Accounting for diffusion in agent based models of reaction-diffusion systems with application to cytoskeletal diffusion

Septin organization is regulated by the Gpa1 Ubiquitination Domain and Endocytic Machinery during the yeast pheromone response

The septin cytoskeleton plays a key role in the morphogenesis of the yeast mating projection, forming structures at the base of the projection. The yeast mating response uses the G-protein coupled receptor (GPCR), Ste2, to detect mating pheromone and initiate mating projection morphogenesis. Desensitization of the Gα, Gpa1, by the Regulator of G-protein Signaling (RGS), Sst2, is required for proper septin organization and morphogenesis. We hypothesized that Gpa1 would utilize known septin regulators to control septin organization. We found that single deletions of the septin chaperone Gic1, the Cdc42 GAP Bem3, and the endocytic adaptor proteins Ent1 and Ent2 rescued the polar cap accumulation of septins in the hyperactive Gα. We hypothesized that hyperactive Gα might increase the rate of endocytosis of a pheromone-responsive cargo, thereby altering where septins are localized. Mathematical modeling predicted that changes in endocytosis could explain the septin organizations we find in WT and mutant cells. Our results show that Gpa1-induced disorganization of septins requires clathrin-mediated endocytosis. Both the GPCR and the Gα are known to be internalized by clathrin-mediated endocytosis during the pheromone response. Deletion of the GPCR C-terminus to block internalization partially rescued septin organization. However, deleting the Gpa1 ubiquitination domain required for its endocytosis completely abrogated septin accumulation at the polarity site. Our data support a model where the location of endocytosis serves as a spatial mark for septin structure assembly and that desensitization of the Gα delays its endocytosis sufficiently that septins are placed peripheral to the site of Cdc42 polarity.

The Effect of Environment on the Evolution and Proliferation of Protocells of Increasing Complexity

The formation, growth, division and proliferation of protocells containing RNA strands is an important step in ensuring the viability of a mixed RNA-lipid world. Experiments and computer simulations indicate that RNA encapsulated inside protocells can favor the protocell, promoting its growth while protecting the system from being over-run by selfish RNA sequences. Recent work has also shown that the rolling-circle replication mechanism can be harnessed to ensure the rapid growth of RNA strands and the probabilistic emergence and proliferation of protocells with functionally diverse ribozymes. Despite these advances in our understanding of a primordial RNA-lipid world, key questions remain about the ideal environment for the formation of protocells and its role in regulating the proliferation of functionally complex protocells. The hot spring hypothesis suggests that mineral-rich regions near hot springs, subject to dry-wet cycles, provide an ideal environment for the origin of primitive protocells. We develop a computational model to study protocellular evolution in such environments that are distinguished by the occurrence of three distinct phases, a wet phase, followed by a gel phase, and subsequently by a dry phase. We determine the conditions under which protocells containing multiple types of ribozymes can evolve and proliferate in such regions. We find that diffusion in the gel phase can inhibit the proliferation of complex protocells with the extent of inhibition being most significant when a small fraction of protocells is eliminated during environmental cycling. Our work clarifies how the environment can shape the evolution and proliferation of complex protocells.

Characterizing Binding Interactions That Are Essential for Selective Transport through the Nuclear Pore Complex

Specific macromolecules are rapidly transported across the nuclear envelope via the nuclear pore complex (NPC). The selective transport process is facilitated when nuclear transport receptors (NTRs) weakly and transiently bind to intrinsically disordered constituents of the NPC, FG Nups. These two types of proteins help maintain the selective NPC barrier. To interrogate their binding interactions in vitro, we deployed an NPC barrier mimic. We created the stationary phase by covalently attaching fragments of a yeast FG Nup called Nsp1 to glass coverslips. We used a tunable mobile phase containing NTR, nuclear transport factor 2 (NTF2). In the stationary phase, three main factors affected binding: the number of FG repeats, the charge of fragments, and the fragment density. We also identified three main factors affecting binding in the mobile phase: the avidity of the NTF2 variant for Nsp1, the presence of nonspecific proteins, and the presence of additional NTRs. We used both experimentally determined binding parameters and molecular dynamics simulations of Nsp1FG fragments to create an agent-based model. The results suggest that NTF2 binding is negatively cooperative and dependent on the density of Nsp1FG molecules. Our results demonstrate the strengths of combining experimental and physical modeling approaches to study NPC-mediated transport.

An overview of diffusion models for intracellular dynamics analysis

We present an overview of diffusion models commonly used for quantifying the dynamics of intracellular particles (e.g. biomolecules) inside eukaryotic living cells. It is established that inference on the modes of mobility of molecules is central in cell biology since it reflects interactions between structures and determines functions of biomolecules in the cell. In that context, Brownian motion is a key component in short distance transportation (e.g. connectivity for signal transduction). Another dynamical process that has been heavily studied in the past decade is the motor-mediated transport (e.g. dynein, kinesin and myosin) of molecules. Primarily supported by actin filament and microtubule network, it ensures spatial organization and temporal synchronization in the intracellular mechanisms and structures. Nevertheless, the complexity of internal structures and molecular processes in the living cell influence the molecular dynamics and prevent the systematic application of pure Brownian or directed motion modeling. On the one hand, cytoskeleton density will hinder the free displacement of the particle, a phenomenon called subdiffusion. On the other hand, the cytoskeleton elasticity combined with thermal bending can contribute a phenomenon called superdiffusion. This paper discusses the basics of diffusion modes observed in eukariotic cells, by introducing the essential properties of these processes. Applications of diffusion models include protein trafficking and transport and membrane diffusion.

Hydrodynamic interactions significantly alter the dynamics of actin networks and result in a length scale dependent loss modulus

Actin, the primary component of the cytoskeleton, is the most studied semiflexible filament. Yet, the dynamics of actin filamentous network is still a subject of debate. Here we show that hydrodynamic interactions may significantly alter the time scale of actin network deformation. The alteration may be easily in the range of 2-20 fold depending on the structural conformations and scales of interest. We show that for a single fiber, hydrodynamic interactions between the cytoskeletal mesh-sized segments can change the net force by up to 7 folds. We also demonstrate that cytoskeletal relaxation times are underestimated if hydrodynamic interaction effects are ignored, but bending mode shapes are not appreciably influenced. Ignoring hydrodynamic interactions can result in up to 20-fold overestimation of shear loss modulus in the 2 μm range we investigated. Moreover, in agreement with experimental studies, our models explain a highly length scale dependent loss modulus. Taken together, our data suggest that including hydrodynamic interactions is key to proper modeling and analysis of actin dynamics at any scales and dimensions, and therefore must not be neglected in future models and experimental analyses of cytoskeletal dynamics.

Quality control of mRNAs at the entry of the nuclear pore: Cooperation in a complex molecular system

Despite extensive research on how mRNAs are quality controlled prior to export into the cytoplasm, the exact underlying mechanisms are still under debate. Specifically, it is unclear how quality control proteins at the entry of the nuclear pore complex (NPC) distinguish normal and aberrant mRNAs. While some of the involved components are suggested to act as switches and recruit different factors to normal versus aberrant mRNAs, some experimental and computational evidence suggests that the combined effect of the regulated stochastic interactions between the involved components could potentially achieve an efficient quality control of mRNAs. In this review, we present a state-of-the-art portrait of the mRNA quality control research and discuss the current hypotheses proposed for dynamics of the cooperation between the involved components and how it leads to their shared goal: mRNA quality control prior to export into the cytoplasm.

Agent-Based Modeling in Molecular Systems Biology

Molecular systems orchestrating the biology of the cell typically involve a complex web of interactions among various components and span a vast range of spatial and temporal scales. Computational methods have advanced our understanding of the behavior of molecular systems by enabling us to test assumptions and hypotheses, explore the effect of different parameters on the outcome, and eventually guide experiments. While several different mathematical and computational methods are developed to study molecular systems at different spatiotemporal scales, there is still a need for methods that bridge the gap between spatially-detailed and computationally-efficient approaches. In this review, we summarize the capabilities of agent-based modeling (ABM) as an emerging molecular systems biology technique that provides researchers with a new tool in exploring the dynamics of molecular systems/pathways in health and disease.

Molecular simulations of cellular processes

It is, nowadays, possible to simulate biological processes in conditions that mimic the different cellular compartments. Several groups have performed these calculations using molecular models that vary in performance and accuracy. In many cases, the atomistic degrees of freedom have been eliminated, sacrificing both structural complexity and chemical specificity to be able to explore slow processes. In this review, we will discuss the insights gained from computer simulations on macromolecule diffusion, nuclear body formation, and processes involving the genetic material inside cell-mimicking spaces. We will also discuss the challenges to generate new models suitable for the simulations of biological processes on a cell scale and for cell-cycle-long times, including non-equilibrium events such as the co-translational folding, misfolding, and aggregation of proteins. A prominent role will be played by the wise choice of the structural simplifications and, simultaneously, of a relatively complex energetic description. These challenging tasks will rely on the integration of experimental and computational methods, achieved through the application of efficient algorithms. Graphical abstract.

Looking "Under the Hood" of Cellular Mechanotransduction with Computational Tools: A Systems Biomechanics Approach across Multiple Scales

Signal modulation has been developed in living cells throughout evolution to promote utilizing the same machinery for multiple cellular functions. Chemical and mechanical modules of signal transmission and transduction are interconnected and necessary for organ development and growth. However, due to the high complexity of the intercommunication of physical intracellular connections with biochemical pathways, there are many missing details in our overall understanding of mechanotransduction processes, i.e., the process by which mechanical signals are converted to biochemical cascades. Cell-matrix adhesions are mechanically coupled to the nucleus through the cytoskeleton. This modulated and tightly integrated network mediates the transmission of mechanochemical signals from the extracellular matrix to the nucleus. Various experimental and computational techniques have been utilized to understand the basic mechanisms of mechanotransduction, yet many aspects have remained elusive. Recently, in silico experiments have made important contributions to the field of mechanobiology. Herein, computational modeling efforts devoted to understanding integrin-mediated mechanotransduction pathways are reviewed, and an outlook is presented for future directions toward using suitable computational approaches and developing novel techniques for addressing important questions in the field of mechanotransduction.

Regulation of RNA-binding proteins affinity to export receptors enables the nuclear basket proteins to distinguish and retain aberrant mRNAs

Export of messenger ribonucleic acids (mRNAs) into the cytoplasm is a fundamental step in gene regulation processes, which is meticulously quality controlled by highly efficient mechanisms in eukaryotic cells. Yet, it remains unclear how the aberrant mRNAs are recognized and retained inside the nucleus. Using a new modelling approach for complex systems, namely the agent-based modelling (ABM) approach, we develop a minimal model of the mRNA quality control (QC) mechanism. Our results demonstrate that regulation of the affinity of RNA-binding proteins (RBPs) to export receptors along with the weak interaction between the nuclear basket protein (Mlp1 or Tpr) and RBPs are the minimum requirements to distinguish and retain aberrant mRNAs. Our results show that the affinity between Tpr and RBPs is optimized to maximize the retention of aberrant mRNAs. In addition, we demonstrate how the length of mRNA affects the QC process. Since longer mRNAs spend more time in the nuclear basket to form a compact conformation and initiate their export, nuclear basket proteins could more easily capture and retain them inside the nucleus.

Single-Cell Migration in Complex Microenvironments: Mechanics and Signaling Dynamics

Cells are highly dynamic and mechanical automata powered by molecular motors that respond to external cues. Intracellular signaling pathways, either chemical or mechanical, can be activated and spatially coordinated to induce polarized cell states and directional migration. Physiologically, cells navigate through complex microenvironments, typically in three-dimensional (3D) fibrillar networks. In diseases, such as metastatic cancer, they invade across physiological barriers and remodel their local environments through force, matrix degradation, synthesis, and reorganization. Important external factors such as dimensionality, confinement, topographical cues, stiffness, and flow impact the behavior of migrating cells and can each regulate motility. Here, we review recent progress in our understanding of single-cell migration in complex microenvironments.

The talin dimer structure orientation is mechanically regulated

Formation of a stable cell-substrate contact can be regulated by mechanical force, especially at the focal adhesion. Individual proteins that make up the focal adhesions, such as talin, can exhibit mechanosensing. We previously described one mode of talin mechanosensing in which the vinculin-binding site of talin is exposed after force-induced stretch of a single talin rod domain. Here, we describe a second mode of talin mechanosensing in which the talin dimer itself can adopt different orientations in response to mechanical stimulation. Using molecular dynamics models, we demonstrate that the C-terminus region of the talin dimer is flexible mainly at the linker between the dimerization helices and the nearby actin-binding helical bundle. Our molecular dynamics simulations reveal two possible orientations of the talin dimer at its C-terminus. The extracellular matrix (ECM)-bound integrins cross-linked by talin can be forced apart leading to an elongated orientation of the talin dimer, and the ECM-bound integrins can be forced together by the ECM producing a collapsed orientation of the talin dimer. Formation of the elongated orientation is shown to be more favorable. Switching between the two talin dimer orientations constitutes a mode of mechanosensing.

β-PIX controls intracellular viscoelasticity to regulate lung cancer cell migration

Cancer metastasis occurs via a progress involving abnormal cell migration. Cell migration, a dynamic physical process, is controlled by the cytoskeletal system, which includes the dynamics of actin organization and cellular adhesive organelles, focal adhesions (FAs). However, it is not known whether the organization of actin cytoskeletal system has a regulatory role in the physiologically relevant aspects of cancer metastasis. In the present studies, it was found that lung adenocarcinoma cells isolated from the secondary lung cancer of the lymph nodes, H1299 cells, show specific dynamics in terms of the actin cytoskeleton and FAs. This results in a higher level of mobility and this is regulated by an immature FA component, β-PIX (PAK-interacting exchange factor-β). In H1299 cells, β-PIX's activity was found not to be down-regulated by sequestration onto stress fibres, as the cells did not bundle actin filaments into stress fibres. Thus, β-PIX mainly remained localized at FAs, which allowed maturation of nascent adhesions into focal complexes; this resulted in actin polymerization, increased actin network integrity, changes in the intracellular microrheology at the peripheral of the cell, and cell polarity, which in turn regulated cell migration. Perturbation of β-PIX caused an inhibition of cell migration, including migration velocity, accumulated distance and directional persistence. Our results demonstrate the importance of β-PIX to the regulation of high mobility of lung adenocarcinoma cell line H1299 and that this occurs via regulation of FA dynamics, changes in actin cytoskeleton organization and cell polarity.

An agent-based model for mRNA export through the nuclear pore complex

On the basis of previously published biophysical and biochemical parameters of mRNA export, a three-dimensional, coarse-grained, agent-based model is developed for the study and characterization of mRNA nucleocytoplasmic export.

mRNA export from the nucleus is an essential step in the expression of every protein- coding gene in eukaryotes, but many aspects of this process remain poorly understood. The density of export receptors that must bind an mRNA to ensure export, as well as how receptor distribution affects transport dynamics, is not known. It is also unclear whether the rate-limiting step for transport occurs at the nuclear basket, in the central channel, or on the cytoplasmic face of the nuclear pore complex. Using previously published biophysical and biochemical parameters of mRNA export, we implemented a three-dimensional, coarse-grained, agent-based model of mRNA export in the nanosecond regime to gain insight into these issues. On running the model, we observed that mRNA export is sensitive to the number and distribution of transport receptors coating the mRNA and that there is a rate-limiting step in the nuclear basket that is potentially associated with the mRNA reconfiguring itself to thread into the central channel. Of note, our results also suggest that using a single location-monitoring mRNA label may be insufficient to correctly capture the time regime of mRNA threading through the pore and subsequent transport. This has implications for future experimental design to study mRNA transport dynamics.

Higher nucleoporin-Importinβ affinity at the nuclear basket increases nucleocytoplasmic import

Several in vitro studies have shown the presence of an affinity gradient in nuclear pore complex proteins for the import receptor Importinβ, at least partially contributing to nucleocytoplasmic transport, while others have historically argued against the presence of such a gradient. Nonetheless, the existence of an affinity gradient has remained an uncharacterized contributing factor. To shed light on the affinity gradient theory and better characterize how the existence of such an affinity gradient between the nuclear pore and the import receptor may influence the nucleocytoplasmic traffic, we have developed a general-purpose agent based modeling (ABM) framework that features a new method for relating rate constants to molecular binding and unbinding probabilities, and used our ABM approach to quantify the effects of a wide range of forward and reverse nucleoporin-Importinβ affinity gradients. Our results indicate that transport through the nuclear pore complex is maximized with an effective macroscopic affinity gradient of 2000 µM, 200 µM and 10 µM in the cytoplasmic, central channel and nuclear basket respectively. The transport rate at this gradient is approximately 10% higher than the transport rate for a comparable pore lacking any affinity gradient, which has a peak transport rate when all nucleoporins have an affinity of 200 µM for Importinβ. Furthermore, this optimal ratio of affinity gradients is representative of the ratio of affinities reported for the yeast nuclear pore complex – suggesting that the affinity gradient seen in vitro is highly optimized.

Spatial pattern dynamics of 3D stem cell loss of pluripotency via rules-based computational modeling

Pluripotent embryonic stem cells (ESCs) have the unique ability to differentiate into cells from all germ lineages, making them a potentially robust cell source for regenerative medicine therapies, but difficulties in predicting and controlling ESC differentiation currently limit the development of therapies and applications from such cells. A common approach to induce the differentiation of ESCs in vitro is via the formation of multicellular aggregates known as embryoid bodies (EBs), yet cell fate specification within EBs is generally considered an ill-defined and poorly controlled process. Thus, the objective of this study was to use rules-based cellular modeling to provide insight into which processes influence initial cell fate transitions in 3-dimensional microenvironments. Mouse embryonic stem cells (D3 cell line) were differentiated to examine the temporal and spatial patterns associated with loss of pluripotency as measured through Oct4 expression. Global properties of the multicellular aggregates were accurately recapitulated by a physics-based aggregation simulation when compared to experimentally measured physical parameters of EBs. Oct4 expression patterns were analyzed by confocal microscopy over time and compared to simulated trajectories of EB patterns. The simulations demonstrated that loss of Oct4 can be modeled as a binary process, and that associated patterns can be explained by a set of simple rules that combine baseline stochasticity with intercellular communication. Competing influences between Oct4+ and Oct4- neighbors result in the observed patterns of pluripotency loss within EBs, establishing the utility of rules-based modeling for hypothesis generation of underlying ESC differentiation processes. Importantly, the results indicate that the rules dominate the emergence of patterns independent of EB structure, size, or cell division. In combination with strategies to engineer cellular microenvironments, this type of modeling approach is a powerful tool to predict stem cell behavior under a number of culture conditions that emulate characteristics of 3D stem cell niches.

Emergence of the mitochondrial reticulum from fission and fusion dynamics

Mitochondria form a dynamic tubular reticulum within eukaryotic cells. Currently, quantitative understanding of its morphological characteristics is largely absent, despite major progress in deciphering the molecular fission and fusion machineries shaping its structure. Here we address the principles of formation and the large-scale organization of the cell-wide network of mitochondria. On the basis of experimentally determined structural features we establish the tip-to-tip and tip-to-side fission and fusion events as dominant reactions in the motility of this organelle. Subsequently, we introduce a graph-based model of the chondriome able to encompass its inherent variability in a single framework. Using both mean-field deterministic and explicit stochastic mathematical methods we establish a relationship between the chondriome structural network characteristics and underlying kinetic rate parameters. The computational analysis indicates that mitochondrial networks exhibit a percolation threshold. Intrinsic morphological instability of the mitochondrial reticulum resulting from its vicinity to the percolation transition is proposed as a novel mechanism that can be utilized by cells for optimizing their functional competence via dynamic remodeling of the chondriome. The detailed size distribution of the network components predicted by the dynamic graph representation introduces a relationship between chondriome characteristics and cell function. It forms a basis for understanding the architecture of mitochondria as a cell-wide but inhomogeneous organelle. Analysis of the reticulum adaptive configuration offers a direct clarification for its impact on numerous physiological processes strongly dependent on mitochondrial dynamics and organization, such as efficiency of cellular metabolism, tissue differentiation and aging.

Yeast mitochondrial interactosome model: metabolon membrane proteins complex involved in the channeling of ADP/ATP

The existence of a mitochondrial interactosome (MI) has been currently well established in mammalian cells but the exact composition of this super-complex is not precisely known, and its organization seems to be different from that in yeast. One major difference is the absence of mitochondrial creatine kinase (MtCK) in yeast, unlike that described in the organization model of MI, especially in cardiac, skeletal muscle and brain cells. The aim of this review is to provide a detailed description of different partner proteins involved in the synergistic ADP/ATP transport across the mitochondrial membranes in the yeast Saccharomyces cerevisiae and to propose a new mitochondrial interactosome model. The ADP/ATP (Aacp) and inorganic phosphate (PiC) carriers as well as the VDAC (or mitochondrial porin) catalyze the import and export of ADP, ATP and Pi across the mitochondrial membranes. Aacp and PiC, which appear to be associated with the ATP synthase, consist of two nanomotors (F₀, F₁) under specific conditions and form ATP synthasome. Identification and characterization of such a complex were described for the first time by Pedersen and co-workers in 2003.