Spatially distributed cell signalling

Cellular diffusion processes in singularly perturbed domains

There are many processes in cell biology that can be modeled in terms of particles diffusing in a two-dimensional (2D) or three-dimensional (3D) bounded domain Ω ⊂ R d containing a set of small subdomains or interior compartments U j , j = 1 , … , N (singularly-perturbed diffusion problems). The domain Ω could represent the cell membrane, the cell cytoplasm, the cell nucleus or the extracellular volume, while an individual compartment could represent a synapse, a membrane protein cluster, a biological condensate, or a quorum sensing bacterial cell. In this review we use a combination of matched asymptotic analysis and Green's function methods to solve a general type of singular boundary value problems (BVP) in 2D and 3D, in which an inhomogeneous Robin condition is imposed on each interior boundary ∂ U j . This allows us to incorporate a variety of previous studies of singularly perturbed diffusion problems into a single mathematical modeling framework. We mainly focus on steady-state solutions and the approach to steady-state, but also highlight some of the current challenges in dealing with time-dependent solutions and randomly switching processes.

Revolutionizing non-melanoma skin cancer treatment: Receptor tyrosine kinase inhibitors take the stage

BACKGROUND

Innovative treatments for non-melanoma skin cancers (NMSCs) are required to enhance patient outcomes.

AIMS

This review examines the effectiveness and safety of receptor tyrosine kinase inhibitors (RTKIs).

METHODS

A comprehensive review was conducted on the treatment potential of several RTKIs, namely cetuximab, erlotinib, gefitinib, panitumumab, and lapatinib.

RESULTS

The findings indicate that these targeted therapies hold great promise for the treatment of NMSCs. However, it is crucial to consider relapse rates and possible adverse effects. Further research is needed to improve treatment strategies, identify patient groups that would benefit the most, and assess the long-term efficacy and safety, despite the favorable results reported in previous studies. Furthermore, it is crucial to investigate the potential benefits of integrating RTKIs with immunotherapy and other treatment modalities to enhance the overall efficacy of therapy for individuals with NMSC.

CONCLUSIONS

Targeted therapies for NMSCs may be possible with the use of RTKIs. The majority of studies focused on utilizing epidermal growth factor receptor inhibitors as the primary class of RTKIs for the treatment of NMSC. Other RTKIs were only employed in experimental investigations. Research indicates that RTKIs could potentially serve as a suitable alternative for elderly patients who are unable to undergo chemotherapy and radiotherapy.

Increased intracellular diffusivity of macromolecules within a mammalian cell by low-intensity pulsed ultrasound

Whilst a number of studies have demonstrated that low-intensity pulsed ultrasound (LIPUS) is a promising therapeutic ultrasound technique that can be used for delivering mild mechanical stimuli to target tissue non-invasively, the underlying biophysical mechanisms still remain unclear. Most mechanism studies have focused explicitly on the effects of LIPUS on the cell membrane and mechanosensitive receptors. In the present study, we propose an additional mechanism by which LIPUS propagation through living cells may directly impact intracellular dynamics, particularly the diffusion transport of biomolecules. To support our hypothesis, human epithelial-like cells (SaOS-2 and HeLa) seeded on a confocal dish placed on a microscope stage were exposed to LIPUS with various exposure conditions (ultrasound frequencies of 0.5, 1 and 3 MHz, peak acoustic pressure of 200 and 400 kPa, a pulse repetition frequency of 1 kHz and a 20 % duty cycle), and the diffusivities of various sizes of biomolecules in the cytoplasm area were measured using fluorescence recovery after photobleaching (FRAP). Furthermore, giant unilamellar vesicles (GUVs) filled with macromolecules were used to examine the physical causal relationship between LIPUS and molecular diffusion changes. Nucleocytoplasmic transport coefficients were also measured by modified FRAP that bleaches the whole cell nuclear region. Extracellular signal-regulated kinases (ERK) activity (the phosphorylation dynamics) was monitored using fluorescence resonance energy transfer (FRET) microscopy. All the measurements were taken during, before and after the LIPUS exposure. Our experimental results clearly showed that the diffusion coefficients of macromolecules within the cell increased with acoustic pressure by 12.1 to 33.5 % during the sonication, and the increments were proportional to their molecular sizes regardless of the ultrasound frequency used. This observation in living cells was consistent with the GUVs exposed to the LIPUS, which indicated that the diffusivity increase was a passive physical response to the acoustic energy of LIPUS. Under the 1 MHz LIPUS exposure with 400 kPa, the passive nucleocytoplasmic transport of enhanced green fluorescent protein (EGFP) was accelerated by 21.4 %. With the same LIPUS exposure condition, both the diffusivity and phosphorylation of ERK induced by EGF treatment were significantly elevated simultaneously, which implied that LIPUS could also modify the kinase kinetics in the signal transduction process. Taken together, this study is the first attempt to uncover the physical link between LIPUS and the dynamics of intracellular macromolecules and related biological processes that LIPUS can possibly increase the diffusivity of intracellular macromolecules, leading to the changes in the basic cellular processes: passive nucleocytoplasmic transport and ERK. Our findings can provide a novel perspective that the mechanotransduction process that the intracellular region, in addition to the cell membrane, can convert the acoustic stimuli of LIPUS to biochemical signals.

NF-kB in Signaling Patterns and Its Temporal Dynamics Encode/Decode Human Diseases

Defects in signaling pathways are the root cause of many disorders. These malformations come in a wide variety of types, and their causes are also very diverse. Some of these flaws can be brought on by pathogenic organisms and viruses, many of which can obstruct signaling processes. Other illnesses are linked to malfunctions in the way that cell signaling pathways work. When thinking about how errors in signaling pathways might cause disease, the idea of signalosome remodeling is helpful. The signalosome may be conveniently divided into two types of defects: phenotypic remodeling and genotypic remodeling. The majority of significant illnesses that affect people, including high blood pressure, heart disease, diabetes, and many types of mental illness, appear to be caused by minute phenotypic changes in signaling pathways. Such phenotypic remodeling modifies cell behavior and subverts normal cellular processes, resulting in illness. There has not been much progress in creating efficient therapies since it has been challenging to definitively confirm this connection between signalosome remodeling and illness. The considerable redundancy included into cell signaling systems presents several potential for developing novel treatments for various disease conditions. One of the most important pathways, NF-κB, controls several aspects of innate and adaptive immune responses, is a key modulator of inflammatory reactions, and has been widely studied both from experimental and theoretical perspectives. NF-κB contributes to the control of inflammasomes and stimulates the expression of a number of pro-inflammatory genes, including those that produce cytokines and chemokines. Additionally, NF-κB is essential for controlling innate immune cells and inflammatory T cells' survival, activation, and differentiation. As a result, aberrant NF-κB activation plays a role in the pathogenesis of several inflammatory illnesses. The activation and function of NF-κB in relation to inflammatory illnesses was covered here, and the advancement of treatment approaches based on NF-κB inhibition will be highlighted. This review presents the temporal behavior of NF-κB and its potential relevance in different human diseases which will be helpful not only for theoretical but also for experimental perspectives.

Can Systems Biology Advance Clinical Precision Oncology?

Precision oncology is perceived as a way forward to treat individual cancer patients. However, knowing particular cancer mutations is not enough for optimal therapeutic treatment, because cancer genotype-phenotype relationships are nonlinear and dynamic. Systems biology studies the biological processes at the systems' level, using an array of techniques, ranging from statistical methods to network reconstruction and analysis, to mathematical modeling. Its goal is to reconstruct the complex and often counterintuitive dynamic behavior of biological systems and quantitatively predict their responses to environmental perturbations. In this paper, we review the impact of systems biology on precision oncology. We show examples of how the analysis of signal transduction networks allows to dissect resistance to targeted therapies and inform the choice of combinations of targeted drugs based on tumor molecular alterations. Patient-specific biomarkers based on dynamical models of signaling networks can have a greater prognostic value than conventional biomarkers. These examples support systems biology models as valuable tools to advance clinical and translational oncological research.

A spatial model of YAP/TAZ signaling reveals how stiffness, dimensionality, and shape contribute to emergent outcomes

YAP/TAZ is a master regulator of mechanotransduction whose functions rely on translocation from the cytoplasm to the nucleus in response to diverse physical cues. Substrate stiffness, substrate dimensionality, and cell shape are all input signals for YAP/TAZ, and through this pathway, regulate critical cellular functions and tissue homeostasis. Yet, the relative contributions of each biophysical signal and the mechanisms by which they synergistically regulate YAP/TAZ in realistic tissue microenvironments that provide multiplexed input signals remain unclear. For example, in simple two-dimensional culture, YAP/TAZ nuclear localization correlates strongly with substrate stiffness, while in three-dimensional (3D) environments, YAP/TAZ translocation can increase with stiffness, decrease with stiffness, or remain unchanged. Here, we develop a spatial model of YAP/TAZ translocation to enable quantitative analysis of the relationships between substrate stiffness, substrate dimensionality, and cell shape. Our model couples cytosolic stiffness to nuclear mechanics to replicate existing experimental trends, and extends beyond current data to predict that increasing substrate activation area through changes in culture dimensionality, while conserving cell volume, forces distinct shape changes that result in nonlinear effect on YAP/TAZ nuclear localization. Moreover, differences in substrate activation area versus total membrane area can account for counterintuitive trends in YAP/TAZ nuclear localization in 3D culture. Based on this multiscale investigation of the different system features of YAP/TAZ nuclear translocation, we predict that how a cell reads its environment is a complex information transfer function of multiple mechanical and biochemical factors. These predictions reveal a few design principles of cellular and tissue engineering for YAP/TAZ mechanotransduction.

Mad dephosphorylation at the nuclear pore is essential for asymmetric stem cell division

Stem cells divide asymmetrically to generate a stem cell and a differentiating daughter cell. Yet, it remains poorly understood how a stem cell and a differentiating daughter cell can receive distinct levels of niche signal and thus acquire different cell fates (self-renewal versus differentiation), despite being adjacent to each other and thus seemingly exposed to similar levels of niche signaling. In the Drosophila ovary, germline stem cells (GSCs) are maintained by short range bone morphogenetic protein (BMP) signaling; the BMP ligands activate a receptor that phosphorylates the downstream molecule mothers against decapentaplegic (Mad). Phosphorylated Mad (pMad) accumulates in the GSC nucleus and activates the stem cell transcription program. Here, we demonstrate that pMad is highly concentrated in the nucleus of the GSC, while it quickly decreases in the nucleus of the differentiating daughter cell, the precystoblast (preCB), before the completion of cytokinesis. We show that a known Mad phosphatase, Dullard (Dd), is required for the asymmetric partitioning of pMad. Our mathematical modeling recapitulates the high sensitivity of the ratio of pMad levels to the Mad phosphatase activity and explains how the asymmetry arises in a shared cytoplasm. Together, these studies reveal a mechanism for breaking the symmetry of daughter cells during asymmetric stem cell division.

Multi-spike solutions of a hybrid reaction–transport model

Simulations of classical pattern-forming reaction–diffusion systems indicate that they often operate in the strongly nonlinear regime, with the final steady state consisting of a spatially repeating pattern of localized spikes. In activator–inhibitor systems such as the two-component Gierer–Meinhardt (GM) model, one can consider the singular limit D a  ≪  D h , where D a and D h are the diffusivities of the activator and inhibitor, respectively. Asymptotic analysis can then be used to analyse the existence and linear stability of multi-spike solutions. In this paper, we analyse multi-spike solutions in a hybrid reaction–transport model, consisting of a slowly diffusing activator and an actively transported inhibitor that switches at a rate α between right-moving and left-moving velocity states. Such a model was recently introduced to account for the formation and homeostatic regulation of synaptic puncta during larval development in Caenorhabditis elegans . We exploit the fact that the hybrid model can be mapped onto the classical GM model in the fast switching limit α  → ∞, which establishes the existence of multi-spike solutions. Linearization about the multi-spike solution yields a non-local eigenvalue problem that is used to investigate stability of the multi-spike solution by combining analytical results for α  → ∞ with a graphical construction for finite α .

System, Method and Software for Calculation of a Cannabis Drug Efficiency Index for the Reduction of Inflammation

There are many varieties of Cannabis sativa that differ from each other by composition of cannabinoids, terpenes and other molecules. The medicinal properties of these cultivars are often very different, with some being more efficient than others. This report describes the development of a method and software for the analysis of the efficiency of various cannabis extracts to detect the anti-inflammatory properties of the various cannabis extracts. The method uses high-throughput gene expression profiling data but can potentially use other omics data as well. According to the signaling pathway topology, the gene expression profiles are convoluted into the signaling pathway activities using a signaling pathway impact analysis (SPIA) method. The method was tested by inducing inflammation in human 3D epithelial tissues, including intestine, oral and skin, and then exposing these tissues to various extracts and then performing transcriptome analysis. The analysis showed a different efficiency of the various extracts in restoring the transcriptome changes to the pre-inflammation state, thus allowing to calculate a different cannabis drug efficiency index (CDEI).

Proofreading through spatial gradients

Key enzymatic processes use the nonequilibrium error correction mechanism called kinetic proofreading to enhance their specificity. The applicability of traditional proofreading schemes, however, is limited because they typically require dedicated structural features in the enzyme, such as a nucleotide hydrolysis site or multiple intermediate conformations. Here, we explore an alternative conceptual mechanism that achieves error correction by having substrate binding and subsequent product formation occur at distinct physical locations. The time taken by the enzyme–substrate complex to diffuse from one location to another is leveraged to discard wrong substrates. This mechanism does not have the typical structural requirements, making it easier to overlook in experiments. We discuss how the length scales of molecular gradients dictate proofreading performance, and quantify the limitations imposed by realistic diffusion and reaction rates. Our work broadens the applicability of kinetic proofreading and sets the stage for studying spatial gradients as a possible route to specificity.

Protein kinase inhibitors in traumatic brain injury and repair: New roles of nanomedicine

Traumatic brain injury (TBI) causes physical injury to the cell membranes of neurons, glial and axons causing the release of several neurochemicals including glutamate and cytokines altering cell-signaling pathways. Upregulation of mitogen associated protein kinase (MAPK) and extracellular signal-regulated kinase (ERK) occurs that is largely responsible for cell death. The pharmacological blockade of these pathways results in cell survival. In this review role of several protein kinase inhibitors on TBI induced oxidative stress, blood-brain barrier breakdown, brain edema formation, and resulting brain pathology is discussed in the light of current literature.

Cell shape regulates subcellular organelle location to control early Ca2+ signal dynamics in vascular smooth muscle cells

The shape of the cell is connected to its function; however, we do not fully understand underlying mechanisms by which global shape regulates a cell's functional capabilities. Using theory, experiments and simulation, we investigated how physiologically relevant cell shape changes affect subcellular organization, and consequently intracellular signaling, to control information flow needed for phenotypic function. Vascular smooth muscle cells going from a proliferative and motile circular shape to a contractile fusiform shape show changes in the location of the sarcoplasmic reticulum, inter-organelle distances, and differential distribution of receptors in the plasma membrane. These factors together lead to the modulation of signals transduced by the M3 muscarinic receptor/Gq/PLCβ pathway at the plasma membrane, amplifying Ca2+ dynamics in the cytoplasm, and the nucleus resulting in phenotypic changes, as determined by increased activity of myosin light chain kinase in the cytoplasm and enhanced nuclear localization of the transcription factor NFAT. Taken together, our observations show a systems level phenomenon whereby global cell shape affects subcellular organization to modulate signaling that enables phenotypic changes.

Subdiffusion-limited fractional reaction-subdiffusion equations with affine reactions: Solution, stochastic paths, and applications

In contrast to normal diffusion, there is no canonical model for reactions between chemical species which move by anomalous subdiffusion. Indeed, the type of mesoscopic equation describing reaction-subdiffusion systems depends on subtle assumptions about the microscopic behavior of individual molecules. Furthermore, the correspondence between mesoscopic and microscopic models is not well understood. In this paper, we study the subdiffusion-limited model, which is defined by mesoscopic equations with fractional derivatives applied to both the movement and the reaction terms. Assuming that the reaction terms are affine functions, we show that the solution to the fractional system is the expectation of a random time change of the solution to the corresponding integer order system. This result yields a simple and explicit algebraic relationship between the fractional and integer order solutions in Laplace space. We then find the microscopic Langevin description of individual molecules that corresponds to such mesoscopic equations and give a computer simulation method to generate their stochastic trajectories. This analysis identifies some precise microscopic conditions that dictate when this type of mesoscopic model is or is not appropriate. We apply our results to several scenarios in cell biology which, despite the ubiquity of subdiffusion in cellular environments, have been modeled almost exclusively by normal diffusion. Specifically, we consider subdiffusive models of morphogen gradient formation, fluctuating mobility, and fluorescence recovery after photobleaching (FRAP) experiments. We also apply our results to fractional ordinary differential equations.

Periodic propagating waves coordinate RhoGTPase network dynamics at the leading and trailing edges during cell migration

Migrating cells need to coordinate distinct leading and trailing edge dynamics but the underlying mechanisms are unclear. Here, we combine experiments and mathematical modeling to elaborate the minimal autonomous biochemical machinery necessary and sufficient for this dynamic coordination and cell movement. RhoA activates Rac1 via DIA and inhibits Rac1 via ROCK, while Rac1 inhibits RhoA through PAK. Our data suggest that in motile, polarized cells, RhoA–ROCK interactions prevail at the rear, whereas RhoA-DIA interactions dominate at the front where Rac1/Rho oscillations drive protrusions and retractions. At the rear, high RhoA and low Rac1 activities are maintained until a wave of oscillatory GTPase activities from the cell front reaches the rear, inducing transient GTPase oscillations and RhoA activity spikes. After the rear retracts, the initial GTPase pattern resumes. Our findings show how periodic, propagating GTPase waves coordinate distinct GTPase patterns at the leading and trailing edge dynamics in moving cells.

Intracellular morphogens: Specifying patterns at the subcellular scale

The notion that graded distributions of signals underlie the spatial organization of biological systems has long been a central pillar in the fields of cell and developmental biology. During morphogenesis, morphogens spread across tissues to guide development of the embryo. Similarly, a variety of dynamic gradients and pattern-forming networks have been discovered that shape subcellular organization. Here we discuss the principles of intracellular pattern formation by these intracellular morphogens and relate them to conceptually similar processes operating at the tissue scale. We will specifically review mechanisms for generating cellular asymmetry and consider how intracellular patterning networks are controlled and adapt to cellular geometry. Finally, we assess the general concept of intracellular gradients as a mechanism for positional control in light of current data, highlighting how the simple readout of fixed concentration thresholds fails to fully capture the complexity of spatial patterning processes occurring inside cells.

Protein concentration gradients and switching diffusions

Morphogen gradients play a vital role in developmental biology by enabling embryonic cells to infer their spatial location and determine their developmental fate accordingly. The standard mechanism for generating a morphogen gradient involves a morphogen being produced from a localized source and subsequently degrading. While this mechanism is effective over the length and time scales of tissue development, it fails over typical subcellular length scales due to the rapid dissipation of spatial asymmetries. In a recent theoretical work, we found an alternative mechanism for generating concentration gradients of diffusing molecules, in which the molecules switch between spatially constant diffusivities at switching rates that depend on the spatial location of a molecule. Independently, an experimental and computational study later found that Caenorhabditis elegans zygotes rely on this mechanism for cell polarization. In this paper, we extend our analysis of switching diffusivities to determine its role in protein concentration gradient formation. In particular, we determine how switching diffusivities modifies the standard theory and show how space-dependent switching diffusivities can yield a gradient in the absence of a localized source. Our mathematical analysis yields explicit formulas for the intracellular concentration gradient which closely match the results of previous experiments and numerical simulations.

New insights into RAS biology reinvigorate interest in mathematical modeling of RAS signaling

RAS is the most frequently mutated gene across human cancers, but developing inhibitors of mutant RAS has proven to be challenging. Given the difficulties of targeting RAS directly, drugs that impact the other components of pathways where mutant RAS operates may potentially be effective. However, the system-level features, including different localizations of RAS isoforms, competition between downstream effectors, and interlocking feedback and feed-forward loops, must be understood to fully grasp the opportunities and limitations of inhibiting specific targets. Mathematical modeling can help us discern the system-level impacts of these features in normal and cancer cells. New technologies enable the acquisition of experimental data that will facilitate development of realistic models of oncogenic RAS behavior. In light of the wealth of empirical data accumulated over decades of study and the advancement of experimental methods for gathering new data, modelers now have the opportunity to advance progress toward realization of targeted treatment for mutant RAS-driven cancers.

Genetically Encoded Fluorescent Biosensors Illuminate the Spatiotemporal Regulation of Signaling Networks

Cellular signaling networks are the foundation which determines the fate and function of cells as they respond to various cues and stimuli. The discovery of fluorescent proteins over 25 years ago enabled the development of a diverse array of genetically encodable fluorescent biosensors that are capable of measuring the spatiotemporal dynamics of signal transduction pathways in live cells. In an effort to encapsulate the breadth over which fluorescent biosensors have expanded, we endeavored to assemble a comprehensive list of published engineered biosensors, and we discuss many of the molecular designs utilized in their development. Then, we review how the high temporal and spatial resolution afforded by fluorescent biosensors has aided our understanding of the spatiotemporal regulation of signaling networks at the cellular and subcellular level. Finally, we highlight some emerging areas of research in both biosensor design and applications that are on the forefront of biosensor development.

Mapping Transient Protein Interactions at the Nanoscale in Living Mammalian Cells

Protein-protein interactions (PPIs) form the basis of cellular processes, regulating cell behavior and fate. PPIs can be extremely transient in nature, which hinders their detection. In addition, traditional biochemical methods provided limited information on the spatial distribution and temporal dynamics of PPIs that is crucial for their regulation in the crowded cellular environment. Given the pivotal role of membrane micro- and nanodomains in the regulation of PPIs at the plasma membrane, the development of methods to visualize PPIs with a high spatial resolution is imperative. Here, we present a super-resolution fluorescence microscopy technique that can detect and map short-lived transient protein-protein interactions on a nanometer scale in the cellular environment. This imaging method is based on single-molecule fluorescence microscopy and exploits the effect of the difference in the mobility between cytosolic and membrane-bound proteins in the recorded fluorescence signals. After the development of the proof of concept using a model system based on membrane-bound modular protein domains and fluorescently labeled peptides, we applied this imaging approach to investigate the interactions of cytosolic proteins involved in the epidermal growth factor signaling pathway (namely, Grb2, c-Raf, and PLCγ1). The detected clusters of Grb2 and c-Raf were correlated with the distribution of the receptor at the plasma membrane. Additionally, the interactions of wild type PLCγ1 were compared with those detected with truncated mutants, which provided important information regarding the role played by specific domains in the interaction with the membrane. The results presented here demonstrate the potential of this technique to unravel the role of membrane heterogeneity in the spatiotemporal regulation of cell signaling.

The Importance of Kinase-Phosphatase Integration: Lessons from Mitosis

Kinases and phosphatases work antagonistically to control the behaviour of individual substrate molecules. This can be incorrectly extrapolated to imply that they also work antagonistically on the signals or processes that these molecules control. In fact, in many situations kinases and phosphatases work together to positively drive signal responses. We explain how this 'cooperativity' is critical for setting the amplitude, localisation, timing, and shape of phosphorylation signals. We use mitosis to illustrate why these properties are important for controlling mitotic entry, sister chromatid cohesion, kinetochore-microtubule attachments, the spindle assembly checkpoint, mitotic spindle elongation, and mitotic exit. These examples provide a rationale to explain how complex signalling behaviour could rely on similar types of integration within many other biological processes.

Diffusive transport in the presence of stochastically gated absorption

We analyze a population of Brownian particles moving in a spatially uniform environment with stochastically gated absorption. The state of the environment at time t is represented by a discrete stochastic variable k(t)∈{0,1} such that the rate of absorption is γ[1-k(t)], with γ a positive constant. The variable k(t) evolves according to a two-state Markov chain. We focus on how stochastic gating affects the attenuation of particle absorption with distance from a localized source in a one-dimensional domain. In the static case (no gating), the steady-state attenuation is given by an exponential with length constant sqrt[D/γ], where D is the diffusivity. We show that gating leads to slower, nonexponential attenuation. We also explore statistical correlations between particles due to the fact that they all diffuse in the same switching environment. Such correlations can be determined in terms of moments of the solution to a corresponding stochastic Fokker-Planck equation.

The Slow Mobility of the ParA Partitioning Protein Underlies Its Steady-State Patterning in Caulobacter

In bacteria, ParABS systems mediate intracellular transport of various cargos, including chromosomal regions in Caulobacter crescentus. Transport of the ParB/parS partition complex requires the DNA-binding activity of ParA, which transiently tethers the partition complex during translocation. In C. crescentus, the directionality of the transport is set up by a gradient of ParA whose concentration gradually increases from one end of the cell (old pole) to the other (new pole). Importantly, this ParA gradient is already observed before DNA replication and segregation are initiated when the partition complex is anchored at the old pole. How such micron-scale ParA pattern is established and maintained before the initiation of chromosome segregation has not been experimentally established. Although the stimulation of ParA ATPase activity by the localized ParB/parS partition complex is thought to be involved, this activity alone cannot quantitatively describe the ParA pattern observed inside cells. Instead, our experimental and theoretical study shows that the missing key component for achieving the experimentally observed steady-state ParA patterning is the slow mobility of ParA dimers (D ∼10(-3)μm(2)/s) due to intermittent DNA binding. Our model recapitulates the entire steady-state ParA distribution observed experimentally, including the shape of the gradient as well as ParA accumulation at the location of the partition complex. Stochastic simulations suggest that cell-to-cell variability in ParA pattern is due to the low ParA copy number in C. crescentus cells. The model also accounts for an apparent exclusion of ParA from regions with small spacing between partition complexes observed in filamentous cells. Collectively, our work demonstrates that in addition to its function in mediating transport, the conserved DNA-binding property of ParA has a critical function before DNA segregation by setting up a ParA pattern required for transport directionality.

Relaxation oscillations and hierarchy of feedbacks in MAPK signaling

We formulated a computational model for a MAPK signaling cascade downstream of the EGF receptor to investigate how interlinked positive and negative feedback loops process EGF signals into ERK pulses of constant amplitude but dose-dependent duration and frequency. A positive feedback loop involving RAS and SOS, which leads to bistability and allows for switch-like responses to inputs, is nested within a negative feedback loop that encompasses RAS and RAF, MEK, and ERK that inhibits SOS via phosphorylation. This negative feedback, operating on a longer time scale, changes switch-like behavior into oscillations having a period of 1 hour or longer. Two auxiliary negative feedback loops, from ERK to MEK and RAF, placed downstream of the positive feedback, shape the temporal ERK activity profile but are dispensable for oscillations. Thus, the positive feedback introduces a hierarchy among negative feedback loops, such that the effect of a negative feedback depends on its position with respect to the positive feedback loop. Furthermore, a combination of the fast positive feedback involving slow-diffusing membrane components with slower negative feedbacks involving faster diffusing cytoplasmic components leads to local excitation/global inhibition dynamics, which allows the MAPK cascade to transmit paracrine EGF signals into spatially non-uniform ERK activity pulses.

Stable DNA-based reaction–diffusion patterns

This paper demonstrates the generation of enzyme free DNA reaction–diffusion gradientsin vitrothat remain stable for tens of hours.

The complexities and versatility of the RAS-to-ERK signalling system in normal and cancer cells

The intricate dynamic control and plasticity of RAS to ERK mitogenic, survival and apoptotic signalling has mystified researches for more than 30 years. Therapeutics targeting the oncogenic aberrations within this pathway often yield unsatisfactory, even undesired results, as in the case of paradoxical ERK activation in response to RAF inhibition. A direct approach of inhibiting single oncogenic proteins misses the dynamic network context governing the network signal processing. In this review, we discuss the signalling behaviour of RAS and RAF proteins in normal and in cancer cells, and the emerging systems-level properties of the RAS-to-ERK signalling network. We argue that to understand the dynamic complexities of this control system, mathematical models including mechanistic detail are required. Looking into the future, these dynamic models will build the foundation upon which more effective, rational approaches to cancer therapy will be developed.

On the importance of modelling the internal spatial dynamics of biological cells

Spatial effects such as cell shape have very often been considered negligible in models of cellular pathways, and many existing simulation infrastructures do not take such effects into consideration. Recent experimental results are reversing this judgement by showing that very small spatial variations can make a big difference in the fate of a cell. This is particularly the case when considering eukaryotic cells, which have a complex physical structure and many subtle control mechanisms, but bacteria are also interesting for the huge variation in shape both between species and in different phases of their lifecycle. In this work we perform simulations that measure the effect of three common bacterial shapes on the behaviour of model cellular pathways. To perform these experiments we develop ReDi-Cell, a highly scalable GPGPU cell simulation infrastructure for the modelling of cellular pathways in spatially detailed environments. ReDi-Cell is validated against known-good simulations, prior to its use in new work. We then use ReDi-Cell to conduct novel experiments that demonstrate the effect that three common bacterial shapes (Cocci, Bacilli and Spirilli) have on the behaviour of model cellular pathways. Pathway wavefront shape, pathway concentration gradients, and chemical species distribution are measured in the three different shapes. We also quantify the impact of internal cellular clutter on the same pathways. Through this work we show that variations in the shape or configuration of these common cell shapes alter model cell behaviour.

Implementation of Complex Biological Logic Circuits Using Spatially Distributed Multicellular Consortia

Engineered synthetic biological devices have been designed to perform a variety of functions from sensing molecules and bioremediation to energy production and biomedicine. Notwithstanding, a major limitation of in vivo circuit implementation is the constraint associated to the use of standard methodologies for circuit design. Thus, future success of these devices depends on obtaining circuits with scalable complexity and reusable parts. Here we show how to build complex computational devices using multicellular consortia and space as key computational elements. This spatial modular design grants scalability since its general architecture is independent of the circuit’s complexity, minimizes wiring requirements and allows component reusability with minimal genetic engineering. The potential use of this approach is demonstrated by implementation of complex logical functions with up to six inputs, thus demonstrating the scalability and flexibility of this method. The potential implications of our results are outlined.

Synthetic biological circuits have been built for different purposes. Nevertheless, the way these devices have been designed so far present several limitations: complex genetic engineering is required to implement complex circuits, and once the parts are built, they are not reusable. We proposed to distribute the computation in several cellular consortia that are physically separated, thus ensuring implementation of circuits independently of their complexity and using reusable components with minimal genetic engineering. This approach allows an easy implementation of multicellular computing devices for secretable inputs or biosensing purposes.

Bistability of a coupled Aurora B kinase-phosphatase system in cell division

Aurora B kinase, a key regulator of cell division, localizes to specific cellular locations, but the regulatory mechanisms responsible for phosphorylation of substrates located remotely from kinase enrichment sites are unclear. Here, we provide evidence that this activity at a distance depends on both sites of high kinase concentration and the bistability of a coupled kinase-phosphatase system. We reconstitute this bistable behavior and hysteresis using purified components to reveal co-existence of distinct high and low Aurora B activity states, sustained by a two-component kinase autoactivation mechanism. Furthermore, we demonstrate these non-linear regimes in live cells using a FRET-based phosphorylation sensor, and provide a mechanistic theoretical model for spatial regulation of Aurora B phosphorylation. We propose that bistability of an Aurora B-phosphatase system underlies formation of spatial phosphorylation patterns, which are generated and spread from sites of kinase autoactivation, thereby regulating cell division.

Dynamics of gradient formation by intracellular shuttling

A number of important cellular functions rely on the formation of intracellular protein concentration gradients. Experimental studies discovered a number of mechanisms for the formation of such gradients. One of the mechanisms relies on the intracellular shuttling of a protein that interconverts between the two states with different diffusivities, under the action of two enzymes, one of which is localized to the plasma membrane, whereas the second is uniformly distributed in the cytoplasm. Recent work reported an analytical solution for the steady state gradient in this mechanism, obtained in the framework of a one-dimensional reaction-diffusion model. Here, we study the dynamics in this model and derive analytical expressions for the Laplace transforms of the time-dependent concentration profiles in terms of elementary transcendental functions. Inverting these transforms numerically, one can obtain time-dependent concentration profiles of the two forms of the protein.

Computational modeling of drug response with applications to neuroscience

The development of novel high-throughput technologies has opened up the opportunity to deeply characterize patient tissues at various molecular levels and has given rise to a paradigm shift in medicine towards personalized therapies. Computational analysis plays a pivotal role in integrating the various genome data and understanding the cellular response to a drug. Based on that data, molecular models can be constructed that incorporate the known downstream effects of drug-targeted receptor molecules and that predict optimal therapy decisions. In this article, we describe the different steps in the conceptual framework of computational modeling. We review resources that hold information on molecular pathways that build the basis for constructing the model interaction maps, highlight network analysis concepts that have been helpful in identifying predictive disease patterns, and introduce the basic concepts of kinetic modeling. Finally, we illustrate this framework with selected studies related to the modeling of important target pathways affected by drugs.

From proteomes to complexomes in the era of systems biology

Protein complexes carry out almost the entire signaling and functional processes in the cell. The protein complex complement of a cell, and its network of complex-complex interactions, is referred to here as the complexome. Computational methods to predict protein complexes from proteomics data, resulting in network representations of complexomes, have recently being developed. In addition, key advances have been made toward understanding the network and structural organization of complexomes. We review these bioinformatics advances, and their discovery-potential, as well as the merits of integrating proteomics data with emerging methods in systems biology to study protein complex signaling. It is envisioned that improved integration of proteomics and systems biology, incorporating the dynamics of protein complexes in space and time, may lead to more predictive models of cell signaling networks for effective modulation.

Complexity of receptor tyrosine kinase signal processing

Our knowledge of molecular mechanisms of receptor tyrosine kinase (RTK) signaling advances with ever-increasing pace. Yet our understanding of how the spatiotemporal dynamics of RTK signaling control specific cellular outcomes has lagged behind. Systems-centered experimental and computational approaches can help reveal how overlapping networks of signal transducers downstream of RTKs orchestrate specific cell-fate decisions. We discuss how RTK network regulatory structures, which involve the immediate posttranslational and delayed transcriptional controls by multiple feed forward and feedback loops together with pathway cross talk, adapt cells to the combinatorial variety of external cues and conditions. This intricate network circuitry endows cells with emerging capabilities for RTK signal processing and decoding. We illustrate how mathematical modeling facilitates our understanding of RTK network behaviors by unraveling specific systems properties, including bistability, oscillations, excitable responses, and generation of intricate landscapes of signaling activities.

Modeling spatiotemporal dynamics of bacterial populations

Quantitative modeling of spatiotemporal dynamics of cells facilitates understanding and engineering of biological systems. Using a synthetic bacterial ecosystem as a workbench, we present the approach to mathematically simulate the spatiotemporal population dynamics of the ecosystem. A description of ecosystem's genetic construction and model development is firstly given. Parameter estimation and computational approach for the derived partial differential equations (PDEs) are then given. Spatiotemporal pattern formation is computed by numerically solving the PDE model. Biodiversity of the ecosystem and its impacts by cellular seeding distance and motility are computed according to the cell distribution patterns.

Dynamics and stability of a three-dimensional model of cell signal transduction

In this paper, we consider a three-dimensional model of cell signal transduction. In this model, the deactivation of signalling proteins occur throughout the cytosol and activation is localized to specific sites in the cell. We use matched asymptotic expansions to construct the dynamic solutions of signalling protein concentrations. The result of the asymptotic analysis is a system of ordinary differential equations. This reduced system is compared to numerical simulations of the full three-dimensional system. As well, we consider the stability of equilibrium solutions. We find that the systems under consideration may undergo sustained oscillations, hysteresis and other complex behaviors. The simulations of the full three-dimensional system agree with simulations of the reduced ordinary differential equations.

Dynamic optimization of distributed biological systems using robust and efficient numerical techniques

Background

Systems biology allows the analysis of biological systems behavior under different conditions through in silico experimentation. The possibility of perturbing biological systems in different manners calls for the design of perturbations to achieve particular goals. Examples would include, the design of a chemical stimulation to maximize the amplitude of a given cellular signal or to achieve a desired pattern in pattern formation systems, etc. Such design problems can be mathematically formulated as dynamic optimization problems which are particularly challenging when the system is described by partial differential equations.

This work addresses the numerical solution of such dynamic optimization problems for spatially distributed biological systems. The usual nonlinear and large scale nature of the mathematical models related to this class of systems and the presence of constraints on the optimization problems, impose a number of difficulties, such as the presence of suboptimal solutions, which call for robust and efficient numerical techniques.

Results

Here, the use of a control vector parameterization approach combined with efficient and robust hybrid global optimization methods and a reduced order model methodology is proposed. The capabilities of this strategy are illustrated considering the solution of a two challenging problems: bacterial chemotaxis and the FitzHugh-Nagumo model.

Conclusions

In the process of chemotaxis the objective was to efficiently compute the time-varying optimal concentration of chemotractant in one of the spatial boundaries in order to achieve predefined cell distribution profiles. Results are in agreement with those previously published in the literature. The FitzHugh-Nagumo problem is also efficiently solved and it illustrates very well how dynamic optimization may be used to force a system to evolve from an undesired to a desired pattern with a reduced number of actuators. The presented methodology can be used for the efficient dynamic optimization of generic distributed biological systems.

Phospholamban and cardiac function: a comparative perspective in vertebrates

Phospholamban (PLN) is a small phosphoprotein closely associated with the cardiac sarcoplasmic reticulum (SR). Dephosphorylated PLN tonically inhibits the SR Ca-ATPase (SERCA2a), while phosphorylation at Ser16 by PKA and Thr17 by Ca(2+) /calmodulin-dependent protein kinase (CaMKII) relieves the inhibition, and this increases SR Ca(2+) uptake. For this reason, PLN is one of the major determinants of cardiac contractility and relaxation. In this review, we attempted to highlight the functional significance of PLN in vertebrate cardiac physiology. We will refer to the huge literature on mammals in order to describe the molecular characteristics of this protein, its interaction with SERCA2a and its role in the regulation of the mechanic and the electric performance of the heart under basal conditions, in the presence of chemical and physical stresses, such as β-adrenergic stimulation, response to stretch, force-frequency relationship and intracellular acidosis. Our aim is to provide the basis to discuss the role of PLN also on the cardiac function of nonmammalian vertebrates, because so far this aspect has been almost neglected. Accordingly, when possible, the literature on PLN will be analysed taking into account the nonuniform cardiac structural and functional characteristics encountered in ectothermic vertebrates, such as the peculiar and variable organization of the SR, the large spectrum of response to stresses and the disaptive absence of crucial proteins (i.e. haemoglobinless and myoglobinless species).

Organization of the ENaC-regulatory machinery

The control of fluid and electrolyte homeostasis in vertebrates requires the integration of a diverse set of signaling inputs, which control epithelial Na(+) transport, the principal ionic component of extracellular fluid. The key site of regulation is a segment of the kidney tubules, frequently termed the aldosterone-sensitive distal nephron, wherein the epithelial Na(+) channel (or ENaC) mediates apical ion entry. Na(+) transport in this segment is strongly regulated by the salt-retaining hormone, aldosterone, which acts through the mineralocorticoid receptor (MR) to influence the expression of a selected set of target genes, most notably the serine-threonine kinase SGK1, which phosphorylates and inhibits the E3 ubiquitin ligase Nedd4-2. It has long been known that ENaC activity is tightly regulated in vertebrate epithelia. Recent evidence suggests that SGK1 and Nedd4-2, along with other ENaC-regulatory proteins, physically associate with each other and with ENaC in a multi-protein complex. The various components of the complex are regulated by diverse signaling networks, including steroid receptor-, PI3-kinase-, mTOR-, and Raf-MEK-ERK-dependent pathways. In this review, we focus on the organization of the targets of these pathways by multi-domain scaffold proteins and lipid platforms into a unified complex, thereby providing a molecular basis for signal integration in the control of ENaC.

How to build a robust intracellular concentration gradient

Concentration gradients of morphogens are critical regulators of patterning in developmental biology. Increasingly, intracellular concentration gradients have also been found to orchestrate spatial organization, but inside single cells, where they regulate processes such as cell division, polarity and mitotic spindle dynamics. Here, we discuss recent progress in understanding how such intracellular gradients can be built robustly. We focus particularly on the Pom1p gradient in fission yeast, elucidating how various buffering mechanisms operate to ensure precise gradient formation. In this case, a systems-level understanding of the entire mechanism of precise gradient construction is now within reach, with important implications for gradients in both intracellular and developmental contexts.

A systems biology approach to model neural stem cell regulation by notch, shh, wnt, and EGF signaling pathways

The Notch, Sonic Hedgehog (Shh), Wnt, and EGF pathways have long been known to influence cell fate specification in the developing nervous system. Here we attempted to evaluate the contemporary knowledge about neural stem cell differentiation promoted by various drug-based regulations through a systems biology approach. Our model showed the phenomenon of DAPT-mediated antagonism of Enhancer of split [E(spl)] genes and enhancement of Shh target genes by a SAG agonist that were effectively demonstrated computationally and were consistent with experimental studies. However, in the case of model simulation of Wnt and EGF pathways, the model network did not supply any concurrent results with experimental data despite the fact that drugs were added at the appropriate positions. This paves insight into the potential of crosstalks between pathways considered in our study. Therefore, we manually developed a map of signaling crosstalk, which included the species connected by representatives from Notch, Shh, Wnt, and EGF pathways and highlighted the regulation of a single target gene, Hes-1, based on drug-induced simulations. These simulations provided results that matched with experimental studies. Therefore, these signaling crosstalk models complement as a tool toward the discovery of novel regulatory processes involved in neural stem cell maintenance, proliferation, and differentiation during mammalian central nervous system development. To our knowledge, this is the first report of a simple crosstalk map that highlights the differential regulation of neural stem cell differentiation and underscores the flow of positive and negative regulatory signals modulated by drugs.

A framework for modeling the relationship between cellular steady-state and stimulus-responsiveness

In cell signaling systems, the abundances of signaling molecules are generally thought to determine the response to stimulation. However, the kinetics of molecular processes, for example receptor trafficking and protein turnover, may also play an important role. Few studies have systematically examined this relationship between the resting state and stimulus-responsiveness. Fewer still have investigated the relative contribution of steady-state concentrations and reaction kinetics. Here we describe a mathematical framework for modeling the resting state of signaling systems. Among other things, this framework allows steady-state concentration measurements to be used in parameterizing kinetic models, and enables comprehensive characterization of the relationship between the resting state and the cellular response to stimulation.

Integrative network biology: graph prototyping for co-expression cancer networks

Network-based analysis has been proven useful in biologically-oriented areas, e.g., to explore the dynamics and complexity of biological networks. Investigating a set of networks allows deriving general knowledge about the underlying topological and functional properties. The integrative analysis of networks typically combines networks from different studies that investigate the same or similar research questions. In order to perform an integrative analysis it is often necessary to compare the properties of matching edges across the data set. This identification of common edges is often burdensome and computational intensive. Here, we present an approach that is different from inferring a new network based on common features. Instead, we select one network as a graph prototype, which then represents a set of comparable network objects, as it has the least average distance to all other networks in the same set. We demonstrate the usefulness of the graph prototyping approach on a set of prostate cancer networks and a set of corresponding benign networks. We further show that the distances within the cancer group and the benign group are statistically different depending on the utilized distance measure.

NMR analysis of a stress response metabolic signaling network

We previously hypothesized that Staphylococcus epidermidis senses a diverse set of environmental and nutritional factors associated with biofilm formation through a modulation in the activity of the tricarboxylic acid (TCA) cycle. Herein, we report our further investigation of the impact of additional environmental stress factors on TCA cycle activity and provide a detailed description of our NMR methodology. S. epidermidis wild-type strain 1457 was treated with stressors that are associated with biofilm formation, a sublethal dose of tetracycline, 5% NaCl, 2% glucose, and autoinducer-2 (AI-2). As controls and to integrate our current data with our previous study, 4% ethanol stress and iron-limitation were also used. Consistent with our prior observations, the effect of many environmental stress factors on the S. epidermidis metabolome was essentially identical to the effect of TCA cycle inactivation in the aconitase mutant strain 1457-acnA::tetM. A detailed quantitative analysis of metabolite concentration changes using 2D (1)H-(13)C HSQC and (1)H-(1)H TOCSY spectra identified a network of 37 metabolites uniformly affected by the stressors and TCA cycle inactivation. We postulate that the TCA cycle acts as the central pathway in a metabolic signaling network.

Colocalization of protein kinase A with adenylyl cyclase enhances protein kinase A activity during induction of long-lasting long-term-potentiation

The ability of neurons to differentially respond to specific temporal and spatial input patterns underlies information storage in neural circuits. One means of achieving spatial specificity is to restrict signaling molecules to particular subcellular compartments using anchoring molecules such as A-Kinase Anchoring Proteins (AKAPs). Disruption of protein kinase A (PKA) anchoring to AKAPs impairs a PKA-dependent form of long term potentiation (LTP) in the hippocampus. To investigate the role of localized PKA signaling in LTP, we developed a stochastic reaction-diffusion model of the signaling pathways leading to PKA activation in CA1 pyramidal neurons. Simulations investigated whether the role of anchoring is to locate kinases near molecules that activate them, or near their target molecules. The results show that anchoring PKA with adenylyl cyclase (which produces cAMP that activates PKA) produces significantly greater PKA activity, and phosphorylation of both inhibitor-1 and AMPA receptor GluR1 subunit on S845, than when PKA is anchored apart from adenylyl cyclase. The spatial microdomain of cAMP was smaller than that of PKA suggesting that anchoring PKA near its source of cAMP is critical because inactivation by phosphodiesterase limits diffusion of cAMP. The prediction that the role of anchoring is to colocalize PKA near adenylyl cyclase was confirmed by experimentally rescuing the deficit in LTP produced by disruption of PKA anchoring using phosphodiesterase inhibitors. Additional experiments confirm the model prediction that disruption of anchoring impairs S845 phosphorylation produced by forskolin-induced synaptic potentiation. Collectively, these results show that locating PKA near adenylyl cyclase is a critical function of anchoring.

The hippocampus is a part of the cerebral cortex involved in formation of certain types of long term memories. Activity-dependent change in the strength of neuronal connections in the hippocampus, known as synaptic plasticity, is one mechanism used to store memories. The ability to form crisp and distinguishable memories of different events implies that learning produces plasticity of specific and distinct subsets of synapses within each neuron. Synaptic activity leads to production of intracellular signaling molecules, which ultimately cause changes in the properties of the synapses. The requirement for synaptic specificity seems incompatible with the diffusibility of intracellular signaling molecules. Anchoring proteins restrict signaling molecules to particular subcellular compartments thereby combating the indiscriminate spread of intracellular signaling molecules. To investigate whether the critical function of anchoring proteins is to localize proteins near their activators or their targets, we developed a stochastic reaction-diffusion model of signaling pathways leading to synaptic plasticity in hippocampal neurons. Simulations demonstrate that colocalizing proteins with their activator molecules is more important due to inactivation mechanisms that limit the spatial extent of the activator molecules.

Diffusive coupling can discriminate between similar reaction mechanisms in an allosteric enzyme system

BACKGROUND

A central question for the understanding of biological reaction networks is how a particular dynamic behavior, such as bistability or oscillations, is realized at the molecular level. So far this question has been mainly addressed in well-mixed reaction systems which are conveniently described by ordinary differential equations. However, much less is known about how molecular details of a reaction mechanism can affect the dynamics in diffusively coupled systems because the resulting partial differential equations are much more difficult to analyze.

RESULTS

Motivated by recent experiments we compare two closely related mechanisms for the product activation of allosteric enzymes with respect to their ability to induce different types of reaction-diffusion waves and stationary Turing patterns. The analysis is facilitated by mapping each model to an associated complex Ginzburg-Landau equation. We show that a sequential activation mechanism, as implemented in the model of Monod, Wyman and Changeux (MWC), can generate inward rotating spiral waves which were recently observed as glycolytic activity waves in yeast extracts. In contrast, in the limiting case of a simple Hill activation, the formation of inward propagating waves is suppressed by a Turing instability. The occurrence of this unusual wave dynamics is not related to the magnitude of the enzyme cooperativity (as it is true for the occurrence of oscillations), but to the sensitivity with respect to changes of the activator concentration. Also, the MWC mechanism generates wave patterns that are more stable against long wave length perturbations.

CONCLUSIONS

This analysis demonstrates that amplitude equations, which describe the spatio-temporal dynamics near an instability, represent a valuable tool to investigate the molecular effects of reaction mechanisms on pattern formation in spatially extended systems. Using this approach we have shown that the occurrence of inward rotating spiral waves in glycolysis can be explained in terms of an MWC, but not with a Hill mechanism for the activation of the allosteric enzyme phosphofructokinase. Our results also highlight the importance of enzyme oligomerization for a possible experimental generation of Turing patterns in biological systems.