Derivation of a velocity equation for a reaction model witwh two binding sites for acetylcholinesterase

The authors suggest a kinetic model with two binding sites for acetylcholinesterase; it is suitable to study particular enzyme forms that show a kinetic pattern which cannot be explained by the model with a single binding site of Krupka and Laidler. The velocity equation was obtained using the algorithm of King and Altman and carrying out elementary calculations.     

On the cooperative binding of large ligands to a one-dimensional homogeneous lattice: the generalized three-state lattice model

We present the general secular equation for three-state lattice models for the cooperative binding of large ligands to a one-dimensional lattice. In addition, a closed-form expression for the isotherm is also obtained, that can be used with all values of the cooperativity parameter omega(0 less than omega less than infinity) thus eliminating the need for multiple equations.     

"Galton's Asset" and "Flower's Problem Cultural Networks and Cultural Units in Cross-Cultural Research Ml (Or, Male Genital Mutilations and Polygyny in Cross-Cultural Perspective)

Edward Tylor had envisioned anthropology to be comprised of ethnology and ethnography in equal parts, but today ethnography dominates the field. In this paper, we examine two reasons for the refugee status of ethnology. First, we look at the notorious "Galton effect." Second, we examine the problem of defining and using cultural units, particularly when positivistic and static theories and methods of culture have been largely discredited by anthropology. We argue against any formulaic solutions to these problems and show that for each research question one needs to reconsider the criteria for how to construct cultural units and how to ensure that the cultures under study are not merely replicas of one another. We show that previous solutions to these issues are limited because they fail to appreciate the contingent and multidimensional nature of culture. We also argue that, instead of a "Galton problem," there is actually a "Galton asset," which can be used to study historical and emergent communicative networks. [Keywords: cross–cultural research, Galton problem, cultural units, methods and theory]     

Theory of interaction of polymer and small molecules which can aggregate in solution

The theory of interaction of small molecules with polymers is extended to the case where the small molecules can aggregate in solution to form dimers, trimers, etc., and where the aggregates can also interact with the polymer. The secular equation is found to be identical in form with that obtained for the binding of nonaggregating monomer to the polymer. Thus, all formulas derived for the latter case apply to the present one also, except that, now the concentration of the free monomer is the relevant factor. It is shown how the experimental data can be analyzed by using information on the molal activity coefficients of the small molecules. As an illustration these formulas are applied to data on the interaction of purines and nucleosides with poly(uridylic acid) in concentrated solutions.     

Determining the DNA sequence elements required for binding integration host factor to two different target sites.

Binding sites for the Escherichia coli protein integration host factor (IHF) include a set of conserved bases that can be summarized by the consensus sequence WATCAANNNNTTR (W is dA or dT, R is dA or dG, and N is any nucleotide). However, additional 5'-proximal bases, whose common feature is a high dA+dT content, are also thought to be required for binding at some sites. We examine the relative contribution of these two sequence elements to IHF binding to the H' and H1 sites in attP of bacteriophage lambda by using the bacteriophage P22-based challenge-phage system. IHF was unable to act as a repressor in the challenge-phage assay at H' sites containing the core consensus element but lacking the dA+dT-rich element. This indicates that both elements are required for IHF to bind to the H' site. In contrast, the core consensus determinant alone is sufficient for IHF binding to the H1 site, which lacks an upstream dA+dT-rich region. Fifty mutants that decreased or eliminated IHF binding to the H1 site were isolated. Sequence analysis showed changes in the bases in the core consensus element only, further indicating that this determinant is sufficient for IHF binding to the H1 site. We found that placement of a dA+dT-rich element upstream of the H1 core consensus element significantly increased the affinity, suggesting that the presence of a dA+dT-rich element enhances IHF binding.     

A continuous cable method for determining the transient potential in passive dendritic trees of known geometry

Models using cable equations are increasingly employed in neurophysiological analyses, but the amount of computer time and memory required for their implementation are prohibitively large for many purposes and many laboratories. A mathematical procedure for determining the transient voltage response to injected current or synaptic input in a passive dendritic tree of known geometry is presented that is simple to implement since it is based on one equation. It proved to be highly accurate when results were compared to those obtained analytically for dendritic trees satisfying equivalent cylinder constraints. In this method the passive cable equation is used to express the potential for each interbranch segment of the dendritic tree. After applying boundary conditions at branch points and terminations, a system of equations for the Laplace transform of the potential at the ends of the segments can be readily obtained by inspection of the dendritic tree. Except for the starting equation, all of the equations have a simple format that varies only with the number of branches meeting at a branch point. The system of equations is solved in the Laplace domain, and the result is numerically inverted back to the time domain for each specified time point (the method is independent of any time increment t). The potential at any selected location in the dendritic tree can be obtained using this method. Since only one equation is required for each interbranch segment, this procedure uses far fewer equations than comparable compartmental approaches. By using significantly less computer memory and time than other methods to attain similar accuracy, this method permits extensive analyses to be performed rapidly on small computers. One hopes that this will involve more investigators in modeling studies and will facilitate their motivation to undertake realistically complex dendritic models.     

Immunological studies on pancreatic phospholipase A2. Antigenic characterization of the NH2-terminal region.

Rabbit antisera elicited against pure pig, horse, ox, and sheep pancreatic phospholipase A2 revealed considerable immunological differences when tested by double immunodiffusion and microcomplement fixation assays. Snake venom phospholipases did not show any detectable cross-reactions with the pancreatic enzymes. Microcomplement fixation also clearly demonstrated conformational differences between porcine phospholipase A2 and its zymogen. NH2 terminally modified analogs of porcine phospholipase A2 could be clearly distinguished using the same assay. Moreover, strong evidence was obtained that Ala1-Arg6 is a part of an antigenic determinant. Radioimmune assay, using monovalent phospholipase-specific Fab fragments revealed a maximum number of three antigenic sites of phospholipase that can simultaneously be occupied by antibody. The Fab fragments were separated into three fractions, using three immunoadsorbent columns in series. These Fab fractions showed different inhibitory properties toward micellar binding of phospholipase A2. They also exhibited different protective effects against active center modification.     

P-Glycoprotein (P-gp) expressed in a confluent monolayer of hMDR1-MDCKII cells has more than one efflux pathway with cooperative binding sites

The multidrug resistance transporter P-glycoprotein (P-gp) effluxes a wide range of substrates and can be affected by a wide range of inhibitors or modulators. Many studies have presented classifications for these binding interactions, within either the context of equilibrium binding or the Michaelis-Menten enzyme analysis of the ATPase activity of P-gp. Our approach is to study P-gp transport and its inhibition using a physiologically relevant confluent monolayer of hMDR1-MDCKII cells. We measure the elementary rate constants for P-gp efflux of substrates and study inhibition using pairwise combinations with a different unlabeled substrate acting as the inhibitor. Our current kinetic model for P-gp has only a single binding site, because a previous study proved that the mass-action kinetics of efflux of a single substrate were not sensitive to whether there are one or more substrate-binding and efflux sites. In this study, using this one-site model, we found that, with "high" concentrations of either a substrate or an inhibitor, the elementary rate constants fitted independently for each of the substrates alone quantitatively predicted the efflux curves, simply applying the assumption that binding at the "one site" was competitive. On the other hand, at "low" concentrations of both the substrate and inhibitor, we found no inhibition of the substrate efflux, despite the fact that both the substrate and inhibitor were being well-effluxed. This was not an effect of excess "empty" P-gp molecules, because the competitive efflux model takes site occupancy into account. Rather, it is quantitative evidence that the substrate and inhibitor are being effluxed by multiple pathways within P-gp. Remarkably, increasing the substrate concentration above the "low" concentration, caused the inhibition to become competitive; i.e., the inhibitor became effective. These data and their analysis show that the binding of these substrates must be cooperative, either positive or negative.     

Determination of binding parameters in the presence of coupled reactions

Components of a binding reaction may undergo nonbinding reactions: receptors may be degraded, internalized, or exchanged with cryptic sites; ligand may be degraded or compartmented. In such cases the parameters that characterize the system are not obtained from the usual equilibrium analyses. We have simulated the reactions of such systems and generated association curves, "Scatchard" plots, and "Scatchard-like" plots that permit the calculation of binding affinity and receptor number not normally calculable under nonequilibrium binding conditions. In particular, we show that certain coupled reactions produce local maxima and sigmoid shapes in association curves and that the maxima can be used to obtain affinities and receptor numbers.     

A singular perturbation approach to diffusion reaction equations containing a point source,with application to the hemolytic plaque assay

Summary Many cells secrete factors which diffuse and bind to receptors on neighboring cells. These processes can be described by a nonlinear diffusion equation with a point source and a spatially distributed binding reaction. We show via perturbation analysis how approximate solutions can be obtained for such equations when the binding reaction is fast compared to diffusive transport. We base our analysis on an example which is of great practical importance in immunology, the hemolytic plaque technique.     

A simple method for the computation of first neighbour frequencies of DNAs from CD spectra

A procedure for the computation of the first neighbour frequencies of DNA's is presented. This procedure is based on the first neighbour approximation of Gray and Tinoco. We show that the knowledge of all the ten elementary CD signals attached to the ten double stranded first neighbour configurations is not necessary. One can obtain the ten frequencies of an unknown DNA with the use of eight elementary CD signals corresponding to eight linearly independent polymer sequences. These signals can be extracted very simply from any eight or more CD spectra of double stranded DNA's of known frequencies. The ten frequencies of a DNA are obtained by least square fit of its CD spectrum with these elementary signals. One advantage of this procedure is that it does not necessitate linear programming, it can be used with CD data digitalized using a large number of wavelengths, thus permitting an accurate resolution of the CD spectra. Under favorable case, the ten frequencies of a DNA (not used as input data) can be determined with an average absolute error < 2%. We have also observed that certain satellite DNA's, those of Drosophila virilis and Callinectes sapidus have CD spectra compatible with those of DNA's of quasi random sequence; these satellite DNA's should adopt also the B-form in solution.     

Modes and cuts in metabolic networks: complexity and algorithms

Constraint-based approaches recently brought new insight into our understanding of metabolism. By making very simple assumptions such as that the system is at steady-state and some reactions are irreversible, and without requiring kinetic parameters, general properties of the system can be derived. A central concept in this methodology is the notion of an elementary mode (EM for short) which represents a minimal functional subsystem. The computation of EMs still forms a limiting step in metabolic studies and several algorithms have been proposed to address this problem leading to increasingly faster methods. However, although a theoretical upper bound on the number of elementary modes that a network may possess has been established, surprisingly, the complexity of this problem has never been systematically studied. In this paper, we give a systematic overview of the complexity of optimisation problems related to modes. We first establish results regarding network consistency. Most consistency problems are easy, i.e., they can be solved in polynomial time. We then establish the complexity of finding and counting elementary modes. We show in particular that finding one elementary mode is easy but that this task becomes hard when a specific EM (i.e. an EM containing some specified reactions) is sought. We then show that counting the number of elementary modes is musical sharpP-complete. We emphasize that the easy problems can be solved using currently existing software packages. We then analyse the complexity of a closely related task which is the computation of so-called minimum reaction cut sets and we show that this problem is hard. We then present two positive results which both allow to avoid computing EMs as a prior to the computation of reaction cuts. The first one is a polynomial approximation algorithm for finding a minimum reaction cut set. The second one is a test for verifying whether a set of reactions constitutes a reaction cut; this test can be readily included in existing algorithms to improve their performance. Finally, we discuss the complexity of other cut-related problems.     

A biologically plausible model of time-scale invariant interval timing

The temporal durations between events often exert a strong influence over behavior. The details of this influence have been extensively characterized in behavioral experiments in different animal species. A remarkable feature of the data collected in these experiments is that they are often time-scale invariant. This means that response measurements obtained under intervals of different durations coincide when plotted as functions of relative time. Here we describe a biologically plausible model of an interval timing device and show that it is consistent with time-scale invariant behavior over a substantial range of interval durations. The model consists of a set of bistable units that switch from one state to the other at random times. We first use an abstract formulation of the model to derive exact expressions for some key quantities and to demonstrate time-scale invariance for any range of interval durations. We then show how the model could be implemented in the nervous system through a generic and biologically plausible mechanism. In particular, we show that any system that can display noise-driven transitions from one stable state to another can be used to implement the timing device. Our work demonstrates that a biologically plausible model can qualitatively account for a large body of data and thus provides a link between the biology and behavior of interval timing.     

Statistical mechanical deconvolution of thermal transitions in macromolecules. I. Theory and application to homogeneous systems

The theoretical basis for the statistical mechanical deconvolution of a thermally induced macromolecular melting profile is presented. It is demonstrated that all the thermodynamic quantities characterizing a multistate macromolecular transition can be obtained from the average excess enthalpy function, 〈ΔH〉, of the system, without any assumption of the particular model or mechanism of the reaction. Experimentally, 〈ΔH〉 is obtained from scanning calorimetric data by direct integration of the excess apparent molar heat capacity function, ΦCp. Once 〈ΔH〉 is known as a continuous function of the temperature, the partition function, Q, of the system can be calculated by means of the equation From the partition function all the thermodynamic quantities of the system can be obtained. It is shown that the number of discrete macroscopic energy states, the enthalpy and entropy changes between them, and the relative population of each state as a function of temperature can be calculated in a recursive form.     

A control theory approach to the analysis and synthesis of the experimentally observed motion primitives

Recent experiments on frogs and rats, have led to the hypothesis that sensory-motor systems are organized into a finite number of linearly combinable modules; each module generates a motor command that drives the system to a predefined equilibrium. Surprisingly, in spite of the infiniteness of different movements that can be realized, there seems to be only a handful of these modules. The structure can be thought of as a vocabulary of "elementary control actions". Admissible controls, which in principle belong to an infinite dimensional space, are reduced to the linear vector space spanned by these elementary controls. In the present paper we address some theoretical questions that arise naturally once a similar structure is applied to the control of nonlinear kinematic chains. First of all, we show how to choose the modules so that the system does not loose its capability of generating a "complete" set of movements. Secondly, we realize a "complete" vocabulary with a minimal number of elementary control actions. Subsequently, we show how to modify the control scheme so as to compensate for parametric changes in the system to be controlled. Remarkably, we construct a set of modules with the property of being invariant with respect to the parameters that model the growth of an individual. Robustness against uncertainties is also considered showing how to optimally choose the modules equilibria so as to compensate for errors affecting the system. Finally, the motion primitive paradigm is extended to locomotion and a related formalization of internal (proprioceptive) and external (exteroceptive) variables is given.     

A light-switchable gene promoter system

Regulatable transgene systems providing easily controlled, conditional induction or repression of expression are indispensable tools in biomedical and agricultural research and biotechnology. Several such systems have been developed for eukaryotes. Most of these rely on the administration of either exogenous chemicals or heat shock. Despite the general success of many of these systems, the potential for problems, such as toxic, unintended, or pleiotropic effects of the inducing chemical or treatment, can impose limitations on their use. We have developed a promoter system that can be induced, rapidly and reversibly, by short pulses of light. This system is based on the known red light-induced binding of the plant photoreceptor phytochrome to the protein PIF3 and the reversal of this binding by far-red light. We show here that yeast cells expressing two chimeric proteins, a phytochrome-GAL4-DNA-binding-domain fusion and a PIF3-GAL4-activation-domain fusion, are induced by red light to express selectable or "scorable" marker genes containing promoters with a GAL4 DNA-binding site, and that this induction is rapidly abrogated by subsequent far-red light. We further show that the extent of induction can be controlled precisely by titration of the number of photons delivered to the cells by the light pulse. Thus, this system has the potential to provide rapid, noninvasive, switchable control of the expression of a desired gene to a preselected level in any suitable cell by simple exposure to a light signal.     

Protein binding specificity versus promiscuity

Interactions between macromolecules in general, and between proteins in particular, are essential for any life process. Examples include transfer of information, inhibition or activation of function, molecular recognition as in the immune system, assembly of macromolecular structures and molecular machines, and more. Proteins interact with affinities ranging from millimolar to femtomolar and, because affinity determines the concentration required to obtain 50% binding, the amount of different complexes formed is very much related to local concentrations. Although the concentration of a specific binding partner is usually quite low in the cell (nanomolar to micromolar), the total concentration of other macromolecules is very high, allowing weak and non-specific interactions to play important roles. In this review we address the question of binding specificity, that is, how do some proteins maintain monogamous relations while others are clearly polygamous. We examine recent work that addresses the molecular and structural basis for specificity versus promiscuity. We show through examples how multiple solutions exist to achieve binding via similar interfaces and how protein specificity can be tuned using both positive and negative selection (specificity by demand). Binding of a protein to numerous partners can be promoted through variation in which residues are used for binding, conformational plasticity and/or post-translational modification. Natively unstructured regions represent the extreme case in which structure is obtained only upon binding. Many natively unstructured proteins serve as hubs in protein-protein interaction networks and such promiscuity can be of functional importance in biology.