Modularity along organism dispersal gradients challenges a prevailing view of abrupt transitions in animal landscape perception

A common property of landscapes and metacommunities is the occurrence of abrupt shifts in connectivity along gradients of individual dispersal abilities. Animals with short‐range dispersal capability perceive fragmented landscapes, but organisms moving across critical thresholds perceive continuous landscapes. This qualitative shift in landscape perception may determine several attributes of local communities and the dynamics of whole metacommunities. Modularity describes the existence in some communities of relatively high numbers of mutual connections favoring the movement of neighboring individuals (even when each individual is able to reach any patch in the landscape). Local patch linkages and metacommunity connectivity along gradients of dispersal ability have been reported frequently. However, the intermediate level of structure captured by modularity has not been considered. We evaluated landscape connectivity and modularity along gradients of individual dispersal abilities. Random landscapes with different degrees of cell aggregation and occupancy were simulated; we also analyzed ten real ecosystems. An expected, a shift in landscape connectivity was always detected; modularity consistently decreased gradually along dispersal gradients in both simulated networks and empirical landscapes. Neutral metacommunities within simulated landscapes demonstrated that modularity and connectivity may reflect landscape traits in the shaping of metacommunity diversity. Average beta‐diversity was strongly associated with modularity, particularly with low migration rates, while connectivity trends tracked changes in beta‐diversity at intermediate to high migrations rates. Consequently, while some species are able to perceive abrupt transitions in the landscape, many others probably experience a gradual continuum in landscape perception, contrary to predictions from previous analyses. Furthermore, the gradual behavior of modularity indicates that it may represent an exceptional early‐warning tool that measures system distance to tipping points. Our study highlights the multiple perceptions that different species may have of a single landscape and shows, for the first time, a theoretical and empirical relationship between landscape modularity, and metacommunity diversity.     

Superstability of the yeast cell-cycle dynamics: ensuring causality in the presence of biochemical stochasticity

Gene regulatory dynamics are governed by molecular processes and therefore exhibits an inherent stochasticity. However, for the survival of an organism it is a strict necessity that this intrinsic noise does not prevent robust functioning of the system. It is still an open question how dynamical stability is achieved in biological systems despite the omnipresent fluctuations. In this paper we investigate the cell cycle of the budding yeast Saccharomyces cerevisiae as an example of a well-studied organism. We study a genetic network model of 11 genes that coordinate the cell-cycle dynamics using a modeling framework which generalizes the concept of discrete threshold dynamics. By allowing for fluctuations in the process times, we introduce noise into the model, accounting for the effects of biochemical stochasticity. We study the dynamical attractor of the cell cycle and find a remarkable robustness against fluctuations of this kind. We identify mechanisms that ensure reliability in spite of fluctuations: 'Catcher states' and persistence of activity levels contribute significantly to the stability of the yeast cell cycle despite the inherent stochasticity.     

A chromosome separation checkpoint

Here we discuss a “chromosome separation checkpoint” that might regulate the anaphase‐telophase transition. The concept of cell cycle checkpoints was originally proposed to account for extrinsic control mechanisms that ensure the order of cell cycle events. Several checkpoints have been shown to regulate major cell cycle transitions, namely at G1‐S and G2‐M. At the onset of mitosis, the prophase‐prometaphase transition is controlled by several potential checkpoints, including the antephase checkpoint, while the spindle assembly checkpoint guards the metaphase‐anaphase transition. Our hypothesis is based on the recently uncovered feedback control mechanism that delays chromosome decondensation and nuclear envelope reassembly until effective separation of sister chromatids during anaphase is achieved. A central player in this potential checkpoint is the establishment of a constitutive, midzone‐based Aurora B phosphorylation gradient that monitors the position of chromosomes along the spindle axis. We propose that this surveillance mechanism represents an additional step towards ensuring mitotic fidelity.     

Observations on rate theory for rugged energy landscapes

The potential energy profile for many complex reactions of proteins, such as folding or allosteric conformational change, involves many different scales of molecular motion along the reaction coordinate. Although it is natural to model the dynamics of motion along such rugged energy landscapes as diffusional (the Smoluchowski equation; SE), problems arise because the frictional forces generated by the molecular surround are typically not strong enough to justify the use of the SE. Here, we discuss the fundamental theory behind the SE and note that it may be justified through a master equation when reduced to its continuum limit. However, the SE cannot be used for rough energy landscapes, where the continuum limit is ill defined. Instead, we suggest that one should use a mean first passage time expression derived from a master equation, and show how this approach can be used to glean information about the underlying dynamics of barrier crossing. We note that the potential profile in the SE is that of the microbarriers between conformational substates, and that there is a temperature-dependent, effective friction associated with the long residence time in the microwells that populate the rough landscape. The number of recrossings of the overall barrier is temperature-dependent, governed by the microbarriers and not by the effective friction. We derive an explicit expression for the mean number of recrossings and its temperature dependence. Finally, we note that the mean first passage time can be used as a departure point for measuring the roughness of the landscape.     

From Understanding the Development Landscape of the Canonical Fate-Switch Pair to Constructing a Dynamic Landscape for Two-Step Neural Differentiation

Recent progress in stem cell biology, notably cell fate conversion, calls for novel theoretical understanding for cell differentiation. The existing qualitative concept of Waddington’s “epigenetic landscape” has attracted particular attention because it captures subsequent fate decision points, thus manifesting the hierarchical (“tree-like”) nature of cell fate diversification. Here, we generalized a recent work and explored such a developmental landscape for a two-gene fate decision circuit by integrating the underlying probability landscapes with different parameters (corresponding to distinct developmental stages). The change of entropy production rate along the parameter changes indicates which parameter changes can represent a normal developmental process while other parameters’ change can not. The transdifferentiation paths over the landscape under certain conditions reveal the possibility of a direct and reversible phenotypic conversion. As the intensity of noise increases, we found that the landscape becomes flatter and the dominant paths more straight, implying the importance of biological noise processing mechanism in development and reprogramming. We further extended the landscape of the one-step fate decision to that for two-step decisions in central nervous system (CNS) differentiation. A minimal network and dynamic model for CNS differentiation was firstly constructed where two three-gene motifs are coupled. We then implemented the SDEs (Stochastic Differentiation Equations) simulation for the validity of the network and model. By integrating the two landscapes for the two switch gene pairs, we constructed the two-step development landscape for CNS differentiation. Our work provides new insights into cellular differentiation and important clues for better reprogramming strategies.     

From mutations to mechanisms and dysfunction via computation and mining of protein energy landscapes

Background

The protein energy landscape underscores the inherent nature of proteins as dynamic molecules interconverting between structures with varying energies. Reconstructing a protein’s energy landscape holds the key to characterizing a protein’s equilibrium conformational dynamics and its relationship to function. Many pathogenic mutations in protein sequences alter the equilibrium dynamics that regulates molecular interactions and thus protein function. In principle, reconstructing energy landscapes of a protein’s healthy and diseased variants is a central step to understanding how mutations impact dynamics, biological mechanisms, and function.

Results

Recent computational advances are yielding detailed, sample-based representations of protein energy landscapes. In this paper, we propose and describe two novel methods that leverage computed, sample-based representations of landscapes to reconstruct them and extract from them informative local structures that reveal the underlying organization of an energy landscape. Such structures constitute landscape features that, as we demonstrate here, can be utilized to detect alterations of landscapes upon mutation.

Conclusions

The proposed methods detect altered protein energy landscape features in response to sequence mutations. By doing so, the methods allow formulating hypotheses on the impact of mutations on specific biological activities of a protein. This work demonstrates that the availability of energy landscapes of healthy and diseased variants of a protein opens up new avenues to harness the quantitative information embedded in landscapes to summarize mechanisms via which mutations alter protein dynamics to percolate to dysfunction.

     

Solvent-induced free energy landscape and solute-solvent dynamic coupling in a multielement solute

Molecular dynamics simulations using a simple multielement model solute with internal degrees of freedom and accounting for solvent-induced interactions to all orders in explicit water are reported. The potential energy landscape of the solute is flat in vacuo. However, the sole untruncated solvent-induced interactions between apolar (hydrophobic) and charged elements generate a rich landscape of potential of mean force exhibiting typical features of protein landscapes. Despite the simplicity of our solute, the depth of minima in this landscape is not far in size from free energies that stabilize protein conformations. Dynamical coupling between configurational switching of the system and hydration reconfiguration is also elicited. Switching is seen to occur on a time scale two orders of magnitude longer than that of the reconfiguration time of the solute taken alone, or that of the unperturbed solvent. Qualitatively, these results are unaffected by a different choice of the water-water interaction potential. They show that already at an elementary level, solvent-induced interactions alone, when fully accounted for, can be responsible for configurational and dynamical features essential to protein folding and function.     

Capturing Transition Paths and Transition States for Conformational Rearrangements in the Ribosome

To reveal the molecular determinants of biological function, one seeks to characterize the interactions that are formed in conformational and chemical transition states. In other words, what interactions govern the molecule’s energy landscape? To accomplish this, it is necessary to determine which degrees of freedom can unambiguously identify each transition state. Here, we perform simulations of large-scale aminoacyl-transfer RNA (aa-tRNA) rearrangements during accommodation on the ribosome and project the dynamics along experimentally accessible atomic distances. From this analysis, we obtain evidence for which coordinates capture the correct number of barrier-crossing events and accurately indicate when the aa-tRNA is on a transition path. Although a commonly used coordinate in single-molecule experiments performs poorly, this study implicates alternative coordinates along which rearrangements are accurately described as diffusive movements across a one-dimensional free-energy profile. From this, we provide the theoretical foundation required for single-molecule techniques to uncover the energy landscape governing aa-tRNA selection by the ribosome.     

Predictability of evolutionary trajectories in fitness landscapes

Experimental studies on enzyme evolution show that only a small fraction of all possible mutation trajectories are accessible to evolution. However, these experiments deal with individual enzymes and explore a tiny part of the fitness landscape. We report an exhaustive analysis of fitness landscapes constructed with an off-lattice model of protein folding where fitness is equated with robustness to misfolding. This model mimics the essential features of the interactions between amino acids, is consistent with the key paradigms of protein folding and reproduces the universal distribution of evolutionary rates among orthologous proteins. We introduce mean path divergence as a quantitative measure of the degree to which the starting and ending points determine the path of evolution in fitness landscapes. Global measures of landscape roughness are good predictors of path divergence in all studied landscapes: the mean path divergence is greater in smooth landscapes than in rough ones. The model-derived and experimental landscapes are significantly smoother than random landscapes and resemble additive landscapes perturbed with moderate amounts of noise; thus, these landscapes are substantially robust to mutation. The model landscapes show a deficit of suboptimal peaks even compared with noisy additive landscapes with similar overall roughness. We suggest that smoothness and the substantial deficit of peaks in the fitness landscapes of protein evolution are fundamental consequences of the physics of protein folding.     

Multiple phosphorylation of Rad9 by CDK is required for DNA damage checkpoint activation

The DNA damage checkpoint controls cell cycle arrest in response to DNA damage, and activation of this checkpoint is in turn cell cycle-regulated. Rad9, the ortholog of mammalian 53BP1, is essential for this checkpoint response and is phosphorylated by the cyclin-dependent kinase (CDK) in the yeast Saccharomyces cerevisiae. Previous studies suggested that the CDK consensus sites of Rad9 are important for its checkpoint activity. However, the precise CDK sites of Rad9 involved have not been determined. Here we show that CDK consensus sites of Rad9 function in parallel to its BRCT domain toward checkpoint activation, analogous to its fission yeast ortholog Crb2. Unlike Crb2, however, mutation of multiple rather than any individual CDK site of Rad9 is required to completely eliminate its checkpoint activity in vivo. Although Dpb11 interacts with CDK-phosphorylated Rad9, we provide evidence showing that elimination of this interaction does not affect DNA damage checkpoint activation in vivo, suggesting that additional pathway(s) exist. Taken together, these findings suggest that the regulation of Rad9 by CDK and the role of Dpb11 in DNA damage checkpoint activation are more complex than previously suggested. We propose that multiple phosphorylation of Rad9 by CDK may provide a more robust system to allow Rad9 to control cell cycle-dependent DNA damage checkpoint activation.     

Multiple phosphorylation of Rad9 by CDK is required for DNA damage checkpoint activation

The DNA damage checkpoint controls cell cycle arrest in response to DNA damage, and activation of this checkpoint is in turn cell cycle-regulated. Rad9, the ortholog of mammalian 53BP1, is essential for this checkpoint response and is phosphorylated by the cyclin-dependent kinase (CDK) in the yeast Saccharomyces cerevisiae. Previous studies suggested that the CDK consensus sites of Rad9 are important for its checkpoint activity. However, the precise CDK sites of Rad9 involved have not been determined. Here we show that CDK consensus sites of Rad9 function in parallel to its BRCT domain toward checkpoint activation, analogous to its fission yeast ortholog Crb2. Unlike Crb2, however, mutation of multiple rather than any individual CDK site of Rad9 is required to completely eliminate its checkpoint activity in vivo. Although Dpb11 interacts with CDK-phosphorylated Rad9, we provide evidence showing that elimination of this interaction does not affect DNA damage checkpoint activation in vivo, suggesting that additional pathway(s) exist. Taken together, these findings suggest that the regulation of Rad9 by CDK and the role of Dpb11 in DNA damage checkpoint activation are more complex than previously suggested. We propose that multiple phosphorylation of Rad9 by CDK may provide a more robust system to allow Rad9 to control cell cycle-dependent DNA damage checkpoint activation.     

Environmental fluctuations: How do they affect the topography of the adaptive landscape?

A Phenotypic Adaptive Landscape is defined with fitness as the ordinate, and longevity of the juvenile phase and duration of disturbances to the adult phase as the horizontal axes. The effect of local environmental perturbations on the landscape’s shape is studied using a semistochastic population model. In this model the intrinsic population dynamics takes the form of a differential-delay nonlinear equation and the environmental disturbance appears as a multiplicativetelegraphic noise. We demonstrate that the landscape has no single characteristic scale. Rather, it shows adaptive peaks corresponding to an integer relation between the biological and the environmental periodicities. Since the system is constrained by a finite time and a finite physiological range, the landscape may have different topographies for different local environmental regimes. A very simple fully deterministic model is presented, predicting landscapes that are similar to those obtained by the semistochastic model. Application to life history strategies are discussed.     

RNA polymerase pushing

Molecular motors can exhibit Brownian ratchet or power stroke mechanisms. These mechanistic categories are related to transition state position: An early transition state suggests that chemical energy is stored and then released during the step (stroke) while a late transition state suggests that the release of chemical energy rectifies thermally activated motion that has already occurred (ratchet). Cellular RNA polymerases are thought to be ratchets that can push each other forward to reduce pausing during elongation. Here, by constructing a two-dimensional energy landscape from the individual landscapes of active and backtracked enzymes, we identify a new pushing mechanism which is the result of a saddle trajectory that arises in the two-dimensional energy landscape of interacting enzymes. We show that this mechanism is more effective with an early transition state suggesting that interacting RNAPs might translocate via a power stroke.     

Specificity and Affinity Quantification of Flexible Recognition from Underlying Energy Landscape Topography

Flexibility in biomolecular recognition is essential and critical for many cellular activities. Flexible recognition often leads to moderate affinity but high specificity, in contradiction with the conventional wisdom that high affinity and high specificity are coupled. Furthermore, quantitative understanding of the role of flexibility in biomolecular recognition is still challenging. Here, we meet the challenge by quantifying the intrinsic biomolecular recognition energy landscapes with and without flexibility through the underlying density of states. We quantified the thermodynamic intrinsic specificity by the topography of the intrinsic binding energy landscape and the kinetic specificity by association rate. We found that the thermodynamic and kinetic specificity are strongly correlated. Furthermore, we found that flexibility decreases binding affinity on one hand, but increases binding specificity on the other hand, and the decreasing or increasing proportion of affinity and specificity are strongly correlated with the degree of flexibility. This shows more (less) flexibility leads to weaker (stronger) coupling between affinity and specificity. Our work provides a theoretical foundation and quantitative explanation of the previous qualitative studies on the relationship among flexibility, affinity and specificity. In addition, we found that the folding energy landscapes are more funneled with binding, indicating that binding helps folding during the recognition. Finally, we demonstrated that the whole binding-folding energy landscapes can be integrated by the rigid binding and isolated folding energy landscapes under weak flexibility. Our results provide a novel way to quantify the affinity and specificity in flexible biomolecular recognition.     

Extended molecular dynamics simulation of the carbon monoxide migration in sperm whale myoglobin

We report the results of an extended molecular dynamics simulation on the migration of photodissociated carbon monoxide in wild-type sperm whale myoglobin. Our results allow following one possible ligand migration dynamics from the distal pocket to the Xe1 cavity via a path involving the other xenon binding cavities and momentarily two additional packing defects along the pathway. Comparison with recent time resolved structural data obtained by Laue crystallography with subnanosecond to millisecond resolution shows a more than satisfactory agreement. In fact, according to time resolved crystallography, CO, after photolysis, can occupy the Xe1 and Xe4 cavities. However, no information on the trajectory of the ligand from the distal pocket to the Xe1 is available. Our results clearly show one possible path within the protein. In addition, although our data refer to a single trajectory, the local dynamics of the ligand in each cavity is sufficiently equilibrated to obtain local structural and thermodynamic information not accessible to crystallography. In particular, we show that the CO motion and the protein fluctuations are strictly correlated: free energy calculations of the migration between adjacent cavities show that the migration is not a simple diffusion but is kinetically or thermodynamically driven by the collective motions of the protein; conversely, the protein fluctuations are influenced by the ligand in such a way that the opening/closure of the passage between adjacent cavities is strictly correlated to the presence of CO in its proximity. The compatibility between time resolved crystallographic experiments and molecular dynamics simulations paves the way to a deeper understanding of the role of internal dynamics and packing defects in the control of ligand binding in heme proteins.     

Time‐to‐kill: measuring attack rates in a heterogenous landscape with multiple prey types

Although spatial heterogeneity of prey and landscapes are known to contribute to variation around predator‐prey functional response models, few studies have quantified these effects. We illustrate a new approach using data from winter movement paths of GPS‐collared wolves in the Rocky Mountains of Canada and time‐to‐event models with competing risks for measuring the effect of prey and landscape characteristics on the time‐to‐kill, which is the reciprocal of attack rate (aN) in a Holling's functional response. We evaluated 13 a priori models representing hypothesized mechanisms influencing attack rates in a heterogeneous landscape with two prey types. Models ranged from variants on Holling's disc equation, including search rate and prey density, to a full model including prey density and patchiness, search rates, satiation, and landscape features, which were measured along the wolf's movement path. Movement rates of wolves while searching explained more of the variation in time‐to‐kill than prey densities. Wolves did not compensate for low prey density by increasing movement rates and there was little evidence that spatial aggregation of prey influenced attack rates in this multi‐prey system. The top model for predicting time‐to‐kill included only search rate and landscape features. Wolves killed prey more quickly in flat terrain, likely due to increased vulnerability from accumulated snow, whereas attack rates were lower when wolves hunted near human‐made features presumably due to human disturbance. Understanding the sources of variation in attack rates provides refinements to functional response models that can lead to more effective predator–prey management in human‐dominated landscapes.     

Early spindle assembly in Drosophila embryos: role of a force balance involving cytoskeletal dynamics and nuclear mechanics

Mitotic spindle morphogenesis depends upon the action of microtubules (MTs), motors and the cell cortex. Previously, we proposed that cortical- and MT-based motors acting alone can coordinate early spindle assembly in Drosophila embryos. Here, we tested this model using microscopy of living embryos to analyze spindle pole separation, cortical reorganization, and nuclear dynamics in interphase-prophase of cycles 11-13. We observe that actin caps remain flat as they expand and that furrows do not ingress. As centrosomes separate, they follow a linear trajectory, maintaining a constant pole-to-furrow distance while the nucleus progressively deforms along the elongating pole-pole axis. These observations are incorporated into a model in which outward forces generated by zones of active cortical dynein are balanced by inward forces produced by nuclear elasticity and during cycle 13, by Ncd, which localizes to interpolar MTs. Thus, the force-balance driving early spindle morphogenesis depends upon MT-based motors acting in concert with the cortex and nucleus.