Structure and Dynamics of ER: Minimal Networks and Biophysical Constraints

The endoplasmic reticulum (ER) in live cells is a highly mobile network whose structure dynamically changes on a number of timescales. The role of such drastic changes in any system is unclear, although there are correlations with ER function. A better understanding of the fundamental biophysical constraints on the system will allow biologists to determine the effects of molecular factors on ER dynamics. Previous studies have identified potential static elements that the ER may remodel around. Here, we use these structural elements to assess biophysical principles behind the network dynamics. By analyzing imaging data of tobacco leaf epidermal cells under two different conditions, i.e., native state (control) and latrunculin B (treated), we show that the geometric structure and dynamics of ER networks can be understood in terms of minimal networks. Our results show that the ER network is well modeled as a locally minimal-length network between the static elements that potentially anchor the ER to the cell cortex over longer timescales; this network is perturbed by a mixture of random and deterministic forces. The network need not have globally minimum length; we observe cases where the local topology may change dynamically between different Euclidean Steiner network topologies. The networks in the treated cells are easier to quantify, because they are less dynamic (the treatment suppresses actin dynamics), but the same general features are found in control cells. Using a Langevin approach, we model the dynamics of the nonpersistent nodes and use this to show that the images can be used to estimate both local viscoelastic behavior of the cytoplasm and filament tension in the ER network. This means we can explain several aspects of the ER geometry in terms of biophysical principles.     

Nonlinear Dynamics of Microtubules: Biophysical Implications

A recently developed model of nonlinear dynamics for microtubules is further expanded based on the biophysical arguments involving the secondary structure of the constitutive protein tubulin and on the ferroelectric properties of microtubules. It is demonstrated that kink excitations arise due to GTP hydrolysis that causes a dynamical transition in the structure of tubulin. The presence of an intrinsic electric field associated with the structure of a microtubule leads to unidirectional propagation of the kink excitation along the microtubule axis. This mechanism offers an explanation of the dynamic instability phenomenon in terms of the electric field effects. Moreover, a possible elucidation of the unidirectional transport of cargo via motor proteins such as kinesin and dynein is proposed within the model developed in this paper.     

Network Dynamics Contribute to Structure: Nestedness in Mutualistic Networks

Both ecological and evolutionary timescales are of importance when considering an ecological system; population dynamics affect the evolution of species traits, and vice versa. Recently, these two timescales have been used to explain structural patterns in host-parasite networks, where the evolution of the manner in which species balance the use of their resources in interactions with each other was examined. One of these patterns was nestedness, in which the set of parasite species within a particular host forms a subset of those within a more species-rich host. Patterns of both nestedness and anti-nestedness have been observed significantly more often than expected due to chance in host-parasite networks. In contrast, mutualistic networks tend to display a significant degree of nestedness, but are rarely anti-nested. Within networks with different interaction types, therefore, there appears to be a feature promoting non-random structural patterns, such as nestedness and anti-nestedness, depending on the interaction types involved. Here, we invoke the co-evolution of species trait-values when allocating resources to interactions to explain the structural pattern of nestedness in a mutualistic community. We look at a bipartite, multi-species system, in which the strength of an interaction between two species is determined by the resources that each species invests in that relationship. We then analyze the evolution of these interactions using adaptive dynamics. We found that the evolution of these interactions, reflecting the trade-off of resources, could be used to accurately predict that nestedness occurs significantly more often than expect due to chance alone in a mutualistic network. This complements previous results applying the same concept to an antagonistic network. We conclude that population dynamics and resource trade-offs could be important promoters of structural patterns in ecological networks of different types.     

Molecular Dynamics Simulation of Protein Folding with Supersecondary Structure Constraints

We integrate molecular dynamics simulation methods with a newly developed supersecondary structure prediction method and compute the structure of a protein molecule, crambin. The computed structure is similar to the crystal structure with an rms error of 3.94 Å.     

Dynamics and Control of Diseases in Networks with Community Structure

The dynamics of infectious diseases spread via direct person-to-person transmission (such as influenza, smallpox, HIV/AIDS, etc.) depends on the underlying host contact network. Human contact networks exhibit strong community structure. Understanding how such community structure affects epidemics may provide insights for preventing the spread of disease between communities by changing the structure of the contact network through pharmaceutical or non-pharmaceutical interventions. We use empirical and simulated networks to investigate the spread of disease in networks with community structure. We find that community structure has a major impact on disease dynamics, and we show that in networks with strong community structure, immunization interventions targeted at individuals bridging communities are more effective than those simply targeting highly connected individuals. Because the structure of relevant contact networks is generally not known, and vaccine supply is often limited, there is great need for efficient vaccination algorithms that do not require full knowledge of the network. We developed an algorithm that acts only on locally available network information and is able to quickly identify targets for successful immunization intervention. The algorithm generally outperforms existing algorithms when vaccine supply is limited, particularly in networks with strong community structure. Understanding the spread of infectious diseases and designing optimal control strategies is a major goal of public health. Social networks show marked patterns of community structure, and our results, based on empirical and simulated data, demonstrate that community structure strongly affects disease dynamics. These results have implications for the design of control strategies.     

Dynamics and Structure in Cell Signaling Networks: Off-State Stability and Dynamically Positive Cycles

The signaling system is a fundamental part of the cell, as it regulates essential functions including growth, differentiation, protein synthesis, and apoptosis. A malfunction in this subsystem can disrupt the cell significantly, and is believed to be involved in certain diseases, with cancer being a very important example. While the information available about intracellular signaling networks is constantly growing, and the network topology is actively being analyzed, the modeling of the dynamics of such a system faces difficulties due to the vast number of parameters, which can prove hard to estimate correctly. As the functioning of the signaling system depends on the parameters in a complex way, being able to make general statements based solely on the network topology could be especially appealing. We study a general kinetic model of the signaling system, giving results for the asymptotic behavior of the system in the case of a network with only activatory interactions. We also investigate the possible generalization of our results for the case of a more general model including inhibitory interactions too. We find that feedback cycles made up entirely of activatory interactions (which we call dynamically positive) are especially important, as their properties determine whether the system has a stable signal-off state, which is desirable in many situations to avoid autoactivation due to a noisy environment. To test our results, we investigate the network topology in the Signalink database, and find that the human signaling network indeed has only significantly few dynamically positive cycles, which agrees well with our theoretical arguments.     

How the Dynamics and Structure of Sexual Contact Networks Shape Pathogen Phylogenies

The characteristics of the host contact network over which a pathogen is transmitted affect both epidemic spread and the projected effectiveness of control strategies. Given the importance of understanding these contact networks, it is unfortunate that they are very difficult to measure directly. This challenge has led to an interest in methods to infer information about host contact networks from pathogen phylogenies, because in shaping a pathogen''s opportunities for reproduction, contact networks also shape pathogen evolution. Host networks influence pathogen phylogenies both directly, through governing opportunities for evolution, and indirectly by changing the prevalence and incidence. Here, we aim to separate these two effects by comparing pathogen evolution on different host networks that share similar epidemic trajectories. This approach allows use to examine the direct effects of network structure on pathogen phylogenies, largely controlling for confounding differences arising from population dynamics. We find that networks with more heterogeneous degree distributions yield pathogen phylogenies with more variable cluster numbers, smaller mean cluster sizes, shorter mean branch lengths, and somewhat higher tree imbalance than networks with relatively homogeneous degree distributions. However, in particular for dynamic networks, we find that these direct effects are relatively modest. These findings suggest that the role of the epidemic trajectory, the dynamics of the network and the inherent variability of metrics such as cluster size must each be taken into account when trying to use pathogen phylogenies to understand characteristics about the underlying host contact network.     

The Biophysical Effects of Neolithic Island Colonization: General Dynamics and Sociocultural Implications

Does anthropogenic environmental change constrain long-term sociopolitical outcomes? It is clear that human colonization of islands radically alters their biological and physical systems. Despite considerable contextual variability in local specificities of this alteration, I argue that these processes are to some extent regular, predictable, and have socio-political implications. Reviewing the data for post-colonization ecodynamics, I show that Neolithic colonization of previously insulated habitats drives biotic homogenization. I argue that we should expect such homogenization to promote regular types of change in biophysical systems, types of change that can be described in sum as environmentally convergent. Such convergence should have significant implications for human social organization over the long term, and general dynamics of this sort are relevant in the context of understanding remarkably similar social evolutionary trajectories towards wealth-inequality not only islands, but also more generally.     

Transmission Dynamics of an SIS Model with Age Structure on Heterogeneous Networks

Infection age is often an important factor in epidemic dynamics. In order to realistically analyze the spreading mechanism and dynamical behavior of epidemic diseases, in this paper, a generalized disease transmission model of SIS type with age-dependent infection and birth and death on a heterogeneous network is discussed. The model allows the infection and recovery rates to vary and depend on the age of infection, the time since an individual becomes infected. We address uniform persistence and find that the model has the sharp threshold property, that is, for the basic reproduction number less than one, the disease-free equilibrium is globally asymptotically stable, while for the basic reproduction number is above one, a Lyapunov functional is used to show that the endemic equilibrium is globally stable. Finally, some numerical simulations are carried out to illustrate and complement the main results. The disease dynamics rely not only on the network structure, but also on an age-dependent factor (for some key functions concerned in the model).     

The Correlation Structure of Local Neuronal Networks Intrinsically Results from Recurrent Dynamics

Correlated neuronal activity is a natural consequence of network connectivity and shared inputs to pairs of neurons, but the task-dependent modulation of correlations in relation to behavior also hints at a functional role. Correlations influence the gain of postsynaptic neurons, the amount of information encoded in the population activity and decoded by readout neurons, and synaptic plasticity. Further, it affects the power and spatial reach of extracellular signals like the local-field potential. A theory of correlated neuronal activity accounting for recurrent connectivity as well as fluctuating external sources is currently lacking. In particular, it is unclear how the recently found mechanism of active decorrelation by negative feedback on the population level affects the network response to externally applied correlated stimuli. Here, we present such an extension of the theory of correlations in stochastic binary networks. We show that (1) for homogeneous external input, the structure of correlations is mainly determined by the local recurrent connectivity, (2) homogeneous external inputs provide an additive, unspecific contribution to the correlations, (3) inhibitory feedback effectively decorrelates neuronal activity, even if neurons receive identical external inputs, and (4) identical synaptic input statistics to excitatory and to inhibitory cells increases intrinsically generated fluctuations and pairwise correlations. We further demonstrate how the accuracy of mean-field predictions can be improved by self-consistently including correlations. As a byproduct, we show that the cancellation of correlations between the summed inputs to pairs of neurons does not originate from the fast tracking of external input, but from the suppression of fluctuations on the population level by the local network. This suppression is a necessary constraint, but not sufficient to determine the structure of correlations; specifically, the structure observed at finite network size differs from the prediction based on perfect tracking, even though perfect tracking implies suppression of population fluctuations.     

Dynamics on Networks: The Role of Local Dynamics and Global Networks on the Emergence of Hypersynchronous Neural Activity

Graph theory has evolved into a useful tool for studying complex brain networks inferred from a variety of measures of neural activity, including fMRI, DTI, MEG and EEG. In the study of neurological disorders, recent work has discovered differences in the structure of graphs inferred from patient and control cohorts. However, most of these studies pursue a purely observational approach; identifying correlations between properties of graphs and the cohort which they describe, without consideration of the underlying mechanisms. To move beyond this necessitates the development of computational modeling approaches to appropriately interpret network interactions and the alterations in brain dynamics they permit, which in the field of complexity sciences is known as dynamics on networks. In this study we describe the development and application of this framework using modular networks of Kuramoto oscillators. We use this framework to understand functional networks inferred from resting state EEG recordings of a cohort of 35 adults with heterogeneous idiopathic generalized epilepsies and 40 healthy adult controls. Taking emergent synchrony across the global network as a proxy for seizures, our study finds that the critical strength of coupling required to synchronize the global network is significantly decreased for the epilepsy cohort for functional networks inferred from both theta (3–6 Hz) and low-alpha (6–9 Hz) bands. We further identify left frontal regions as a potential driver of seizure activity within these networks. We also explore the ability of our method to identify individuals with epilepsy, observing up to 80 predictive power through use of receiver operating characteristic analysis. Collectively these findings demonstrate that a computer model based analysis of routine clinical EEG provides significant additional information beyond standard clinical interpretation, which should ultimately enable a more appropriate mechanistic stratification of people with epilepsy leading to improved diagnostics and therapeutics.     

Multimodal Networks: Structure and Operations

A multimodal network (MMN) is a novel graph-theoretic formalism designed to capture the structure of biological networks and to represent relationships derived from multiple biological databases. MMNs generalize the standard notions of graphs and hypergraphs, which are the bases of current diagrammatic representations of biological phenomena and incorporate the concept of mode. Each vertex of an MMN is a biological entity, a biot, while each modal hyperedge is a typed relationship, where the type is given by the mode of the hyperedge. The current paper defines MMNs and concentrates on the structural aspects of MMNs. A companion paper develops MMNs as a representation of the semantics of biological networks and discusses applications of the MMNs in managing complex biological data. The MMN model has been implemented in a database system containing multiple kinds of biological networks.     

Biophysical Constraints on Optimal Patch Lengths for Settlement of a Reef-Building Bivalve

Reef-building species form discrete patches atop soft sediments, and reef restoration often involves depositing solid material as a substrate for larval settlement and growth. There have been few theoretical efforts to optimize the physical characteristics of a restored reef patch to achieve high recruitment rates. The delivery of competent larvae to a reef patch is influenced by larval behavior and by physical habitat characteristics such as substrate roughness, patch length, current speed, and water depth. We used a spatial model, the “hitting-distance” model, to identify habitat characteristics that will jointly maximize both the settlement probability and the density of recruits on an oyster reef (Crassostrea virginica). Modeled larval behaviors were based on laboratory observations and included turbulence-induced diving, turbulence-induced passive sinking, and neutral buoyancy. Profiles of currents and turbulence were based on velocity profiles measured in coastal Virginia over four different substrates: natural oyster reefs, mud, and deposited oyster and whelk shell. Settlement probabilities were higher on larger patches, whereas average settler densities were higher on smaller patches. Larvae settled most successfully and had the smallest optimal patch length when diving over rough substrates in shallow water. Water depth was the greatest source of variability, followed by larval behavior, substrate roughness, and tidal current speed. This result suggests that the best way to maximize settlement on restored reefs is to construct patches of optimal length for the water depth, whereas substrate type is less important than expected. Although physical patch characteristics are easy to measure, uncertainty about larval behavior remains an obstacle for predicting settlement patterns. The mechanistic approach presented here could be combined with a spatially explicit metapopulation model to optimize the arrangement of reef patches in an estuary or region for greater sustainability of restored habitats.     

Adaptive Dynamics of Regulatory Networks: Size Matters

To accomplish adaptability, all living organisms are constructed of regulatory networks on different levels which are capable to differentially respond to a variety of environmental inputs. Structure of regulatory networks determines their phenotypical plasticity, that is, the degree of detail and appropriateness of regulatory replies to environmental or developmental challenges. This regulatory network structure is encoded within the genotype. Our conceptual simulation study investigates how network structure constrains the evolution of networks and their adaptive abilities. The focus is on the structural parameter network size. We show that small regulatory networks adapt fast, but not as good as larger networks in the longer perspective. Selection leads to an optimal network size dependent on heterogeneity of the environment and time pressure of adaptation. Optimal mutation rates are higher for smaller networks. We put special emphasis on discussing our simulation results on the background of functional observations from experimental and evolutionary biology.     

Dynamics and retention of misfolded proteins in native ER membranes

When co-translationally inserted into endoplasmic reticulum (ER) membranes, newly synthesized proteins encounter the lumenal environment of the ER, which contains chaperone proteins that facilitate the folding reactions necessary for protein oligomerization, maturation and export from the ER. Here we show, using a temperature-sensitive variant of vesicular stomatitis virus G protein tagged with green fluorescent protein (VSVG-GFP), and fluorescence recovery after photobleaching (FRAP), the dynamics of association of folded and misfolded VSVG complexes with ER chaperones. We also investigate the potential mechanisms underlying protein retention in the ER. Misfolded VSVG-GFP complexes at 40 degrees C are highly mobile in ER membranes and do not reside in post-ER compartments, indicating that they are not retained in the ER by immobilization or retrieval mechanisms. These complexes are immobilized in ATP-depleted or tunicamycin-treated cells, in which VSVG-chaperone interactions are no longer dynamic. These results provide insight into the mechanisms of protein retention in the ER and the dynamics of protein-folding complexes in native ER membranes.