Effects of Na+and Mg2+on the Structures of Supercoiled DNAs: Comparison of Simulations with Experiments

Recent cryo-electron microscopy (cryo-EM) results suggest that sufficient NaCl concentration (≤0.1 M) and superhelix density (≤−0.05) cause circular DNAs to adopt highly extended, tightly interwound configur ations, in which the strands are laterally contiguous along almost their entire length. Millimolar levels of MgCl₂reportedly act synergistically with NaCl to produce similar conformations. However, Monte Carlo simulations with purely repulsive interduplex forces failed to reproduce such structures. In the present work, solution measurements of particular physical properties were performed both to characterize the effects of Na⁺and Mg²⁺on DNA structure and to provide quantitative tests of Monte Carlo simulations of circular DNAs. Supercoiled p30δ DNAs in 10 mM Tris plus 0, 0.122, and 0.1 M NaCl, and 0.1 M NaCl plus 4 mM Mg²⁺were examined by static and dynamic light scattering (LS and DLS), time- resolved fluorescence polarization anisotropy (FPA) of intercalated ethidium, and circular dichroism (CD) spectroscopy. Upon addition of 0.122 M NaCl, the radius of gyration (R_g) decreased substantially, which indicates that p30δ adopts a more compact structure. This contradicts the cryo-EM studies, where molecular extension andR_gboth increase upon adding 0.1 M NaCl. In 0.1 M NaCl, the torsion constant measured by FPA is practically invariant to superhelix density, and the plateau diffusion coefficient at large scattering vector (D_plat) is likewise nearly the same at both relaxed and native superhelix densities. Such invariance is difficult to reconcile with any transition from relaxed circles to tightly interwound structures with laterally contiguous strands. Metropolis Monte Carlo simulations were performed to generate canonically distributed sets of structures, from which averageD₀values and scattered intensity ratios,〈I(0)〉/〈I(k)〉, were calculated. Agreement between simulations and experiments in regard to 〈I(0)|〉/〈I(k)〉,D₀and the supercoiling free energy, ΔG_sc(Δl ), is remarkably good for the most extensively studied p30δ samples. The simulated structures exhibit no sign of very tight interwinding with extensive lateral contacts, but instead exhibit most probable superhelix diameters of 85 to 90 Å. When 4 mM Mg²⁺was added to native supercoiled p30δ in 0.1 M NaCl,R_gdecreased,D₀increased, and the longest internal relaxation rate (1/τ₂(0)) increased, all of which indicate a further overall contraction of the molecular envelope. The torsion constant exhibited a slight increase that is hardly statistically significant. In this case, agreement between the simulations and experiments was only semi-quantitative for most samples investigated, although the predicted contraction was exhibited by all five samples of p30δ and one of pBR322 DNA. The simulated structures in 0.1 M NaCl plus 4 mM Mg²⁺again showed no sign of extensive lateral contacts. A plausible explanation is proposed for the highly extended, tightly interwound structures seen in cryo-EM, and explicitly tested by Monte Carlo simulations of a 1000 bp circular DNA at +25 and −50°C. Structures identical to those seen in cyro-EM are in fact the equilibrium structures in the simulations at −50°C, and the estimated time for equilibration (2.3×10⁻⁶second) is much smaller than the estimated time for vitrification (1×10⁻⁴second).     

Boundaries of the universal K3 region and plateau region of the dynamic structure factor for DNA

A sufficiently long semiflexible filamentous macromolecule is theroretically expected to exhibit three different domains of behavior of its apparent diffusion coefficient D_app(K) as a function of scattering vector K: (1) the small wave vector limit, where D_app(K) = D₀ is the translational diffusion coefficient of the center-of-mass; (2) the universal K³ region, where D_app(K) = (k_BT/6πη)K is a universal function of K independent of any property of the molecule itself; (c) the plateau region at large K², where D_app(K) approaches either a plateau, or gradually sloping quasiplateau, characteristic of local (elastic) rigid-body motions of the filament. The existence of each of these different domains has now been established experimentally for at least some polymers. The boundaries of the universal K³ region and the plateau region are determined theoretically here using precise quantitative criteria for universal or plateau behavior of D_app(K) for a Rouse-Zimm model containing N + 1 subchains with rms subchain extension b. Allowing a maximum of 13% nonuniversal behavior, the domain of the universal K³ region is given by K²R²_G = K²Nb²/6 ≥ 7 and K²b² ? 0.54. Allowing as much as 10% nonplateau behavior, the boundary for onset of plateau behavior is K²b² = 18.3. D_app(K) is at least 50% nonuniversal when K²b²/6 = 6 ln 3. Extension of these results to DNA is examined theoretically, and good agreement of the pertinent predictions with published experimental data is demonstrated. It is concluded that no truly universal K³ region exists for DNA with M_r ? 10⁷ and persistence length a ≥ 450 Å, although marginally (?17% nonuniversal) universal behavior, is exhibited in a very narrow domain 0.64 × 10¹⁰ ? K² ? 0.84 × 10¹⁰ cm^?2 for ?29 DNA (M_r = 11.5 × 10⁶). More than 50% of D_app(K) is governed by local (elastic) rigid-body motions when K² = 5.23 × 10¹⁰ cm^?2. The existence of a very wide region of nonuniversal apparent K³ behavior extending up to very large K², far into the plateau region, is demonstrated in a plot of D_app(K)/K vs K² for the Rouse-Zimm model. This is shown to stem in part from visual artifacts of plotting D_app(K)/K vs K², even for rigid species.     

The titratable joint phenomenon in ΦW-14 DNA

Dynamic light scattering (DLS) studies are carried out on native ΦW-14 DNA, which has putrescines covalently attached at the methyl groups of half its thymines, and on a chemically modified form of the same DNA in which the ammonium groups of its putrescines are almost completely acetylated. From neutrality to pH 9.6, both forms of ΦW-14 DNA exhibit the same curve of D_app vs K² over the range K² = 0.5 × 10¹⁰ to K² = 20 × 10¹⁰ cm^?2, and this coincides with curves that we have observed for other DNAs. (D_app, apparent diffusion coefficient; K, scattering vector). However, when the pH is raised to pH 10.0–10.2, native ΦW-14 exhibits a spectacular decrease in D_app at large wave vector, whereas the acetylated form shows no sign of such behavior. It is inferred that bound ammonium groups make an essential contribution to the stabilization of titratable joints. Comparing the pH profiles of the absorbance (A₂₆₀) for these two DNAs gives some evidence that base unstacking may be involved in titratable joint formation.     

Dynamic light scattering from thin rigid rods: Anisotropy of translational diffusion of tobacco mosaic virus

An Exact theoretical expression for the apparent diffusion coefficient D_app(K) of a thin rigid rod with arbitrary anisotropy of its translational diffusion diffusion coefficient is derived from the first cumulant of its dynamic structure factor. D_app(K) is predicted to reach a limiting plateau value at extermely large values of KL, where K is the scattering vector and L the rod length. Howerver, that limiting plateau value is approached only very slowly along a quasi-plateau with a very gradual slope. Dynamic light-scattering studies have been performed on tobacco mosaic virus from K² = (0.4–20) × 10¹⁰ cm^?2 using 632-8-nm laser radiation. The present data yield D₀ = (4.19 ± 0.10) × 10^?8 cm²/s (corrected to 20,w conditions) and, with literature data to establish L = 2980 Å and the rotational diffusion coefficient D_R = 318s^?1, yield also Δ ≡ D_∥ ? D_⊥ = (1.79 ± 0.38) × 10^?8 cm²/s. The experimental data closely follow the curve of D_app(K) vs K² calcuated for these parameters. The present value of D₀ substantially exceeds all previous dynamic light-scattering values, but is in good aggreement with previous sedimentation data, which were confirmed for the presemt sample. The anisotropy ratio Δ/D₀ = 0.43 ± 0.09 is in accord with theoretical predictions based on the modified Kirkwood algorithm, despite the fact the D₀ lies significantly below its corresponding theoretical value. The present data largely predlude the possibility that both D₀ and Δ/D₀ could simultaneously match their theoretical predictions. We present a detailed comparison of the experimental data with the calculations of Tirado and Garcia de la Torre based on the modified Kirkwood algorithm and with the Broersma formulas.     

Dynamic light-scattering studies of internal motions in DNA. I. Applicability of the rouse-zimm model

The intermediate scattering function G(K,t) for any polymer model obeying a linear separable Langevin equation can be expressed in terms of the eigenvalues and eigenvectors of its normal coordinate transformation. An algorithm for the extract numerical evaluation of G(K,t) for linear Rouse-Zimm chains in the presence of hydrodynamic interaction has been developed. The computed G(K,t)² were fit to C(t) = A exp(?t/τA) + B, and apparent diffusion coefficients calculated according to D_app ≡ 1/(2τ_AK²). G(K,t)² was surprisingly well-fit by single-exponential decays, especially at both small and large values of Kb, where K is the scattering vector and b the root-mean-squared subunit extension. Plots of D_app vs K² in-variably showed a sigmoidal rise from D₀ at K² = O up to a constant plateau value at large K²b². Analytical expression for G(K,t), exact in the limit of short times, were obtained for circular Rouse-Zimm chains with and without hydrodynamic interaction, and also for free-draining linear chains, and in addition for the independent-segment-mean-force (ISMF) model. The predicted behaviors for G(K,t) at large Kb (or KR_G) was found in all cases to be single-exponential with 1/τ ∝ K² at large Kb, in agreement with the computational results. A simple procedure for estamating all parameter of the Rouse-Zimm model from a plot of D_app vs K² is proposed. Experimental data for both native and pH-denatured calf-thymus DNA in 1.0M Nacl with and without EDTA clearly plateau behavior of D_app at large values of K, in harmony with the present Rouse-Zimm and ISMF theories, and in sharp contrast to previous predictions based on the Rouse-Zimm model.     

Intramolecular interference effects in dynamic light scattering from rigid rings

A formula for the apparent diffusion coefficient [D_app(κ)] of a rigid ring is derived from the exact first cumulant of its dynamic structure factor. D_app(κ) is expressed in terms of the ring radius, the diffusion coefficients (D_zz and D_xx) for translation parallel and perpendicular, respectively, to the symmetry axis, and the diffusion coefficients (D and D) for rotation around the symmetry and transverse axes, respectively. D_app(κ) exhibits oscillations as a function of the scattering vector k , which depend on D and the anisotropy of translational diffusion (D_zz ? D_xx). The maxima in D_app(κ) are associated with minima in the static structure factor S(κ, 0), which are due to destructive intramolecular interference. The oscillations in D_app(κ) result from periodic variations in the relative intensities of scattered light from different orientations of the ring, which manifest the various motions to different extents. The orientations contributing most to the scattered intensity are those that exhibit the least destructive interference and consequently contribute most to the decay of the dynamic structure factor. © 1993 John Wiley & Sons, Inc.     

QELS-SEF study on poly(lysine) in the extraordinary phase: Effect of electric field strength on the apparent diffusion coefficient

The technique of quasielastic light scattering (QELS) in the presence of a sinusoidal electric field (QELS-SEF) was used to examine the diffusion of poly(lysine) in the extraordinary phase, which is defined by the anomalously small value in the apparent diffusion coefficient (D_app, obtained by QELS methods) as the added salt concentration is lowered below 10 mM. Spectra were obtained for high-molecular-weight poly(lysine) (800,000) in 0.5 mM KCl, using a driving frequency of 90 Hz. It was observed that the linewidth, hence apparent diffusion coefficient (D_SF), increased with electric field strength (E) over the range 6 < E < 30 V/cm. As might be anticipated, the asymptotic limit, D_SF(E = 0), was almost numerically equivalent to D_app at this KCl concentration. As E approached the upper limit value of 31 V/cm, the value of D_SF approached the high salt (500 mM KCl) value of D_app. These observations are discussed in terms of small-ion dispersion effects.     

Diffusion properties of bacteriophages through agarose gel membrane

A simple two‐chamber diffusion method was developed to study the diffusion properties of bacteriophages (phages). The apparent diffusion coefficients (D_app) of Myoviridae phage T4 and filamentous phage fNEL were investigated, and the diffusion of the phages was found to be much slower than the diffusion of three antibiotics, ciprofloxacin, penicillin G, and tetracycline. D_app of T4 and fNEL in water through filter paper were calculated to be 2.8 × 10^?11 m²/s and 6.8 × 10^?12 m²/s, respectively, and D_app of fNEL through agarose gel membrane, an artificial biofilm, was also calculated to be smaller than that of T4. In addition, D_app of phages through agarose gel was dependent on agarose concentration due to the similar size of phage and agarose gel mesh. We concluded that D_app of phages through an artificial biofilm is dependent on both phage morphology and biofilm density, and suggest the use of this method to study diffusion properties through real biofilms. © 2010 American Institute of Chemical Engineers Biotechnol. Prog., 2010     

Quasielastic light scattering by biopolymers. V. Interparticle interactions between polynucleosomes

Quasielastic light scattering and electrophoretic light scattering experiments were performed on chicken erythrocyte polynucleosome solutions at various temperatures and ionic strengths. The apparent diffusion coefficient, D_app, was found to depend on the scattering vector K. In general, D_app can be described as a damped oscillatory function of K in the ionic strength range of 10 to 60 mM and over the temperature range of 10 to 40°C. Electrophoretic light scattering studies on total digest chromatin samples indicate the apparent charge on the polynucleosomes increases as the ionic strength is lowered from 10 to 1 mM. These data are interpreted in terms of fluctuations in the surface charge distribution of the polyion and subsequent inducement of an asymmetric distribution of small ions about the polyion. These fluctuation components lead to the formation of “clusters” of polyions.     

Nonradiative energy transfer in oligopeptide chains generated by a monte-cralo mehod including long-range interactions

A Monte-Carlo method including long-range interactions is used to oligopeptide chains in random-coil state. The chains are composed of 4, 9, or 14 repeating units and are labeled with the luminopheres tyrosine or tryptophan. Interactions with a solvent (water) are taken into account in the calculations through modifications of the semiempirical potential-energy functions. The chains represent oligopeptides composed of hydrophobic or hydrophilic amino acid residues. Various properties relavent to the interpretaiton of nonradiative enrgy-transfer experiments, such as the average value of the orientation factor for dipole-dipole interaction of the luminophores, 〈k²〉, the distribution function of the distances between the luminophores f(r_l), the efficiences of energy transfer in the static and dyamic averaging regimes, 〈T〉_s amnd 〈T〉_d, as well as the fluorescence decay I(t) of the donor luminophore in various averaging conditions, are computed. It is shown that, for all chains considered, 〈k²〉 is not vary far form 0.67 and that 〈T〉_s and 〈T〉_d have completely different values. Due to the small extent of correlation between the distances r_l and the mutual orientations of the lumninophores, the decay kinetics 〈I(t)_s corresponding to a static averaging regime can be expressed in terms of distribution functions f(r_l). These results are in agrrement with those obtained previously for the unperturbed chain model.     

Temperature dependence of the dynamic light scattering of linear phi 29 DNA: implications for spontaneous opening of the double-helix

The apparent diffusion coefficient D_app(K) of a single sample of linear ?29 DNA (M_r = 11.5 × 10⁶) has been measured as a function of K² from 0.21 × 10¹⁰ to 20 × 10¹⁰ cm^?2 at a variety of temperatures from ?0.5 to +70°C. D_app(K) scales closely as T/η at every value of K². All of these data are simulated by a particular Rouse-Zimm model comprised of a constant number of subchains with constant rms subchain extension b = 1057 Å and an apparent subchain diffusion coefficient D_plat that scales at T/η from ?0.5 to +70°C. It is inferred from these results that any temperature dependence of the flexural and torsional rigidities of DNA must be rather weak. A less firm inference is that these rigidities actually increase slightly with temperature, possibly in proportion to T, which is weak T dependence in this context. These findings eliminate the possibility that spontaneous transient opening of the DNA structure has any significant effect on the flexural and torsional rigidities of the DNA filament. A review of the most pertinent available data from other experiments concerning spontaneous transient opening of the DNA is presented. The formaldehyde kinetics data do not unequivocally implicate an open base-pair intermediate and provide only an upper limit to the fraction of open base pairs. An alternative nonopening model with a protonated doorway state is proposed to accommodate the hydrogen-exchange data. It is concluded that there is presently no incontrovertible evidence for a fraction of unstacked open base pairs greater than about 10^?4.     

A dynamic laser light-scattering study of chitosan in aqueous solution

The solution behavior of four chitosans (91% deacetylated chitin) with different molecular weights in 0.2M CH₃COOH/0.1M CH₃COONa aqueous solution was investigated at 25°C by dynamic laser light scattering (LLS). The Laplace inversion of the precisely measured intensity-intensity lime correlation function leads us to an estimate of the line-width distribution G(Γ), which could be further reduced too translational diffusion coefficient distributions G(D). By using a combination of static and dynamic LLS results, i.e., M_w and G (D), we were able to establish a calibration of D = k_DM with k_D = (3.14 ± 0.20) × 10⁻⁴ and α_D = 0.655 ± 0.015. By using this calibration, we successfully converted G(D) into a molecular weight distribution f_w(M). The larger α_D value confirms that the chitosan chain is slightly extended in aqueous solution even in the presence of salts. This is mainly due to its backbone and polyelectrolytes nature. As a very sensitive technique, our dynamic LLS results also revealed that even in dilute solution chitosan still forms a small amount of larger sized aggregates that have been overlooked in previous studies. The calibration obtained in this study will provide another way to characterize the molecular weight distribution of chitosan in aqueous solution at room temperature. © 1995 John Wiley & Sons, Inc.     

Measurement of diffusion coefficients of meningococcal polysaccharide by optical mixing spectroscopy. I. A preliminary characterization on the aggregation of the group C polysaccharide

The angular distribution of scattered intensity and decay times of concentration fluctuations have been measured by means of digital photon counting and single-clipped photon correlation for solutions of Group C meningococcal polysaccharides at 31°C. The z-average diffusion coefficient 〈D〉_z and its second moment 〈D²〉_z have been determined from the time-dependent correlation function using the cumulant expansion technique. Very low observed values of 〈D〉_z and the tremendous width of the polydispersity index, which is the z-average normalized variance, suggest a higher degree of aggregation than the monomer–dimer type self-association at finite concentrations.     

Light scattering and viscosity study of heat aggregation of insulin

Aggregation behavior and hydrodynamic parameters of insulin have been determined from static and dynamic light scattering experiments and intrinsic viscosity measurements carried out at pH 4.0, 7.5, and 9.0 in the temperature range 20–40°C in aqueous solutions. The protein aggregated extensively at elevated temperatures in the acidic solutions. Intermolecular interactions were found to be attractive and to increase with temperature. The measured intrinsic viscosity [η], diffusion coefficient D₀, molecular weight M, and radius of gyration R_g exhibited the universal behavior: M[η] = (2.4 ± 02) × 10⁻²⁷ (R_e,η/R_e,D)³(D_0η/T)⁻³ and (D₀√n)₋₁ ≃ (√6 πη₀ζβ/k_BT) [1 + 0.201)(v/β³)√n], where n is the number of segments in the polypeptide. The effective hydrodynamic radii deduced from [η], (R_e, η) and the same deduced from D₀, (R_e,D) showed a constant ratio, (R_e,η/R_e,D = 1.1 ± 0.1). R_e,D/R_g = ξ was found to be (0.76 ± 0.07). From the known solvent viscosity η₀, the segment length β was deduced to be (10 ± 1) Å. The excluded volume was deduced to be (5 Å)³ regardless of pH. The Flory-Huggins interaction parameter was found to be χ = 0.45 ± 0.04, independent of pH and temperature. © 1998 John Wiley & Sons, Inc. Biopoly 45: 1–8, 1998     

Solvent‐dependent conformation of amylose tris(phenylcarbamate) as deduced from scattering and viscosity data

The z‐average mean‐square radius of gyration 〈S²〉_z, the particle scattering function P(k), the second virial coefficient, and the intrinsic viscosity [η] have been determined for amylose tris(phenylcarbamate) (ATPC) in methyl acetate (MEA) at 25°C, in ethyl acetate (EA) at 33°C, and in 4‐methyl‐2‐pentanone (MIBK) at 25°C by light and small‐angle X‐ray scattering and viscometry as functions of the weight‐average molecular weight in a range from 2 × 10⁴ to 3 × 10⁶. The first two solvents attain the theta state, whereas the last one is a good solvent for the amylose derivative. Analysis of the 〈S²〉_z, P(k), and [η] data based on the wormlike chain yields h (the contour length or helix pitch per repeating unit) = 0.37 ± 0.02 and λ^?1 (the Kuhn segment length) = 15 ± 2 nm in MEA, h = 0.39 ± 0.02 and λ^?1 = 17 ± 2 nm in EA, and h = 0.42 ± 0.02 nm and λ^?1 = 24 ± 2 nm in MIBK. These h values, comparable with the helix pitches (0.37–0.40 nm) per residue of amylose triesters in the crystalline state, are somewhat larger than the previously determined h of 0.33 ± 0.02 nm for ATPC in 1,4‐dioxane and 2‐ethoxyethanol, in which intramolecular hydrogen bonds are formed between the C?O and NH groups of the neighbor repeating units. The slightly extended helices of ATPC in the ketone and ester solvents are most likely due to the replacement of those hydrogen bonds by intermolecular hydrogen bonds between the NH groups of the polymer and the carbonyl groups of the solvent. © 2009 Wiley Periodicals, Inc. Biopolymers 91: 729–736, 2009. This article was originally published online as an accepted preprint. The “Published Online” date corresponds to the preprint version. You can request a copy of the preprint by emailing the Biopolymers editorial office at biopolymers@wiley.com     

Size adaptation of turing prepatterns

Spontaneous pattern formation may arise in biological systems as primary and secondary bifurcations to nonlinear parabolic partial differential equations describing chemical reaction-diffusion systems. Such Turing prepatterns have a specified geometry as long as D/R ² (the diffusion coefficient of the morphogen D divided by the square of a characteristic length) is confined to a (usually) limited interval. As real biochemical systems like cleaving eggs or early embryos vary considerably in size, Turing prepatterns are unable to maintain a specified prepattern-geometry, unless D/R ² is varied as well. We show, that actual biochemical control systems may vary D _app/R², where D _app(k) is an apparent diffusion constant, dependent on enzyme regulated rate constants, and that such simple control systems allow Turing structures to adapt to size variations of at least a factor 10³ (linearly), not only in large connected cell systems, but in single cells as well.     

Stochastic processes in particle-number fluctuations in an electron-photon shower

The paper is concerned with the existence and asymptotic character of the nonlinear boundary value problemdG/dt=F(t,G,F, ¦α?β¦) (1) ¦α?β¦dF/dt=g(t,G,F, ¦α?β¦)G(o,¦α?β¦)=k ₁,G(∞,¦α?β¦)=k ₂ (2) as ¦α?β¦→ o+ The discussion is related to the problem of particle-number fluctuations in the theory of cosmic radiation andG andF denote respectively the probability generating functions for the electron distribution in an electron-initiated and a photon-initiated shower. A solution of the system (1) satisfying the boundary conditions (2) is constructed so that specified limiting conditions are fulfilled.     

Bacillus subtilis aminopeptidase: specificity toward amino acyl-beta-naphthylamides.

The kinetic parameters for the hydrolyses of different l-α-amino acid-β-naphthylamides by Bacillus subtilis aminopeptidase have been measured for the native enzyme and for the enzyme activated in 5 mm Co(NO₃)₂. In most cases Co²⁺ activation decreased K_m(app) values and increased k_cat values, in other cases k_m(app) and k_cat values were increased; for the remainder of the substrates tested k_m(app) values and k_cat values were decreased. In all cases tested the ratios of $\text{(}\text{k}\text{cat}\text{K}{}_{\mathrm{<mtext>m(</mtext><mtext>app</mtext><mtext>)</mtext>}}\text{)}\text{CO}{}^{\mathrm{2+}}\text{/(}\text{k}{}_{\mathrm{<mtext>cat</mtext>}}\text{K}{}_{\mathrm{<mtext>m(</mtext><mtext>app</mtext><mtext>)nativ</mtext>}}\text{)}$ were increased (2- to 108-fold). For the native enzyme the order of specificity toward the l-amino acid-β-naphthylamides was Arg > Met > Trp > Lys > Leu and for the Co²⁺ activated enzyme the order of specificity was Lys > Arg > Met > Trp > Leu. The native enzyme hydrolyzed Pro-β-naphthylamide, but not α-Glu-β-naphthylamide; Co²⁺ activation of the enzyme affected an appreciable rate of hydrolysis of the latter substrate.     

A systematic comparison of summary characteristics for quantifying point patterns in ecology

Many functional summary characteristics such as Ripley's K function have been used in ecology to describe the spatial structure of point patterns to aid understanding of the underlying processes. However, their use is poorly guided in ecology because little is understood how well single summary characteristics, or a combination of them, capture the spatial structure of real world patterns. Here, we systematically tested the performance of combinations of eight summary characteristics [i.e. pair correlation function g(r), K‐function K(r), the proportion E(r) of points with no neighbor at distance r, the nearest neighbor distribution function D(r), the spherical contact distribution H_s(r), the kth nearest‐neighbor distribution functions D_k(r), the mean distance nn(k) to the kth neighbor, and the intensity function λ( x )]. To this end we used point pattern data covering a wide range of spatial structures including simulated (stationary) as well as real, possibly non‐stationary, patterns on tree species in a tropical forest in Panamá. To measure the information contained in a given combination of summary characteristics we used simulated annealing to reconstruct the observed patterns based only on the limited information provided by this combination and assessed how well other characteristics of the observed pattern were recovered. We found that the number of summary characteristics required to capture the spatial structure of stationary patterns varied between one (for patterns with near random structures) and three (for patterns with complex cluster and superposition structures), but with a robust ranking g(r), D_k(r), and H_s(r) that was largely independent on pattern idiosyncrasies. Stationary summary characteristics [with ranking g(r), D_k(r), H_s(r), E(r)] captured small‐ to intermediate scale properties of non‐stationary patterns, but for describing large‐scale spatial structures the intensity function was required. Our finding revealed that the current practice in ecology of using only one or two summary characteristics bears danger that essential characteristics of more complex patterns would not be detected. The technique of pattern reconstruction presented here has wide applications in ecology.