Response analysis in biochemical chain reactions with negative feedforward and feedbackward loops

Finite difference equations can be used to study the responses of biochemical chain reactions at any step of the chain to an external stimulus. In this study, we developed mathematical models for two hypothetical chain reactions involving loops to study the responses in the chain as the length of the chain gets longer, so called transient and steady state responses. The first model is for a chain with a negative feedforward loop, and the second one is for a chain that has a negative feedback loop. Although both of the models have the same steady state equations and values, we showed that the chain with negative feedforward and negative feedback loops can produce significantly different behaviors. The former can bring the chain into oscillations with various periods and eventually chaos when the feedback is strong enough as the length of the reaction chain increases, whereas the latter is not capable of producing oscillations and more complicated dynamics.     

Experimental strategy for characterization of essential dynamical variables in oscillatory systems: effect of double-layer capacitance on the stability of electrochemical oscillators

An experimentally accessible algorithm for changing the time scale associated with a dynamical variable is proposed. In general, a differential controller can be applied to (a) identify the essential species in oscillatory systems and (b) explore their role in the feedback loops. Here, we report on classifying electrochemical oscillators by changing the time scale over which the electrode potential varies; the type of different electrochemical oscillators is identified based on whether the controlled modification of pseudo-capacitance induces or suppresses current oscillations.     

Delay induced oscillations in a turbidostat with feedback control

A model of competition between two species in a turbidostat with delayed feedback control is investigated. By choosing the delay in the measurement of the optical sensor to the turbidity of the fluid as a bifurcation parameter, we show that Hopf bifurcations can occur as the delay crosses some critical values. The direction and stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem. Computer simulations illustrate the results.     

Bifurcation analysis and chaos control in discrete-time glycolysis models

In this paper, the qualitative behavior of two discrete-time glycolysis models is discussed. The discrete-time models are obtained by implementing forward Euler’s scheme and nonstandard finite difference method. The parametric conditions for local asymptotic stability of positive steady-states are investigated. Moreover, we discuss the existence and directions of period-doubling and Neimark–Sacker bifurcations with the help of center manifold theorem and bifurcation theory. OGY feedback control and hybrid control methods are implemented in order to control chaos in discrete-time glycolysis model due to emergence of period-doubling and Neimark–Sacker bifurcations. Numerical simulations are provided to illustrate theoretical discussion.     

Bifurcations of dividing surfaces in chemical reactions

We study the dynamical behavior of the unstable periodic orbit (NHIM) associated to the non-return transition state (TS) of the H(2) + H collinear exchange reaction and their effects on the reaction probability. By means of the normal form of the Hamiltonian in the vicinity of the phase space saddle point, we obtain explicit expressions of the dynamical structures that rule the reaction. Taking advantage of the straightforward identification of the TS in normal form coordinates, we calculate the reaction probability as a function of the system energy in a more efficient way than the standard Monte Carlo method. The reaction probability values computed by both methods are not in agreement for high energies. We study by numerical continuation the bifurcations experienced by the NHIM as the energy increases. We find that the occurrence of new periodic orbits emanated from these bifurcations prevents the existence of a unique non-return TS, so that for high energies, the transition state theory cannot be longer applied to calculate the reaction probability.     

Light-Driven Continual Oscillatory Rocking of a Polymer Film

Achieving oscillatory motion in polymers without requiring on/off switching of stimuli is a current challenge. Hereby, a free-standing liquid crystal polymer (LCP) is demonstrated to undergo a sustained oscillatory motion when triggered by light, moving back and forth, resembling the motion of a rocking-chair. Two polymer films having different azobenzene photo-switches have been studied, revealing photoswitch requirements as well as illumination conditions necessary to sustain oscillations. The motion presented here shows how feedback loops involving light-triggered actuation, self-shadowing and a shifting center of gravity can be utilized to achieve self-sustained motion in free-standing polymers.     

Nuclear magnetic resonance studies of adsorbed polymer layers

Nuclear magnetic resonance spectroscopy (NMR) encompasses a large range of techniques which can probe both the structure and dynamics of materials in detail. Of particular interest to the study of polymer adsorption is the ability to distinguish adsorbed segments (trains) from free segments (loops and tails) in a quantitative way. This may he achieved by a variety of experimental approaches and the background to those will be discussed. A brief overview of the necessary NMR theory will be given but for a more detailed treatment, the reader is referred to the large number of texts available [1].     

Discrete state model and accurate estimation of loop entropy of RNA secondary structures

Conformational entropy makes important contribution to the stability and folding of RNA molecule, but it is challenging to either measure or compute conformational entropy associated with long loops. We develop optimized discrete k-state models of RNA backbone based on known RNA structures for computing entropy of loops, which are modeled as self-avoiding walks. To estimate entropy of hairpin, bulge, internal loop, and multibranch loop of long length (up to 50), we develop an efficient sampling method based on the sequential Monte Carlo principle. Our method considers excluded volume effect. It is general and can be applied to calculating entropy of loops with longer length and arbitrary complexity. For loops of short length, our results are in good agreement with a recent theoretical model and experimental measurement. For long loops, our estimated entropy of hairpin loops is in excellent agreement with the Jacobson-Stockmayer extrapolation model. However, for bulge loops and more complex secondary structures such as internal and multibranch loops, we find that the Jacobson-Stockmayer extrapolation model has large errors. Based on estimated entropy, we have developed empirical formulae for accurate calculation of entropy of long loops in different secondary structures. Our study on the effect of asymmetric size of loops suggest that loop entropy of internal loops is largely determined by the total loop length, and is only marginally affected by the asymmetric size of the two loops. Our finding suggests that the significant asymmetric effects of loop length in internal loops measured by experiments are likely to be partially enthalpic. Our method can be applied to develop improved energy parameters important for studying RNA stability and folding, and for predicting RNA secondary and tertiary structures. The discrete model and the program used to calculate loop entropy can be downloaded at http://gila.bioengr.uic.edu/resources/RNA.html.     

Biological significance of polymorphism in legume protease inhibitors from the Bowman-Birk family

Naturally occurring protease inhibitors (PI) of the Bowman-Birk type constitute a major PI family in cereal and legume seeds. The family name is derived from the names of the two investigators who characterised the first inhibitor of this type, the Bowman-Birk inhibitor from soybean (BBI). These proteins have the capacity to inhibit one or more of a range of serine proteases, including the digestive enzymes trypsin and chymotrypsin. PI from this family interact with the active sites of serine proteases in a 'canonical', i.e. substrate-like, manner via exposed reactive site loops of conserved conformation within the inhibitor. Multiple BBI variants can be found within and among species. A limited number of amino acids located within the inhibitory domain is responsible for the primary functional and biological activities of BBI-like proteins. However, sequence variation in binding loops, post-translational modifications at the amino- and carboxy-terminal ends, as well as differences in the multimeric nature of the inhibitors may act in combination to influence the functional properties and the physiological role of BBI-like proteins. Recently, BBI and proteins homologous to BBI (BBI-like proteins) have emerged as highly promising cancer chemopreventive agents. BBI has been shown to be capable of preventing or suppressing carcinogenic processes in a wide variety of in vitro and in vivo animal model systems. The potential exploitation of BBI-like proteins in human health-promotion programmes will depend on elucidating in detail the molecular basis for the variation in biological activities among the many variant forms. New knowledge, derived both from the use of synthetic cyclic peptides that mimic the inhibitory loops of BBI-like proteins, and from genomic data pertaining to the structure of BBI gene classes, together facilitate the manipulation, screening and selection of appropriate variants through biotechnology.     

Multi-element optical waveguide sensor: General concept and design

A prototype of a self-contained multi-element optical waveguide sensor for detection and identification of the constituents of gaseous or liquid mixtures has been fabricated. The device consists of eight optical waveguides, each coated with a thin film known to react specifically with one or more components in a multicomponent system. An array of eight sequentially-activated light-emitting diodes is attached to the waveguide assembly in such a fashion as to activate each detection channel separately. Each waveguide is a fiber-optic coupled to a single high-gain, low-noise photomultiplier tube or photodiode/operational amplifier detector. The amplified signals can be displayed visually or input to a microprocessor pattern-recognition algorithm. CMOS analog switches/multiplexers are used in feedback loops to control automatic gain-ranging, light-level adjustment and channel-sequencing. Preliminary experiments involving the monitoring of redox/pH changes are discussed.     

Advances in homology protein structure modeling

Homology modeling plays a central role in determining protein structure in the structural genomics project. The importance of homology modeling has been steadily increasing because of the large gap that exists between the overwhelming number of available protein sequences and experimentally solved protein structures, and also, more importantly, because of the increasing reliability and accuracy of the method. In fact, a protein sequence with over 30% identity to a known structure can often be predicted with an accuracy equivalent to a low-resolution X-ray structure. The recent advances in homology modeling, especially in detecting distant homologues, aligning sequences with template structures, modeling of loops and side chains, as well as detecting errors in a model, have contributed to reliable prediction of protein structure, which was not possible even several years ago. The ongoing efforts in solving protein structures, which can be time-consuming and often difficult, will continue to spur the development of a host of new computational methods that can fill in the gap and further contribute to understanding the relationship between protein structure and function.     

Molecular recognition via base-pairing

Hydrogen-bonding interactions in DNA/RNA systems are a defining feature of double helical systems. They also play a critical role in stabilizing other higher-order structures, such as hairpin loops, and thus in the broadest sense can be considered as key requisites to the successful translation and replication of genetic information. This importance, coupled with the aesthetic appeal of nucleic acid base (nucleobase) hydrogen-bond interactions, has inspired the use of such motifs to stabilize a range of synthetic structures. This, in turn, has led to the formation of a number of novel ensembles. This tutorial review will discuss these structures, both from a synthetic perspective and in terms of their potential application in areas that include, but are not limited to, self-assembled macrocyclic and high-order ensemble synthesis, supramolecular polymer preparation, molecular cage construction, and energy and electron transfer modeling.     

Steady-state fluctuations of a genetic feedback loop: an exact solution

Genetic feedback loops in cells break detailed balance and involve bimolecular reactions; hence, exact solutions revealing the nature of the stochastic fluctuations in these loops are lacking. We here consider the master equation for a gene regulatory feedback loop: a gene produces protein which then binds to the promoter of the same gene and regulates its expression. The protein degrades in its free and bound forms. This network breaks detailed balance and involves a single bimolecular reaction step. We provide an exact solution of the steady-state master equation for arbitrary values of the parameters, and present simplified solutions for a number of special cases. The full parametric dependence of the analytical non-equilibrium steady-state probability distribution is verified by direct numerical solution of the master equations. For the case where the degradation rate of bound and free protein is the same, our solution is at variance with a previous claim of an exact solution [J. E. M. Hornos, D. Schultz, G. C. P. Innocentini, J. Wang, A. M. Walczak, J. N. Onuchic, and P. G. Wolynes, Phys. Rev. E 72, 051907 (2005), and subsequent studies]. We show explicitly that this is due to an unphysical formulation of the underlying master equation in those studies.     

Analysis of a model scheme incorporating reactant inhibition: Instability of homogeneous solution and formation of spatio–temporal structures

A model scheme incorporating reactant inhibition in the rate process has been analyzed with a view to study the instability of homogeneous solution due to diffusion. Conditions for the occurrence of Turing as well as phase instability are derived and show the existence of multiplicity in the parameter space. The Ginzburg-Landau equation for the system is developed and solved numerically in various regions of the parameter space. The simple model system shows the existence of very rich behavior including normal and inverted bifurcations in the super and subcritical regimes. The various results are analyzed and discussed. © 1993 John Wiley & Sons, Inc.     

Classification of protein disulphide-bridge topologies

The preferential occurrence of certain disulphide-bridge topologies in proteins has prompted us to design a method and a program, KNOT-MATCH, for their classification. The program has been applied to a database of proteins with less than 65% homology and more than two disulphide bridges. We have investigated whether there are topological preferences that can be used to group proteins and if these can be applied to gain insight into the structural or functional relationships among them. The classification has been performed by Density Search and Hierarchical Clustering Techniques, yielding thirteen main protein classes from the superimposition and clustering process. It is noteworthy that besides the disulphide bridges, regular secondary structures and loops frequently become correctly aligned. Although the lack of significant sequence similarity among some clustered proteins precludes the easy establishment of evolutionary relationships, the program permits us to find out important structural or functional residues upon the superimposition of two protein structures apparently unrelated. The derived classification can be very useful for finding relationships among proteins which would escape detection by current sequence or topology-based analytical algorithms.     

Effect of proline and glycine residues on dynamics and barriers of loop formation in polypeptide chains

Glycine and proline residues are frequently found in turn and loop structures of proteins and are believed to play an important role during chain compaction early in folding. We investigated their effect on the dynamics of intrachain loop formation in various unstructured polypeptide chains. Loop formation is significantly slower around trans prolyl peptide bonds and faster around glycine residues compared to any other amino acid. However, short loops are formed fastest around cis prolyl bonds with a time constant of 6 ns for end-to-end contact formation in a four-residue loop. Formation of short loops encounters activation energies in the range of 15 to 30 kJ/mol. The altered dynamics around glycine and trans prolyl bonds can be mainly ascribed to their effects on the activation energy. The fast dynamics around cis prolyl bonds, in contrast, originate in a higher Arrhenius pre-exponential factor, which compensates for an increased activation energy for loop formation compared to trans isomers. All-atom simulations of proline-containing peptides indicate that the conformational space for cis prolyl isomers is largely restricted compared to trans isomers. This leads to decreased average end-to-end distances and to a smaller loss in conformational entropy upon loop formation in cis isomers. The results further show that glycine and proline residues only influence formation of short loops containing between 2 and 10 residues, which is the typical loop size in native proteins. Formation of larger loops is not affected by the presence of a single glycine or proline residue.     

Sucrose-based fabrication of 3D-networked, cylindrical microfluidic channels for rapid prototyping of lab-on-a-chip and vaso-mimetic devices

We present a new fabrication scheme for 3D-networked, cylindrical microfluidic (MF) channels based on shaping, bonding, and assembly of sucrose fibers. It is a simple, cleanroom-free, and environment-friendly method, ideal for rapid prototyping of lab-on-a-chip devices. Despite its simplicity, it can realize complex 3D MF channel architectures such as cylindrical tapers, internal loops, end-to-side junctions, tapered junctions, and stenosis. The last two will be of special use for realizing vaso-mimetic MF structures. It also enables molding with polymers incompatible with high-temperature processing.     

Visualisation of inter loop tertiary base pairing and stacking interactions in an unusual slipped loop DNA structure

The conformation of an unusual slipped loop DNA structure exhibited by the sequence d(GAATTCCCGAATTC)₂ is determined using a combination of geometrical and molecular mechanics methods. This sequence is known to form a B-DNA-like duplex with the central non-complementary cytosines extruded into single stranded loop regions. The unusual feature is that the interior guanine does not pair with the cytosine across, instead, it pairs with the cytosine upstream by skipping two cytosines, leading to a slipped loop DNA structure with the loops staggered by two base pairs. The two loops, despite being very small, can fold across minor or major groove symmetrically or asymmetrically disposed, with one of the loop bases partially blocking the major or minor groove. Most interestingly, for certain conformations, the loop bases approach one another at close proximity so as to engage even in base pairing as well as base stacking interactions across the major groove. While such pairing and stacking are common in the tertiary folds of RNA, this is the first time that such an interaction is visualized in a DNA. This observation demonstrates that a W-C pair can readily be accomplished in a typical slipped loop structure postulated for DNA. Such tertiary loop interaction may prevent access to regulatory proteins across the major groove of the duplex DNA, thus providing a structure-function relation for the occurrence of slipped loop structure in DNA. Contribution no. 839 from this department