide repeating subunit of the cell wall polysaccharide from Streptococcus mitis J22 are correlated with individual glycosidic dihedral angles, effectively uncoupling the degrees of freedom of the oligosaccharide and allowing a search for combinations of dihedral angles which are energetically reasonable, i.e., with no bad van der Waals contacts, and which can be combined to satisfy all the measured J values. Allowed values of the individual angles can then be combined to search for overall oligosaccharide conformations which contribute to the ensemble. We show that while the polysaccharide from S. mitis J22 is flexible, requiring multiple conformations, most of the flexibility is localized to a few bonds and only a rather small number of conformations is required to reproduce the experimental NOE and scalar coupling data.

Carbohydrate Conformation↗

PubMed2006

NMR structure of the full-length linear dimer of stem-loop-1 RNA in the HIV-1 dimer initiation site.

The packaging signal of HIV-1 RNA contains a stem-loop structure, SL1, which serves as the dimerization initiation site for two identical copies of the genome and is important for packaging of the RNA genome into the budding virion and for overall infectivity. SL1 spontaneously dimerizes via a palindromic hexanucleotide sequence in its apical loop, forming a metastable kissing dimer form. Incubation with nucleocapsid protein causes this form to refold to a thermodynamically stable mature linear dimer. Here, we present an NMR structure of the latter form of the full-length SL1 sequence of the Lai HIV-1 isolate. The structure was refined using nuclear Overhauser effect and residual dipolar coupling data. The structure presents a symmetric homodimer of two RNA strands of 35 nucleotides each; it includes five stems separated by four internal loops. The central palindromic stem is surrounded by two symmetric adenine-rich 1-2 internal loops, A-bulges. All three adenines in each A-bulge are stacked inside the helix, consistent with the solution structures of shorter SL1 constructs determined previously. The outer 4-base pair stems and, proximal to them, purine-rich 1-3 internal loops, or G-bulges, are the least stable parts of the molecule. The G-bulges display high conformational variability in the refined ensemble of structures, despite the availability of many structural restraints for this region. Nevertheless, most conformations share a similar structural motif: a guanine and an adenine from opposite strands form a GA mismatch stacked on the top of the neighboring stem. The two remaining guanines are exposed, one in the minor groove and another in the major groove side of the helix, consistent with secondary structure probing data for SL1. These guanines may be recognized by the nucleocapsid protein, which binds tightly to the G-bulge in vitro.

Base Sequence↗

PubMed2001

Unusual conformational changes in 6-hydroxymethyl-7,8-dihydropterin pyrophosphokinase as revealed by X-ray crystallography and NMR.

The crystal structure of Escherichia coli 6-hydroxymethyl-7,8-dihydropterin pyrophosphokinase (HPPK) in complex with MgADP has been determined at 1.5-A resolution with a crystallographic R factor of 0.191. The solution structure of HPPK in complex with Mg(2+) and beta,gamma-methyleneadenosine 5'-triphosphate (MgAMPPCP) has been determined using a simulated annealing protocol with 3,523 experimental NMR restraints. The root mean square deviation of the ensemble of 20 refined conformers that represent the solution structure from the mean coordinate set derived from them is 0.74 +/- 0.26 A for all backbone atoms and 0.49 +/- 0.22 A when residues Pro(14), Pro(44)-Gln(50), and Arg(84)-Pro(91) are excluded. Binding of MgADP causes significant changes in the conformation and dynamical property of three loops of HPPK that are involved in catalysis. A dramatic, unusual conformational change is that loop 3 moves away from the active center significantly with some residues moving by >17 A. The binding of MgADP also stabilizes loop 1 and loop 3 but makes loop 2 more mobile. Very similar conformational and dynamical changes are observed in the NMR solution structure of HPPK.MgAMPPCP. The conformational and dynamical changes may play important roles in both substrate binding and product release in the catalytic cycle.

Adenosine Diphosphate↗

PubMed2000

Both native conformers of rabbit muscle adenylate kinase are active.

There are two forms of rabbit muscle adenylate kinase (AK) with different 8-anilino-1-naphthalenesulfonic acid (ANS) binding properties in equilibrium solution. One form (about 70%, denoted N1) binds rapidly with ANS, whereas the other (about 30%, denoted N2) does not. Furthermore, native forms of AK should adopt different conformations for binding with substrates and products, which should be pre-existing for performing its catalytic function. The present experiments demonstrate both forms of AK distinguished by ANS probe are active. The activity of N2 is about 0.8 fold higher than N1 and shows higher susceptibility to proteolysis by trypsin. This means that the native state of AK might be an ensemble of kinetically attainable conformers and the energy landscapes of AK folding should be rugged with more than one local minimum.

Adenylate Kinase↗

PubMed2004

Thermodynamic profiling of conformationally constrained cyclic ligands for the PDZ domain.

Inspired by structure-based design and tailored for combinatorial preparation, a series of novel cyclic peptides has been developed to yield binding ligands for the third PDZ domain (PDZ3) of PSD-95. These side chain-side chain bridged peptides permit the systematic expansion or contraction of ring size, which is intended to maximize the conformational diversity of the ensemble. Isothermal titration calorimetry (ITC) was used to measure the dissociation constants (K(d)) and associated thermodynamic binding parameters.

Adaptor Proteins, Signal Transducing↗

PubMed2006

Accounting for loop flexibility during protein-protein docking.

Although reliable docking can now be achieved for systems that do not undergo important induced conformational change upon association, the presence of flexible surface loops, which must adapt to the steric and electrostatic properties of a partner, generally presents a major obstacle. We report here the first docking method that allows large loop movements during a systematic exploration of the possible arrangements of the two partners in terms of position and rotation. Our strategy consists in taking into account an ensemble of possible loop conformations by a multi-copy representation within a reduced protein model. The docking process starts from regularly distributed positions and orientations of the ligand around the whole receptor. Each starting configuration is submitted to energy minimization during which the best-fitting loop conformation is selected based on the mean-field theory. Trials were carried out on proteins with significant differences in the main-chain conformation of the binding loop between isolated form and complexed form, which were docked to their partner considered in their bound form. The method is able to predict complexes very close to the crystal complex both in terms of relative position of the two partners and of the geometry of the flexible loop. We also show that introducing loop flexibility on the isolated protein form during systematic docking largely improves the predictions of relative position of the partners in comparison with rigid-body docking.

Binding Sites↗

PubMed1995

The use of the AMBER force field in conformational analysis of carbohydrate molecules: determination of the solution conformation of methyl alpha-lactoside by NMR spectroscopy, assisted by molecular mechanics and dynamics calculations.

The solution conformation of methyl alpha-lactoside has been studied through nmr spectroscopy and molecular mechanics calculations using the assisted model building with energy refinement (AMBER) force field. The nmr data have included nuclear Overhauser effect (NOE) measurements both in the laboratory and rotating frames, longitudinal relaxation times, and homonuclear and heteronuclear coupling constants. The steady-state and transient NOEs have been interpreted in terms of an ensemble average distribution of conformers, making use of the complete relaxation matrix approach. The molecular mechanics calculations have been performed at two dielectric constants [epsilon = 1*r and 80 Debyes (D)] in an exhaustive way, and have been complemented with specific calculations at intermediate epsilon values. Relaxed energy maps and adiabatic surfaces have been generated for the different dielectric constants. The probability distribution of conformers has been estimated from these steric energy maps. Molecular dynamics simulations in vacuo have also been performed. The experimental results indicate that the beta (1-->4)-glycosidic linkage shows some fluctuations among three low energy regions, although spends ca. 85% of its time in the region close to the global minimum. It is shown that the overestimation of the electrostatic contributions in AMBER is responsible for the failure of this force field to explain the experimental results when used at low dielectric constant (epsilon < 20 D). The matching between the expected and observed facts increases for epsilon > 40 D. Different conditions have been tested to perform temperature constant molecular dynamics simulations in vacuo, which have indicated that, when used without explicit solvent, this force field should only be employed in a qualitatively way when analyzing dynamical properties of oligosaccharides.

Carbohydrate Conformation↗

PubMed2004

Nature of structural inhomogeneities on folding a helix and their influence on spectral measurements.

Extensive conformational sampling and calculations of vibrational coupling provide a quantitative basis for the structurally inhomogeneous spectra of the amide unit in aqueous solutions containing folded and unfolded state distributions of helices. Replica exchange molecular dynamics simulations of the capped helical peptide, AA(AAKAA)(3)AAY, is carried out over a range of temperatures, where the system populates the folded and unfolded states. This sampling defines a set of ensembles that characterizes the conformational variability for configurations identified by their fraction of helical content. The effects of hydrogen bonding, both internal and external (with water), and the coupling between amide-I modes are computed as a function of temperature and helical content. End-to-end distance and coupling distributions are also computed. The solvent H-bonding, which is present at all temperatures, shifts the amide-I band toward lower frequency compared with the unsolvated band. Upon thermal denaturation of the peptide, the amide-I band shifts to higher frequency because the increase in solvent H-bonding fails to compensate for the loss in internal (helical) H-bonds. The loss of uniformity of the mode coupling along the helix at higher temperatures accounts for the well-known thermal broadening of the amide IR spectrum. The calculated inhomogeneities of segments of the peptide predict experimental properties of isotope-edited helices.

Amides↗

PubMed2005

A conformational two-state peptide model system containing an ultrafast but soft light switch.

Combining an azobenzene chromophore with the bis-cysteinyl active-site sequence of the protein disulfide isomerase (PDI) we constructed a simple but promising model for allosteric conformational rearrangements. Paralleling cellular signaling events, an external trigger, here absorption of a photon, leads to a structural change in one part of the molecule, namely the azobenzene-based chromophore. The change in geometry translates to the effector site, in our case the peptide sequence, where it modifies covalent and nonbonded interactions and thus leads to a conformational rearrangement. NMR spectroscopy showed that the trans-azo and cis-azo isomer of the cyclic PDI peptide exhibit different, but well-defined structures when the two cystine residues form a disulfide bridge. Without this intramolecular cross-link conformationally more variable structural ensembles are obtained that again differ for the two isomeric states. Ultrafast UV/Vis spectroscopy confirmed that the rapid isomerization of azobenzene is not significantly slowed down when incorporated into the cyclic peptides, although the amplitudes of ballistic and diffusive pathways are changed. The observation that most of the energy of an absorbed photon is dissipated to the solvent in the first few picoseconds when the actual azo-isomerization takes place is important. The conformational rearrangement is weakly driven due to the absence of appreciable excess energy and can be described as biased diffusion similar to natural processes.

Computer Simulation↗