Evaluations of reduction potential data in relation to coupling, kinetics and function

 This commentary addresses the effect and measurement of time-dependent contributions to reduction potentials. Reduction potentials form the basis for many quantitative or semi-quantitative judgements in biological redox chemistry. However, since data are obtained under an assumption of equilibrium being established, their relevance to biological functions requires consideration of the kinetics of the subprocesses that contribute to or influence the overall free energy change. Initial and final states effective in rapid and complex biological functions may differ considerably from those analysed after slow equilibration in a sample tube. A shortcoming of traditional potentiometric measurements is that the time domain is not probed. Voltammetry, a technique that has been much less widely applied in biological chemistry than in chemistry, examines redox transformations in both potential and time domains, and may enable a more realistic picture to be derived. Received, accepted: 26 November 1996     

Peptide binding to the PDZ3 domain by conformational selection

The PDZ domains, a large family of peptide recognition proteins, bind to the C‐terminal segment of membrane ion channels and receptors thereby mediating their localization. The peptide binding process is not known in detail and seems to differ among different PDZ domains. For the third PDZ domain of the synaptic protein PSD‐95 (PDZ3), a lock‐and‐key mechanism was postulated on the basis of the almost perfect overlap of the crystal structures in the presence and absence of its peptide ligand. Here, peptide binding to PDZ3 is investigated by explicit solvent molecular dynamics (MD) simulations (for a total of 1.3 μs) and the cut‐based free energy profile method for determining free energy barriers and basins. The free energy landscape of apo PDZ3 indicates that there are multiple basins within the native state. These basins differ by the relative orientation of the α2 helix and β2 strand, the two secondary structure elements that make up the peptide binding site. Only the structure with the smallest aperture of the binding site is populated in the MD simulations of the complex whose analysis reveals that the peptide ligand binds to PDZ3 by selecting one of three conformations. Thus, the dynamical information obtained by the atomistic simulations increment the static, that is, partial, picture of the PDZ3 binding mechanism based on the X‐ray crystallography data. Importantly, the simulation results show for the first time that conformational selection is a possible mechanism of peptide binding by PDZ domains in general. Proteins 2012. © 2012 Wiley Periodicals, Inc.     

The steady state kinetics of some biological systems: III. Thermodynamic aspects

Some thermodynamic aspects of steady systems are considered. The time rates of changes, “flux”, of various thermodynamic quantities are formulated. In particular the free energy flux in the steady state, the difference between the free energy flux in the steady and time dependent states and the change in free energy flux upon transition between steady states are discussed. Equations are derived which exhibit the formal similarities and differences between the free energy flux and the conventional free energy change. The temperature dependence of the steady state rate is examined and conditions for “mastery” by a single step discussed. A brief discussion of the role ofrate in the coupling of exergonic and endergonic reactions is given.     

8 Using pseudorotation as a reaction coordinate in free energy simulations of nucleic acids

Backbone sugar groups are central components of nucleic acids. The conformations of the ribose/deoxyribose can be elegantly described using the concept of pseudorotation (Altona and Sundaralingam, 1972), and are dominated by the C2′- and C3′-endo conformers. The free energy barrier of the transition between these two major puckering modes can be probed by NMR relaxation experiments (Johnson and Hoogstraten, 2008), but an atomic picture of the transition path per se is only available for several truncated nucleoside analogues (Brameld & Goddard III, 1999). Here, we implemented a new free energy simulation method for Molecular Dynamics simulations using pseudorotation as the reaction coordinate (Cremer and Pople, 1975). This allowed us to compute the free energy landscape of a complete pseudorotation cycle. The free energy landscape revealed not only the relative stability of C2′- and C3′-endo conformers, but also the main transition path and its free energy barrier. As a validation of our new approach, we calculated free energy surface of the pseudorotation of guanosine monophosphate. The free energy surface revealed that the C2′-endo conformation is ?1?kcal/mol that is more stable and the free energy barrier for the transition is 4.5–5?kcal/mol. These are in excellent agreement with previous NMR measurements (Zhang et al., 2012; Röder et al., 1975). We have further applied this method to other systems that are important in pre-biotic chemistry, including an RNA duplex with unique 2′, 5′-phosphodiester linkages.     

Gibbs free energy as a measure of complexity correlates with time within <Emphasis Type="Italic">C. elegans</Emphasis> embryonic development

We investigate free energy behavior in the nematode Caenorhabditis elegans during embryonic development. Our approach utilizes publicly available gene expression data, which gives us a picture of developmental changes in protein concentration and, resultantly, chemical potential and free energy. Our results indicate a clear global relationship between Gibbs free energy and time spent in development and provide thermodynamic indicators of the large-scale biological events of cell division and differentiation.     

Ligand binding to the voltage-gated Kv1.5 potassium channel in the open state--docking and computer simulations of a homology model

The binding of blockers to the human voltage-gated Kv1.5 potassium ion channel is investigated using a three-step procedure consisting of homology modeling, automated docking, and binding free energy calculations from molecular dynamics simulations, in combination with the linear interaction energy method. A reliable homology model of Kv1.5 is constructed using the recently published crystal structure of the Kv1.2 channel as a template. This model is expected to be significantly more accurate than earlier ones based on less similar templates. Using the three-dimensional homology model, a series of blockers with known affinities are docked into the cavity of the ion channel and their free energies of binding are calculated. The predicted binding free energies are in very good agreement with experimental data and the binding is predicted to be mainly achieved through nonpolar interactions, whereas the relatively small differences in the polar contribution determine the specificity. Apart from confirming the importance of residues V505, I508, V512, and V516 for ligand binding in the cavity, the results also show that A509 and P513 contribute significantly to the nonpolar binding interactions. Furthermore, we find that pharmacophore models based only on optimized free ligand conformations may not necessarily capture the geometric features of ligands bound to the channel cavity. The calculations herein give a detailed structural and energetic picture of blocker binding to Kv1.5 and this model should thus be useful for further ligand design efforts.     

Kinetics of sickle hemoglobin polymerization. II. A double nucleation mechanism

A double nucleation mechanism for the polymerization of sickle hemoglobin is described. The mechanism accounts for all of the major kinetic observations: the appearance of a delay, the high concentration dependence of the delay time, and the stochastic behavior of slowly polymerizing samples in small volumes. The mechanism postulates that there are two pathways for polymer formation: polymerization is initiated by homogeneous nucleation in the solution phase, followed by nucleation of additional polymers on the surface of existing ones. This second pathway is called heterogeneous nucleation. Since the surface of polymers is continuously increasing with time, heterogeneous nucleation provides a mechanism for the extreme autocatalysis that is manifested as an apparent delay in the kinetic progress curves. In this mechanism, each spherulitic domain of polymers is considered to be initiated by a single homogeneous nucleation event. The mechanism explains the irreproducibility of the delay time for single domain formation as arising from stochastic fluctuations in the time at which the homogeneous nucleus for the first polymer is formed. Integration of the linearized rate equations that describe this model results in a simple kinetic form: A[cosh(Bt)-1] (Bishop & Ferrone, 1984). In the accompanying paper (Ferrone et al., 1985) it was shown that the initial 10 to 15% of progress curves, with delay times varying from a few milliseconds to over 10(5) seconds, is well fit by this equation. In this paper, we present an approximate statistical thermodynamic treatment of the equilibrium nucleation processes that shows how the nucleus sizes and nucleation equilibrium constants depend on monomer concentration. The equilibrium model results in expressions for B and B2A as a function of monomer concentration in terms of five adjustable parameters: the bimolecular addition rate of a monomer to the growing aggregate, the fraction of polymerized monomers that serve as heterogeneous nucleation sites, the free energy of intermolecular bonding within the polymer, and two parameters that describe the free energy change as a function of size for the bonding of the heterogeneous nucleus to a polymer surface. This model provides an excellent fit to the data for B and B2A as a function of concentration using physically reasonable parameters. The model also correctly predicts the time regime in which stochastic behavior is observed for polymerization in small volumes.     

The folding funnel landscape for the peptide Met-enkephalin

We study the free energy landscape of the small peptide Met-enkephalin. Our data were obtained from a generalized-ensemble Monte Carlo simulation taking the interactions among all atoms into account. We show that the free energy landscape resembles that of a funnel, indicating that this peptide is a good folder. Our work demonstrates that the energy landscape picture and folding concept, developed in the context of simplified protein models, can also be used to describe the folding in more realistic models.     

Excitation energy trapping in anoxygenic photosynthetic bacteria*

Various aspects of excitation energy conversion in anoxygenic photosynthetic bacteria are surveyed. This minireview discusses different models that have been proposed during the past 60 years to describe excitation energy transfer from an antenna molecule to the reaction center. First, a simple one-dimensional model was suggested, but over time the models became more detailed when structural and dynamic information was included. This review focuses mainly on the picture of purple bacteria and green sulfur bacteria developed during the past decades. This revised version was published online in June 2006 with corrections to the Cover Date.     

Electrostatic contributions to the binding free energy of the lambdacI repressor to DNA.

A model based on the nonlinear Poisson-Boltzmann (NLPB) equation is used to study the electrostatic contribution to the binding free energy of the lambdacI repressor to its operator DNA. In particular, we use the Poisson-Boltzmann model to calculate the pKa shift of individual ionizable amino acids upon binding. We find that three residues on each monomer, Glu34, Glu83, and the amino terminus, have significant changes in their pKa and titrate between pH 4 and 9. This information is then used to calculate the pH dependence of the binding free energy. We find that the calculated pH dependence of binding accurately reproduces the available experimental data over a range of physiological pH values. The NLPB equation is then used to develop an overall picture of the electrostatics of the lambdacI repressor-operator interaction. We find that long-range Coulombic forces associated with the highly charged nucleic acid provide a strong driving force for the interaction of the protein with the DNA. These favorable electrostatic interactions are opposed, however, by unfavorable changes in the solvation of both the protein and the DNA upon binding. Specifically, the formation of a protein-DNA complex removes both charged and polar groups at the binding interface from solvent while it displaces salt from around the nucleic acid. As a result, the electrostatic contribution to the lambdacI repressor-operator interaction opposes binding by approximately 73 kcal/mol at physiological salt concentrations and neutral pH. A variety of entropic terms also oppose binding. The major force driving the binding process appears to be release of interfacial water from the protein and DNA surfaces upon complexation and, possibly, enhanced packing interactions between the protein and DNA in the interface. When the various nonelectrostatic terms are described with simple models that have been applied previously to other binding processes, a general picture of protein/DNA association emerges in which binding is driven by the nonpolar interactions, whereas specificity results from electrostatic interactions that weaken binding but are necessary components of any protein/DNA complex.     

A model for calculating the Bohr effect in hemoglobin equilibria.

The unusual aspects of the reaction of oxygen with hemoglobin are believed to be due to the free energy of the conformational change in the hemoglobin molecule upon oxygenation. The conformational free energy change due to oxygenation can be estimated in terms of the surface free energy of an emuslion droplet of the same size as the hemoglobin molecule. Calculations on the basis of this model lead to an equilibrium constant that varies with pH as in the acid and alkaline Bohr Effects, and that also varies with the ionic strength. The model used in this paper provides a simple way of estimating the variation of the equilibrium constant of a reaction involving a globular protein where the free energy of conformational changes can be evaluated in terms of surface properties.     

Theoretical model of reticulocyte to erythrocyte shape transformation

A theoretical model describing the kinetics of reticulocyte shape transformation was developed. The model considers the evolution of a simple cellular shape under transmembrane pressure difference, and proposes a four-parameter axisymmetric approximation of the cell surface. The mathematical analysis considers plasma membrane tension in the plane of bilayer leaflets, membrane spontaneous curvature and transmembrane transport of water. Cytoskeleton dilatational and shear rigidity, and the energetic barrier preventing the decrease of cell volume below a certain minimum are also incorporated. The set of adequate physical assumptions allowed for formulation of the equation for free energy of the investigated system. Computer simulations of cell shape changes, down to the state of free energy minimum, together with estimation of the time needed for the resulting transport of water, revealed a complex, three-phase picture of temporal alterations in cellular geometry with a wide spectrum of final results, and led to propose a standard model of reticulocyte-erythrocyte transformation. According to the model, both cell volume and surface undergo changes, and the work of the pressure, initially accumulated in the cytoskeleton, is consumed for local bending of the cell membrane. Further simulations with modified initial shape or parameters of the standard model show the trajectories of system evolution and help in better understanding the conditions for the erythro-, sphero-, ovalo-, stomato-, and leptoidal metamorphosis of maturing red blood cells. The stability of the final biconcave shape was also verified. Spherogenic modifications were discussed in the context of spherocytosis. Future development of the model was proposed.     

An Attempt to Increase the Longevity of Cut Daffodils (Narcissus pseudonarcissus) by Chemical Treatments

The use of pictures to illustrate science text is not usually taken to be problematic. However, the ‘picture superiority effect’ (PSE), whereby pictures are deemed to enhance learning from text, has been examined systematically over the last decade and has been found to be more equivocal than was hitherto believed. Part 1 of this review of the PSE in learning biology examines a number of perceptual considerations that need to be given to picture construction. It examines the major parameters which appear to attract the learner's attention to the picture in the first place, and then directs their subsequent viewing. These parameters are important because they exert control over the information the learner extracts from the picture. They are also important because, once recognized, it should be possible to control their influence in such a way as to optimize learning. These parameters fall into two main categories: those residing within the picture itself (for example, figure-ground differentiation) and those within the learner (for example, cultural bias). The review discusses ways in which within-picture variables such as depth of field and colour can be manipulated to re-inforce the intended message. It also suggests that more explicit instructions need to be given to learners to guide their use of texts with picture adjuncts. The importance of teaching children how to read pictures is complicated by the ways in which picture and text interact in the mind of the learner, and future comment on this aspect of the learning process is deferred to Part 2 of the article, which deals specifically with aspects of picture-text processing.     

Evaluation of catalytic free energies in genetically modified proteins

A combination of the empirical valence bond method and a free energy perturbation approach is used to simulate the activity of genetically modified enzymes. The simulations reproduce in a semiquantitative way the observed effects of mutations on the activity and binding free energies of trypsin and subtilisin. This suggests that we are approaching a stage of quantitative structure-function correlation of enzymes. The analysis of the calculations points towards the electrostatic energy of the reacting system as the key factor in enzyme catalysis. The changes in the charges of the reacting system and the corresponding changes in "solvation" free energy (generalized here as the interaction between the charges and the given microenvironment) are emphasized. It is argued that a reliable evaluation of these changes might be sufficient for correlating structure and catalysis. The use of free energy perturbation methods and thermodynamic cycles for evaluation of solvation energies and reactivity is discussed, pointing out our early contributions. The apparent elaborated nature of our treatment is clarified, explaining that such a treatment is essential for consistent calculations of chemical reactions in polar environments. The problems associated with seemingly more rigorous quantum mechanical methods are discussed, emphasizing the inconsistency associated with using gas phase charge distributions. The importance of dynamic aspects is examined by evaluating the autocorrelation of the protein "reaction field" on the reacting substrate. It is found that, at least in the present case, dynamic effects are not important. The nature of the catalytic free energy is considered, arguing that the protein provides preoriented dipoles (polarized to stabilize the transition state charge distribution) and small reorganization energy, thus reducing the activation free energy. The corresponding catalytic free energy is related to the folding free energy, which is being invested in aligning the active site dipoles.     

A Physical Picture of Protein Dynamics and Conformational Changes

A physical model is reviewed which explains different aspects of protein dynamics consistently. At low temperatures, the molecules are frozen in conformational substates. Their average energy is 3/2RT. Solid-state vibrations occur on a time scale of femtoseconds to nanoseconds. Above a characteristic temperature, often called the dynamical transition temperature, slow modes of motions can be observed occurring on a time scale between about 140 and 1 ns. These motions are overdamped, quasidiffusive, and involve collective motions of segments of the size of an α-helix. Molecules performing these types of motion are in the “flexible state”. This state is reached by thermal activation. It is shown that these motions are essential for conformational relaxation. Based on this picture, a new approach is proposed to understand conformational changes. It connects structural fluctuations and conformational transitions.     

Induced fit or conformational selection? The role of the semi-closed state in the maltose binding protein

A full characterization of the thermodynamic forces underlying ligand-associated conformational changes in proteins is essential for understanding and manipulating diverse biological processes, including transport, signaling, and enzymatic activity. Recent experiments on the maltose binding protein (MBP) have provided valuable data about the different conformational states implicated in the ligand recognition process; however, a complete picture of the accessible pathways and the associated changes in free energy remains elusive. Here we describe results from advanced accelerated molecular dynamics (aMD) simulations, coupled with adaptively biased force (ABF) and thermodynamic integration (TI) free energy methods. The combination of approaches allows us to track the ligand recognition process on the microsecond time scale and provides a detailed characterization of the protein's dynamic and the relative energy of stable states. We find that an induced-fit (IF) mechanism is most likely and that a mechanism involving both a conformational selection (CS) step and an IF step is also possible. The complete recognition process is best viewed as a "Pac Man" type action where the ligand is initially localized to one domain and naturally occurring hinge-bending vibrations in the protein are able to assist the recognition process by increasing the chances of a favorable encounter with side chains on the other domain, leading to a population shift. This interpretation is consistent with experiments and provides new insight into the complex recognition mechanism. The methods employed here are able to describe IF and CS effects and provide formally rigorous means of computing free energy changes. As such, they are superior to conventional MD and flexible docking alone and hold great promise for future development and applications to drug discovery.     

Ultraviolet B radiation-induced immunosuppression: molecular mechanisms and cellular alterations.

About 30 years ago, the discovery of the connection between UV radiation and the immune system triggered the field of photoimmunology. In that time, many aspects were studied, and a complex picture emerged. UV absorption results in multi-tiered molecular and cellular UV radiation-induced events, eventually affecting the immune system. The shorter wavelengths of the UV spectrum, i.e. UVB appear to be the most critical players for impairing immune reactions. This review summarizes and discusses UVB radiation-induced effects on the skin, considering the primary efferent molecular events following energy absorption of UVB radiation, ending with the various afferent cellular changes, such as induction of regulatory T cells.     

Molecular docking study and development of an empirical binding free energy model for phosphodiesterase 4 inhibitors

In the present work, several computational methodologies were combined to develop a model for the prediction of PDE4B inhibitors' activity. The adequacy of applying the ligand docking approach, keeping the enzyme rigid, to the study of a series of PDE4 inhibitors was confirmed by a previous molecular dynamics analysis of the complete enzyme. An exhaustive docking procedure was performed to identify the most probable binding modes of the ligands to the enzyme, including the active site metal ions and the surrounding structural water molecules. The enzyme-inhibitor interaction enthalpies, refined by using the semiempirical molecular orbital approach, were combined with calculated solvation free energies and entropy considerations in an empirical free energy model that enabled the calculation of binding free energies that correlated very well with experimentally derived binding free energies. Our results indicate that both the inclusion of the structural water molecules close to the ions in the binding site and the use of a free energy model with a quadratic dependency on the ligand free energy of solvation are important aspects to be considered for molecular docking investigations involving the PDE4 enzyme family.     

Sensitivity of membranes to their environment. Role of stochastic processes

Ionic flow through biomembranes often exhibits a sensitivity to the environment, which is difficult to explain by classical theory, that usually assumes that the free energy available to change the membrane permeability results from the environmental change acting directly on the permeability control mechanism. This implies, for example, that a change delta V in the trans-membrane potential can produce a maximum free energy change, delta V X q, on a gate (control mechanism) carrying a charge q. The analysis presented here shows that when stochastic fluctuations are considered, under suitable conditions (gate cycle times rapid compared with the field relaxation time within a channel), the change in free energy is limited, not by the magnitude of the stimulus, but by the electrochemical potential difference across the membrane, which may be very much greater. Conformational channel gates probably relax more slowly than the field within the channel; this would preclude appreciable direct amplification of the stimulus. It is shown, however, that the effect of impermeable cations such as Ca++ is to restore the amplification of the stimulus through its interaction with the electric field. The analysis predicts that the effect of Ca++ should be primarily to affect the number of channels that are open, while only slightly affecting the conductivity of an open channel.     

Importance of main-chain hydrophobic free energy to the stability of thermophilic proteins

Living organisms are found in the most unexpected places, including deep-sea vents at 100 degrees C and several hundred bars pressure, in hot springs. Needless to say, the proteins found in thermophilic species are much more stable than their mesophilic counterparts. There are no obvious reasons to say that one would be more stable than others. Even examination of the amino acids and comparison of structural features of thermophiles with mesophilies cannot bring satisfactory explanation for the thermal stability of such proteins. In order to bring out the hidden information behind the thermal stabilization of such proteins in terms of energy factors and their combinations, analysis were made on good resolution structures of thermophilic and their mesophilic homologous from 23 different families. From the structural coordinates, free energy contributions due to hydrophobic, electrostatic, hydrogen bonding, disulfide bonding and van der Waals interactions are computed. In this analysis, a vast majority of thermophilic proteins adopt slightly lower free energy contribution in each energy terms than its mesophilic counterparts. The major observation noted from this study is the lower hydrophobic free energy contribution due to carbon atoms and main-chain nitrogen atoms in all the thermophilic proteins. The possible combination of different free energy terms shows majority of the thermophilic proteins have lower free energy strategy than their mesophilic homologous. The derived results show that the hydrophobic free energy due to carbon and nitrogen atoms and such combinations of free energy components play a vital role in the thermostablisation of such proteins.