Diffusion-controlled reactions of enzymes. An approximate analytic solution of Chou's model

Phosphate removal and recovery using immobilized phosphate binding proteins

Progress towards a more circular phosphorus economy necessitates development of innovative water treatment systems which can reversibly remove inorganic phosphate (P_i) to ultra-low levels (<100 μg L^-1), and subsequently recover the P_i for reuse. In this study, a novel approach using the high-affinity E. coli phosphate binding protein (PBP) as a reusable P_i bio-adsorbent was investigated. PBP was expressed, extracted, purified and immobilized on NHS-activated Sepharose beads. The resultant PBP beads were saturated with P_i and exposed to varying pH (pH 4.7 to 12.5) and temperatures (25-45 °C) to induce P_i release. Increase in temperature from 25 to 45 °C and pH conditions between 4.7 and 8.5 released less than 20% of adsorbed P_i. However, 62% and 86% of the adsorbed P_i was released at pH 11.4 and 12.5, respectively. Kinetic experiments showed that P_i desorption occurred nearly instantaneously (<5 min), regardless of pH conditions, which is advantageous for P_i recovery. Additionally, no loss in P_i adsorption or desorption capacity was observed when the PBP beads were exposed to 10 repeated cycles of adsorption/desorption using neutral and high pH (≥12.5) washes, respectively. The highest average P_i adsorption using the PBP beads was 83 ± 5%, with 89 ± 4.1% average desorption using pH 12.5 washes over 10 wash cycles at room temperature. Thermal shift assay of the PBP showed that the protein was structurally stable after 10 cycles, with statistically similar melting temperatures between pH 4 and 12.5. These results indicate that immobilized high-affinity PBP has the potential to be an effective and reversible bio-adsorbent suitable for P_i recovery from water/wastewater.

High Resolution 31P NMR Spectroscopy Generates a Quantitative Evolution Profile of Phosphorous Translocation in Germinating Sesame Seed

Phosphorus metabolism and circulation are essential bio-physicochemical processes during development of a plant and have been extensively studied and known to be affected by temperature, humidity, lighting, hormones etc. However, a quantitative description of how various phosphorous species evolve over time has not been reported. In this work, a combined ³¹P liquid and solid state NMR spectroscopic methodology is employed, supported by a new extraction scheme and data analysis method, to carry out a quantitative investigation of phosphorous circulation in germinating sesame seeds in dark and under illumination with and without adding a growth hormone. The spectra show that only slight changes occur for phosphorous metabolism at the initial stage but a rapid change takes place between 48–96 hours after germination is started. The metabolism is found to be temperature dependent and affected by illumination and hormone. However, neither illumination nor hormone affects the final residual concentration of phytin. Moreover, phytin does not flow out of cotyledon and the phosphorous flowing to other parts of the plant is always in the inorganic form. The overall evolution profile of phytate consumption is found to be a Gaussian decaying function. These findings can be explained with a dynamic model on phytin conversion.

A Quantitative Model for cAMP Binding to the Binding Domain of MloK1

Ligand-protein binding processes are essential in biological systems. A well-studied system is the binding of cyclic adenosine monophosphate to the cyclic nucleotide binding domain of the bacterial potassium channel MloK1. Strikingly, the measured on-rate for cyclic adenosine monophosphate binding is two orders of magnitude slower than a simple Smoluchowski diffusion model would suggest. To resolve this discrepancy and to characterize the ligand-binding path in structural and energetic terms, we calculated 1100 ligand-binding molecular dynamics trajectories and tested two scenarios: In the first scenario, the ligand transiently binds to the protein surface and then diffuses along the surface into the binding site. In the second scenario, only ligands that reach the protein surface in the vicinity of the binding site proceed into the binding site. Here, a binding funnel, which increasingly confines the translational as well as the rotational degrees of freedom, determines the binding pathways and limits the on-rate. From the simulations, we identified five surface binding states and calculated the rates between these surface binding states, the binding site, and the bulk. We find that the transient binding of the ligands to the surface binding states does not affect the on-rate, such that this effect alone cannot explain the observed low on-rate. Rather, by quantifying the translational and rotational degrees of freedom and by calculating the binding committor, our simulations confirmed the existence of a binding funnel as the main bottleneck. Direct binding via the binding funnel dominates the binding kinetics, and only ∼10% of all ligands proceed via the surface into the binding site. The simulations further predict an on-rate between 15 and 40μs-1(mol/l)-1, which agrees with the measured on-rate.

Investigation of Intradomain Motions of a Y-Family DNA Polymerase during Substrate Binding and Catalysis

DNA polymerases catalyze DNA synthesis through a stepwise kinetic mechanism that begins with binding to DNA, followed by selection, binding, and incorporation of a nucleotide into an elongating primer. It is hypothesized that subtle active site adjustments in a polymerase to align reactive moieties limit the rate of correct nucleotide incorporation. DNA damage can impede this process for many DNA polymerases, causing replication fork stalling, genetic mutations, and potentially cell death. However, specialized Y-family DNA polymerases are structurally evolved to efficiently bypass DNA damage in vivo, albeit at the expense of replication fidelity. Dpo4, a model Y-family polymerase from Sulfolobus solfataricus, has been well-studied kinetically, structurally, and computationally, which yielded a mechanistic understanding of how the Y-family DNA polymerases achieve their unique catalytic properties. We previously employed a real-time Förster resonance energy transfer (FRET) technique to characterize the global conformational motions of Dpo4 during DNA binding as well as nucleotide binding and incorporation by monitoring changes in distance between sites on the polymerase and DNA, and even between domains of Dpo4. Here, we extend the utility of our FRET methodology to observe conformational transitions within individual domains of Dpo4 during DNA binding and nucleotide incorporation. The results of this novel, intradomain FRET approach unify findings from many studies to fully clarify the complex DNA binding mechanism of Dpo4. Furthermore, intradomain motions in the Finger domain during nucleotide binding and incorporation, for the first time, report on the rate-limiting step of a single-nucleotide addition catalyzed by Dpo4.

Two-level QSAR network (2L-QSAR) for peptide inhibitor design based on amino acid properties and sequence positions

In the design of peptide inhibitors the huge possible variety of the peptide sequences is of high concern. In collaboration with the fast accumulation of the peptide experimental data and database, a statistical method is suggested for peptide inhibitor design. In the two-level peptide prediction network (2L-QSAR) one level is the physicochemical properties of amino acids and the other level is the peptide sequence position. The activity contributions of amino acids are the functions of physicochemical properties and the sequence positions. In the prediction equation two weight coefficient sets {ak} and {bl} are assigned to the physicochemical properties and to the sequence positions, respectively. After the two coefficient sets are optimized based on the experimental data of known peptide inhibitors using the iterative double least square (IDLS) procedure, the coefficients are used to evaluate the bioactivities of new designed peptide inhibitors. The two-level prediction network can be applied to the peptide inhibitor design that may aim for different target proteins, or different positions of a protein. A notable advantage of the two-level statistical algorithm is that there is no need for host protein structural information. It may also provide useful insight into the amino acid properties and the roles of sequence positions.

Tethered particle motion reveals that LacI·DNA loops coexist with a competitor-resistant but apparently unlooped conformation

The lac repressor protein (LacI) efficiently represses transcription of the lac operon in Escherichia coli by binding to two distant operator sites on the bacterial DNA and causing the intervening DNA to form a loop. We employed single-molecule tethered particle motion to observe LacI-mediated loop formation and breakdown in DNA constructs that incorporate optimized operator binding sites and intrinsic curvature favorable to loop formation. Previous bulk competition assays indirectly measured the loop lifetimes in these optimized DNA constructs as being on the order of days; however, we measured these same lifetimes to be on the order of minutes for both looped and unlooped states. In a range of single-molecule DNA competition experiments, we found that the resistance of the LacI-DNA complex to competitive binding is a function of both the operator strength and the interoperator sequence. To explain these findings, we present what we believe to be a new kinetic model of loop formation and DNA competition. In this proposed new model, we hypothesize a new unlooped state in which the unbound DNA-binding domain of the LacI protein interacts nonspecifically with nonoperator DNA adjacent to the operator site at which the second LacI DNA-binding domain is bound.

Characterization of [(3) H]LS-3-134, a novel arylamide phenylpiperazine D3 dopamine receptor selective radioligand

LS-3-134 is a substituted N-phenylpiperazine derivative that has been reported to exhibit: (i) high-affinity binding (Ki value 0.2 nM) at human D3 dopamine receptors, (ii) > 100-fold D3 versus D2 dopamine receptor subtype binding selectivity, and (iii) low-affinity binding (Ki  > 5000 nM) at sigma 1 and sigma 2 receptors. Based upon a forskolin-dependent activation of the adenylyl cyclase inhibition assay, LS-3-134 is a weak partial agonist at both D2 and D3 dopamine receptor subtypes (29% and 35% of full agonist activity, respectively). In this study, [(3) H]-labeled LS-3-134 was prepared and evaluated to further characterize its use as a D3 dopamine receptor selective radioligand. Kinetic and equilibrium radioligand binding studies were performed. This radioligand rapidly reaches equilibrium (10-15 min at 37°C) and binds with high affinity to both human (Kd  = 0.06 ± 0.01 nM) and rat (Kd  = 0.2 ± 0.02 nM) D3 receptors expressed in HEK293 cells. Direct and competitive radioligand binding studies using rat caudate and nucleus accumbens tissue indicate that [(3) H]LS-3-134 selectively binds a homogeneous population of binding sites with a dopamine D3 receptor pharmacological profile. Based upon these studies, we propose that [(3) H]LS-3-134 represents a novel D3 dopamine receptor selective radioligand that can be used for studying the expression and regulation of the D3 dopamine receptor subtype.

Harnessing catalysis to enhance scanning probe nanolithography

The use of scanning probes bearing catalysts to perform surface nanolithography combines the exquisite spatial precision of scanning probe microscopy with the synthetic capabilities of (bio)chemical catalysis. The ability to use these probes to direct a variety of localised chemical reactions enables the generation of nanoscale features with a high degree of chemical complexity in a "direct-write" manner. This article surveys the range of reactions that have been employed and the key factors necessary for the successful use of such catalytic scanning probes. These factors include the experimental parameters such as write speed, force applied to the probes and temperature; as well as the processes involved in the preparation of the catalysts on the probes and the surface that is to be fabricated. Where possible, the various reactions are also compared and contrasted; and future perspectives are discussed.

Prioritization of candidate disease genes by enlarging the seed set and fusing information of the network topology and gene expression

The identification of disease genes is very important not only to provide greater understanding of gene function and cellular mechanisms which drive human disease, but also to enhance human disease diagnosis and treatment. Recently, high-throughput techniques have been applied to detect dozens or even hundreds of candidate genes. However, experimental approaches to validate the many candidates are usually time-consuming, tedious and expensive, and sometimes lack reproducibility. Therefore, numerous theoretical and computational methods (e.g. network-based approaches) have been developed to prioritize candidate disease genes. Many network-based approaches implicitly utilize the observation that genes causing the same or similar diseases tend to correlate with each other in gene-protein relationship networks. Of these network approaches, the random walk with restart algorithm (RWR) is considered to be a state-of-the-art approach. To further improve the performance of RWR, we propose a novel method named ESFSC to identify disease-related genes, by enlarging the seed set according to the centrality of disease genes in a network and fusing information of the protein-protein interaction (PPI) network topological similarity and the gene expression correlation. The ESFSC algorithm restarts at all of the nodes in the seed set consisting of the known disease genes and their k-nearest neighbor nodes, then walks in the global network separately guided by the similarity transition matrix constructed with PPI network topological similarity properties and the correlational transition matrix constructed with the gene expression profiles. As a result, all the genes in the network are ranked by weighted fusing the above results of the RWR guided by two types of transition matrices. Comprehensive simulation results of the 10 diseases with 97 known disease genes collected from the Online Mendelian Inheritance in Man (OMIM) database show that ESFSC outperforms existing methods for prioritizing candidate disease genes. The top prediction results of Alzheimer's disease are consistent with previous literature reports.

Thermodynamic and kinetic analysis of peptides derived from CapZ, NDR, p53, HDM2, and HDM4 binding to human S100B

S100B is a member of the S100 subfamily of EF-hand proteins that has been implicated in malignant melanoma and neurodegenerative conditions such as Alzheimer's disease and Parkinson's disease. Calcium-induced conformational changes expose a hydrophobic binding cleft, facilitating interactions with a wide variety of nuclear, cytoplasmic, and extracellular target proteins. Previously, peptides derived from CapZ, p53, NDR, HDM2, and HDM4 have been shown to interact with S100B in a calcium-dependent manner. However, the thermodynamic and kinetic basis of these interactions remains largely unknown. To gain further insight, we screened these peptides against the S100B protein using isothermal titration calorimetry and nuclear magnetic resonance. All peptides were found to have binding affinities in the low micromolar to nanomolar range. Binding-induced changes in the line shapes of S100B backbone (1)H and (15)N resonances were monitored to obtain the dissociation constants and the kinetic binding parameters. The large microscopic K(on) rate constants observed in this study (≥1 × 10(7) M(-1) s(-1)) suggest that S100B utilizes a "fly casting mechanism" in the recognition of these peptide targets.

Experimental and theoretical evaluation of multisite cadmium(II) exchange in designed three-stranded coiled-coil peptides

An important factor that defines the toxicity of elements such as cadmium(II), mercury(II), and lead(II) with biological macromolecules is metal ion exchange dynamics. Intriguingly, little is known about the fundamental rates and mechanisms of metal ion exchange into proteins, especially helical bundles. Herein, we investigate the exchange kinetics of Cd(II) using de novo designed three-stranded coiled-coil peptides that contain metal complexing cysteine thiolates as a model for the incorporation of this ion into trimeric, parallel coiled coils. Peptides were designed containing both a single Cd(II) binding site, GrandL12AL16C [Grand = AcG-(LKALEEK)(5)-GNH(2)], GrandL26AL30C, and GrandL26AE28QL30C, as well as GrandL12AL16CL26AL30C with two Cd(II) binding sites. The binding of Cd(II) to any of these sites is of high affinity (K(A) > 3 × 10(7) M(-1)). Using (113)Cd NMR spectroscopy, Cd(II) binding to these designed peptides was monitored. While the Cd(II) binding is in extreme slow exchange regime without showing any chemical shift changes, incremental line broadening for the bound (113)Cd(II) signal is observed when excess (113)Cd(II) is titrated into the peptides. Most dramatically, for one site, L26AL30C, all (113)Cd(II) NMR signals disappear once a 1.7:1 ratio of Cd(II)/(peptide)(3) is reached. The observed processes are not compatible with a simple "free-bound" two-site exchange kinetics at any time regime. The experimental results can, however, be simulated in detail with a multisite binding model, which features additional Cd(II) binding site(s) which, once occupied, perturb the primary binding site. This model is expanded into differential equations for five-site NMR chemical exchange. The numerical integration of these equations exhibits progressive loss of the primary site NMR signal without a chemical shift change and with limited line broadening, in good agreement with the observed experimental data. The mathematical model is interpreted in molecular terms as representing binding of excess Cd(II) to surface Glu residues located at the helical interfaces. In the absence of Cd(II), the Glu residues stabilize the three-helical structure though salt bridge interactions with surface Lys residues. We hypothesize that Cd(II) interferes with these surface ion pairs, destabilizing the helical structure, and perturbing the primary Cd(II) binding site. This hypothesis is supported by the observation that the Cd(II)-excess line broadening is attenuated in GrandL26AE28QL30C, where a surface Glu(28), close to the metal binding site, was changed to Gln. The external binding site may function as an entry pathway for Cd(II) to find its internal binding site following a molecular rearrangement which may serve as a basis for our understanding of metal complexation, transport, and exchange in complex native systems containing α-helical bundles.

Application of density similarities to predict membrane protein types based on pseudo-amino acid composition

Cell membranes provide integrity of living cells. Although the stability of biological membrane is maintained by the lipid bilayer, membrane proteins perform most of the specific functions such as signal transduction, transmembrane transport, etc. Then it is plausible membrane proteins being attractive drug targets. In this article, based on the concept of using the pseudo-amino acid composition to define a protein, three different density similarities are developed for predicting the membrane protein type. The predicted results showed that the proposed approach can remarkably improve the accuracy, and might become a useful tool for predicting the other attributes of proteins as well.

Some remarks on protein attribute prediction and pseudo amino acid composition

With the accomplishment of human genome sequencing, the number of sequence-known proteins has increased explosively. In contrast, the pace is much slower in determining their biological attributes. As a consequence, the gap between sequence-known proteins and attribute-known proteins has become increasingly large. The unbalanced situation, which has critically limited our ability to timely utilize the newly discovered proteins for basic research and drug development, has called for developing computational methods or high-throughput automated tools for fast and reliably identifying various attributes of uncharacterized proteins based on their sequence information alone. Actually, during the last two decades or so, many methods in this regard have been established in hope to bridge such a gap. In the course of developing these methods, the following things were often needed to consider: (1) benchmark dataset construction, (2) protein sample formulation, (3) operating algorithm (or engine), (4) anticipated accuracy, and (5) web-server establishment. In this review, we are to discuss each of the five procedures, with a special focus on the introduction of pseudo amino acid composition (PseAAC), its different modes and applications as well as its recent development, particularly in how to use the general formulation of PseAAC to reflect the core and essential features that are deeply hidden in complicated protein sequences.

Analysis of protein pathway networks using hybrid properties

Given a protein-forming system, i.e., a system consisting of certain number of different proteins, can it form a biologically meaningful pathway? This is a fundamental problem in systems biology and proteomics. During the past decade, a vast amount of information on different organisms, at both the genetic and metabolic levels, has been accumulated and systematically stored in various specific databases, such as KEGG, ENZYME, BRENDA, EcoCyc and MetaCyc. These data have made it feasible to address such an essential problem. In this paper, we have analyzed known regulatory pathways in humans by extracting different (biological and graphic) features from each of the 17,069 protein-formed systems, of which 169 are positive pathways, i.e., known regulatory pathways taken from KEGG; while 16,900 were negative, i.e., not formed as a biologically meaningful pathway. Each of these protein-forming systems was represented by 352 features, of which 88 are graph features and 264 biological features. To analyze these features, the "Minimum Redundancy Maximum Relevance" and the "Incremental Feature Selection" techniques were utilized to select a set of 22 optimal features to query whether a protein-forming system is able to form a biologically meaningful pathway or not. It was found through cross-validation that the overall success rate thus obtained in identifying the positive pathways was 79.88%. It is anticipated that, this novel approach and encouraging result, although preliminary yet, may stimulate extensive investigations into this important topic.

Trends in global warming and evolution of nucleoproteins from influenza A viruses since 1918

Global warming affects not only the environment where we live, but also all living species to different degree, including influenza A virus. We recently conducted several studies on the possible impact of global warming on the protein families of influenza A virus. More studies are needed in order to have a full picture of the impact of global warming on living organisms, especially its effect on viruses. In this study, we correlate trends in global warming with evolution of the nucleoprotein from influenza A virus and then analyse the trends with respect to northern/southern hemispheres, virus subtypes and sampling species. The results suggest that global warming may have an impact on the evolution of the nucleoprotein from influenza A virus.

Dynamic modeling of cellular response to DNA damage based on p53 stress response networks

Under acute perturbations from the outside, cells can trigger self-defensive mechanisms to fight against genome stress. To investigate the cellular response to continuous ion radiation (IR), a dynamic model for p53 stress response networks at the cellular level is proposed. The model can successfully be used to simulate the dynamic processes of double-strand breaks (DSBs) generation and their repair, switch-like ataxia telangiectasia mutated (ATM) activation, oscillations occurring in the p53-MDM2 feedback loop, as well as toxins elimination triggered by p53 stress response networks. Especially, the model can predict the plausible outcomes of cellular response under different IR dose regimes.

A dynamic model for the p53 stress response networks under ion radiation

P53 controls the cell cycle arrest and cell apoptosis through interaction with the downstream genes and their signal pathways. To stimulate the investigation into the complicated responses of p53 under the circumstance of ion radiation (IR) in the cellular level, a dynamic model for the p53 stress response networks is proposed. The model can be successfully used to simulate the dynamic processes of generating the double-strand breaks (DSBs) and their repairing, ataxia telangiectasia mutated (ATM) activation, as well as the oscillations occurring in the p53-MDM2 feedback loop.

Mechanisms of discrimination between cobalamins and their natural analogues during their binding to the specific B12-transporting proteins

Three proteins, intrinsic factor (IF), transcobalamin (TC), and haptocorrin (HC), all have an extremely high affinity for the cobalamins (Cbls, Kd approximately 5 fM) but discriminate these physiological ligands from Cbl analogues with different efficiencies decreasing in the following order: IF > TC > HC. We investigated interactions of these proteins with a number of ligands: Cbl, fluorescent conjugate CBC, two base-off analogues [pseudo-coenzyme B12 (pB) and adenosyl factor A (fA)], and a baseless corrinoid cobinamide. Protein-ligand encounter and the following internal rearrangements in both molecules were registered as a change in the fluorescence of CBC (alone or mixed with other ligands), a transition in absorbance of pB and fA (base-off --> on-base conversion), and alterations in the molecular mass of two split IF domains. The greater complexity of the binding kinetics followed better Cbl specificity (HC < TC < IF). On the basis of the experimental results, we propose a general binding model with three major steps: (1) initial attachment of the ligand to the high-affinity C-domain, (2) primary assembly of N- and C-domains, and (3) slow adjustments and fixation of the ligand at the domain-domain interface. Since step 3 was characteristic of highly specific TC and especially IF, we suggest its particular importance for ligand recognition. The designed models revealed the absolute Kd values for a group of analogues. Calculations show that most of them could potentially bind to the specific transporters IF and TC under physiological conditions. Implications of this finding and the protective role of HC are discussed.

Evolutionary optimization of the catalytic efficiency of enzymes

1. The rate equation for a generalized Michaelian type of enzymic reaction mechanism has been analyzed in order to establish how the mechanism should be kinetically designed in order to optimize the catalytic efficiency of the enzyme for a given average magnitude of true and apparent first-order rate constants in the mechanism at given concentrations of enzyme, substrate and product. 2. As long as on-velocity constants for substrate and product binding to the enzyme have not reached the limiting value for a diffusion-controlled association process, the optimal state of enzyme operation will be characterized by forward (true and apparent) first-order rate constants of equal magnitude and reverse rate constants of equal magnitude. The drop in free energy driving the catalysed reaction will occur to an equal extent for each reaction step in the mechanism. All internal equilibrium constants will be of equal magnitude and reflect only the closeness of the catalysed reaction to equilibrium conditions. 3. When magnitudes of on-velocity constants for substrate and product binding have reached their upper limits, the optimal kinetic design of the reaction mechanism becomes more complex and has to be established by numerical methods. Numerical solutions, calculated for triosephosphate isomerase, indicate that this particular enzyme may or may not be considered to exhibit close to maximal efficiency, depending on what value is assigned to the upper limit for a ligand association rate constant. 4. Arguments are presented to show that no useful information on the evolutionary optimization of the catalytic efficiency of enzymes can be obtained by previously taken approaches that are based on the application of linear free-energy relationships for rate and equilibrium constants in the reaction mechanism.

Low-frequency collective motion in biomacromolecules and its biological functions

The occurrence of low-frequency motion in biomacromolecules, which had long been speculated upon with a great deal of skepticism, is now a clearly established phenomenon and has been convincingly demonstrated. The next stage in the process of its elucidation appropriately concerns the determination of its origin, the development of a feasible and effective model for the calculations involved and, more importantly, the extending of investigations on its biological roles in order to gain insights into the various interesting mechanisms underlying the dynamic processes occurring in biomacromolecules. Confronted with such a task, this review has been written with the aim of stimulating further, through a systematic and comprehensive description, developments to open up this exciting frontier of molecular biology, especially from the viewpoint of biological functions.

The biological functions of low-frequency vibrations (phonons) 5. A phenomenological theory

Low-frequency internal motions of a biomacromolecule are thought to possess significant biological function from the dynamic point of view. In this paper, a general phenomenological theory is established by which it is clearly verified that low-frequency resonance plays a central role in the energy transmission required during the cooperative interaction between subunits in a protein oligomer. According to the present theory, it is found that the energy transmission between a pair of diagonal subunits in a protein oligomer with a polygon arrangement is the most efficient, so as to in a sense further predict that after a ligand is bound to a subunit by random collision, its diagonal subunit in the same protein oligomer will possess the greatest probability of binding with the next ligand. Furthermore, based on the concept of the 'resonance-controlled trigger' derived from the phenomenological theory, it is feasible to estimate the lower time limit of allosteric transition from one subunit to the other. Such a time limit depends on the dominant low-frequency mode of each subunit, the ratio of the coupling force constant to the corresponding inherent force constant, as well as the geometrical arrangement of subunits in a protein oligomer. So far none of the allosteric transitions observed in proteins has exceeded the time limit as defined here, indicating a logical consistency between our theory and the experiments.