Population Dynamics of <Emphasis Type="Italic">Agave marmorata</Emphasis> Roezl. under Two Contrasting Management Systems in Central Mexico

Population Dynamics of Agave marmorata Roezl. under Two Contrasting Management Systems in Central Mexico. This paper evaluates the impacts of traditional management on the population dynamics of Agave marmorata, a multipurpose, useful species that is dominant in the Zapotitlán Salinas Valley, Puebla, Mexico. During 2002–2003 and 2003–2004, we constructed matrix models for two populations—one unmanaged, the other subject to plant extraction and cutting of flowering stalks. We also conducted prospective (elasticity) and retrospective (life table response experiments) analyses. Overall, the unmanaged population had higher finite rates of increase (λ) than the managed one. This variation in λ was the result of a decrease in the individual growth and fecundity in the managed population. Survival and growth were the demographic processes with the highest contribution to λ in the unmanaged population, while survival was the most important in the managed one. Our results suggest that management and plant extraction practices could be having negative effects on the population dynamics of this plant species. Recommendations are provided in order to promote positive effects on its vital rates and regeneration capacity.     

Evolutionary tradeoff and equilibrium in an aquatic predator-prey system

Due to the conventional distinction between ecological (rapid) and evolutionary (slow) timescales, ecological and population models have typically ignored the effects of evolution. Yet the potential for rapid evolutionary change has been recently established and may be critical to understanding how populations persist in changing environments. In this paper we examine the relationship between ecological and evolutionary dynamics, focusing on a well-studied experimental aquatic predator-prey system (Fussmann et al., 2000, Science, 290, 1358–1360; Shertzer et al., 2002, J. Anim. Ecol., 71, 802–815; Yoshida et al., 2003, Nature, 424, 303–306). Major properties of predator-prey cycles in this system are determined by ongoing evolutionary dynamics in the prey population. Under some conditions, however, the populations tend to apparently stable steady-state densities. These are the subject of the present paper. We examine a previously developed model for the system, to determine how evolution shapes properties of the equilibria, in particular the number and identity of coexisting prey genotypes. We then apply these results to explore how evolutionary dynamics can shape the responses of the system to ‘management’: externally imposed alterations in conditions. Specifically, we compare the behavior of the system including evolutionary dynamics, with predictions that would be made if the potential for rapid evolutionary change is neglected. Finally, we posit some simple experiments to verify our prediction that evolution can have significant qualitative effects on observed population-level responses to changing conditions.     

A calcium-based phantom bursting model for pancreatic islets

Insulin-secreting β-cells, located within the pancreatic islets of Langerhans, are excitable cells that produce regular bursts of action potentials when stimulated by glucose. This system has been the focus of mathematical investigation for two decades, spawning an array of mathematical models. Recently, a new class of models has been introduced called ‘phantom bursters’ [Bertram et al. (2000) Biophys. J. 79, 2880–2892], which accounts for the wide range of burst frequencies exhibited by islets via the interaction of more than one slow process. Here, we describe one implementation of the phantom bursting mechanism in which intracellular Ca²⁺ controls the oscillations through both direct and indirect negative feedback pathways. We show how the model dynamics can be understood through an extension of the fast/slow analysis that is typically employed for bursting oscillations. From this perspective, the model makes use of multiple degrees of freedom to generate the full range of bursting oscillations exhibited by β-cells. The model also accounts for a wide range of experimental phenomena, including the ubiquitous triphasic response to the step elevation of glucose and responses to perturbations of internal Ca²⁺ stores. Although it is not presently a complete model of all β-cell properties, it demonstrates the design principles that we anticipate will underlie future progress in β-cell modeling.     

Linearized oscillations in population dynamics

A linearized oscillation theorem due to Kulenović, Ladas and Meimaridou (1987,Quart. appl. Math. XLV, 155–164) and an extension of it are applied to obtain the oscillation of solutions of several equations which have appeared in population dynamics. They include the logistic equation with several delays, Nicholson's blowflies model as described by Gurney, Blythe and Nisbet (1980,Nature, Lond. 287, 17–21) and the Lasota-Wazewska model of the red blood cell supply in an animal. We also developed a linearized oscillation result for difference equations and applied it to several equations taken from the biological literature.     

A theoretical explanation of “Concomitant resistance”

Concomitant resistance is a tumor growth dynamic which results when the growth of a second tumor implant is inhibited by the presence of the first. Recently, we modeled tumor growth in the presence of a regenerating liver after partial hepatectomy (Michelson and Leith,Bull. Math. Biol. 57, 345–366, 1995), with an interlocking pair of growth control triads to account for the accelerated growth observed in both tissues. We also modeled tumor dormancy and recurrence as a dynamic equilibrium achieved between proliferating and quiescent subpopulations. In this paper those studies are extended to initially model the concomitant resistance case. Two interlocking model systems are proposed. In one an interactive competition between the tumor implants is described, while in the other purely proportional growth inhibition is described. The equilibria and dynamics of each system when the coefficients are held constant are presented for three subcases of model parameters. We show that the dynamic called concomitant resistance can be real or apparent, and that if the model coefficients are held constant, the only way to truly achieve concomitant resistance is by forcing one of the tumors into total quiescence. If this is the true state of the inhibited implant, then a non-constant recruitment signal is required to insure regrowth when the inhibitor mass is excised. We compare these theoretical results to a potential explanation of the phenomenon provided by Prehn (Cancer Res. 53, 3266–3269, 1993).     

Homology modeling and dynamics of the extracellular domain of rat and human neuronal nicotinic acetylcholine receptor subtypes α4β2 and α7

In recent years, it has become clear that the neuronal nicotinic acetylcholine receptor (nAChR) is a valid target in the treatment of a variety of diseases, including Alzheimer’s disease, anxiety, and nicotine addiction. As with most membrane proteins, information on the three-dimensional (3D) structure of nAChR is limited to data from electron microscopy, at a resolution that makes the application of structure-based design approaches to develop specific ligands difficult. Based on a high-resolution crystal structure of AChBP, homology models of the extracellular domain of the neuronal rat and human nAChR subtypes α4β2 and α7 (the subtypes most abundant in brain) were built, and their stability assessed with molecular dynamics (MD). All models built showed conformational stability over time, confirming the quality of the starting 3D model. Lipophilicity and electrostatic potential studies performed on the rat and human α4β2 and α7 nicotinic models were compared to AChBP, revealing the importance of the hydrophobic aromatic pocket and the critical role of the α-subunit Trp—the homolog of AChBP-Trp 143—for ligand binding. The models presented provide a valuable framework for the structure-based design of specific α4β2 nAChR subtype ligands aimed at improving therapeutic and diagnostic applications. Figure Electrostatic surface potential of the binding site cavity of the neuronal nicotinic acetylcholine receptor (nAChR). Nicotinic models performed with the MOLCAD program: a rat α7, b rat α4β2, c human α7, d human α4β2. All residues labeled are part of the α7 (a,c) or α4 (b,d) subunit with the exception of Phe 117, which belongs to subunit β2 (d). Violet Very negative, blue negative, yellow neutral, red very positive     

The role of cortical area MST in a model of combined smooth eye-head pursuit

The cortical medial superior temporal area (MST) is essential for the normal execution of smooth pursuit eye movements. Many pursuit-related neurons (visual-tracking neurons = VT neurons) in the lateral part of area MST (MSTl) are responsive to retinal image slip (r) as well as to eye (e) and head velocity (h) with similar preferred directions (isodirectionality). We show, by running a connectionist network with VT neuron-like elements, that an assembly of MSTl-VT neurons is able to reconstruct target motion in world-centered coordinates (t′). When t′ is fed into a subsequent model stage, converting t′ into gaze velocity (g′) with varying contributions of e and h, the overall model is able to account for many of the salient properties of visually guided pursuit including the consequences of MSTl lesions. However, the analysis of the MSTl network also clearly indicates that isodirectionality is not a prerequisite for its performance. The investigation of a second model suggests that isodirectionality indeed does not result from functional but from developmental constraints. This second model is a connectionist network with hidden units, which similar to MSTl-VT neurons receive input from modality specific units encoding retinal slip, eye and head velocity. After training this network to offer t′ as output, two subsets of hidden units emerged, one exhibiting isodirectionality, but not the other. Since only isodirectional hidden units contributed to the flow of information, the preponderance of isodirectional MSTl-VT neurons might be the result of developmental pruning, eliminating the second group. Received: 17 April 1998 / Accepted in revised form: 28 July 1998     

Window automata analysis of population dynamics in the immune system

A formalism based on window automata is proposed as a method to analyse complex population dynamics. The method is applied to a model of the immune network (Weisbuch, G.et al., 1990.J. theor. Biol. 146, 483–499), and used to predict which attractor the system reaches after antigenic stimulation, as a function of the parameters. The attractors of the dynamics are interpreted in terms of immune conditions such as vaccination or tolerance. Scaling laws that define the regimes in the parameter space corresponding to the specific attractor reached under antigenic stimulation are derived.     

The neuronal dynamics underlying cognitive flexibility in set shifting tasks

The ability to switch attention from one aspect of an object to another or in other words to switch the “attentional set” as investigated in tasks like the “Wisconsin Card Sorting Test” is commonly referred to as cognitive flexibility. In this work we present a biophysically detailed neurodynamical model which illustrates the neuronal base of the processes related to this cognitive flexibility. For this purpose we conducted behavioral experiments which allow the combined evaluation of different aspects of set shifting tasks: uninstructed set shifts as investigated in Wisconsin-like tasks, effects of stimulus congruency as investigated in Stroop-like tasks and the contribution of working memory as investigated in “Delayed-Match-to-Sample” tasks. The work describes how general experimental findings are usable to design the architecture of a biophysical detailed though minimalistic model with a high orientation on neurobiological findings and how, in turn, the simulations support experimental investigations. The resulting model is able to account for experimental and individual response times and error rates and enables the switch of attention as a system inherent model feature: The switching process suggested by the model is based on the memorization of the visual stimuli and does not require any synaptic learning. The operation of the model thus demonstrates with at least a high probability the neuronal dynamics underlying a key component of human behavior: the ability to adapt behavior according to context requirements—cognitive flexibility. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. Action Editor: Peter Dayan     

On the quantitative relationship between survival rate of larvae and their food supply

The survival rate of fishes in their earlier stages of development and the influencing factors present one of the most fundamental problems of fish population dynamics. After I. Hjort's (Cons. L.'explor. Ner.,20, 3–228, 1914) work, there have been many investigators in this field and there is no doubt about the very important role of ova and larvae mortality in the fate of a given fish generation. Less clear are the ideas concerning factors determining the high mortality of fishes in their earlier stages of development; especially the factor of food supply of larvae during the period of transition to exogenic nutrition. The value of this factor has been estimated differently from different points of view. For example, R. J. H. Beverton and S. J. Holt (On the Dynamics of Exploited Fish Population, 1957) have given to the food supply factor its deserved importance. On the other hand, T. V. Dekhnik (Trudy Sevastopolskoi Biologicheskoi Stantsii,13, 216–244, 1960;Ibid.,14, 222–243, 1961) has proved in her investigations that at least for pelagic larvae of Black Sea fishes there is an excessive amount of food, and that therefore food cannot play an important role in larva survival. Not wanting to stop to review the literature of the problem (see Dekhnik,Trudy Sevastopolskoi Biologicheskoi Stantsii,13, 216–244, 1960), we will only remark that the problem as a whole needs further investigation. Not only new data are needed, but also methods for following up analysis have to be worked out.     

Optimal deep brain stimulation of the subthalamic nucleus—a computational study

Deep brain stimulation (DBS) of the subthalamic nucleus, typically with periodic, high frequency pulse trains, has proven to be an effective treatment for the motor symptoms of Parkinson’s disease (PD). Here, we use a biophysically-based model of spiking cells in the basal ganglia (Terman et al., Journal of Neuroscience, 22, 2963–2976, 2002; Rubin and Terman, Journal of Computational Neuroscience, 16, 211–235, 2004) to provide computational evidence that alternative temporal patterns of DBS inputs might be equally effective as the standard high-frequency waveforms, but require lower amplitudes. Within this model, DBS performance is assessed in two ways. First, we determine the extent to which DBS causes Gpi (globus pallidus pars interna) synaptic outputs, which are burstlike and synchronized in the unstimulated Parkinsonian state, to cease their pathological modulation of simulated thalamocortical cells. Second, we evaluate how DBS affects the GPi cells’ auto- and cross-correlograms. In both cases, a nonlinear closed-loop learning algorithm identifies effective DBS inputs that are optimized to have minimal strength. The network dynamics that result differ from the regular, entrained firing which some previous studies have associated with conventional high-frequency DBS. This type of optimized solution is also found with heterogeneity in both the intrinsic network dynamics and the strength of DBS inputs received at various cells. Such alternative DBS inputs could potentially be identified, guided by the model-free learning algorithm, in experimental or eventual clinical settings. Action Editor: Steven J. Schiff Xiao-Jiang Feng and Eric Shea-Brown contributed equally to this work.     

Molecular modeling and biophysical analysis of the c-MYC NHE-III<Subscript>1</Subscript> silencer element

G-Quadruplex and i-Motif-forming sequences in the promoter regions of several oncogenes show promise as targets for the regulation of oncogenes. In this study, molecular models were created for the c-MYC NHE-III₁ (nuclease hypersensitivity element III₁) from two 39-base complementary sequences. The NHE modeled here consists of single folded conformers of the polypurine intramolecular G-Quadruplex and the polypyrimidine intramolecular i-Motif structures, flanked by short duplex DNA sequences. The G-Quadruplex was based on published NMR structural data for the c-MYC 1:2:1 loop isomer. The i-Motif structure is theoretical (with five cytosine–cytosine pairs), where the central intercalated cytosine core interactions are based on NMR structural data obtained for a tetramolecular [d(A₂C₄)₄] model i-Motif. The loop structures are in silico predictions of the c-MYC i-motif loops. The porphyrin meso-tetra(N-methyl-4-pyridyl)porphine (TMPyP4), as well as the ortho and meta analogs TMPyP2 and TMPyP3, were docked to six different locations in the complete c-MYC NHE. Comparisons are made for drug binding to the NHE and the isolated G-Quadruplex and i-Motif structures. NHE models both with and without bound cationic porphyrin were simulated for 100 ps using molecular dynamics techniques, and the non-bonded interaction energies between the DNA and porphyrins calculated for all of the docking interactions. Figure Molecular models of the average structure of the final 20 ps of the molecular dynamics simulation of the c-MYC NHE-III₁ (nuclease hypersensitivity element III₁) “silencer” element. The G-Quadruplex structure is at the top-center, and the i-Motif is at the bottom-center of each picture. a “Rotation #1” of the G-Quadruplex, with the T15 loop at the top and rear and the G19/A20 loop at the top and front of the picture. b “Rotation #2” of the G-Quadruplex, with the T15 loop at the top and front of the image, and the G19/A20 loop at the front and adjacent to the G-Quadruplex/i-Motif interface     

Modeling species richness controlled by community-intrinsic and community-extrinsic processes: coastal fish communities as an example

 This article focuses on the analysis of coastal fish communities along the Norwegian Skagerrak coast. Species numbers are estimated based on annual samples of the fish communities within 12 fjords from 1953 to 1994. On this basis, a community dynamics model (incorporating both community-intrinsic and community-extrinsic processes) was developed and analyzed. This model is then discussed on the basis of other community models available through the literature, both phenomenologically oriented and process-oriented models. Received: January 17, 2002 / Accepted: May 13, 2002 Acknowledgments We thank Dr. Masakado Kawata for the invi-tation to present this paper at the 19th Symposium of the Society of Population Ecology held in Yamagata, Japan, October 26–28, 2001: “Evolution of Biodiversity: Theories and Facts.” Valuable input was provided after the presentation at this meeting, which we greatly appreciated. The reformulation of the model in terms of ΔS was kindly suggested to us by Prof. Joan Roughgarden. Thanks to Dr. Hildegunn Viljugrein for advice on the BUGS analyses and to two anonymous reviewers for constructive comments. This work has been supported by grants from the Norwegian Science Council (NFR). Correspondence to:N.C. Stenseth     

Residue Specific Ribose and Nucleobase Dynamics of the cUUCGg RNA Tetraloop Motif by MNMR 13C Relaxation

The dynamics of the nucleobase and the ribose moieties in a 14-nt RNA cUUCGg hairpin-loop uniformly labeled with ¹³C and ¹⁵N were studied by ¹³C spin relaxation experiments. R₁, R_1ρ and the ¹³C-{¹H} steady-state NOE of C₆ and C_1′ in pyrimidine and C₈ and C_1′ in purine residues were obtained at 298 K. The relaxation data were analyzed by the model-free formalism to yield dynamic information on timescales of pico-, nano- and milli-seconds. An axially symmetric diffusion tensor with an overall rotational correlation time τ_c of 2.31±0.13 ns and an axial ratio of 1.35±0.02 were determined. Both findings are in agreement with hydrodynamic calculations. For the nucleobase carbons, the validity of different reported ¹³C chemical shift anisotropy values (Stueber, D. and Grant, D. M., 2002 J. Am. Chem. Soc. 124, 10539–10551; Fiala et al., 2000 J. Biomol. NMR 16, 291–302; Sitkoff, D. and Case, D. A., 1998 Prog. NMR Spectroscopy 32, 165–190) is discussed. The resulting dynamics are in agreement with the structural features of the cUUCGg motif in that all residues are mostly rigid (0.82 < S² < 0.96) in both the nucleobase and the ribose moiety except for the nucleobase of U7, which is protruding into solution (S² = 0.76). In general, ribose mobility follows nucleobase dynamics, but is less pronounced. Nucleobase dynamics resulting from the analysis of ¹³C relaxation rates were found to be in agreement with ¹⁵N relaxation data derived dynamic information (Akke et al., 1997 RNA 3, 702–709). Electronic supplementary material Electronic supplementary material is available for this article at and accessible for authorised users.     

Simultaneous interpretation of Mössbauer, EPR and 57Fe ENDOR spectra of the [Fe4S4] cluster in the high-potential iron protein I Ectothiorhodospira halophila

4 S₄]^3 + and the reduced [Fe₄S₄]^2 + clusters in the high-potential iron protein I from Ectothiorhodospira halophila were measured in a temperature range from 5 K to 240 K. EPR measurements and ⁵⁷Fe electron-nuclear double resonance (ENDOR) experiments were carried out with the oxidized protein. In the oxidized state the cluster has a net spin S = 1/2 and is paramagnetic. As common in [Fe₄S₄]^3 + clusters, the M?ssbauer spectrum was simulated with two species contributing equally to the absorption area: two Fe^3 + atoms couple to the “ferric-ferric” pair, and one Fe^2 + and one Fe^3 + atom give the “ferric-ferrous pair”. For the simulation of the M?ssbauer spectrum, g-values were taken from EPR measurements. A-tensor components were determined by ⁵⁷Fe ENDOR experiments that turned out to be a necessary source of estimating parameters independently. In order to obtain a detailed agreement of M?ssbauer and ENDOR data, electronic relaxation has to be taken into account. Relaxing the symmetry condition in a way that the electric field gradient tensor does not coincide with g- and A-tensors yielded an even better agreement of experimental and theoretical M?ssbauer spectra. Spin-spin and spin-lattice relaxation times were estimated by pulsed EPR; the former turned out to be the dominating mechanism at T = 5 K. Relaxation times measured by pulsed EPR and obtained from the M?ssbauer fit were compared and yield nearly identical values. The reduced cluster has one additional electron and has a diamagnetic (S = 0) ground state. All the four irons are indistinguishable in the M?ssbauer spectrum, indicating a mixed-valence state of Fe^2.5 + for each. Received: 15 February 1999 / Accepted: 31 August 1999     

Sequential and synchronous growth models related to vertex analysis and branching ratios

Two models of binary tree growth are examined in terms of the Strahler order branching ratio (Rb) and the types of vertex produced during growth, and their inter-relationship. The sequential growth model is that described by Van Pelt and Verwer (1985,Bull. math. Biol. 47, 323–336) in which random growth occurs according to attributed probabilities on terminal or internal segments, one branch at a time. This model generates values ofRb≥3. The synchronous growth model is new and permits more than one segment to branch at a time, again randomly with attributed probabilities. This model generates values ofRb≥2 and in particular, when only terminal branching is permitted, gives 2≤Rb<3. Such a model might explain the branching in the human bronchial tree, in which 2.5≤Rb≤2.8. Our synchronous model is an alternative to the centrifugal-order-dependent sequential model of Van Pelt and Verwer.     

Resource allocation,hyperphagia and compensatory growth

Organisms often shown enhanced growth during recovery from starvation, and can even overtake continuously fed conspecifics (overcompensation). In an earlier paper (Ecology 84, 2777–2787), we studied the relative role played by hyperphagia and resource allocation in producing overcompensation in juvenile (non-reproductive) animals. We found that, although hyperphagia always produces growth compensation, overcompensation additionally requires protein allocation control which routes assimilate preferentially to structure during recovery. In this paper we extend our model to cover reproductively active individuals and demonstrate that growth rate overcompensation requires a similar combination of hyperphagia and allocation control which routes the part of enhanced assimilation not used for reproduction preferentially towards structural growth. We compare the properties of our dynamic energy budget model with an earlier proposal, due to Kooijman, which we extend to include hyperphagia. This formulation assumes that the rate of allocation to reserves is controlled by instantaneous feeding rate, and one would thus expect that an extension to include hyperphagia would not predict growth overcompensation. However, we show that a self-consistent representation of the hyperphagic response in Kooijman’s model overrides its fundamental dynamics, leading to preferential allocation to structural growth during recovery and hence to growth overcompensation.     

Conformation of the C-terminal pentapeptide—the ‘message sequence’—of tachykinins as determined by consensus dynamic

The tachykinins are a family of gastrointestinal peptides comprising eight members: substance P, neurokinin A, neurokinin B, eledoisin, physalemin, uperolein, kassinin and phyllomedusin. Consensus dynamics was carried out on an ensemble of seven tachykinins to determine the binding conformation of the common C-terminal fragment: Phe-X-Gly-Leu-Met-NH ₂ ,the ’message sequence’ of tachykinins. Three binding modes for the C-terminal pentapeptide were determined. The first binding conformation is folded due to an intramolecular H-bond between the NH of the variable residue (X) and CO of Met. Other features include γ-bends at both the variable amino acid (X) and at Gly. The global minimum of the simulation has this conformation for the C-terminal pentapeptide. The other two binding modes have slightly higher energies. The second is chiefly characterized by a β-turn around the segment X-Gly-Leu-Met, with additional β-bends at the variable amino acid (X) and Met. The final binding conformation is composed of β-bends around the variable amino acid (X) and Leu, and a ’pseudo’ γ-bend at the terminal Met. This paper was presented at the MBU Silver Jubilee Symposium on Structural Biology and 24th Annual Meeting of the Indian Biophysical Society held at Indian Institute of Science, Bangalore, Dec. 9–12, 1996.     

Engineering of betabellin 15D: Copper(II)-induced folding of a fibrillar β-sandwich protein

Summary The inverse protein-folding problem has been explored by designing de novo the betabellin target structure (a 64-residue β-sandwich protein), synthesizing a 32-residue peptide chain (HSLTAKIpkLTFSIAphTYTCAVpkYTAKVSH, wherep=DPro,k=DLys, andh=DHis) that might fold into this structure, and studying how its disulfide-bridged form (betabellin 15D) folds in 10 mM ammonium acetate with and without Cu²⁺. Circular dichroic spectropolarimetry indicated that at pH 5.8, 6.4, or 6.7 betabellin 15D exhibited β-sheet structure in the presence of Cu²⁺ but not in its absence. Electrospray mass spectrometry demonstrated that at pH 6.3 each molecule of betabellin 15D bound one or two Cu(II) ions. Electron microscopy showed that at pH 6.7 betabellin 15D formed short broad fibrils in the presence of Cu²⁺ but not in its absence. The observed width of the fibrils (7±2 nm) was consistent with the width (6.8nm) of a structural model of a fibril that contained two adjacent rows of betabellin 15D β-sandwiches joined lengthwise by multiple intersheet hydrogen bonds and widthwise by multiple Cu(II)-imidazole bonds. Electron paramagnetic resonance spectrometry revealed that some pairs of Cu(II) ions in a Cu(II)/betabellin 15D complex were magnetically coupled, which is consistent with the structural model of the Cu(II)/betabellin 15D fibril.