How do digits emerge? – mathematical models of limb development

The mechanism that controls digit formation has long intrigued developmental and theoretical biologists, and many different models and mechanisms have been proposed. Here we review models of limb development with a specific focus on digit and long bone formation. Decades of experiments have revealed the basic signaling circuits that control limb development, and recent advances in imaging and molecular technologies provide us with unprecedented spatial detail and a broader view of the regulatory networks. Computational approaches are important to integrate the available information into a consistent framework that will allow us to achieve a deeper level of understanding, and that will help with the future planning and interpretation of complex experiments, paving the way to in silico genetics. Previous models of development had to be focused on very few, simple regulatory interactions. Algorithmic developments and increasing computing power now enable the generation and validation of increasingly realistic models that can be used to test old theories and uncover new mechanisms. Birth Defects Research (Part C) 102:1–12, 2014. © 2014 Wiley Periodicals, Inc.     

How do biological systems discriminate among physically similar ions?

This paper reviews the history of understanding how biological systems can discriminate so strikingly among physically similar ions, especially alkali cations. Appreciation of qualitative regularities ("permitted sequences") and quantitative regularities ("selectivity isotherms") in ion selectivity grew first from studies of ion exchangers and glass electrodes, then of biological systems such as enzymes and cell membranes, and most recently of lipid bilayers doped with model pores and carriers. Discrimination of ions depends on both electrostatic and steric forces. "Black-box" studies on intact biological membranes have in some cases yielded molecular clues to the structure of the actual biological pores and carriers. Major current problems involve the extraction of these molecules; how to do it, what to do when it is achieved, and how (and if) it is relevant to the central problems of membrane function. Further advances are expected soon from studies of rate barriers within membranes, of voltage-dependent ("excitable") conducting channels, and of increasingly complex model systems and biological membranes.     

How do biomolecular systems speed up and regulate rates?

The viability of a biological system depends upon careful regulation of the rates of various processes. These rates have limits imposed by intrinsic chemical or physical steps (e.g., diffusion). These limits can be expanded by interactions and dynamics of the biomolecules. For example, (a) a chemical reaction is catalyzed when its transition state is preferentially bound to an enzyme; (b) the folding of a protein molecule is speeded up by specific interactions within the transition-state ensemble and may be assisted by molecular chaperones; (c) the rate of specific binding of a protein molecule to a cellular target can be enhanced by mechanisms such as long-range electrostatic interactions, nonspecific binding and folding upon binding; (d) directional movement of motor proteins is generated by capturing favorable Brownian motion through intermolecular binding energy; and (e) conduction and selectivity of ions through membrane channels are controlled by interactions and the dynamics of channel proteins. Simple physical models are presented here to illustrate these processes and provide a unifying framework for understanding speed attainment and regulation in biomolecular systems.     

How do adaptive immune systems control pathogens while avoiding autoimmunity?

Immune systems face a daunting control challenge. On the one hand, they need to minimize damage from pathogens, without wasting energy and resources, but on the other must avoid initiating or perpetuating autoimmune responses. Finally, because pathogens interfere with immune function, immune systems must be robust against sabotage. We describe here how these challenges are met by two immune systems, the intracellular RNA interference system and the vertebrate CD8 T-cell response. We extrapolate from these two systems to propose principles for strategically robust control.     

How close to the theoretical diffusion limit do bacterial uptake systems function?

Using a 10cm flow-through cuvette in a high precision spectrophotometer linked to a mini-computer, the growth rate dependence of Escherichia coli on glucose concentration has been studied. The specific growth rate vs bacterial mass of single cultures consuming small amounts of glucose was followed. The data were analyzed with the computer programs described previously. For neither batch nor chemostat-cultured organisms did growth follow the monod growth law. Rather, the growth rate vs residual glucose concentration has an almost abrupt change in slope, indicative of a passive diffusion barrier prior to an uptake system possessing hyperbolic dependency. Calculations showed that the diffusion through the outer membrane via the porin channels could quantitatively account for the deviations from hyperbolic dependency. Long term chemostat culture alters the bacteria so that the maximum specific growth rate is reduced, but the initial dependence on glucose concentration is increased approaching more closely the theoretical limit. Therefore there was both a change in the outer membrane channels and the uptake activity of the cytoplasmic membrane.Deceased     

How do proteins fold?

This article emphasizes the importance of getting students to understand the ways in which polypeptides fold to form protein molecules with complex higher-ordered structures. Modern views on how this folding occurs in vitro and in the cell are summarized and set within an appropriate biological context.     

How do spores germinate?

Spore germination, as defined as those events that result in the loss of the spore-specific properties, is an essentially biophysical process. It occurs without any need for new macromolecular synthesis, so the apparatus required is already present in the mature dormant spore. Germination in response to specific chemical nutrients requires specific receptor proteins, located at the inner membrane of the spore. After penetrating the outer layers of spore coat and cortex, germinant interacts with its receptor: one early consequence of this binding is the movement of monovalent cations from the spore core, followed by Ca2(+) and dipicolinic acid (DPA). In some species, an ion transport protein is also required for these early stages. Early events - including loss of heat resistance, ion movements and partial rehydration of the spore core - can occur without cortex hydrolysis, although the latter is required for complete core rehydration and colony formation from a spore. In Bacillus subtilis two crucial cortex lytic enzymes have been identified: one is CwlJ, which is DPA-responsive and is located at the cortex-coat junction. The second, SleB, is present both in outer layers and at the inner spore membrane, and is more resistant to wet heat than is CwlJ. Cortex hydrolysis leads to the complete rehydration of the spore core, and then enzyme activity within the spore protoplast resumes. We do not yet know what activates SleB activity in the spore, and neither do we have any information at all on how the spore coat is degraded.     

How do nutrients drive growth?

The relationship between plant nutrient concentration and relative growth rate (RGR) was studied under non-steady state conditions using data from a new N interruption experiment with young lettuce plants grown hydroponically in the glasshouse. RGRs estimated from the fit of a versatile growth model were shown to decline curvilinearly with plant N concentration as N deficiency increased. Similar curvilinear relationships were also derived when the same model was used to reanalyse data for N, P and K interruption treatments from other experiments previously published in the literature. These results clearly indicate that the rate of remobilisation of nutrient reserves varies with the nutrient status of the plant. This contrasts with the linear relationships observed where the changes in plant N concentration occurred solely as a response to increasing plant age, or when plants were grown under steady state conditions with constant relative nutrient addition rates. These differences in the pattern of response provide strong evidence to support the hypothesis that the form of the relationship between RGR and plant nutrient concentration can vary depending upon whether a plant's external supplies or internal reserves of a particular nutrient are more limiting.     

How do spinal segments move?

PurposeTo study and clarify the kinematics of spinal segments following cyclic torques causing axial rotation (T_z (t)), lateral-flexion (T_x (t)), flexion/extension (T_y (t)).MethodsA 6D--Measurement of location, alignment, and migration of the instantaneous helical axis (IHA) as a function of rotational angle in cervical, thoracic, and lumbar segments subjected to axially directed preloads.ResultsIHA retained an almost constant alignment, but migrated along distinct centrodes.Thoracic segmentsIHA was almost parallel to T_z (t), T_x (t), or T_y (t), stationary for T_x (t) or T_y (t), and migrating for T_z (t) along dorsally opened bows. IHA locations hardly depended on the position or size of axial preload.Lumbar segmentsIHA was also almost parallel to T_z (t), T_x (t), or T_y (t). In axial rotation IHA-migration along wide, ventrally or dorsally bent bows depending on segmental flexional/extensional status. Distances covered: 20–60 mm. In lateral-flexion: IHA-migration to the left/right joint and vice versa. In flexion/extension IHA-migration from the facets to the centre of the disc.Cervical segmentsIn flexion/flexion IHA was almost stationary for and parallel to T_y (t). In axial rotation or lateral-flexion IHA intersected T_z (t)/T_x (t) under approximately ?30°/+30°.ConclusionsGenerally joints alternate in guidance. Lumbar segments: in axial rotation and lateral-flexion parametrical control of IHA-position and IHA-migration by axial preload position. Cervical segments: kinematical coupling between axial rotation and lateral-flexion.The IHA-migration guided by the joints should be taken into account in the design of non-fusion implants. FE-calculations of spinal mechanics and kinematics should be based on detailed data of curvature morphology of the articulating surfaces of the joint facets.     

How do plants make mitochondria?

Plant mitochondria can differ in size, shape, number and protein content across different tissue types and over development. These differences are a result of signaling and regulatory processes that ensure mitochondrial function is tuned in a cell-specific manner to support proper plant growth and development. In the last decade, the processes involved in mitochondrial biogenesis are becoming clearer, including; how dormant seeds transition from empty promitochondria to fully functional mitochondria with extensive cristae structures and various biochemical activities, the regulation of nuclear genes encoding mitochondrial proteins via regulators of the diurnal cycle in plants, the mitochondrial stress response, the targeting of proteins to mitochondria and other organelles and connections between the respiratory chain and protein import complexes. All these findings indicate that mitochondrial function is a part of an integrated cellular network, and communication between mitochondria and other cellular processes extends beyond the known exchange or transport of metabolites. Our current knowledge now needs to be used to gain more insight into the molecular components at various levels of this hierarchical and complex regulatory and communication network, so that mitochondrial function can be predicted and modified in a rational manner.     

How do prokaryotic cells cycle?

This issue of Current Biology features five reviews covering various key aspects of the eukaryotic cell cycle. The topics include initiation of chromosome replication, assembly of the mitotic spindle, cytokinesis, the regulation of cell-cycle progression, and cell-cycle modeling, focusing mainly on budding yeast, fission yeast and animal cell model systems. The reviews underscore common themes as well as key differences in the way these processes are carried out and regulated among the different model organisms. Consequently, an important question is how cell-cycle mechanisms and controls have evolved, particularly in the broader perspective of the three domains of life.     

How do cross-migration models arise?

In this paper we present a general method to derive spatio-temporal population models mechanistically. We consider a system of multiple species living in a patchy habitat in which the local population of each species consists of some behavioural groups. We then formulate a continuous-time model where a small positive parameter is present, measuring the time scale of behavioural transitions relative to that of giving birth, death and migration among patches. By the singular perturbation method the model is reduced to a lower dimensional one in which the migration terms are, in general, nonlinear and related to the reaction terms describing the local dynamics. Two examples demonstrating the emergence of cross-migration models, i.e., the models in which the per-capita migration rate of one species depends on the density of some other species, are given.     

How do fishes manage disease?

Disease drives the evolution of proactive and reactive mitigation behaviours in fishes as for terrestrial animals. Understanding fish self-remedy behaviours could discover algal bioactives, reveal novel strategies for disease management, identify new habitats or ecosystems critical to population health and conservation, and enhance knowledge of interspecific evolutionary relationships and communication.     

How do uncoupling proteins uncouple?

According to the proton buffering model, introduced by Klingenberg, UCP1 conducts protons through a hydrophilic pathway lined with fatty acid head groups that buffer the protons as they move across the membrane. According to the fatty acid protonophore model, introduced by Garlid, UCPs do not conduct protons at all. Rather, like all members of this gene family, they are anion carriers. A variety of anions are transported, but the physiological substrates are fatty acid (FA) anions. Because the carboxylate head group is translocated by UCP, and because the protonated FA rapidly diffuses across the membrane, this mechanism permits FA to behave as regulated cycling protonophores. Favoring the latter mechanism is the fact that the head group of long-chain alkylsulfonates, strong acid analogues of FA, is also translocated by UCP.     

How do you RUN on?

RUN domain is present in several proteins related to the functions of Rap and Rab family GTPases. Accumulating evidence supports the hypothesis that RUN domain-containing proteins act as a component of vesicle traffic and might be responsible for an interaction with a filamentous network linked to actin cytoskeleton or microtubules. That is to say, on one hand, RUN domains associate with Rab or Rap family proteins, on the other hand, they also might interact with motor proteins such as kinesin or myosin via intervention molecules. In this review, we summarize the background and current status of RUN domain research with an emphasis on the interaction between RUN domain and motor proteins with respect to the vesicle traffic on filamentous network.