Project description:When the state of the whole reaction network can be inferred by just measuring the dynamics of a limited set of nodes the system is said to be fully observable. However, as the number of all possible combinations of measured variables and time derivatives spanning the reconstructed state of the system exponentially increases with its dimension, the observability becomes a computationally prohibitive task. Our approach consists in computing the observability coefficients from a symbolic Jacobian matrix whose elements encode the linear, nonlinear polynomial or rational nature of the interaction among the variables. The novelty we introduce in this paper, required for treating large-dimensional systems, is to identify from the symbolic Jacobian matrix the minimal set of variables (together with their time derivatives) candidate to be measured for completing the state space reconstruction. Then symbolic observability coefficients are computed from the symbolic observability matrix. Our results are in agreement with the analytical computations, evidencing the correctness of our approach. Its application to efficiently exploring the dynamics of real world complex systems such as power grids, socioeconomic networks or biological networks is quite promising.
Project description:In many complex systems encountered in the natural and social sciences, mechanisms governing system dynamics at a microscale depend upon the values of state variables characterizing the system at coarse-grained, macroscale (Goldenfeld and Woese, 2011, Noble et al., 2019, and Chater and Loewenstein, 2023). State variables, in turn, are averages over relevant probability distributions of the microscale variables. Neither inferential Top-Down nor mechanistic Bottom-Up modeling alone can predict responses of such scale-entwined systems to perturbations. We describe and explore the properties of a dynamic theory that combines Top-Down information-theoretic inference with Bottom-Up, state-variable-dependent mechanisms. The theory predicts the functional form of nonstationary probability distributions over microvariables and relates the trajectories of time-evolving macrovariables to the form of those distributions. Analytic expressions for the time evolution of Lagrange multipliers from Maxent solutions allow for rapid calculation of the time trajectories of state variables even in high dimensional systems. Examples of possible applications to scale-entwined systems in nonequilibrium chemical thermodynamics, epidemiology, economics, and ecology exemplify the potential multidisciplinary scope of the theory. A worked-out low-dimension example illustrates the structure of the theory and demonstrates how scale entwinement can result in slowed recovery from perturbations, reddened time series spectra in response to white-noise input, and hysteresis upon parameter displacement and subsequent restoration.
Project description:Mental disorders like major depressive disorder can be modeled as complex dynamical systems. In this study we investigate the dynamic behavior of individuals to see whether or not we can expect a transition to another mood state. We introduce a mean field model to a binomial process, where we reduce a dynamic multidimensional system (stochastic cellular automaton) to a one-dimensional system to analyse the dynamics. Using maximum likelihood estimation, we can estimate the parameter of interest which, in combination with a bifurcation diagram, reflects the expectancy that someone has to transition to another mood state. After numerically illustrating the proposed method with simulated data, we apply this method to two empirical examples, where we show its use in a clinical sample consisting of patients diagnosed with major depressive disorder, and a general population sample. Results showed that the majority of the clinical sample was categorized as having an expectancy for a transition, while the majority of the general population sample did not have this expectancy. We conclude that the mean field model has great potential in assessing the expectancy for a transition between mood states. With some extensions it could, in the future, aid clinical therapists in the treatment of depressed patients.
Project description:The "developmental hourglass" concept suggests that intermediate developmental stages are most resistant to evolutionary changes and that differences between species arise through divergence later in development. This high conservation during middevelopment is illustrated by the "waist" of the hourglass and it represents a low probability of evolutionary change. Earlier molecular surveys both on animals and on plants have shown that the genes expressed at the waist stage are more ancient and more conserved in their expression. The existence of such a developmental hourglass has not been explored in fungi, another eukaryotic kingdom. In this study, we generated a series of transcriptomic data covering the entire lifecycle of a model mushroom-forming fungus, Coprinopsis cinerea, and we observed a molecular hourglass over its development. The "young fruiting body" is the stage that expresses the evolutionarily oldest (lowest transcriptome age index) transcriptome and gives the strongest signal of purifying selection (lowest transcriptome divergence index). We also demonstrated that all three kingdoms-animals, plants, and fungi-display high expression levels of genes in "information storage and processing" at the waist stages, whereas the genes in "metabolism" become more highly expressed later. Besides, the three kingdoms all show underrepresented "signal transduction mechanisms" at the waist stages. The synchronic existence of a molecular "hourglass" across the three kingdoms reveals a mutual strategy for eukaryotes to incorporate evolutionary innovations.
Project description:The M-bM-^@M-^Xdevelopmental hourglassM-bM-^@M-^Y concept suggests that intermediate developmental stages are most resistant to evolutionary changes and that differences between species arise through divergence later in development. This high conservation during mid-development is illustrated by the M-bM-^@M-^XwaistM-bM-^@M-^Y of the hourglass and it represents a low probability of evolutionary change. Earlier molecular surveys both on animals and plants have shown that the genes expressed at the waist stage are more ancient and more conserved in their expression. The existence of such a developmental hourglass has not been explored in fungi, another eukaryotic kingdom. In this study, we generated a series of transcriptomic data covering the entire lifecycle of a model mushroom-forming fungus, Coprinopsis cinerea, and we observed a molecular hourglass over its development. The M-bM-^@M-^Xyoung fruiting bodyM-bM-^@M-^Y (YFB) is the stage that expresses the evolutionarily oldest (lowest transcriptome age index, TAI) transcriptome and gives the strongest signal of purifying selection (lowest transcriptome divergence index, TDI). We also demonstrated that all three kingdoms M-bM-^@M-^S animals, plants and fungi M-bM-^@M-^S display high expression levels of genes in M-bM-^@M-^Xinformation storage and processingM-bM-^@M-^Y at the waist stages, whereas the genes in M-bM-^@M-^XmetabolismM-bM-^@M-^Y become more highly expressed later. Besides, the three kingdoms all show underrepresented M-bM-^@M-^Xsignal transductionM-bM-^@M-^Y at the waist stages. The synchronic existence of a molecular M-bM-^@M-^XhourglassM-bM-^@M-^Y across the three kingdoms reveals a mutual strategy for eukaryotes to incorporate evolutionary innovations. NimbleGen custom microarray with total RNAs extracted from two biological replicates for each stage of mycelium, fruiting initials (~2mm tall), stage 2 primordium (~1cm tall), young fruiting body (~2cm tall) and the fully-expanded cap of the mature fruiting body (~4cm tall). Mycelia from 5 agar plates were collected and pooled to form one replicate. For the other stages, 4-5 independent structures were isolated and their RNA extracted as one replicate sample.
Project description:Waddington's epigenetic landscape, a famous metaphor in developmental biology, depicts how a stem cell progresses from an undifferentiated phenotype to a differentiated one. The concept of "landscape" in the context of dynamical systems theory represents a high-dimensional space, in which each cell phenotype is considered as an "attractor" that is determined by interactions between multiple molecular players, and is buffered against environmental fluctuations. In addition, biological noise is thought to play an important role during these cell-fate decisions and in fact controls transitions between different phenotypes. Here, we discuss the phenotypic transitions in cancer from a dynamical systems perspective and invoke the concept of "cancer attractors"-hidden stable states of the underlying regulatory network that are not occupied by normal cells. Phenotypic transitions in cancer occur at varying levels depending on the context. Using epithelial-to-mesenchymal transition (EMT), cancer stem-like properties, metabolic reprogramming and the emergence of therapy resistance as examples, we illustrate how phenotypic plasticity in cancer cells enables them to acquire hybrid phenotypes (such as hybrid epithelial/mesenchymal and hybrid metabolic phenotypes) that tend to be more aggressive and notoriously resilient to therapies such as chemotherapy and androgen-deprivation therapy. Furthermore, we highlight multiple factors that may give rise to phenotypic plasticity in cancer cells, such as (a) multi-stability or oscillatory behaviors governed by underlying regulatory networks involved in cell-fate decisions in cancer cells, and (b) network rewiring due to conformational dynamics of intrinsically disordered proteins (IDPs) that are highly enriched in cancer cells. We conclude by discussing why a therapeutic approach that promotes "recanalization", i.e., the exit from "cancer attractors" and re-entry into "normal attractors", is more likely to succeed rather than a conventional approach that targets individual molecules/pathways.
Project description:How genetic changes are linked to morphological novelties and developmental constraints remains elusive. Here, we investigate genetic apparatuses that distinguish fish fins from tetrapod limbs by analyzing transcriptomes and open-chromatin regions (OCRs). Specifically, we compared mouse forelimb buds with the pectoral fin buds of an elasmobranch, the brown-banded bamboo shark (Chiloscyllium punctatum). A transcriptomic comparison with an accurate orthology map revealed both a mass heterochrony and hourglass-shaped conservation of gene expression between fins and limbs. Furthermore, open-chromatin analysis suggested that access to conserved regulatory sequences is transiently increased during mid-stage limb development. During this stage, stage-specific and tissue-specific OCRs were also enriched. Together, early and late stages of fin/limb development are more permissive to mutations than middle stages, which may have contributed to major morphological changes during the fin-to-limb evolution. We hypothesize that the middle stages are constrained by regulatory complexity that results from dynamic and tissue-specific transcriptional controls.
Project description:Synthetic constructs in biotechnology, biocomputing, and modern gene therapy interventions are often based on plasmids or transfected circuits which implement some form of "on-off" switch. For example, the expression of a protein used for therapeutic purposes might be triggered by the recognition of a specific combination of inducers (e.g., antigens), and memory of this event should be maintained across a cell population until a specific stimulus commands a coordinated shut-off. The robustness of such a design is hampered by molecular ("intrinsic") or environmental ("extrinsic") noise, which may lead to spontaneous changes of state in a subset of the population and is reflected in the bimodality of protein expression, as measured for example using flow cytometry. In this context, a "majority-vote" correction circuit, which brings deviant cells back into the required state, is highly desirable, and quorum-sensing has been suggested as a way for cells to broadcast their states to the population as a whole so as to facilitate consensus. In this paper, we propose what we believe is the first such a design that has mathematically guaranteed properties of stability and auto-correction under certain conditions. Our approach is guided by concepts and theory from the field of "monotone" dynamical systems developed by M. Hirsch, H. Smith, and others. We benchmark our design by comparing it to an existing design which has been the subject of experimental and theoretical studies, illustrating its superiority in stability and self-correction of synchronization errors. Our stability analysis, based on dynamical systems theory, guarantees global convergence to steady states, ruling out unpredictable ("chaotic") behaviors and even sustained oscillations in the limit of convergence. These results are valid no matter what are the values of parameters, and are based only on the wiring diagram. The theory is complemented by extensive computational bifurcation analysis, performed for a biochemically-detailed and biologically-relevant model that we developed. Another novel feature of our approach is that our theorems on exponential stability of steady states for homogeneous or mixed populations are valid independently of the number N of cells in the population, which is usually very large (N ≫ 1) and unknown. We prove that the exponential stability depends on relative proportions of each type of state only. While monotone systems theory has been used previously for systems biology analysis, the current work illustrates its power for synthetic biology design, and thus has wider significance well beyond the application to the important problem of coordination of toggle switches.
Project description:Open-ended evolution (OEE) is relevant to a variety of biological, artificial and technological systems, but has been challenging to reproduce in silico. Most theoretical efforts focus on key aspects of open-ended evolution as it appears in biology. We recast the problem as a more general one in dynamical systems theory, providing simple criteria for open-ended evolution based on two hallmark features: unbounded evolution and innovation. We define unbounded evolution as patterns that are non-repeating within the expected Poincare recurrence time of an isolated system, and innovation as trajectories not observed in isolated systems. As a case study, we implement novel variants of cellular automata (CA) where the update rules are allowed to vary with time in three alternative ways. Each is capable of generating conditions for open-ended evolution, but vary in their ability to do so. We find that state-dependent dynamics, regarded as a hallmark of life, statistically out-performs other candidate mechanisms, and is the only mechanism to produce open-ended evolution in a scalable manner, essential to the notion of ongoing evolution. This analysis suggests a new framework for unifying mechanisms for generating OEE with features distinctive to life and its artifacts, with broad applicability to biological and artificial systems.
Project description:Pain caused by nerve injury (i.e. neuropathic pain) is associated with development of neuronal hyperexcitability at several points along the pain pathway. Within primary afferents, numerous injury-induced changes have been identified but it remains unclear which molecular changes are necessary and sufficient to explain cellular hyperexcitability. To investigate this, we built computational models that reproduce the switch from a normal spiking pattern characterized by a single spike at the onset of depolarization to a neuropathic one characterized by repetitive spiking throughout depolarization. Parameter changes that were sufficient to switch the spiking pattern also enabled membrane potential oscillations and bursting, suggesting that all three pathological changes are mechanistically linked. Dynamical analysis confirmed this prediction by showing that excitability changes co-develop when the nonlinear mechanism responsible for spike initiation switches from a quasi-separatrix-crossing to a subcritical Hopf bifurcation. This switch stems from biophysical changes that bias competition between oppositely directed fast- and slow-activating conductances operating at subthreshold potentials. Competition between activation and inactivation of a single conductance can be similarly biased with equivalent consequences for excitability. "Bias" can arise from a multitude of molecular changes occurring alone or in combination; in the latter case, changes can add or offset one another. Thus, our results identify pathological change in the nonlinear interaction between processes affecting spike initiation as the critical determinant of how simple injury-induced changes at the molecular level manifest complex excitability changes at the cellular level. We demonstrate that multiple distinct molecular changes are sufficient to produce neuropathic changes in excitability; however, given that nerve injury elicits numerous molecular changes that may be individually sufficient to alter spike initiation, our results argue that no single molecular change is necessary to produce neuropathic excitability. This deeper understanding of degenerate causal relationships has important implications for how we understand and treat neuropathic pain.