Smooth bistable S-systems

S-systems have been used as models of biochemical systems for over 30 years. One of their hallmarks is that, although they are highly non-linear, their steady states are characterised by linear equations. This allows streamlined analyses of stability, sensitivities and gains as well as objective, mathematically controlled comparisons of similar model designs. Regular S-systems have a unique steady state at which none of the system variables is zero. This makes it difficult to represent switching phenomena, as they occur, for instance, in the expression of genes, cell cycle phenomena and signal transduction. Previously, two strategies were proposed to account for switches. One was based on a technique called recasting, which permits the modelling of any differentiable non-linearities, including bistability, but typically does not allow steady-state analyses based on linear equations. The second strategy formulated the switching system in a piece-wise fashion, where each piece consisted of a regular S-system. A representation gleaned from a simplified form of recasting is proposed and it is possible to divide the characterisation of the steady states into two phases, the first of which is linear, whereas the other is non-linear, but easy to execute. The article discusses a representative pathway with two stable states and one unstable state. The pathway model exhibits strong separation between the stable states as well as hysteresis.     

Plant reproductive systems and evolution during biological invasion

Recent biological invasions provide opportunities to investigate microevolution during contemporary timescales. The tempo and scope of local adaptation will be determined by the intensity of natural selection and the amounts and kinds of genetic variation within populations. In flowering plants, genetic diversity is strongly affected by interactions between reproductive systems and stochastic forces associated with immigration history and range expansion. Here, we explore the significance of reproductive system diversity for contemporary evolution during plant invasion. We focus in particular on how reproductive modes influence the genetic consequences of long-distance colonization and determine the likelihood of adaptive responses during invasion. In many clonal invaders, strong founder effects and restrictions on sexual reproduction limit opportunities for local adaptation. In contrast, adaptive changes to life-history traits should be a general expectation in both outbreeding and inbreeding species. We provide evidence that evolutionary modifications to reproductive systems promote the colonizing ability of invading populations and that reproductive timing is an important target of selection during range expansion. Knowledge of the likelihood and speed at which local adaptation evolves in invasive plants will be particularly important for management practices when evolutionary changes enhance ecological opportunities and invasive spread.     

State-dependent invasion windows for prey in size-structured predator-prey systems: whole lake experiments

1. In size-structured communities where individuals grow in size over their life cycle, interactions between species will shift between competitive and predatory interactions depending on size relationships. The outcome of interactions will subsequently depend on the strength of competitive and predatory interactions, respectively. 2. In a whole lake experiment including four experimental lakes, it was tested under which conditions the competing prey, roach Rutilus rutilus, could successfully recruit into systems previously occupied by the predator, perch Perca fluviatilis. Two replicated introduction experiments were carried out 3 years apart. 3. Roach were able to successfully recruit into three of the four experimental lakes of which two were also inhabited by the top predator pike Esox lucius. Resource levels were unrelated to whether roach could successfully recruit into the systems as recruiting roach in all years were feeding close to their maximum rate. 4. High population fecundity of roach and low predation pressure by perch combined were necessary ingredients for successful recruitment and the presence of only one of these conditions did not result in successful recruitment. 5. It is hypothesized that, although roach were able to successfully recruit into one lake with only perch present in addition to the two lakes that also inhabited pike, long-term coexistence of roach and perch depends on the presence of another top predator (e.g. pike) selectively preying on perch. This hypothesis was supported by data on co-occurrence of perch and roach in different lakes. 6. Overall, the results are in accordance with expectation of size-structured life-history omnivory theory suggesting that coexistence between top predator and intermediate consumer is fragile.     

Reversing Drug Resistance In Vivo

Apoptotic defects occur in oncogenesis and contribute to drug resistance. We have shown that Bcl-2, Akt, and the translational regulator eIF4E cooperate with Myc during lymphomagenesis and are potent inducers of drug resistance. Interestingly, lymphomas expressing Akt, but not those expressing Bcl-2 are sensitized tochemotherapy-induced apoptosis by the mTOR inhibitor rapamycin, an effect that is countered by eIF4E. These results provide in vivo validation for a strategy to reverse drug resistance in human cancers and highlight the potential role of translational deregulation in oncogenesis and resistance. They also illustrate the importance of tailoring cancer therapy based on tumor genotype.     

Reversing opinions on Dollo's Law

Dollo's Law, the idea that the loss of complex features in evolution is irreversible, is a popular concept in evolutionary biology. Here we review how application of recent phylogenetic methods, genomics and evo-devo approaches is changing our view of Dollo's Law and its underlying mechanisms. Phylogenetic studies have recently demonstrated cases where seemingly complex features such as digits and wings have been reacquired. Meanwhile, large genomics databases and evo-devo studies are showing how the underlying developmental pathways and genetic architecture can be retained after the loss of a character. With dwindling evidence for the law-like nature of Dollo's Law, we anticipate a return to Dollo's original focus on irreversibility of all kinds of changes, not exclusively losses.     

Computational dynamics of gradient bistable networks

We describe a neural-like, homogeneous network consisting of coupled bistable elements and we study its abilities of learning, pattern recognition and computation. The technique allows new possibilities of pattern recognition, including the memorization and perfect recall of several memory patterns, without interference from spurious states. When the coupling strength between elements exceeds a critical value, the network readily converges to a unique attractor. Below this critical value one could perfectly recall all memorized patterns.     

Soliton behaviour in a bistable reaction diffusion model

We analyze a generic reaction-diffusion model that contains the important features of Turing systems and that has been extensively used in the past to model biological interesting patterns. This model presents various fixed points. Analysis of this model has been made in the past only in the case when there is only a single fixed point, and a phase diagram of all the possible instabilities shows that there is a place where a Turing-Hopf bifurcation occurs producing oscillating Turing patterns. In here we focus on the interesting situation of having several fixed points, particularly when one unstable point is in between two equally stable points. We show that the solutions of this bistable system are traveling front waves, or solitons. The predictions and results are tested by performing extensive numerical calculations in one and two dimensions. The dynamics of these solitons is governed by a well defined spatial scale, and collisions and interactions between solitons depend on this scale. In certain regions of parameter space the wave fronts can be stationary, forming a pattern resembling spatial chaos. The patterns in two dimensions are particularly interesting because they can present a coherent dynamics with pseudo spiral rotations that simulate the myocardial beat quite closely. We show that our simple model can produce complicated spatial patterns with many different properties, and could be used in applications in many different fields.      

Quantum Zeno features of bistable perception

A generalized quantum theoretical framework, not restricted to the validity domain of standard quantum physics, is used to model the dynamics of the bistable perception of ambiguous visual stimuli such as the Necker cube. The central idea is to treat the perception process in terms of the evolution of an unstable two-state system. This gives rise to a Necker-Zeno effect, in analogy to the quantum Zeno effect. A quantitative relation between the involved time scales is theoretically derived. This relation is found to be satisfied by empirically obtained cognitive time scales relevant for bistable perception.     

A bistable model of cell polarity

Ultrasensitivity, as described by Goldbeter and Koshland, has been considered for a long time as a way to realize bistable switches in biological systems. It is not as well recognized that when ultrasensitivity and reinforcing feedback loops are present in a spatially distributed system such as the cell plasmamembrane, they may induce bistability and spatial separation of the system into distinct signaling phases. Here we suggest that bistability of ultrasensitive signaling pathways in a diffusive environment provides a basic mechanism to realize cell membrane polarity. Cell membrane polarization is a fundamental process implicated in several basic biological phenomena, such as differentiation, proliferation, migration and morphogenesis of unicellular and multicellular organisms. We describe a simple, solvable model of cell membrane polarization based on the coupling of membrane diffusion with bistable enzymatic dynamics. The model can reproduce a broad range of symmetry-breaking events, such as those observed in eukaryotic directional sensing, the apico-basal polarization of epithelium cells, the polarization of budding and mating yeast, and the formation of Ras nanoclusters in several cell types.     

Traveling waves in the discrete fast buffered bistable system

We study the existence and uniqueness of traveling wave solutions of the discrete buffered bistable equation. Buffered excitable systems are used to model, among other things, the propagation of waves of increased calcium concentration, and discrete models are often used to describe the propagation of such waves across multiple cells. We derive necessary conditions for the existence of waves, and, under some restrictive technical assumptions, we derive sufficient conditions. When the wave exists it is unique and stable.      

Transduction in photoreceptors with bistable pigments: Intermediate processes

The prolonged depolarizing after potential (PDA) in the R1–6 receptors of the fly was used to isolate intermediate processes in phototransduction which are not manifested directly in the voltage response. It is first demonstrated that a pigment shift by light from metarhodopsin to rhodopsin in four species of the flies: Drosophila, Calliphora, Chrysomya and Musca induces an independent antagonistic process to the PDA, which is manifested in a strong inhibitory effect on PDA induction and is called the anti-PDA.By using mutants of Drosophila the existence of processes underlying the PDA were examined. The norpA ^H52and the trp mutant were used in which the voltage response of the photoreceptors could be reversibly abolished by elavated temperature and long intense light respectively. It is shown that the excitatory process underlying the PDA could be induced and depressed in conditions that block the voltage response of the photoreceptors, thus indicating the existance of intermediate processes which link the pigment activation by light to the PDA voltage response.Based on material presented at the European Neurosciences Meeting, Florence, September 1978     

The branching structure of the bistable dendrite

A branching structure consisting of three bistable cylindrical branches was considered. Both stable and unstable solutions for the voltage distribution in such a structure, were obtained using the method developed in our laboratory. This made it possible to calculate the input current-voltage characteristic of the bistable branching structure, including unstable segments of this characteristic. Possible stable states of the structure when its proximal end is loaded by a resistance were determined. It is shown that the binary exclusive-OR could be accomplished by the elementary branching structure of a bistable dendrite. A model with overexcitation carried out by Ca-dependent K channels was developed. It is shown that the model parameters do not fall outside the physiological range of values.     

Reversing disability of irreversible lung disease.

Pulmonary rehabilitation is a comprehensive multifaceted team approach for integrating medical management, coping skills, self-management techniques, and exercise reconditioning. It provides patients with chronic lung disease the ability to adapt and live full and nearly normal lives. These changes are possible because the overall disability includes significant reversible components: Patients have bronchospasm, infection, and cor pulmonale; they respond to progressively impaired lungs by progressive inactivity, leading to physical deconditioning. Both factors contribute to dyspnea. Because patients naturally fear dyspnea, they panic easily. During panic, their work of breathing may increase and respiratory failure may result. Pulmonary rehabilitation provides good medical management; provides exercises to increase strength, endurance, and tolerance to dyspnea; and trains patients in panic control. These programs have not been shown to lengthen life span or improve static lung function. They increase exercise performance and render patients functional, independent, and subject to fewer hospital admissions. Pulmonary rehabilitation is the only approach to chronic lung disease short of lung transplantation that improves the long-term outlook for these patients.     

Interlinked bistable mechanisms generate robust mitotic transitions

The transitions between phases of the cell cycle have evolved to be robust and switch-like, which ensures temporal separation of DNA replication, sister chromatid separation, and cell division. Mathematical models describing the biochemical interaction networks of cell cycle regulators attribute these properties to underlying bistable switches, which inherently generate robust, switch-like, and irreversible transitions between states. We have recently presented new mathematical models for two control systems that regulate crucial transitions in the cell cycle: mitotic entry and exit,¹ Mochida S, Rata S, Hino H, Nagai T, Novák B. Two Bistable Switches Govern M Phase Entry. Curr Biol. 2016;26:3361-3367. doi:10.1016/j.cub.2016.10.022. PMID:27889260[Crossref], [PubMed], [Web of Science ®] [Google Scholar] and the mitotic checkpoint.² Mirkovic M, Hutter LH, Novák B, Oliveira RA. Premature sister chromatid separation is poorly detected by the spindle assembly checkpoint as a result of system-level feedback. Cell Rep. 2015;13:469-478. doi:10.1016/j.celrep.2015.09.020[Crossref], [PubMed], [Web of Science ®] [Google Scholar] Each of the two control systems is characterized by two interlinked bistable switches. In the case of mitotic checkpoint control, these switches are mutually activating, whereas in the case of the mitotic entry/exit network, the switches are mutually inhibiting. In this Perspective we describe the qualitative features of these regulatory motifs and show that having two interlinked bistable mechanisms further enhances robustness and irreversibility. We speculate that these network motifs also underlie other cell cycle transitions and cellular transitions between distinct biochemical states.