Implications of a zinc uptake and transport model

While physicists regularly use mathematical equations to describe natural phenomena, mathematical modeling of biological systems is still not well established and is hampered by communication barriers between experimental and theoretical biologists. In a recent study we developed a mathematical model of zinc uptake and radial transport in Arabidopsis thaliana roots. By refraining from writing many equations in the main text and confining the derivation of formulas to a supplemental file, we attempted to reach both experimentalists and theoreticians likewise. Here, we give a short summary of our results on the accumulation pattern of zinc and the importance of transporter regulation, water flow and geometry. For a better understanding of the dynamics of adaptation to changes in external conditions, we plead for more detailed and frequent measurements. As a new aspect, we analyzed the effect of buffering. Simulations indicate that it dampens oscillations and may therefore play a key role in zinc homeostasis.     

Question 8: Bridging the Gap Between In Silico and In Vitro Approaches to Minimal Cells

In this short paper we argue for the relevance and value of theoretical models in the field of origins of life, but also claim that both theoreticians and experimentalists should make an effort to come together and interact more closely to obtain more fruitful and significant results. As an example, we present our own modeling approach to protocell dynamics, including some simulation results, to show that it is possible to develop computational tools that start bridging that traditional gap between theory and experiments. Presented at: International School of Complexity – 4th Course: Basic Questions on the Origins of Life; “Ettore Majorana” Foundation and Centre for Scientific Culture, Erice, Italy, 1–6 October 2006.     

The effect of ATP-sensitive K+ channels on the electrical burst activity and insulin secretion in pancreatic beta-cells.

In recent years, the electrical burst activity of the insulin releasing pancreatic beta-cells has attracted many experimentalists and theoreticians, largely because of its functional importance, but also because of the nonlinear nature of the burst activity. The ATP-sensitive K+ channels are believed to play an important role in electrical activity and insulin release. In this paper, we show by computer simulation how ATP and antidiabetic drugs can lengthen the plateau fraction of bursting and how these chemicals can increase the intracellular Ca2+ level in the pancreatic beta-cell.     

Uncovering mechanisms of bistability in biological systems

As the systems biology era progresses, theoreticians and experimentalists continue uncovering the molecular mechanisms that underlie the regulation of complex cellular phenomena, including those governing proliferation, differentiation, and death. The discovery of bistability in cellular responses and their signaling pathways has become a recurring theme, and prompted strong interest in understanding both the design and function of these networks. Modeling these systems has been crucial in assisting experimentalists to better understand how this and other types of behavior can emerge from a subset of regulators, and also to analyze and identify systems-level characteristics that would otherwise be difficult to intuit. In this review, recent advances in both theoretical and experimental work investigating the mechanistic as well as biological basis for bistability will be presented. These will include the role of positive feedback loops, the potential function of dual phosphorylation cycles, and substrate competition as a means of generating ultrasensitivity.     

GLASS: A tool to visualize protein structure prediction data in three dimensions and evaluate their consistency

When a protein sequence does not share any significant sequence similarity with a protein of known structure, homology modeling cannot be applied. However, many novel and interesting methods, such as secondary structure prediction, fold recognition, and prediction of long-range interactions, are being developed and have been shown to be reasonably successful in predicting protein structures from sequence data and evolutionary information. The a priori evaluation of the correctness of a prediction obtained by one of these methods is however often problematic. Consequently, it is important to use all available information provided by as many different methods as possible and all the available experimental data about the protein of interest, since the consistency of the results is indicative of the reliability of the prediction. Hence the need has arisen for suitable tools able to compare results provided by different methods and evaluate their consistency. We have therefore constructed GLASS, a general platform to read, visualize, compare, and evaluate prediction results from many different sources and to project these prediction results into three dimensions. In addition, GLASS allows the comparison of selected parameters calculated for a model with the distribution observed in real protein structures, thus providing an easy way to test new methods for evaluating the likelihood of different structural models. GLASS can be considered as a “workbench” for structural predictions useful to both experimentalists and theoreticians. Proteins 30:339–351, 1998. © 1998 Wiley-Liss, Inc.     

Hydrogen bonds involving sulfur atoms in proteins.

Intrachain hydrogen bonds are a hallmark of globular proteins. Traditionally, these involve oxygen and nitrogen atoms. The electronic structure of sulfur is compatible with hydrogen bond formation as well. We surveyed a set of 85 high-resolution protein structures in order to evaluate the prevalence and geometry of sulfur-containing hydrogen bonds. This information should be of interest to experimentalists and theoreticians interested in protein structure and protein engineering.     

The effect of ATP-sensitive K+ channels on the electrical burst activity and insulin secretion in pancreatic β-cells

In recent years, the electrical burst activity of the insulin releasing pancreatic β-cells has attracted many experimentalists and theoreticians, largely because of its functional importance, but also because of the nonlinear nature of the burst activity. The ATP-sensitive K⁺ channels are believed to play an important role in electrical activity and insulin release. In this paper, we show by computer simulation how ATP and antidiabetic drugs can lengthen the plateau fraction of bursting and how these chemicals can increase the intracellular Ca²⁺ level in the pancreatic β-cell.     

The stability of predator-prey systems subject to the Allee effects

In recent years, many theoreticians and experimentalists have concentrated on the processes that affect the stability of predator-prey systems. But few papers have addressed the Allee effect with focus on the their stability. In this paper, we select two classical models describing predator-prey systems and introduce the Allee effects into the dynamics of both the predator and prey populations in these models, respectively. By combining mathematical analysis with numerical simulation, we have shown that the Allee effect may be a destabilizing force in predator-prey systems: the equilibrium point of the system could be changed from stable to unstable or otherwise, the system, even when it is stable, will take much longer time to reach the stable state. We also conclude that the equilibrium of the prey population will be enlarged due to the Allee effect of the predator, but the Allee effects of the prey may decrease the equilibrium value of the predator, or that of both the predator and prey. It should also be pointed out that the impact of the Allee effects of predator and prey due to different mechanisms on different predator-prey systems could also vary.     

Endocytosis optimizes the dynamic localization of membrane proteins that regulate cortical polarity

Diverse cell types require the ability to maintain dynamically polarized membrane-protein distributions through balancing transport and diffusion. However, design principles underlying dynamically maintained cortical polarity are not well understood. Here we constructed a mathematical model for characterizing the morphology of dynamically polarized protein distributions. We developed analytical approaches for measuring all model parameters from single-cell experiments. We applied our methods to a well-characterized system for studying polarized membrane proteins: budding yeast cells expressing activated Cdc42. We found that a balance of diffusion, directed transport, and endocytosis was sufficient for accurately describing polarization morphologies. Surprisingly, the model predicts that polarized regions are defined with a precision that is nearly optimal for measured endocytosis rates and that polarity can be dynamically stabilized through positive feedback with directed transport. Our approach provides a step toward understanding how biological systems shape spatially precise, unambiguous cortical polarity domains using dynamic processes.     

“Essentially,all models are wrong,but some are useful”<Emphasis Type="Italic">—</Emphasis>a cross-disciplinary agenda for building useful models in cell biology and biophysics

Intuition alone often fails to decipher the mechanisms underlying the experimental data in Cell Biology and Biophysics, and mathematical modeling has become a critical tool in these fields. However, mathematical modeling is not as widespread as it could be, because experimentalists and modelers often have difficulties communicating with each other, and are not always on the same page about what a model can or should achieve. Here, we present a framework to develop models that increase the understanding of the mechanisms underlying one’s favorite biological system. Development of the most insightful models starts with identifying a good biological question in light of what is known and unknown in the field, and determining the proper level of details that are sufficient to address this question. The model should aim not only to explain already available data, but also to make predictions that can be experimentally tested. We hope that both experimentalists and modelers who are driven by mechanistic questions will find these guidelines useful to develop models with maximum impact in their field.     

Feedback models for polarized auxin transport: an emerging trend

The phytohormone auxin is vital to plant growth and development. A unique property of auxin among all other plant hormones is its cell-to-cell polar transport that requires activity of polarly localized PIN-FORMED (PIN) auxin efflux transporters. Despite the substantial molecular insight into the cellular PIN polarization, the mechanistic understanding for developmentally and environmentally regulated PIN polarization is scarce. The long-standing belief that auxin modulates its own transport by means of a positive feedback mechanism has inspired both experimentalists and theoreticians for more than two decades. Recently, theoretical models for auxin-dependent patterning in plants include the feedback between auxin transport and the PIN protein localization. These computer models aid to assess the complexity of plant development by testing and predicting plausible scenarios for various developmental processes that occur in planta. Although the majority of these models rely on purely heuristic principles, the most recent mechanistic models tentatively integrate biologically testable components into known cellular processes that underlie the PIN polarity regulation. The existing and emerging computational approaches to describe PIN polarization are presented and discussed in the light of recent experimental data on the PIN polar targeting.     

Computational Approaches for Predicting Biomedical Research Collaborations

Biomedical research is increasingly collaborative, and successful collaborations often produce high impact work. Computational approaches can be developed for automatically predicting biomedical research collaborations. Previous works of collaboration prediction mainly explored the topological structures of research collaboration networks, leaving out rich semantic information from the publications themselves. In this paper, we propose supervised machine learning approaches to predict research collaborations in the biomedical field. We explored both the semantic features extracted from author research interest profile and the author network topological features. We found that the most informative semantic features for author collaborations are related to research interest, including similarity of out-citing citations, similarity of abstracts. Of the four supervised machine learning models (naïve Bayes, naïve Bayes multinomial, SVMs, and logistic regression), the best performing model is logistic regression with an ROC ranging from 0.766 to 0.980 on different datasets. To our knowledge we are the first to study in depth how research interest and productivities can be used for collaboration prediction. Our approach is computationally efficient, scalable and yet simple to implement. The datasets of this study are available at https://github.com/qingzhanggithub/medline-collaboration-datasets.     

A theoretical and empirical investigation of delayed growth response in the continuous culture of bacteria

When the growth of bacteria in a chemostat is controlled by limiting the supply of a single essential nutrient, the growth rate is affected both by the concentration of this nutrient in the culture medium and by the amount of time that it takes for the chemical and physiological processes that result in the production of new biomass. Thus, although the uptake of nutrient by cells is an essentially instantaneous process, the addition of new biomass is delayed by the amount of time that it takes to metabolize the nutrient. Mathematical models that incorporate this "delayed growth response" (DGR) phenomenon have been developed and analysed. However, because they are formulated in terms of parameters that are difficult to measure directly, these models are of limited value to experimentalists. In this paper, we introduce a DGR model that is formulated in terms of measurable parameters. In addition, we provide for this model a complete set of criteria for determining persistence versus extinction of the bacterial culture in the chemostat. Specifically, we show that DGR plays a role in determining persistence versus extinction only under certain ranges of chemostat operating parameters. It is also shown, however, that DGR plays a role in determining the steady-state nutrient and bacteria concentrations in all instances of persistence. The steady state and transient behavior of solutions of our model is found to be in agreement with data that we obtained in growing Escherichia coli 23716 in a chemostat with glucose as a limiting nutrient. One of the theoretical predictions of our model that does not occur in other DGR models is that under certain conditions a large delay in growth response might actually have a positive effect on the bacteria's ability to persist.     

Pigmentation pattern formation in butterflies: experiments and models

Butterfly pigmentation patterns are one of the most spectacular and vivid examples of pattern formation in biology. They have attracted much attention from experimentalists and theoreticians, who have tried to understand the underlying genetic, chemical and physical processes that lead to patterning. In this paper, we present a brief review of this field by first considering the generation of the localised, eyespot, patterns and then the formation of more globally controlled patterns. We present some new results applied to pattern formation on the wing of the mimetic butterfly Papilio dardanus.     

Modeling developmental patterns of spontaneous activity

Spontaneous activity is found in many regions of the developing nervous system; such activity is thought to be instructive for guiding developmental processes. In particular, the developing retina generates correlated patterns of activity known as retinal waves. We review the main theoretical models that have been developed to study the mechanisms for generation and propagation of retinal waves. Much of the progress in this field has been due to the close interaction between experimentalists and theorists in analyzing and modeling spontaneous activity. We conclude by describing spontaneous activity models in other systems and suggestions for future modeling work.     

Systems biology by the rules: hybrid intelligent systems for pathway modeling and discovery

Background  

Expert knowledge in journal articles is an important source of data for reconstructing biological pathways and creating new hypotheses. An important need for medical research is to integrate this data with high throughput sources to build useful models that span several scales. Researchers traditionally use mental models of pathways to integrate information and development new hypotheses. Unfortunately, the amount of information is often overwhelming and these are inadequate for predicting the dynamic response of complex pathways. Hierarchical computational models that allow exploration of semi-quantitative dynamics are useful systems biology tools for theoreticians, experimentalists and clinicians and may provide a means for cross-communication.     

Looking inside the box: bacterial transistor arrays

One often compares cells to computers, and signalling proteins to transistors. Location and wiring of those molecular transistors is paramount in defining the function of the subcellular chips. The bacterial chemotactic sensing apparatus is a large, stable assembly consisting of thousands of receptors, signal transducing kinases and linking proteins, and is responsible for the motile response of the bacterium to environmental signals, whether chemical, mechanical, or thermal. Because of its rich functional repertoire despite its relative simplicity, this chemosome has attracted much attention from both experimentalists and theoreticians, and the bacterial chemotaxis response becoming a benchmark in Systems Biology. Structural and functional models of the chemotactic device have been developed, often based on particular assumptions regarding the topology of the receptor lattice. In this issue of Molecular Microbiology, Briegel et al. provide a detailed view of the receptor arrangement, unravelling the wiring of the molecular signal processors.     

Endocytosis and sorting of ErbB2 and the site of action of cancer therapeutics trastuzumab and geldanamycin

ErbB2 is a transmembrane tyrosine kinase whose surface overexpression is linked to tumorigenesis and poor prognosis in breast cancer patients. Two models have emerged that account for the high surface distribution of ErbB2. In one model, the surface pool is dynamic and governed by a balance between endocytosis and recycling, whereas in the other it is retained, static, and excluded from endocytosis. These models have contrasting implications for how ErbB2 exerts its biological function and how cancer therapies might down-regulate surface ErbB2, such as the antibody trastuzumab (Herceptin) or the Hsp90 inhibitor geldanamycin. Little is known, however, about how these treatments affect ErbB2 endocytic trafficking. To investigate this issue, we examined breast carcinoma cells by immunofluorescence and quantitative immunoelectron microscopy and developed imaging and trafficking kinetics assays using cell surface fluorescence quenching. Surprisingly, trastuzumab does not influence ErbB2 distribution but instead recycles passively with internalized ErbB2. By contrast, geldanamycin down-regulates surface ErbB2 through improved degradative sorting in endosomes exclusively rather than through increased endocytosis. These results reveal substantial dynamism in the surface ErbB2 pool and clearly demonstrate the significance of endosomal sorting in the maintenance of ErbB2 surface distribution, a critical feature of its biological function.     

Influence of target concentration and background binding on in vitro selection of affinity reagents

Nucleic acid-based aptamers possess many useful features that make them a promising alternative to antibodies and other affinity reagents, including well-established chemical synthesis, reversible folding, thermal stability and low cost. However, the selection process typically used to generate aptamers (SELEX) often requires significant resources and can fail to yield aptamers with sufficient affinity and specificity. A number of seminal theoretical models and numerical simulations have been reported in the literature offering insights into experimental factors that govern the effectiveness of the selection process. Though useful, these previous models have not considered the full spectrum of experimental factors or the potential impact of tuning these parameters at each round over the course of a multi-round selection process. We have developed an improved mathematical model to address this important question, and report that both target concentration and the degree of non-specific background binding are critical determinants of SELEX efficiency. Although smaller target concentrations should theoretically offer superior selection outcome, we show that the level of background binding dramatically affect the target concentration that will yield maximum enrichment at each round of selection. Thus, our model enables experimentalists to determine appropriate target concentrations as a means for protocol optimization. Finally, we perform a comparative analysis of two different selection methods over multiple rounds of selection, and show that methods with inherently lower background binding offer dramatic advantages in selection efficiency.     

Gene network models robust to spatial scaling and noisy input

Many biological systems are inherently noisy, yet demonstrate robustness to perturbations and changes in external influences. Such is the case in the Bicoid-Hunchback (Bcd-Hb) system, which is critical to axis specification in the developing Drosophila embryo. We use this system as motivation to explore the larger problem of how precise patterning can be achieved under imprecise conditions. While evidence suggests Bicoid gradients are uncorrelated with respect to embryo length, downstream genes, such as Hb, are expressed in a precise manner with regard to position along the anterior-posterior (AP)-axis. In addition to precision under variability of embryo length, Hb also exhibits robustness to perturbations to the regulatory network, gene dosage, and temperature. Understanding the reduced variability of patterns in this system is of interest to both experimentalists and theoreticians, lending itself well to the field of mathematical modeling. In this paper, a class of reaction-diffusion models is presented, which produce precise patterns, despite receiving noisy input and other perturbations to the system. An essential property of the network includes the existence of a strong inhibitor for the Hb representative, where the strength of the inhibition is directly related to the amount of variation that can be tolerated. With a higher inhibitory effect, larger perturbations of Bcd can be made with relatively small changes to the location of the Hb boundary. Network topology and interaction strength are the essential properties of the minimal model giving rise to the robust features, and possible interpretations are made with regard to the Bcd-Hb system.