Generation of nonidentical compartments in vesicular transport systems

Potential based, spatial simulation of dynamically nested particles

BACKGROUND

To study cell biological phenomena which depend on diffusion, active transport processes, or the locations of species, modeling and simulation studies need to take space into account. To describe the system as a collection of discrete objects moving and interacting in continuous space, various particle-based reaction diffusion simulators for cell-biological system have been developed. So far the focus has been on particles as solid spheres or points. However, spatial dynamics might happen at different organizational levels, such as proteins, vesicles or cells with interrelated dynamics which requires spatial approaches that take this multi-levelness of cell biological systems into account.

RESULTS

Based on the perception of particles forming hollow spheres, ML-Force contributes to the family of particle-based simulation approaches: in addition to excluded volumes and forces, it also supports compartmental dynamics and relating dynamics between different organizational levels explicitly. Thereby, compartmental dynamics, e.g., particles entering and leaving other particles, and bimolecular reactions are modeled using pair-wise potentials (forces) and the Langevin equation. In addition, forces that act independently of other particles can be applied to direct the movement of particles. Attributes and the possibility to define arbitrary functions on particles, their attributes and content, to determine the results and kinetics of reactions add to the expressiveness of ML-Force. Its implementation comprises a rudimentary rule-based embedded domain-specific modeling language for specifying models and a simulator for executing models continuously. Applications inspired by cell biological models from literature, such as vesicle transport or yeast growth, show the value of the realized features. They facilitate capturing more complex spatial dynamics, such as the fission of compartments or the directed movement of particles, and enable the integration of non-spatial intra-compartmental dynamics as stochastic events.

CONCLUSIONS

By handling all dynamics based on potentials (forces) and the Langevin equation, compartmental dynamics, such as dynamic nesting, fusion and fission of compartmental structures are handled continuously and are seamlessly integrated with traditional particle-based reaction-diffusion dynamics within the cell. Thereby, attributes and arbitrary functions allow to flexibly describe diverse spatial phenomena, and relate dynamics across organizational levels. Also they prove crucial in modeling intra-cellular or intra-compartmental dynamics in a non-spatial manner, and, thus, to abstract from spatial dynamics, on demand which increases the range of multi-compartmental processes that can be captured.

Dynamic balance between vesicle transport and microtubule growth enables neurite outgrowth

Whole cell responses involve multiple subcellular processes (SCPs). To understand how balance between SCPs controls the dynamics of whole cell responses we studied neurite outgrowth in rat primary cortical neurons in culture. We used a combination of dynamical models and experiments to understand the conditions that permitted growth at a specified velocity and when aberrant growth could lead to the formation of dystrophic bulbs. We hypothesized that dystrophic bulb formation is due to quantitative imbalances between SCPs. Simulations predict redundancies between lower level sibling SCPs within each type of high level SCP. In contrast, higher level SCPs, such as vesicle transport and exocytosis or microtubule growth characteristic of each type need to be strictly coordinated with each other and imbalances result in stalling of neurite outgrowth. From these simulations, we predicted the effect of changing the activities of SCPs involved in vesicle exocytosis or microtubule growth could lead to formation of dystrophic bulbs. siRNA ablation experiments verified these predictions. We conclude that whole cell dynamics requires balance between the higher-level SCPs involved and imbalances can terminate whole cell responses such as neurite outgrowth.

Mechanisms that cause a change of state of a cell arise from unique patterns of interactions between multiple subcellular processes (SCPs). Neurite outgrowth (NOG) is such a change of cell state where a neuron puts out a long process that eventually becomes the axon. We used a top-down based approach to mathematically model interactions between SCPs involved in NOG. These include membrane production at the cell body, membrane delivery from the cell body to the neurite tip and microtubule growth within the neurite. Our analyses show how the different SCPs interact with each other to enable NOG at a given velocity under physiological conditions. This approach is different from the commonly used bottom-up approaches that focus on predicting cell functions based on the activity of molecular interaction networks. Our simulations predict that lower-level sibling SCPs (e.g. vesicle tethering at and vesicle fusion with the plasma membrane) within a group can compensate for each other under physiological conditions, while such simple relationships do not exist between higher level SCPs (e.g. vesicle exocytosis and vesicle transport along microtubules). We predicted that imbalances of activities between higher-level SCPs induce dystrophic bulbs (a pathological response) and validated these predictions via siRNA ablation experiments.

Reconstruction of endosomal organization and function by a combination of ODE and agent-based modeling strategies

BACKGROUND

Reproducing cell processes using an in silico system is an essential tool for understanding the underlying mechanisms and emergent properties of this extraordinary complex biological machine. However, computational models are seldom applied in the field of intracellular trafficking. In a cell, numerous molecular interactions occur on the surface or in the interior of membrane-bound compartments that continually change position and undergo dynamic processes of fusion and fission. At present, the available simulation tools are not suitable to develop models that incorporate the dynamic evolution of the cell organelles.

RESULTS

We developed a modeling platform combining Repast (Agent-Based Modeling, ABM) and COPASI (Differential Equations, ODE) that can be used to reproduce complex networks of molecular interactions. These interactions occur in dynamic cell organelles that change position and composition over the course of time. These two modeling strategies are fundamentally different and comprise of complementary capabilities. The ODEs can easily model the networks of molecular interactions, signaling cascades, and complex metabolic reactions. On the other hand, ABM software is especially suited to simulate the movement, interaction, fusion, and fission of dynamic organelles. We used the combined ABM-ODE platform to simulate the transport of soluble and membrane-associated cargoes that move along an endocytic route composed of early, sorting, recycling and late endosomes. We showed that complex processes that strongly depend on transport can be modeled. As an example, the hydrolysis of a GM2-like glycolipid was programmed by adding a trans-Golgi network compartment, lysosomal enzyme trafficking, endosomal acidification, and cholesterol processing to the simulation model.

CONCLUSIONS

The model captures the highly dynamic nature of cell compartments that fuse and divide, creating different conditions for each organelle. We expect that this modeling strategy will be useful to understand the logic underlying the organization and function of the endomembrane system.

REVIEWERS

This article was reviewed by Drs. Rafael Fernández-Chacón, James Faeder, and Thomas Simmen.

Trisomy 21 Represses Cilia Formation and Function

Trisomy 21 (T21) is the most prevalent human chromosomal disorder, causing a range of cardiovascular, musculoskeletal, and neurological abnormalities. However, the cellular processes disrupted by T21 are poorly understood. Consistent with the clinical overlap between T21 and ciliopathies, we discovered that T21 disrupts cilia formation and signaling. Cilia defects arise from increased expression of Pericentrin, a centrosome scaffold and trafficking protein encoded on chromosome 21. Elevated Pericentrin is necessary and sufficient for T21 cilia defects. Pericentrin accumulates at centrosomes and dramatically in the cytoplasm surrounding centrosomes. Centrosome Pericentrin recruits more γ-tubulin and enhances microtubules, whereas cytoplasmic Pericentrin assembles into large foci that do not efficiently traffic. Moreover, the Pericentrin-associated cilia assembly factor IFT20 and the ciliary signaling molecule Smoothened do not efficiently traffic to centrosomes and cilia. Thus, increased centrosome protein dosage produces ciliopathy-like outcomes in T21 cells by decreasing trafficking between the cytoplasm, centrosomes, and cilia.

Cargo induces retromer-mediated membrane remodeling on membranes

Endosomes serve as a central sorting station of lipids and proteins that arrive via vesicular carrier from the plasma membrane and the Golgi complex. At the endosome, retromer complexes sort selected receptors and membrane proteins into tubules or vesicles that bud off the endosome. The mature endosome finally fuses with the lysosome. Retromer complexes consist of a cargo selection complex (CSC) and a membrane remodeling part (sorting nexin [SNX]-Bin/amphiphysin/Rvs [BAR], or Snx3 in yeast) and different assemblies of retromer mediate recycling of different cargoes. Due to this complexity, the exact order of events that results in carrier formation is not yet understood. Here, we reconstituted this process on giant unilamellar vesicles together with purified retromer complexes from yeast and selected cargoes. Our data reveal that the membrane remodeling activity of both Snx3 and the SNX-BAR complex is strongly reduced at low concentrations, which can be reactivated by CSC. At even lower concentrations, these complexes still associate with membranes, but only remodel membranes in the presence of their specific cargoes. Our data thus favor a simple model, where cargo functions as a specific trigger of retromer-mediated sorting on endosomes.

Stochastic Model of Maturation and Vesicular Exchange in Cellular Organelles

The dynamical organization of membrane-bound organelles along intracellular transport pathways relies on vesicular exchange between organelles and on the maturation of the organelle's composition by enzymatic reactions or exchange with the cytoplasm. The relative importance of each mechanism in controlling organelle dynamics remains controversial, in particular for transport through the Golgi apparatus. Using a stochastic model, we identify two classes of dynamical behavior that can lead to full maturation of membrane-bound compartments. In the first class, maturation corresponds to the stochastic escape from a steady state in which export is dominated by vesicular exchange, and is very unlikely for large compartments. In the second class, it occurs in a quasi-deterministic fashion and is almost size independent. Whether a system belongs to the first or second class is largely controlled by homotypic fusion.

Stochastic Model of Vesicular Sorting in Cellular Organelles

The proper sorting of membrane components by regulated exchange between cellular organelles is crucial to intracellular organization. This process relies on the budding and fusion of transport vesicles, and should be strongly influenced by stochastic fluctuations, considering the relatively small size of many organelles. We identify the perfect sorting of two membrane components initially mixed in a single compartment as a first passage process, and we show that the mean sorting time exhibits two distinct regimes as a function of the ratio of vesicle fusion to budding rates. Low ratio values lead to fast sorting but result in a broad size distribution of sorted compartments dominated by small entities. High ratio values result in two well-defined sorted compartments but sorting is exponentially slow. Our results suggest an optimal balance between vesicle budding and fusion for the rapid and efficient sorting of membrane components and highlight the importance of stochastic effects for the steady-state organization of intracellular compartments.

Agents and networks to model the dynamic interactions of intracellular transport

Cell biology is increasingly evolving to become a more formal and quantitative science. The field of intracellular transport is no exception. However, it is extremely challenging to formulate mathematical and computational models for processes that involve dynamic structures that continuously change their shape, position and composition, leading to information transfer and functional outcomes. The two major strategies employed to represent intracellular trafficking are based on "ordinary differential equations" and "agent-" based modeling. Both approaches have advantages and drawbacks. Combinations of both modeling strategies have promising characteristics to generate meaningful simulations for intracellular transport and allow the formulation of new hypotheses and provide new insights. In the near future, cell biologists will encounter and hopefully overcome the challenge of translating descriptive cartoon representations of biological systems into mathematical network models.

Nonequilibrium description of de novo biogenesis and transport through Golgi-like cisternae

A central issue in cell biology is the physico-chemical basis of organelle biogenesis in intracellular trafficking pathways, its most impressive manifestation being the biogenesis of Golgi cisternae. At a basic level, such morphologically and chemically distinct compartments should arise from an interplay between the molecular transport and chemical maturation. Here, we formulate analytically tractable, minimalist models, that incorporate this interplay between transport and chemical progression in physical space, and explore the conditions for de novo biogenesis of distinct cisternae. We propose new quantitative measures that can discriminate between the various models of transport in a qualitative manner–this includes measures of the dynamics in steady state and the dynamical response to perturbations of the kind amenable to live-cell imaging.

Model of Growth Cone Membrane Polarization via Microtubule Length Regulation

We present a mathematical model of membrane polarization in growth cones. We proceed by coupling an active transport model of cytosolic proteins along a two-dimensional microtubule (MT) network with a modified Dogterom-Leibler model of MT growth. In particular, we consider a Rac1-stathmin-MT pathway in which the growth and catastrophe rates of MTs are regulated by cytosolic stathmin, while the stathmin is regulated by Rac1 at the membrane. We use regular perturbation theory and numerical simulations to determine the steady-state stathmin concentration, the mean MT length distribution, and the resulting distribution of membrane-bound proteins. We thus show how a nonuniform Rac1 distribution on the membrane generates a polarized distribution of membrane proteins. The mean MT length distribution and hence the degree of membrane polarization are sensitive to the precise form of the Rac1 distribution and parameters such as the catastrophe-promoting constant and tubulin association rate. This is a consequence of the fact that the lateral diffusion of stathmin tends to weaken the effects of Rac1 on the distribution of mean MT lengths.

Stacking the odds for Golgi cisternal maturation

What is the minimal set of cell-biological ingredients needed to generate a Golgi apparatus? The compositions of eukaryotic organelles arise through a process of molecular exchange via vesicle traffic. Here we statistically sample tens of thousands of homeostatic vesicle traffic networks generated by realistic molecular rules governing vesicle budding and fusion. Remarkably, the plurality of these networks contain chains of compartments that undergo creation, compositional maturation, and dissipation, coupled by molecular recycling along retrograde vesicles. This motif precisely matches the cisternal maturation model of the Golgi, which was developed to explain many observed aspects of the eukaryotic secretory pathway. In our analysis cisternal maturation is a robust consequence of vesicle traffic homeostasis, independent of the underlying details of molecular interactions or spatial stacking. This architecture may have been exapted rather than selected for its role in the secretion of large cargo.

DOI:http://dx.doi.org/10.7554/eLife.16231.001

Wine glasses and hourglasses: Non-adaptive complexity of vesicle traffic in microbial eukaryotes

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We are motivated by the diversity of vesicle traffic systems in microbial parasites.

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We present a mathematical model of vesicle traffic in a manner accessible to a broad audience.

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We show that many complex features of vesicle traffic systems arise spontaneously due to molecular interactions.

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Traffic features such as compartmental maturation might arise non-adaptively and later be selected for function.

Microbial eukaryotes present a stunning diversity of endomembrane organization. From specialized secretory organelles such as the rhoptries and micronemes of apicomplexans, to peroxisome-derived metabolic compartments such as the glycosomes of kinetoplastids, different microbial taxa have explored different solutions to the compartmentalization and processing of cargo. The basic secretory and endocytic system, comprising the ER, Golgi, endosomes, and plasma membrane, as well as diverse taxon-specific specialized endomembrane organelles, are coupled by a complex network of cargo transport via vesicle traffic. It is tempting to connect form to function, ascribing biochemical roles to each compartment and vesicle of such a system. Here we argue that traffic systems of high complexity could arise through non-adaptive mechanisms via purely physical constraints, and subsequently be exapted for various taxon-specific functions. Our argument is based on a Boolean mathematical model of vesicle traffic: we specify rules of how compartments exchange vesicles; these rules then generate hypothetical cells with different types of endomembrane organization. Though one could imagine a large number of hypothetical vesicle traffic systems, very few of these are consistent with molecular interactions. Such molecular constraints are the bottleneck of a metaphorical hourglass, and the rules that make it through the bottleneck are expected to generate cells with many special properties. Sampling at random from among such rules represents an evolutionary null hypothesis: any properties of the resulting cells must be non-adaptive. We show by example that vesicle traffic systems generated in this random manner are reminiscent of the complex trafficking apparatus of real cells.

Signaling at the Golgi: sensing and controlling the membrane fluxes

Over the past few decades, it has emerged that the Golgi (and other secretory stations) is host to a variety of signaling molecules and can act as a signaling hub that receives, emits and elaborates signals. This endomembrane-based signaling apparatus appears to have more than one purpose. Its most fundamental function appears to be the auto-regulation of the biosynthetic apparatus to maintain and/or optimize its own activities and to coordinate such activities with those of other cellular modules.(1) This is achieved by dedicated control devices that provide stability, robustness, precision, sensitivity and complexity to cellular behaviors.

Synthetic biology outside the cell: linking computational tools to cell-free systems

As mathematical models become more commonly integrated into the study of biology, a common language for describing biological processes is manifesting. Many tools have emerged for the simulation of in vivo synthetic biological systems, with only a few examples of prominent work done on predicting the dynamics of cell-free synthetic systems. At the same time, experimental biologists have begun to study dynamics of in vitro systems encapsulated by amphiphilic molecules, opening the door for the development of a new generation of biomimetic systems. In this review, we explore both in vivo and in vitro models of biochemical networks with a special focus on tools that could be applied to the construction of cell-free expression systems. We believe that quantitative studies of complex cellular mechanisms and pathways in synthetic systems can yield important insights into what makes cells different from conventional chemical systems.

Control systems of membrane transport at the interface between the endoplasmic reticulum and the Golgi

A fundamental property of cellular processes is to maintain homeostasis despite varying internal and external conditions. Within the membrane transport apparatus, variations in membrane fluxes from the endoplasmic reticulum (ER) to the Golgi complex are balanced by opposite fluxes from the Golgi to the ER to maintain homeostasis between the two organelles. Here we describe a molecular device that balances transport fluxes by integrating transduction cascades with the transport machinery. Specifically, ER-to-Golgi transport activates the KDEL receptor at the Golgi, which triggers a cascade that involves Gs and adenylyl cyclase and phosphodiesterase isoforms and then PKA activation and results in the phosphorylation of transport machinery proteins. This induces retrograde traffic to the ER and balances transport fluxes between the ER and Golgi. Moreover, the KDEL receptor activates CREB1 and other transcription factors that upregulate transport-related genes. Thus, a Golgi-based control system maintains transport homeostasis through both signaling and transcriptional networks.

Control systems and coordination protocols of the secretory pathway

Like other cellular modules, the secretory pathway and the Golgi complex are likely to be supervised by control systems that support homeostasis and optimal functionality under all conditions, including external and internal perturbations. Moreover, the secretory apparatus must be functionally connected with other cellular modules, such as energy metabolism and protein degradation, via specific rules of interaction, or “coordination protocols”. These regulatory devices are of fundamental importance for optimal function; however, they are generally “hidden” at steady state. The molecular components and the architecture of the control systems and coordination protocols of the secretory pathway are beginning to emerge through studies based on the use of controlled transport-specific perturbations aimed specifically at the detection and analysis of these internal regulatory devices.

Models in biology: 'accurate descriptions of our pathetic thinking'

In this essay I will sketch some ideas for how to think about models in biology. I will begin by trying to dispel the myth that quantitative modeling is somehow foreign to biology. I will then point out the distinction between forward and reverse modeling and focus thereafter on the former. Instead of going into mathematical technicalities about different varieties of models, I will focus on their logical structure, in terms of assumptions and conclusions. A model is a logical machine for deducing the latter from the former. If the model is correct, then, if you believe its assumptions, you must, as a matter of logic, also believe its conclusions. This leads to consideration of the assumptions underlying models. If these are based on fundamental physical laws, then it may be reasonable to treat the model as 'predictive', in the sense that it is not subject to falsification and we can rely on its conclusions. However, at the molecular level, models are more often derived from phenomenology and guesswork. In this case, the model is a test of its assumptions and must be falsifiable. I will discuss three models from this perspective, each of which yields biological insights, and this will lead to some guidelines for prospective model builders.

New organelles by gene duplication in a biophysical model of eukaryote endomembrane evolution

Extant eukaryotic cells have a dynamic traffic network that consists of diverse membrane-bound organelles exchanging matter via vesicles. This endomembrane system arose and diversified during a period characterized by massive expansions of gene families involved in trafficking after the acquisition of a mitochondrial endosymbiont by a prokaryotic host cell >1.8 billion years ago. Here we investigate the mechanistic link between gene duplication and the emergence of new nonendosymbiotic organelles, using a minimal biophysical model of traffic. Our model incorporates membrane-bound compartments, coat proteins and adaptors that drive vesicles to bud and segregate cargo from source compartments, and SNARE proteins and associated factors that cause vesicles to fuse into specific destination compartments. In simulations, arbitrary numbers of compartments with heterogeneous initial compositions segregate into a few compositionally distinct subsets that we term organelles. The global structure of the traffic system (i.e., the number, composition, and connectivity of organelles) is determined completely by local molecular interactions. On evolutionary timescales, duplication of the budding and fusion machinery followed by loss of cross-interactions leads to the emergence of new organelles, with increased molecular specificity being necessary to maintain larger organellar repertoires. These results clarify potential modes of early eukaryotic evolution as well as more recent eukaryotic diversification.

Retromer and the dynamin Vps1 cooperate in the retrieval of transmembrane proteins from vacuoles

Endosomes are dynamic organelles that need to combine the ability to successfully deliver proteins and lipids to the lysosome-like vacuole, and recycle others to the Golgi or the plasma membrane. We now show that retromer, implicated in retrieval of proteins from endosomes to the Golgi or to the plasma membrane, can act on vacuoles. We explore its function using an assay that allows us to dissect the required cofactors during recycling. We demonstrate that recycling of the transmembrane receptor Vps10 from vacuoles requires the retromer, the dynamin-like Vps1, and the Rab7 GTPase Ypt7. While retromer and Vps1 leave the vacuole together with the cargo, Ypt7 stays behind, in agreement with its regulatory function. Recycled cargo then accumulates at endosomes and later at the Golgi, implying consecutive sorting steps to the final destination. Our data further suggest that retromer and Vps1 are essential to maintain vacuole membrane organization. All together, our data demonstrate that retromer can cooperate with Vps1 and the Rab Ypt7 to clear the vacuole of selected membrane proteins.

Transient domain formation in membrane-bound organelles undergoing maturation

The membrane components of cellular organelles have been shown to segregate into domains as the result of biochemical maturation. We propose that the dynamical competition between maturation and lateral segregation of membrane components regulates domain formation. We study a two-component fluid membrane in which enzymatic reaction irreversibly converts one component into another and phase separation triggers the formation of transient membrane domains. The maximum domain size is shown to depend on the maturation rate as a power law similar to the one observed for domain growth with time in the absence of maturation, despite this time dependence not being verified in the case of irreversible maturation. This control of domain size by enzymatic activity could play a critical role in regulating exchange between organelles or within compartmentalized organelles such as the Golgi apparatus.

Mesoscopic behavior from microscopic Markov dynamics and its application to calcium release channels

A major challenge in biology is to understand how molecular processes determine phenotypic features. We address this fundamental problem in a class of model systems by developing a general mathematical framework that allows the calculation of mesoscopic properties from the knowledge of microscopic Markovian transition probabilities. We show how exact analytic formulae for the first and second moments of resident time distributions in mesostates can be derived from microscopic resident times and transition probabilities even for systems with a large number of microstates. We apply our formalism to models of the inositol trisphosphate receptor, which plays a key role in generating calcium signals triggering a wide variety of cellular responses. We demonstrate how experimentally accessible quantities, such as opening and closing times and the coefficient of variation of inter-spike intervals, and other, more elaborated, quantities can be analytically calculated from the underlying microscopic Markovian dynamics. A virtue of our approach is that we do not need to follow the detailed time evolution of the whole system, as we derive the relevant properties of its steady state without having to take into account the often extremely complicated transient features. We emphasize that our formulae fully agree with results obtained by stochastic simulations and approaches based on a full determination of the microscopic system's time evolution. We also illustrate how experiments can be devised to discriminate between alternative molecular models of the inositol trisphosphate receptor. The developed approach is applicable to any system described by a Markov process and, owing to the analytic nature of the resulting formulae, provides an easy way to characterize also rare events that are of particular importance to understand the intermittency properties of complex dynamic systems.

A model for the self-organization of vesicular flux and protein distributions in the Golgi apparatus

The generation of two non-identical membrane compartments via exchange of vesicles is considered to require two types of vesicles specified by distinct cytosolic coats that selectively recruit cargo, and two membrane-bound SNARE pairs that specify fusion and differ in their affinities for each type of vesicles. The mammalian Golgi complex is composed of 6-8 non-identical cisternae that undergo gradual maturation and replacement yet features only two SNARE pairs. We present a model that explains how distinct composition of Golgi cisternae can be generated with two and even a single SNARE pair and one vesicle coat. A decay of active SNARE concentration in aging cisternae provides the seed for a cis[Formula: see text]trans SNARE gradient that generates the predominantly retrograde vesicle flux which further enhances the gradient. This flux in turn yields the observed inhomogeneous steady-state distribution of Golgi enzymes, which compete with each other and with the SNAREs for incorporation into transport vesicles. We show analytically that the steady state SNARE concentration decays exponentially with the cisterna number. Numerical solutions of rate equations reproduce the experimentally observed SNARE gradients, overlapping enzyme peaks in cis, medial and trans and the reported change in vesicle nature across the Golgi: Vesicles originating from younger cisternae mostly contain Golgi enzymes and SNAREs enriched in these cisternae and extensively recycle through the Endoplasmic Reticulum (ER), while the other subpopulation of vesicles contains Golgi proteins prevalent in older cisternae and hardly reaches the ER.

Transport logistics in pollen tubes

Cellular organelles move within the cellular volume and the effect of the resulting drag forces on the liquid causes bulk movement in the cytosol. The movement of both organelles and cytosol leads to an overall motion pattern called cytoplasmic streaming or cyclosis. This streaming enables the active and passive transport of molecules and organelles between cellular compartments. Furthermore, the fusion and budding of vesicles with and from the plasma membrane (exo/endocytosis) allow for transport of material between the inside and the outside of the cell. In the pollen tube, cytoplasmic streaming and exo/endocytosis are very active and fulfill several different functions. In this review, we focus on the logistics of intracellular motion and transport processes as well as their biophysical underpinnings. We discuss various modeling attempts that have been performed to understand both long-distance shuttling and short-distance targeting of organelles. We show how the combination of mechanical and mathematical modeling with cell biological approaches has contributed to our understanding of intracellular transport logistics.

(Re)modeling the Golgi

In this chapter, we summarize recent theoretical efforts to address a variety of issues in Golgi morphogenesis: de novo biogenesis of compartments with precise chemical identity, the transport of proteins through the Golgi, the maintenance of chemical identity, and the morphology of Golgi compartments, from the perspective of nonequilibrium physics.

Two-pool model of cooperative vesicular transport

We present a model of bidirectional vesicular transport between two intracellular organelles, which takes into account intermediate stages of transport that occur between vesicular budding from one organelle and subsequent fusion with the other organelle. These are incorporated into the model by associating with each organelle a donor pool of newly budded vesicles and an acceptor pool of transported vesicles ready for fusion. By constructing a system of differential equations that keeps track of the distribution of vesicles and protein concentrations within the various pools and along cytoskeletal tracks, we show how a stable steady state can emerge that consists of organelles that maintain different protein concentrations in spite of the continuous exchange of materials. In particular, exploiting the fact that the surface area of individual vesicles is much smaller than the surface area of organelles, we use an adiabatic approximation to eliminate the vesicular variables. This results in a major simplification of the dynamics and provides a systematic procedure for deriving phenomenological models of cooperative transport.

A hypothetical model of cargo-selective rab recruitment during organelle maturation

Rabs constitute a group of small GTPases that confer directionality to intracellular vesicle transport by promoting on the membrane of transport vesicles in the formation of specific protein complexes allowing for efficient fusion with a selected set of target organelles. The molecular mechanism controlling recruitment of the correct Rab at the right time is not fully understood. We propose a model according to which the residence time of a given Rab on the membrane of an organelle is determined by its transient trapping into a Rab effector complex (REC) composed of cargo receptor, SNAREs and further effectors. The stability of REC is controlled by the conformational state of the receptor which may change due to binding and release of cargo or changes in the luminal ion milieu. We use a conceptual mathematical model to calculate temporal changes in the Rab decoration of an organelle brought about by exchange with a cytosolic pool of Rabs or alternatively by budding and uptake of Rab-carrying vesicles. Considering the time-dependent drop in pH as one crucial factor for the conformational change of endocytic cargo receptors, our model provides a good quantitative description of the switch from Rab5 to Rab7 during the early-to-late endosome transition and correctly explains the arrest of this transition at insufficient luminal acidification. Model simulations suggest that a switch from one Rab to another may be continuous or abrupt. We discuss mechanisms, e.g. specific signalling pathways, which may restore an arrested organelle maturation.

The KDEL receptor couples to Gαq/11 to activate Src kinases and regulate transport through the Golgi

Membrane trafficking involves large fluxes of cargo and membrane across separate compartments. These fluxes must be regulated by control systems to maintain homoeostasis. While control systems for other key functions such as protein folding or the cell cycle are well known, the mechanisms that control secretory transport are poorly understood. We have previously described a signalling circuit operating at the Golgi complex that regulates intra-Golgi trafficking and is initiated by the KDEL receptor (KDEL-R), a protein previously known to mediate protein recycling from the Golgi to the endoplasmic reticulum (ER). Here, we investigated the KDEL-R signalling mechanism. We show that the KDEL-R is predicted to fold like a G-protein-coupled receptor (GPCR), and that it binds and activates the heterotrimeric signalling G-protein Gα(q/11) which, in turn, regulates transport through the Golgi complex. These findings reveal an unexpected GPCR-like mode of action of the KDEL-R and shed light on a core molecular control mechanism of intra-Golgi traffic.

Endocytosis and signaling: cell logistics shape the eukaryotic cell plan

Our understanding of endocytosis has evolved remarkably in little more than a decade. This is the result not only of advances in our knowledge of its molecular and biological workings, but also of a true paradigm shift in our understanding of what really constitutes endocytosis and of its role in homeostasis. Although endocytosis was initially discovered and studied as a relatively simple process to transport molecules across the plasma membrane, it was subsequently found to be inextricably linked with almost all aspects of cellular signaling. This led to the notion that endocytosis is actually the master organizer of cellular signaling, providing the cell with understandable messages that have been resolved in space and time. In essence, endocytosis provides the communications and supply routes (the logistics) of the cell. Although this may seem revolutionary, it is still likely to be only a small part of the entire story. A wealth of new evidence is uncovering the surprisingly pervasive nature of endocytosis in essentially all aspects of cellular regulation. In addition, many newly discovered functions of endocytic proteins are not immediately interpretable within the classical view of endocytosis. A possible framework, to rationalize all this new knowledge, requires us to "upgrade" our vision of endocytosis. By combining the analysis of biochemical, biological, and evolutionary evidence, we propose herein that endocytosis constitutes one of the major enabling conditions that in the history of life permitted the development of a higher level of organization, leading to the actuation of the eukaryotic cell plan.

Spatial modeling of vesicle transport and the cytoskeleton: the challenge of hitting the right road

The membrane trafficking machinery provides a transport and sorting system for many cellular proteins. We propose a mechanistic agent-based computer simulation to integrate and test the hypothesis of vesicle transport embedded into a detailed model cell. The method tracks both the number and location of the vesicles. Thus both the stochastic properties due to the low numbers and the spatial aspects are preserved. The underlying molecular interactions that control the vesicle actions are included in a multi-scale manner based on the model of Heinrich and Rapoport (2005). By adding motor proteins we can improve the recycling process of SNAREs and model cell polarization. Our model also predicts that coat molecules should have a high turnover at the compartment membranes, while the turnover of motor proteins has to be slow. The modular structure of the underlying model keeps it tractable despite the overall complexity of the vesicle system. We apply our model to receptor-mediated endocytosis and show how a polarized cytoskeleton structure leads to polarized distributions in the plasma membrane both of SNAREs and the Ste2p receptor in yeast. In addition, we can couple signal transduction and membrane trafficking steps in one simulation, which enables analyzing the effect of receptor-mediated endocytosis on signaling.

Trafficking motifs as the basis for two-compartment signaling systems to form multiple stable states

Transport of molecules in cells is a central part of cell biology. Frequently such trafficking is not just for material transport, but also for information propagation, and serves to couple signaling circuits across cellular compartments. Here, I show that trafficking transforms simple local signaling pathways into self-organizing systems that span compartments and confer distinct states and identities to these compartments. I find that three motifs encapsulate the responses of most single-compartment signaling pathways in the context of trafficking. These motifs combine with different trafficking reactions to generate a diverse set of cellular functions. For example, trafficked bistable switches can oscillate or become quad- or tristable, depending on trafficking mechanisms and rates. Furthermore, the analysis shows how compartments participating in traffic can settle to distinct molecular compositions characteristic of distinct organelle identities. This general framework shows how the interplay between molecular movement and local reactions can generate many system functions, and give distinct identities to different parts of the cell.

Mechanisms of protein retention in the Golgi

The protein composition of the Golgi is intimately linked to its structure and function. As the Golgi serves as the major protein-sorting hub for the secretory pathway, it faces the unique challenge of maintaining its protein composition in the face of constant influx and efflux of transient cargo proteins. Much of our understanding of how proteins are retained in the Golgi has come from studies on glycosylation enzymes, largely because of the compartment-specific distributions these proteins display. From these and other studies of Golgi membrane proteins, we now understand that a variety of retention mechanisms are employed, the majority of which involve the dynamic process of iterative rounds of retrograde and anterograde transport. Such mechanisms rely on protein conformation and amino acid-based sorting signals as well as on properties of transmembrane domains and their relationship with the unique lipid composition of the Golgi.

Cooperative protein transport in cellular organelles

Compartmentalization into biochemically distinct organelles constantly exchanging material is one of the hallmarks of eukaryotic cells. In the most naive picture of interorganelle transport driven by concentration gradients, concentration differences between organelles should relax. We determine the conditions under which cooperative transport, i.e., based on molecular recognition, allows for the existence and maintenance of distinct organelle identities. Cooperative transport is also shown to control the flux of material transiting through a compartmentalized system, dramatically increasing the transit time under high incoming flux. By including chemical processing of the transported species, we show that this property provides a strong functional advantage to a system responsible for protein maturation and sorting.

Conserved molecular mechanisms underlying homeostasis of the Golgi complex

The Golgi complex performs a central function in the secretory pathway in the sorting and sequential processing of a large number of proteins destined for other endomembrane organelles, the plasma membrane, or secretion from the cell, in addition to lipid metabolism and signaling. The Golgi apparatus can be regarded as a self-organizing system that maintains a relatively stable morphofunctional organization in the face of an enormous flux of lipids and proteins. A large number of the molecular players that operate in these processes have been identified, their functions and interactions defined, but there is still debate about many aspects that regulate protein trafficking and, in particular, the maintenance of these highly dynamic structures and processes. Here, we consider how an evolutionarily conserved underlying mechanism based on retrograde trafficking that uses lipids, COPI, SNAREs, and tethers could maintain such a homeodynamic system.

A modeling approach to the self-assembly of the Golgi apparatus

The dynamic compartmentalization of eukaryotic cells is a fascinating phenomenon that is not yet understood. A prominent example of this challenge is the Golgi apparatus, the central hub for protein sorting and lipid metabolism in the secretory pathway. Despite major advances in elucidating its molecular biology, the fundamental question of how the morphogenesis of this organelle is organized on a system level has remained elusive. Here, we have formulated a coarse-grained computational model that captures key features of the dynamic morphogenesis of a Golgi apparatus. In particular, our model relates the experimentally observed Golgi phenotypes, the typical turnover times, and the size and number of cisternae to three basic, experimentally accessible quantities: the rates for material influx from the endoplasmic reticulum, and the anterograde and retrograde transport rates. Based on these results, we propose which molecular factors should be mutated to alter the organelle's phenotype and dynamics.

A systems model of vesicle trafficking in Arabidopsis pollen tubes

A systems model that describes vesicle trafficking during pollen tube growth in Arabidopsis (Arabidopsis thaliana) was constructed. The model is composed of ordinary differential equations that connect the molecular functions of genes expressed in pollen. The current model requires soluble N-ethylmaleimide-sensitive fusion protein attachment protein receptors (SNAREs) and small GTPases, Arf or Rab, to reasonably predict tube growth as a function of time. Tube growth depends on vesicle trafficking that transports phospholipid and pectin to the tube tip. The vesicle trafficking genes identified by analyzing publicly available transcriptome data comprised 328 genes. Fourteen of them are up-regulated by the gibberellin signaling pathway during pollen development, which includes the SNARE genes SYP124 and SYP125 and the Rab GTPase gene RABA4D. The model results adequately fit the pollen tube growth of both previously reported wild-type and raba4d knockout lines. Furthermore, the difference of pollen tube growth in syp124/syp125 single and double mutations was quantitatively predicted based on the model analysis. In general, a systems model approach to vesicle trafficking arguably demonstrated the importance of the functional connections in pollen tube growth and can help guide future research directions.

Discrete, continuous, and stochastic models of protein sorting in the Golgi apparatus

The Golgi apparatus plays a central role in processing and sorting proteins and lipids in eukaryotic cells. Golgi compartments constantly exchange material with each other and with other cellular components, allowing them to maintain and reform distinct identities despite dramatic changes in structure and size during cell division, development, and osmotic stress. We have developed three minimal models of membrane and protein exchange in the Golgi-a discrete, stochastic model, a continuous ordinary differential equation model, and a continuous stochastic differential equation model-each based on two fundamental mechanisms: vesicle-coat-mediated selective concentration of cargoes and soluble N-ethylmaleimide-sensitive factor attachment protein receptor (SNARE) proteins during vesicle formation and SNARE-mediated selective fusion of vesicles. By exploring where the models differ, we hope to discover whether the discrete, stochastic nature of vesicle-mediated transport is likely to have appreciable functional consequences for the Golgi. All three models show similar ability to restore and maintain distinct identities over broad parameter ranges. They diverge, however, in conditions corresponding to collapse and reassembly of the Golgi. The results suggest that a continuum model provides a good description of Golgi maintenance but that considering the discrete nature of vesicle-based traffic is important to understanding assembly and disassembly of the Golgi. Experimental analysis validates a prediction of the models that altering guanine nucleotide exchange factor expression levels will modulate Golgi size.

A conceptual mathematical model of the dynamic self-organisation of distinct cellular organelles

Formation, degradation and renewal of cellular organelles is a dynamic process based on permanent budding, fusion and inter-organelle traffic of vesicles. These processes include many regulatory proteins such as SNAREs, Rabs and coats. Given this complex machinery, a controversially debated issue is the definition of a minimal set of generic mechanisms necessary to enable the self-organization of organelles differing in number, size and chemical composition. We present a conceptual mathematical model of dynamic organelle formation based on interacting vesicles which carry different types of fusogenic proteins (FP) playing the role of characteristic marker proteins. Our simulations (ODEs) show that a de novo formation of non-identical organelles, each accumulating a different type of FP, requires a certain degree of disproportionation of FPs during budding. More importantly however, the fusion kinetics must indispensably exhibit positive cooperativity among these FPs, particularly for the formation of larger organelles. We compared different types of cooperativity: sequential alignment of corresponding FPs on opposite vesicle/organelles during fusion and pre-formation of FP-aggregates (equivalent, e.g., to SNARE clusters) prior to fusion described by Hill kinetics. This showed that the average organelle size in the system is much more sensitive to the disproportionation strength of FPs during budding if the vesicular transport system gets along with a fusion mechanism based on sequential alignments of FPs. Therefore, pre-formation of FP aggregates within the membranes prior to fusion introduce robustness with respect to organelle size. Our findings provide a plausible explanation for the evolution of a relatively large number of molecules to confer specificity on the fusion machinery compared to the relatively small number involved in the budding process. Moreover, we could speculate that a specific cooperativity which may be described by Hill kinetics (aggregates or Rab/SNARE complex formation) is suitable if maturation/identity switching of organelles play a role (bistability).

Predation and eukaryote cell origins: a coevolutionary perspective

Cells are of only two kinds: bacteria, with DNA segregated by surface membrane motors, dating back approximately 3.5Gy; and eukaryotes, which evolved from bacteria, possibly as recently as 800-850My ago. The last common ancestor of eukaryotes was a sexual phagotrophic protozoan with mitochondria, one or two centrioles and cilia. Conversion of bacteria (=prokaryotes) into a eukaryote involved approximately 60 major innovations. Numerous contradictory ideas about eukaryogenesis fail to explain fundamental features of eukaryotic cell biology or conflict with phylogeny. Data are best explained by the intracellular coevolutionary theory, with three basic tenets: (1) the eukaryotic cytoskeleton and endomembrane system originated through cooperatively enabling the evolution of phagotrophy; (2) phagocytosis internalised DNA-membrane attachments, unavoidably disrupting bacterial division; recovery entailed the evolution of the nucleus and mitotic cycle; (3) the symbiogenetic origin of mitochondria immediately followed the perfection of phagotrophy and intracellular digestion, contributing greater energy efficiency and group II introns as precursors of spliceosomal introns. Eukaryotes plus their archaebacterial sisters form the clade neomura, which evolved from a radically modified derivative of an actinobacterial posibacterium that had replaced the ancestral eubacterial murein peptidoglycan by N-linked glycoproteins, radically modified its DNA-handling enzymes, and evolved cotranslational protein secretion, but not the isoprenoid-ether lipids of archaebacteria. I focus on this phylogenetic background and on explaining how in response to novel phagotrophic selective pressures and ensuing genome internalisation this prekaryote evolved efficient digestion of prey proteins by retrotranslocation and 26S proteasomes, then internal digestion by phagocytosis, lysosomes, and peroxisomes, and eukaryotic vesicle trafficking and intracellular compartmentation.

A traffic-activated Golgi-based signalling circuit coordinates the secretory pathway

As with other complex cellular functions, intracellular membrane transport involves the coordinated engagement of a series of organelles and machineries; however, the molecular basis of this coordination is unknown. Here we describe a Golgi-based signalling system that is activated by traffic and is involved in monitoring and balancing trafficking rates into and out of the Golgi complex. We provide evidence that the traffic signal is due to protein chaperones that leave the endoplasmic reticulum and reach the Golgi complex where they bind to the KDEL receptor. This initiates a signalling reaction that includes the activation of a Golgi pool of Src kinases and a phosphorylation cascade that in turn activates intra-Golgi trafficking, thereby maintaining the dynamic equilibrium of the Golgi complex. The concepts emerging from this study should help to understand the control circuits that coordinate high-order cellular functions.

Membrane identity and GTPase cascades regulated by toggle and cut-out switches

Key cellular functions and developmental processes rely on cascades of GTPases. GTPases of the Rab family provide a molecular ID code to the generation, maintenance and transport of intracellular compartments. Here, we addressed the molecular design principles of endocytosis by focusing on the conversion of early endosomes into late endosomes, which entails replacement of Rab5 by Rab7. We modelled this process as a cascade of functional modules of interacting Rab GTPases. We demonstrate that intermodule interactions share similarities with the toggle switch described for the cell cycle. However, Rab5-to-Rab7 conversion is rather based on a newly characterized ‘cut-out switch' analogous to an electrical safety-breaker. Both designs require cooperativity of auto-activation loops when coupled to a large pool of cytoplasmic proteins. Live cell imaging and endosome tracking provide experimental support to the cut-out switch in cargo progression and conversion of endosome identity along the degradative pathway. We propose that, by reconciling module performance with progression of activity, the cut-out switch design could underlie the integration of modules in regulatory cascades from a broad range of biological processes.

Simulated de novo assembly of golgi compartments by selective cargo capture during vesicle budding and targeted vesicle fusion

The Golgi apparatus is comprised of stacked cisternal membranes forming subcompartments specialized for posttranslational processing of newly synthesized secretory cargo. Recent experimental evidence indicates that the Golgi apparatus can undergo de novo biogenesis from the endoplasmic reticulum, but the mechanism by which the membranes self assemble into compartmentalized structures remains unknown. We developed a discrete-event computer simulation model to test whether two fundamental mechanisms-vesicle-coat-mediated selective concentration of soluble N-ethylmaleimide-sensitive factor attachment protein receptor (SNARE) proteins during vesicle formation, and SNARE-mediated selective fusion of vesicles-suffice to generate and maintain compartments. Simulations verified that this minimal model is adequate for homeostasis of preestablished compartments, even in response to small perturbations, and for de novo formation of stable compartments. The model led to a novel prediction that Golgi size is in part dependent on target SNARE expression level. This prediction was supported by a demonstration that exogenous expression of the Golgi target SNARE syntaxin-5 alters Golgi size in living cells.

Building functional modules from molecular interactions

The main reaction pathways in the living cell are carried out by functional modules--namely, macromolecular machines with compact structure or ensembles that change their composition and/or organization during function. Modules define themselves by spatial sequestration, chemical specificity and a characteristic time domain within which their function proceeds. On receiving a specific input, modules go through functional cycles, with phases of increasing and decreasing complexity of molecular interactions. Here, we discuss how such modules are formed and the experimental and theoretical approaches that can be used to investigate them, using examples from polynucleotide-protein interactions, vesicle transport and signal transduction to illustrate the underlying principles. Further progress in this field, where systems biology and biochemistry meet, will depend on iterative validation of the experimental and theoretical approaches.

The physiology of membrane transport and endomembrane-based signalling

Some of the important open questions concerning the physiology of the secretory pathway relate to its homeostasis. Secretion involves a number of separate compartments for which their transport activities should be precisely cross-coordinated to avoid gross imbalances in the trafficking system. Moreover, the membrane fluxes across these compartments should be able to adapt to environmental 'requests' and to respond to extracellular signals. How is this regulation effected? Here, we consider evidence that endomembrane-based signalling cascades that are similar in organization to those used at the plasma membrane coordinate membrane traffic. If this is the case, this would also represent a model for a more general inter-organelle signalling network for functionally interconnecting different intracellular activities, a necessity for the maintenance of cellular homeostasis and to express harmonic global cellular responses.

Functions of SNAREs in intracellular membrane fusion and lipid bilayer mixing

Intracellular membrane fusion occurs with exquisite coordination and specificity. Each fusion event requires three basic components: Rab-GTPases organize the fusion site; SNARE proteins act during fusion; and N-ethylmaleimide-sensitive factor (NSF) plus its cofactor alpha-SNAP are required for recycling or activation of the fusion machinery. Whereas Rab-GTPases seem to mediate the initial membrane contact, SNAREs appear to lie at the center of the fusion process. It is known that formation of complexes between SNAREs from apposed membranes is a prerequisite for lipid bilayer mixing; however, the biophysics and many details of SNARE function are still vague. Nevertheless, recent observations are shedding light on the role of SNAREs in membrane fusion. Structural studies are revealing the mechanisms by which SNARES form complexes and interact with other proteins. Furthermore, it is now apparent that the SNARE transmembrane segment not only anchors the protein but engages in SNARE-SNARE interactions and plays an active role in fusion. Recent work indicates that the fusion process itself may comprise two stages and proceed via a hemifusion intermediate.

Subcompartmentalizing the Golgi apparatus

The subcompartmentalized structure of the Golgi apparatus contributes to efficient glycosylation in the secretory pathway. Subcompartmentalization driven by maturation relies primarily on constant and accurate vesicle-mediated local recycling of Golgi residents. The precision of this vesicle transport is dependent on the interplay between the key factors that mediate vesicle budding and fusion--the coat proteins and the SNARE fusion machinery. These alone, however, may not be sufficient to ensure establishment of compartments de novo, and additional regulatory mechanisms operate to modify their activity.