Journal articles on the topic 'Computational neuroscience (incl. mathematical neuroscience and theoretical neuroscience)'
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1
Gerstner, Wulfram, Henning Sprekeler, and Gustavo Deco. "Theory and Simulation in Neuroscience." Science 338, no. 6103 (October 4, 2012): 60–65. http://dx.doi.org/10.1126/science.1227356.
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Modeling work in neuroscience can be classified using two different criteria. The first one is the complexity of the model, ranging from simplified conceptual models that are amenable to mathematical analysis to detailed models that require simulations in order to understand their properties. The second criterion is that of direction of workflow, which can be from microscopic to macroscopic scales (bottom-up) or from behavioral target functions to properties of components (top-down). We review the interaction of theory and simulation using examples of top-down and bottom-up studies and point to some current developments in the fields of computational and theoretical neuroscience.
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Medaglia, John D., Mary-Ellen Lynall, and Danielle S. Bassett. "Cognitive Network Neuroscience." Journal of Cognitive Neuroscience 27, no. 8 (August 2015): 1471–91. http://dx.doi.org/10.1162/jocn_a_00810.
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Network science provides theoretical, computational, and empirical tools that can be used to understand the structure and function of the human brain in novel ways using simple concepts and mathematical representations. Network neuroscience is a rapidly growing field that is providing considerable insight into human structural connectivity, functional connectivity while at rest, changes in functional networks over time (dynamics), and how these properties differ in clinical populations. In addition, a number of studies have begun to quantify network characteristics in a variety of cognitive processes and provide a context for understanding cognition from a network perspective. In this review, we outline the contributions of network science to cognitive neuroscience. We describe the methodology of network science as applied to the particular case of neuroimaging data and review its uses in investigating a range of cognitive functions including sensory processing, language, emotion, attention, cognitive control, learning, and memory. In conclusion, we discuss current frontiers and the specific challenges that must be overcome to integrate these complementary disciplines of network science and cognitive neuroscience. Increased communication between cognitive neuroscientists and network scientists could lead to significant discoveries under an emerging scientific intersection known as cognitive network neuroscience.
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KOCH, PAUL, and GERALD LEISMAN. "Numbers, models, and understanding of natural intelligence: Computational neuroscience in the service of clinical neuropsychology." Journal of the International Neuropsychological Society 6, no. 5 (July 2000): 580–82. http://dx.doi.org/10.1017/s1355617700655078.
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What we call computational neuroscience involves construction of mathematical and numerical models for understanding cognitive phenomena. This issue is devoted to showing how it can also be used to help in the analysis of cognitive defects. Although the models may seem abstract to clinicians, they are based on the reality of brain anatomy. The theoretical papers presented here are connectionist: They posit a network of cells connected by synapses whose weights are modified during learning. Architecture of connectionist models has progressed and ramified considerably since they were first introduced, and we include some examples of the current state of the art. The final work presented here is concerned with the connection of the constructed models with clinical experience and experiment.
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Fellous, Jean-Marc, and Christiane Linster. "Computational Models of Neuromodulation." Neural Computation 10, no. 4 (May 1, 1998): 771–805. http://dx.doi.org/10.1162/089976698300017476.
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Computational modeling of neural substrates provides an excellent theoretical framework for the understanding of the computational roles of neuromodulation. In this review, we illustrate, with a large number of modeling studies, the specific computations performed by neuromodulation in the context of various neural models of invertebrate and vertebrate preparations. We base our characterization of neuromodulations on their computational and functional roles rather than on anatomical or chemical criteria. We review the main framework in which neuromodulation has been studied theoretically (central pattern generation and oscillations, sensory processing, memory and information integration). Finally, we present a detailed mathematical overview of how neuromodulation has been implemented at the single cell and network levels in modeling studies. Overall, neuromodulation is found to increase and control computational complexity.
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Poznanski, Roman R. "Book Review: "Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems", P. Dayan and L. F. Abbott, eds., (2001)." Journal of Integrative Neuroscience 05, no. 03 (September 2006): 489–91. http://dx.doi.org/10.1142/s0219635206001197.
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Vyas, Saurabh, Matthew D. Golub, David Sussillo, and Krishna V. Shenoy. "Computation Through Neural Population Dynamics." Annual Review of Neuroscience 43, no. 1 (July 8, 2020): 249–75. http://dx.doi.org/10.1146/annurev-neuro-092619-094115.
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Significant experimental, computational, and theoretical work has identified rich structure within the coordinated activity of interconnected neural populations. An emerging challenge now is to uncover the nature of the associated computations, how they are implemented, and what role they play in driving behavior. We term this computation through neural population dynamics. If successful, this framework will reveal general motifs of neural population activity and quantitatively describe how neural population dynamics implement computations necessary for driving goal-directed behavior. Here, we start with a mathematical primer on dynamical systems theory and analytical tools necessary to apply this perspective to experimental data. Next, we highlight some recent discoveries resulting from successful application of dynamical systems. We focus on studies spanning motor control, timing, decision-making, and working memory. Finally, we briefly discuss promising recent lines of investigation and future directions for the computation through neural population dynamics framework.
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Georgopoulos, Apostolos P. "Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems. Computational Neuroscience. By Peter Dayan and , L F Abbott. Cambridge (Massachusetts): MIT Press. $50.00. xv + 460 p; ill.; index. ISBN: 0–262–04199–5. 2001." Quarterly Review of Biology 79, no. 1 (March 2004): 113. http://dx.doi.org/10.1086/421681.
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Nieus, Thierry, Elisabetta Sola, Jonathan Mapelli, Elena Saftenku, Paola Rossi, and Egidio D'Angelo. "LTP Regulates Burst Initiation and Frequency at Mossy Fiber–Granule Cell Synapses of Rat Cerebellum: Experimental Observations and Theoretical Predictions." Journal of Neurophysiology 95, no. 2 (February 2006): 686–99. http://dx.doi.org/10.1152/jn.00696.2005.
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Long-term potentiation (LTP) is a synaptic change supposed to provide the cellular basis for learning and memory in brain neuronal circuits. Although specific LTP expression mechanisms could be critical to determine the dynamics of repetitive neurotransmission, this important issue remained largely unexplored. In this paper, we have performed whole cell patch-clamp recordings of mossy fiber–granule cell LTP in acute rat cerebellar slices and studied its computational implications with a mathematical model. During LTP, stimulation with short impulse trains at 100 Hz revealed earlier initiation of granule cell spike bursts and a smaller nonsignificant spike frequency increase. In voltage-clamp recordings, short AMPA excitatory postsynaptic current (EPSC) trains showed short-term facilitation and depression and a sustained component probably generated by spillover. During LTP, facilitation disappeared, depression accelerated, and the sustained current increased. The N-methyl-d-aspartate (NMDA) current also increased. In agreement with a presynaptic expression caused by increased release probability, similar changes were observed by raising extracellular [Ca2+]. A mathematical model of mossy fiber–granule cell neurotransmission showed that increasing release probability efficiently modulated the first-spike delay. Glutamate spillover, by causing tonic NMDA and AMPA receptor activation, accelerated excitatory postsynaptic potential (EPSP) temporal summation and maintained a sustained spike discharge. The effect of increasing neurotransmitter release could not be replicated by increasing receptor conductance, which, like postsynaptic manipulations enhancing intrinsic excitability, proved very effective in raising granule cell output frequency. Independent regulation of spike burst initiation and frequency during LTP may provide mechanisms for temporal recoding and gain control of afferent signals at the input stage of cerebellar cortex.
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Engbert, Ralf, and Reinhold Kliegl. "The game of word skipping: Who are the competitors?" Behavioral and Brain Sciences 26, no. 4 (August 2003): 481–82. http://dx.doi.org/10.1017/s0140525x03270102.
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Computational models such as E-Z Reader and SWIFT are ideal theoretical tools to test quantitatively our current understanding of eye-movement control in reading. Here we present a mathematical analysis of word skipping in the E-Z Reader model by semianalytic methods, to highlight the differences in current modeling approaches. In E-Z Reader, the word identification system must outperform the oculomotor system to induce word skipping. In SWIFT, there is competition among words to be selected as a saccade target. We conclude that it is the question of competitors in the “game” of word skipping that must be solved in eye movement research.
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Geisler, Caroline, Nicolas Brunel, and Xiao-Jing Wang. "Contributions of Intrinsic Membrane Dynamics to Fast Network Oscillations With Irregular Neuronal Discharges." Journal of Neurophysiology 94, no. 6 (December 2005): 4344–61. http://dx.doi.org/10.1152/jn.00510.2004.
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During fast oscillations in the local field potential (40–100 Hz gamma, 100–200 Hz sharp-wave ripples) single cortical neurons typically fire irregularly at rates that are much lower than the oscillation frequency. Recent computational studies have provided a mathematical description of such fast oscillations, using the leaky integrate-and-fire (LIF) neuron model. Here, we extend this theoretical framework to populations of more realistic Hodgkin–Huxley-type conductance-based neurons. In a noisy network of GABAergic neurons that are connected randomly and sparsely by chemical synapses, coherent oscillations emerge with a frequency that depends sensitively on the single cell's membrane dynamics. The population frequency can be predicted analytically from the synaptic time constants and the preferred phase of discharge during the oscillatory cycle of a single cell subjected to noisy sinusoidal input. The latter depends significantly on the single cell's membrane properties and can be understood in the context of the simplified exponential integrate-and-fire (EIF) neuron. We find that 200-Hz oscillations can be generated, provided the effective input conductance of single cells is large, so that the single neuron's phase shift is sufficiently small. In a two-population network of excitatory pyramidal cells and inhibitory neurons, recurrent excitation can either decrease or increase the population rhythmic frequency, depending on whether in a neuron the excitatory synaptic current follows or precedes the inhibitory synaptic current in an oscillatory cycle. Detailed single-cell properties have a substantial impact on population oscillations, even though rhythmicity does not originate from pacemaker neurons and is an emergent network phenomenon.
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DiMattina, Christopher, and Kechen Zhang. "Active Data Collection for Efficient Estimation and Comparison of Nonlinear Neural Models." Neural Computation 23, no. 9 (September 2011): 2242–88. http://dx.doi.org/10.1162/neco_a_00167.
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The stimulus-response relationship of many sensory neurons is nonlinear, but fully quantifying this relationship by a complex nonlinear model may require too much data to be experimentally tractable. Here we present a theoretical study of a general two-stage computational method that may help to significantly reduce the number of stimuli needed to obtain an accurate mathematical description of nonlinear neural responses. Our method of active data collection first adaptively generates stimuli that are optimal for estimating the parameters of competing nonlinear models and then uses these estimates to generate stimuli online that are optimal for discriminating these models. We applied our method to simple hierarchical circuit models, including nonlinear networks built on the spatiotemporal or spectral-temporal receptive fields, and confirmed that collecting data using our two-stage adaptive algorithm was far more effective for estimating and comparing competing nonlinear sensory processing models than standard nonadaptive methods using random stimuli.
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Ben-Yosef, Guy, and Ohad Ben-Shahar. "Tangent Bundle Curve Completion with Locally Connected Parallel Networks." Neural Computation 24, no. 12 (December 2012): 3277–316. http://dx.doi.org/10.1162/neco_a_00365.
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We propose a theory for cortical representation and computation of visually completed curves that are generated by the visual system to fill in missing visual information (e.g., due to occlusions). Recent computational theories and physiological evidence suggest that although such curves do not correspond to explicit image evidence along their length, their construction emerges from corresponding activation patterns of orientation-selective cells in the primary visual cortex. Previous theoretical work modeled these patterns as least energetic 3D curves in the mathematical continuous space [Formula: see text], which abstracts the mammalian striate cortex. Here we discuss the biological plausibility of this theory and present a neural architecture that implements it with locally connected parallel networks. Part of this contribution is also a first attempt to bridge the physiological literature on curve completion with the shape problem and a shape theory. We present completion simulations of our model in natural and synthetic scenes and discuss various observations and predictions that emerge from this theory in the context of curve completion.
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Brogin, João Angelo Ferres, Jean Faber, and Douglas Domingues Bueno. "Burster Reconstruction Considering Unmeasurable Variables in the Epileptor Model." Neural Computation 33, no. 12 (November 12, 2021): 3288–333. http://dx.doi.org/10.1162/neco_a_01443.
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Abstract Epilepsy is one of the most common brain disorders worldwide, affecting millions of people every year. Although significant effort has been put into better understanding it and mitigating its effects, the conventional treatments are not fully effective. Advances in computational neuroscience, using mathematical dynamic models that represent brain activities at different scales, have enabled addressing epilepsy from a more theoretical standpoint. In particular, the recently proposed Epileptor model stands out among these models, because it represents well the main features of seizures, and the results from its simulations have been consistent with experimental observations. In addition, there has been an increasing interest in designing control techniques for Epileptor that might lead to possible realistic feedback controllers in the future. However, such approaches rely on knowing all of the states of the model, which is not the case in practice. The work explored in this letter aims to develop a state observer to estimate Epileptor's unmeasurable variables, as well as reconstruct the respective so-called bursters. Furthermore, an alternative modeling is presented for enhancing the convergence speed of an observer. The results show that the proposed approach is efficient under two main conditions: when the brain is undergoing a seizure and when a transition from the healthy to the epileptiform activity occurs.
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Stephan, Klaas E., Karl Zilles, and Rolf Kötter. "Coordinate–independent mapping of structural and functional data by objective relational transformation (ORT)." Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 355, no. 1393 (January 29, 2000): 37–54. http://dx.doi.org/10.1098/rstb.2000.0548.
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Neuroscience has produced an enormous amount of structural and functional data. Powerful database systems are required to make these data accessible for computational approaches such as higher–order analyses and simulations. Available databases for key data such as anatomical and functional connectivity between cortical areas, however, are still hampered by methodological problems. These problems arise predominantly from the parcellation problem, the use of incongruent parcellation schemes by different authors.We here present a coordinate–independent mathematical method to overcome this problem: objective relational transformation (ORT). Based on new classifications for brain data and on methods from theoretical computer science, ORT represents a formally defined, transparent transformation method for reproducible, coordinate–independent mapping of brain data to freely chosen parcellation schemes. We describe the methodology of ORTand discuss its strengths and limitations. Using two practical examples, we show that ORT in conjunction with connectivity databases like CoCoMac (http://www.cocomac.org) is an important tool for analyses of cortical organization and structure–function relationships.
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Wu-Yan, Elena, Richard F. Betzel, Evelyn Tang, Shi Gu, Fabio Pasqualetti, and Danielle S. Bassett. "Benchmarking Measures of Network Controllability on Canonical Graph Models." Journal of Nonlinear Science 30, no. 5 (March 9, 2018): 2195–233. http://dx.doi.org/10.1007/s00332-018-9448-z.
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Abstract The control of networked dynamical systems opens the possibility for new discoveries and therapies in systems biology and neuroscience. Recent theoretical advances provide candidate mechanisms by which a system can be driven from one pre-specified state to another, and computational approaches provide tools to test those mechanisms in real-world systems. Despite already having been applied to study network systems in biology and neuroscience, the practical performance of these tools and associated measures on simple networks with pre-specified structure has yet to be assessed. Here, we study the behavior of four control metrics (global, average, modal, and boundary controllability) on eight canonical graphs (including Erdős–Rényi, regular, small-world, random geometric, Barábasi–Albert preferential attachment, and several modular networks) with different edge weighting schemes (Gaussian, power-law, and two nonparametric distributions from brain networks, as examples of real-world systems). We observe that differences in global controllability across graph models are more salient when edge weight distributions are heavy-tailed as opposed to normal. In contrast, differences in average, modal, and boundary controllability across graph models (as well as across nodes in the graph) are more salient when edge weight distributions are less heavy-tailed. Across graph models and edge weighting schemes, average and modal controllability are negatively correlated with one another across nodes; yet, across graph instances, the relation between average and modal controllability can be positive, negative, or nonsignificant. Collectively, these findings demonstrate that controllability statistics (and their relations) differ across graphs with different topologies and that these differences can be muted or accentuated by differences in the edge weight distributions. More generally, our numerical studies motivate future analytical efforts to better understand the mathematical underpinnings of the relationship between graph topology and control, as well as efforts to design networks with specific control profiles.
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Hiraga, Takahiro, Yasufumi Yamada, and Ryo Kobayashi. "Theoretical investigation of active listening behavior based on the echolocation of CF-FM bats." PLOS Computational Biology 18, no. 10 (October 7, 2022): e1009784. http://dx.doi.org/10.1371/journal.pcbi.1009784.
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Bats perceive the three-dimensional environment by emitting ultrasound pulses from their nose or mouth and receiving echoes through both ears. To determine the position of a target object, it is necessary to know the distance and direction of the target. Certain bat species that use a combined signal of long constant frequency and short frequency modulated ultrasounds synchronize their pinnae movement with pulse emission, and this behavior has been regarded as helpful for localizing the elevation angle of a reflective sound source. However, the significance of bats’ ear motions remains unclear. In this study, we construct a model of an active listening system including the motion of the ears, and conduct mathematical investigations to clarify the importance of ear motion in direction detection of the reflective sound source. In the simulations, direction detection under rigid ear movements with interaural level differences was mathematically investigated by assuming that bats accomplish direction detection using the amplitude modulation in the echoes caused by ear movements. In particular, the ear motion conditions required for direction detection are theoretically investigated through exhaustive simulations of the pseudo-motion of the ears, rather than simulations of the actual ear motions of bats. The theory suggests that only certain ear motions, namely three-axis rotation, allow for accurate and robust direction detection. Our theoretical analysis also strongly supports the behavior whereby bats move their pinnae in the antiphase mode. In addition, we suggest that simple shaped hearing directionality and well-selected uncomplicated ear motions are sufficient to achieve precise and robust direction detection. Our findings and mathematical approach have the potential to be used in the design of active sensing systems in various engineering fields.
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Tung, Hwai-Ray, and Rick Durrett. "Signatures of neutral evolution in exponentially growing tumors: A theoretical perspective." PLOS Computational Biology 17, no. 2 (February 11, 2021): e1008701. http://dx.doi.org/10.1371/journal.pcbi.1008701.
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Recent work of Sottoriva, Graham, and collaborators have led to the controversial claim that exponentially growing tumors have a site frequency spectrum that follows the 1/f law consistent with neutral evolution. This conclusion has been criticized based on data quality issues, statistical considerations, and simulation results. Here, we use rigorous mathematical arguments to investigate the site frequency spectrum in the two-type model of clonal evolution. If the fitnesses of the two types are λ0 < λ1, then the site frequency spectrum is c/fα where α = λ0/λ1. This is due to the advantageous mutations that produce the founders of the type 1 population. Mutations within the growing type 0 and type 1 populations follow the 1/f law. Our results show that, in contrast to published criticisms, neutral evolution in an exponentially growing tumor can be distinguished from the two-type model using the site frequency spectrum.
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Christensen, Samuel, Yitong Huang, Olivia J. Walch, and Daniel B. Forger. "Optimal adjustment of the human circadian clock in the real world." PLOS Computational Biology 16, no. 12 (December 28, 2020): e1008445. http://dx.doi.org/10.1371/journal.pcbi.1008445.
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Which suggestions for behavioral modifications, based on mathematical models, are most likely to be followed in the real world? We address this question in the context of human circadian rhythms. Jet lag is a consequence of the misalignment of the body’s internal circadian (~24-hour) clock during an adjustment to a new schedule. Light is the clock’s primary synchronizer. Previous research has used mathematical models to compute light schedules that shift the circadian clock to a new time zone as quickly as possible. How users adjust their behavior when provided with these optimal schedules remains an open question. Here, we report data collected by wearables from more than 100 travelers as they cross time zones using a smartphone app, Entrain. We find that people rarely follow the optimal schedules generated through mathematical modeling entirely, but travelers who better followed the optimal schedules reported more positive moods after their trips. Using the data collected, we improve the optimal schedule predictions to accommodate real-world constraints. We also develop a scheduling algorithm that allows for the computation of approximately optimal schedules "on-the-fly" in response to disruptions. User burnout may not be critically important as long as the first parts of a schedule are followed. These results represent a crucial improvement in making the theoretical results of past work viable for practical use and show how theoretical predictions based on known human physiology can be efficiently used in real-world settings.
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D’Alessandro, Marco, Stefan T. Radev, Andreas Voss, and Luigi Lombardi. "A Bayesian brain model of adaptive behavior: an application to the Wisconsin Card Sorting Task." PeerJ 8 (November 30, 2020): e10316. http://dx.doi.org/10.7717/peerj.10316.
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Adaptive behavior emerges through a dynamic interaction between cognitive agents and changing environmental demands. The investigation of information processing underlying adaptive behavior relies on controlled experimental settings in which individuals are asked to accomplish demanding tasks whereby a hidden regularity or an abstract rule has to be learned dynamically. Although performance in such tasks is considered as a proxy for measuring high-level cognitive processes, the standard approach consists in summarizing observed response patterns by simple heuristic scoring measures. With this work, we propose and validate a new computational Bayesian model accounting for individual performance in the Wisconsin Card Sorting Test (WCST), a renowned clinical tool to measure set-shifting and deficient inhibitory processes on the basis of environmental feedback. We formalize the interaction between the task’s structure, the received feedback, and the agent’s behavior by building a model of the information processing mechanisms used to infer the hidden rules of the task environment. Furthermore, we embed the new model within the mathematical framework of the Bayesian Brain Theory (BBT), according to which beliefs about hidden environmental states are dynamically updated following the logic of Bayesian inference. Our computational model maps distinct cognitive processes into separable, neurobiologically plausible, information-theoretic constructs underlying observed response patterns. We assess model identification and expressiveness in accounting for meaningful human performance through extensive simulation studies. We then validate the model on real behavioral data in order to highlight the utility of the proposed model in recovering cognitive dynamics at an individual level. We highlight the potentials of our model in decomposing adaptive behavior in the WCST into several information-theoretic metrics revealing the trial-by-trial unfolding of information processing by focusing on two exemplary individuals whose behavior is examined in depth. Finally, we focus on the theoretical implications of our computational model by discussing the mapping between BBT constructs and functional neuroanatomical correlates of task performance. We further discuss the empirical benefit of recovering the assumed dynamics of information processing for both clinical and research practices, such as neurological assessment and model-based neuroscience.
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Cody, Jonathan W., Amy L. Ellis-Connell, Shelby L. O’Connor, and Elsje Pienaar. "Mathematical modeling of N-803 treatment in SIV-infected non-human primates." PLOS Computational Biology 17, no. 7 (July 28, 2021): e1009204. http://dx.doi.org/10.1371/journal.pcbi.1009204.
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Immunomodulatory drugs could contribute to a functional cure for Human Immunodeficiency Virus (HIV). Interleukin-15 (IL-15) promotes expansion and activation of CD8+ T cell and natural killer (NK) cell populations. In one study, an IL-15 superagonist, N-803, suppressed Simian Immunodeficiency Virus (SIV) in non-human primates (NHPs) who had received prior SIV vaccination. However, viral suppression attenuated with continued N-803 treatment, partially returning after long treatment interruption. While there is evidence of concurrent drug tolerance, immune regulation, and viral escape, the relative contributions of these mechanisms to the observed viral dynamics have not been quantified. Here, we utilize mathematical models of N-803 treatment in SIV-infected macaques to estimate contributions of these three key mechanisms to treatment outcomes: 1) drug tolerance, 2) immune regulation, and 3) viral escape. We calibrated our model to viral and lymphocyte responses from the above-mentioned NHP study. Our models track CD8+ T cell and NK cell populations with N-803-dependent proliferation and activation, as well as viral dynamics in response to these immune cell populations. We compared mathematical models with different combinations of the three key mechanisms based on Akaike Information Criterion and important qualitative features of the NHP data. Two minimal models were capable of reproducing the observed SIV response to N-803. In both models, immune regulation strongly reduced cytotoxic cell activation to enable viral rebound. Either long-term drug tolerance or viral escape (or some combination thereof) could account for changes to viral dynamics across long breaks in N-803 treatment. Theoretical explorations with the models showed that less-frequent N-803 dosing and concurrent immune regulation blockade (e.g. PD-L1 inhibition) may improve N-803 efficacy. However, N-803 may need to be combined with other immune therapies to countermand viral escape from the CD8+ T cell response. Our mechanistic model will inform such therapy design and guide future studies.
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Schindler, Daniel, Ted Moldenhawer, Maike Stange, Valentino Lepro, Carsten Beta, Matthias Holschneider, and Wilhelm Huisinga. "Analysis of protrusion dynamics in amoeboid cell motility by means of regularized contour flows." PLOS Computational Biology 17, no. 8 (August 23, 2021): e1009268. http://dx.doi.org/10.1371/journal.pcbi.1009268.
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Amoeboid cell motility is essential for a wide range of biological processes including wound healing, embryonic morphogenesis, and cancer metastasis. It relies on complex dynamical patterns of cell shape changes that pose long-standing challenges to mathematical modeling and raise a need for automated and reproducible approaches to extract quantitative morphological features from image sequences. Here, we introduce a theoretical framework and a computational method for obtaining smooth representations of the spatiotemporal contour dynamics from stacks of segmented microscopy images. Based on a Gaussian process regression we propose a one-parameter family of regularized contour flows that allows us to continuously track reference points (virtual markers) between successive cell contours. We use this approach to define a coordinate system on the moving cell boundary and to represent different local geometric quantities in this frame of reference. In particular, we introduce the local marker dispersion as a measure to identify localized membrane expansions and provide a fully automated way to extract the properties of such expansions, including their area and growth time. The methods are available as an open-source software package called AmoePy, a Python-based toolbox for analyzing amoeboid cell motility (based on time-lapse microscopy data), including a graphical user interface and detailed documentation. Due to the mathematical rigor of our framework, we envision it to be of use for the development of novel cell motility models. We mainly use experimental data of the social amoeba Dictyostelium discoideum to illustrate and validate our approach.
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Tournus, Magali, Miguel Escobedo, Wei-Feng Xue, and Marie Doumic. "Insights into the dynamic trajectories of protein filament division revealed by numerical investigation into the mathematical model of pure fragmentation." PLOS Computational Biology 17, no. 9 (September 3, 2021): e1008964. http://dx.doi.org/10.1371/journal.pcbi.1008964.
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The dynamics by which polymeric protein filaments divide in the presence of negligible growth, for example due to the depletion of free monomeric precursors, can be described by the universal mathematical equations of ‘pure fragmentation’. The rates of fragmentation reactions reflect the stability of the protein filaments towards breakage, which is of importance in biology and biomedicine for instance in governing the creation of amyloid seeds and the propagation of prions. Here, we devised from mathematical theory inversion formulae to recover the division rates and division kernel information from time dependent experimental measurements of filament size distribution. The numerical approach to systematically analyze the behaviour of pure fragmentation trajectories was also developed. We illustrate how these formulae can be used, provide some insights on their robustness, and show how they inform the design of experiments to measure fibril fragmentation dynamics. These advances are made possible by our central theoretical result on how the length distribution profile of the solution to the pure fragmentation equation aligns with a steady distribution profile for large times.
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Ratti, Vardayani, Seema Nanda, Susan K. Eszterhas, Alexandra L. Howell, and Dorothy I. Wallace. "A mathematical model of HIV dynamics treated with a population of gene-edited haematopoietic progenitor cells exhibiting threshold phenomenon." Mathematical Medicine and Biology: A Journal of the IMA 37, no. 2 (July 2, 2019): 212–42. http://dx.doi.org/10.1093/imammb/dqz011.
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Abstract The use of gene-editing technology has the potential to excise the CCR5 gene from haematopoietic progenitor cells, rendering their differentiated CD4-positive (CD4+) T cell descendants HIV resistant. In this manuscript, we describe the development of a mathematical model to mimic the therapeutic potential of gene editing of haematopoietic progenitor cells to produce a class of HIV-resistant CD4+ T cells. We define the requirements for the permanent suppression of viral infection using gene editing as a novel therapeutic approach. We develop non-linear ordinary differential equation models to replicate HIV production in an infected host, incorporating the most appropriate aspects found in the many existing clinical models of HIV infection, and extend this model to include compartments representing HIV-resistant immune cells. Through an analysis of model equilibria and stability and computation of $R_0$ for both treated and untreated infections, we show that the proposed therapy has the potential to suppress HIV infection indefinitely and return CD4+ T cell counts to normal levels. A computational study for this treatment shows the potential for a successful ‘functional cure’ of HIV. A sensitivity analysis illustrates the consistency of numerical results with theoretical results and highlights the parameters requiring better biological justification. Simulations of varying level production of HIV-resistant CD4+ T cells and varying immune enhancements as the result of these indicate a clear threshold response of the model and a range of treatment parameters resulting in a return to normal CD4+ T cell counts.
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RIBBA, B., K. MARRON, Z. AGUR, T. ALARCON, and P. MAINI. "A mathematical model of Doxorubicin treatment efficacy for non-Hodgkin?s lymphoma: investigation of the current protocol through theoretical modelling results." Bulletin of Mathematical Biology 67, no. 1 (January 2005): 79–99. http://dx.doi.org/10.1016/j.bulm.2004.06.007.
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Perkins, Melinda Liu. "Implications of diffusion and time-varying morphogen gradients for the dynamic positioning and precision of bistable gene expression boundaries." PLOS Computational Biology 17, no. 6 (June 1, 2021): e1008589. http://dx.doi.org/10.1371/journal.pcbi.1008589.
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The earliest models for how morphogen gradients guide embryonic patterning failed to account for experimental observations of temporal refinement in gene expression domains. Following theoretical and experimental work in this area, dynamic positional information has emerged as a conceptual framework to discuss how cells process spatiotemporal inputs into downstream patterns. Here, we show that diffusion determines the mathematical means by which bistable gene expression boundaries shift over time, and therefore how cells interpret positional information conferred from morphogen concentration. First, we introduce a metric for assessing reproducibility in boundary placement or precision in systems where gene products do not diffuse, but where morphogen concentrations are permitted to change in time. We show that the dynamics of the gradient affect the sensitivity of the final pattern to variation in initial conditions, with slower gradients reducing the sensitivity. Second, we allow gene products to diffuse and consider gene expression boundaries as propagating wavefronts with velocity modulated by local morphogen concentration. We harness this perspective to approximate a PDE model as an ODE that captures the position of the boundary in time, and demonstrate the approach with a preexisting model for Hunchback patterning in fruit fly embryos. We then propose a design that employs antiparallel morphogen gradients to achieve accurate boundary placement that is robust to scaling. Throughout our work we draw attention to tradeoffs among initial conditions, boundary positioning, and the relative timescales of network and gradient evolution. We conclude by suggesting that mathematical theory should serve to clarify not just our quantitative, but also our intuitive understanding of patterning processes.
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Barra Avila, Diego, Juan R. Melendez-Alvarez, and Xiao-Jun Tian. "Control of tissue homeostasis, tumorigenesis, and degeneration by coupled bidirectional bistable switches." PLOS Computational Biology 17, no. 11 (November 19, 2021): e1009606. http://dx.doi.org/10.1371/journal.pcbi.1009606.
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The Hippo-YAP/TAZ signaling pathway plays a critical role in tissue homeostasis, tumorigenesis, and degeneration disorders. The regulation of YAP/TAZ levels is controlled by a complex regulatory network, where several feedback loops have been identified. However, it remains elusive how these feedback loops contain the YAP/TAZ levels and maintain the system in a healthy physiological state or trap the system in pathological conditions. Here, a mathematical model was developed to represent the YAP/TAZ regulatory network. Through theoretical analyses, three distinct states that designate the one physiological and two pathological outcomes were found. The transition from the physiological state to the two pathological states is mechanistically controlled by coupled bidirectional bistable switches, which are robust to parametric variation and stochastic fluctuations at the molecular level. This work provides a mechanistic understanding of the regulation and dysregulation of YAP/TAZ levels in tissue state transitions.
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Chizhov, Anton V., and Lyle J. Graham. "A strategy for mapping biophysical to abstract neuronal network models applied to primary visual cortex." PLOS Computational Biology 17, no. 8 (August 16, 2021): e1009007. http://dx.doi.org/10.1371/journal.pcbi.1009007.
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A fundamental challenge for the theoretical study of neuronal networks is to make the link between complex biophysical models based directly on experimental data, to progressively simpler mathematical models that allow the derivation of general operating principles. We present a strategy that successively maps a relatively detailed biophysical population model, comprising conductance-based Hodgkin-Huxley type neuron models with connectivity rules derived from anatomical data, to various representations with fewer parameters, finishing with a firing rate network model that permits analysis. We apply this methodology to primary visual cortex of higher mammals, focusing on the functional property of stimulus orientation selectivity of receptive fields of individual neurons. The mapping produces compact expressions for the parameters of the abstract model that clearly identify the impact of specific electrophysiological and anatomical parameters on the analytical results, in particular as manifested by specific functional signatures of visual cortex, including input-output sharpening, conductance invariance, virtual rotation and the tilt after effect. Importantly, qualitative differences between model behaviours point out consequences of various simplifications. The strategy may be applied to other neuronal systems with appropriate modifications.
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Lindstrom, Michael R., Manuel B. Chavez, Elijah A. Gross-Sable, Eric Y. Hayden, and David B. Teplow. "From reaction kinetics to dementia: A simple dimer model of Alzheimer’s disease etiology." PLOS Computational Biology 17, no. 7 (July 19, 2021): e1009114. http://dx.doi.org/10.1371/journal.pcbi.1009114.
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Oligomers of the amyloid β-protein (Aβ) have been implicated in the pathogenesis of Alzheimer’s disease (AD) through their toxicity towards neurons. Understanding the process of oligomerization may contribute to the development of therapeutic agents, but this has been difficult due to the complexity of oligomerization and the metastability of the oligomers thus formed. To understand the kinetics of oligomer formation, and how that relates to the progression of AD, we developed models of the oligomerization process. Here, we use experimental data from cell viability assays and proxies for rate constants involved in monomer-dimer-trimer kinetics to develop a simple mathematical model linking Aβ assembly to oligomer-induced neuronal degeneration. This model recapitulates the rapid growth of disease incidence with age. It does so through incorporation of age-dependent changes in rates of Aβ monomer production and elimination. The model also describes clinical progression in genetic forms of AD (e.g., Down’s syndrome), changes in hippocampal volume, AD risk after traumatic brain injury, and spatial spreading of the disease due to foci in which Aβ production is elevated. Continued incorporation of clinical and basic science data into the current model will make it an increasingly relevant model system for doing theoretical calculations that are not feasible in biological systems. In addition, terms in the model that have particularly large effects are likely to be especially useful therapeutic targets.
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Martinez-Rabert, Eloi, Chiel van Amstel, Cindy Smith, William T. Sloan, and Rebeca Gonzalez-Cabaleiro. "Environmental and ecological controls of the spatial distribution of microbial populations in aggregates." PLOS Computational Biology 18, no. 12 (December 19, 2022): e1010807. http://dx.doi.org/10.1371/journal.pcbi.1010807.
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In microbial communities, the ecological interactions between species of different populations are responsible for the spatial distributions observed in aggregates (granules, biofilms or flocs). To explore the underlying mechanisms that control these processes, we have developed a mathematical modelling framework able to describe, label and quantify defined spatial structures that arise from microbial and environmental interactions in communities. An artificial system of three populations collaborating or competing in an aggregate is simulated using individual-based modelling under different environmental conditions. In this study, neutralism, competition, commensalism and concurrence of commensalism and competition have been considered. We were able to identify interspecific segregation of communities that appears in competitive environments (columned stratification), and a layered distribution of populations that emerges in commensal (layered stratification). When different ecological interactions were considered in the same aggregate, the resultant spatial distribution was identified as the one controlled by the most limiting substrate. A theoretical modulus was defined, with which we were able to quantify the effect of environmental conditions and ecological interactions to predict the most probable spatial distribution. The specific microbial patterns observed in our results allowed us to identify the optimal spatial organizations for bacteria to thrive when building a microbial community and how this permitted co-existence of populations at different growth rates. Our model reveals that although ecological relationships between different species dictate the distribution of bacteria, the environment controls the final spatial distribution of the community.
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Mor, Uria, Yotam Cohen, Rafael Valdés-Mas, Denise Kviatcovsky, Eran Elinav, and Haim Avron. "Dimensionality reduction of longitudinal ’omics data using modern tensor factorizations." PLOS Computational Biology 18, no. 7 (July 15, 2022): e1010212. http://dx.doi.org/10.1371/journal.pcbi.1010212.
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Longitudinal ’omics analytical methods are extensively used in the field of evolving precision medicine, by enabling ‘big data’ recording and high-resolution interpretation of complex datasets, driven by individual variations in response to perturbations such as disease pathogenesis, medical treatment or changes in lifestyle. However, inherent technical limitations in biomedical studies often result in the generation of feature-rich and sample-limited datasets. Analyzing such data using conventional modalities often proves to be challenging since the repeated, high-dimensional measurements overload the outlook with inconsequential variations that must be filtered from the data in order to find the true, biologically relevant signal. Tensor methods for the analysis and meaningful representation of multi-way data may prove useful to the biological research community by their advertised ability to tackle this challenge. In this study, we present tcam—a new unsupervised tensor factorization method for the analysis of multi-way data. Building on top of cutting-edge developments in the field of tensor-tensor algebra, we characterize the unique mathematical properties of our method, namely, 1) preservation of geometric and statistical traits of the data, which enables uncovering information beyond the inter-individual variation that often takes-over the focus, especially in human studies. 2) Natural and straightforward out-of-sample extension, making tcam amenable for integration in machine learning workflows. A series of re-analyses of real-world, human experimental datasets showcase these theoretical properties, while providing empirical confirmation of tcam’s utility in the analysis of longitudinal ’omics data.
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Cunniffe, Nik J., Nick P. Taylor, Frédéric M. Hamelin, and Michael J. Jeger. "Epidemiological and ecological consequences of virus manipulation of host and vector in plant virus transmission." PLOS Computational Biology 17, no. 12 (December 30, 2021): e1009759. http://dx.doi.org/10.1371/journal.pcbi.1009759.
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Many plant viruses are transmitted by insect vectors. Transmission can be described as persistent or non-persistent depending on rates of acquisition, retention, and inoculation of virus. Much experimental evidence has accumulated indicating vectors can prefer to settle and/or feed on infected versus noninfected host plants. For persistent transmission, vector preference can also be conditional, depending on the vector’s own infection status. Since viruses can alter host plant quality as a resource for feeding, infection potentially also affects vector population dynamics. Here we use mathematical modelling to develop a theoretical framework addressing the effects of vector preferences for landing, settling and feeding–as well as potential effects of infection on vector population density–on plant virus epidemics. We explore the consequences of preferences that depend on the host (infected or healthy) and vector (viruliferous or nonviruliferous) phenotypes, and how this is affected by the form of transmission, persistent or non-persistent. We show how different components of vector preference have characteristic effects on both the basic reproduction number and the final incidence of disease. We also show how vector preference can induce bistability, in which the virus is able to persist even when it cannot invade from very low densities. Feedbacks between plant infection status, vector population dynamics and virus transmission potentially lead to very complex dynamics, including sustained oscillations. Our work is supported by an interactive interface https://plantdiseasevectorpreference.herokuapp.com/. Our model reiterates the importance of coupling virus infection to vector behaviour, life history and population dynamics to fully understand plant virus epidemics.
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Arthur, Ronan F., James H. Jones, Matthew H. Bonds, Yoav Ram, and Marcus W. Feldman. "Adaptive social contact rates induce complex dynamics during epidemics." PLOS Computational Biology 17, no. 2 (February 10, 2021): e1008639. http://dx.doi.org/10.1371/journal.pcbi.1008639.
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Epidemics may pose a significant dilemma for governments and individuals. The personal or public health consequences of inaction may be catastrophic; but the economic consequences of drastic response may likewise be catastrophic. In the face of these trade-offs, governments and individuals must therefore strike a balance between the economic and personal health costs of reducing social contacts and the public health costs of neglecting to do so. As risk of infection increases, potentially infectious contact between people is deliberately reduced either individually or by decree. This must be balanced against the social and economic costs of having fewer people in contact, and therefore active in the labor force or enrolled in school. Although the importance of adaptive social contact on epidemic outcomes has become increasingly recognized, the most important properties of coupled human-natural epidemic systems are still not well understood. We develop a theoretical model for adaptive, optimal control of the effective social contact rate using traditional epidemic modeling tools and a utility function with delayed information. This utility function trades off the population-wide contact rate with the expected cost and risk of increasing infections. Our analytical and computational analysis of this simple discrete-time deterministic strategic model reveals the existence of an endemic equilibrium, oscillatory dynamics around this equilibrium under some parametric conditions, and complex dynamic regimes that shift under small parameter perturbations. These results support the supposition that infectious disease dynamics under adaptive behavior change may have an indifference point, may produce oscillatory dynamics without other forcing, and constitute complex adaptive systems with associated dynamics. Implications for any epidemic in which adaptive behavior influences infectious disease dynamics include an expectation of fluctuations, for a considerable time, around a quasi-equilibrium that balances public health and economic priorities, that shows multiple peaks and surges in some scenarios, and that implies a high degree of uncertainty in mathematical projections.
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Gérard, Claude, Laurane De Mot, Sabine Cordi, Jonathan van Eyll, and Frédéric P. Lemaigre. "Temporal dynamics of a CSF1R signaling gene regulatory network involved in epilepsy." PLOS Computational Biology 17, no. 4 (April 5, 2021): e1008854. http://dx.doi.org/10.1371/journal.pcbi.1008854.
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Colony Stimulating Factor 1 Receptor (CSF1R) is a potential target for anti-epileptic drugs. However, inhibition of CSF1R is not well tolerated by patients, thereby prompting the need for alternative targets. To develop a framework for identification of such alternatives, we here develop a mathematical model of a pro-inflammatory gene regulatory network (GRN) involved in epilepsy and centered around CSF1R. This GRN comprises validated transcriptional and post-transcriptional regulations involving STAT1, STAT3, NFκB, IL6R, CSF3R, IRF8, PU1, C/EBPα, TNFR1, CSF1 and CSF1R. The model was calibrated on mRNA levels of all GRN components in lipopolysaccharide (LPS)-treated mouse microglial BV-2 cells, and allowed to predict that STAT1 and STAT3 have the strongest impact on the expression of the other GRN components. Microglial BV-2 cells were selected because, the modules from which the GRN was deduced are enriched for microglial marker genes. The function of STAT1 and STAT3 in the GRN was experimentally validated in BV-2 cells. Further, in silico analysis of the GRN dynamics predicted that a pro-inflammatory stimulus can induce irreversible bistability whereby the expression level of GRN components occurs as two distinct states. The irreversibility of the switch may enforce the need for chronic inhibition of the CSF1R GRN in order to achieve therapeutic benefit. The cell-to-cell heterogeneity driven by the bistability may cause variable therapeutic response. In conclusion, our modeling approach uncovered a GRN controlling CSF1R that is predominantly regulated by STAT1 and STAT3. Irreversible inflammation-induced bistability and cell-to-cell heterogeneity of the GRN provide a theoretical foundation to the need for chronic GRN control and the limited potential for disease modification via inhibition of CSF1R.
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Bhattacharya, Priyan, Karthik Raman, and Arun K. Tangirala. "Discovering adaptation-capable biological network structures using control-theoretic approaches." PLOS Computational Biology 18, no. 1 (January 21, 2022): e1009769. http://dx.doi.org/10.1371/journal.pcbi.1009769.
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Constructing biological networks capable of performing specific biological functionalities has been of sustained interest in synthetic biology. Adaptation is one such ubiquitous functional property, which enables every living organism to sense a change in its surroundings and return to its operating condition prior to the disturbance. In this paper, we present a generic systems theory-driven method for designing adaptive protein networks. First, we translate the necessary qualitative conditions for adaptation to mathematical constraints using the language of systems theory, which we then map back as ‘design requirements’ for the underlying networks. We go on to prove that a protein network with different input–output nodes (proteins) needs to be at least of third-order in order to provide adaptation. Next, we show that the necessary design principles obtained for a three-node network in adaptation consist of negative feedback or a feed-forward realization. We argue that presence of a particular class of negative feedback or feed-forward realization is necessary for a network of any size to provide adaptation. Further, we claim that the necessary structural conditions derived in this work are the strictest among the ones hitherto existed in the literature. Finally, we prove that the capability of producing adaptation is retained for the admissible motifs even when the output node is connected with a downstream system in a feedback fashion. This result explains how complex biological networks achieve robustness while keeping the core motifs unchanged in the context of a particular functionality. We corroborate our theoretical results with detailed and thorough numerical simulations. Overall, our results present a generic, systematic and robust framework for designing various kinds of biological networks.
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Andrade, Jair, and Jim Duggan. "Inferring the effective reproductive number from deterministic and semi-deterministic compartmental models using incidence and mobility data." PLOS Computational Biology 18, no. 6 (June 27, 2022): e1010206. http://dx.doi.org/10.1371/journal.pcbi.1010206.
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The effective reproduction number (ℜt) is a theoretical indicator of the course of an infectious disease that allows policymakers to evaluate whether current or previous control efforts have been successful or whether additional interventions are necessary. This metric, however, cannot be directly observed and must be inferred from available data. One approach to obtaining such estimates is fitting compartmental models to incidence data. We can envision these dynamic models as the ensemble of structures that describe the disease’s natural history and individuals’ behavioural patterns. In the context of the response to the COVID-19 pandemic, the assumption of a constant transmission rate is rendered unrealistic, and it is critical to identify a mathematical formulation that accounts for changes in contact patterns. In this work, we leverage existing approaches to propose three complementary formulations that yield similar estimates for ℜt based on data from Ireland’s first COVID-19 wave. We describe these Data Generating Processes (DGP) in terms of State-Space models. Two (DGP1 and DGP2) correspond to stochastic process models whose transmission rate is modelled as Brownian motion processes (Geometric and Cox-Ingersoll-Ross). These DGPs share a measurement model that accounts for incidence and transmission rates, where mobility data is assumed as a proxy of the transmission rate. We perform inference on these structures using Iterated Filtering and the Particle Filter. The final DGP (DGP3) is built from a pool of deterministic models that describe the transmission rate as information delays. We calibrate this pool of models to incidence reports using Hamiltonian Monte Carlo. By following this complementary approach, we assess the tradeoffs associated with each formulation and reflect on the benefits/risks of incorporating proxy data into the inference process. We anticipate this work will help evaluate the implications of choosing a particular formulation for the dynamics and observation of the time-varying transmission rate.
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"Mathematical/computational/ theoretical neuroscience research awards." Neural Networks 2, no. 2 (January 1989): 153. http://dx.doi.org/10.1016/0893-6080(89)90032-4.
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Hipólito, Inês. "Cognition Without Neural Representation: Dynamics of a Complex System." Frontiers in Psychology 12 (January 12, 2022). http://dx.doi.org/10.3389/fpsyg.2021.643276.
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This paper proposes an account of neurocognitive activity without leveraging the notion of neural representation. Neural representation is a concept that results from assuming that the properties of the models used in computational cognitive neuroscience (e.g., information, representation, etc.) must literally exist the system being modelled (e.g., the brain). Computational models are important tools to test a theory about how the collected data (e.g., behavioural or neuroimaging) has been generated. While the usefulness of computational models is unquestionable, it does not follow that neurocognitive activity should literally entail the properties construed in the model (e.g., information, representation). While this is an assumption present in computationalist accounts, it is not held across the board in neuroscience. In the last section, the paper offers a dynamical account of neurocognitive activity with Dynamical Causal Modelling (DCM) that combines dynamical systems theory (DST) mathematical formalisms with the theoretical contextualisation provided by Embodied and Enactive Cognitive Science (EECS).
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Stoliar, Pablo, Olivier Schneegans, and Marcelo J. Rozenberg. "A Functional Spiking Neural Network of Ultra Compact Neurons." Frontiers in Neuroscience 15 (February 25, 2021). http://dx.doi.org/10.3389/fnins.2021.635098.
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We demonstrate that recently introduced ultra-compact neurons (UCN) with a minimal number of components can be interconnected to implement a functional spiking neural network. For concreteness we focus on the Jeffress model, which is a classic neuro-computational model proposed in the 40’s to explain the sound directionality detection by animals and humans. In addition, we introduce a long-axon neuron, whose architecture is inspired by the Hodgkin-Huxley axon delay-line and where the UCNs implement the nodes of Ranvier. We then interconnect two of those neurons to an output layer of UCNs, which detect coincidences between spikes propagating down the long-axons. This functional spiking neural neuron circuit with biological relevance is built from identical UCN blocks, which are simple enough to be made with off-the-shelf electronic components. Our work realizes a new, accessible and affordable physical model platform, where neuroscientists can construct arbitrary mid-size spiking neuronal networks in a lego-block like fashion that work in continuous time. This should enable them to address in a novel experimental manner fundamental questions about the nature of the neural code and to test predictions from mathematical models and algorithms of basic neurobiology research. The present work aims at opening a new experimental field of basic research in Spiking Neural Networks to a potentially large community, which is at the crossroads of neurobiology, dynamical systems, theoretical neuroscience, condensed matter physics, neuromorphic engineering, artificial intelligence, and complex systems.
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Höfner, Nora, Jan-Hendrik Storm, Peter Hömmen, Antonino Mario Cassarà, and Rainer Körber. "Computational and Phantom-Based Feasibility Study of 3D dcNCI With Ultra-Low-Field MRI." Frontiers in Physics 9 (April 26, 2021). http://dx.doi.org/10.3389/fphy.2021.647376.
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The possibility to directly and non-invasively localize neuronal activities in the human brain, as for instance by performing neuronal current imaging (NCI) via magnetic resonance imaging (MRI), would be a breakthrough in neuroscience. In order to assess the feasibility of 3-dimensional (3D) NCI, comprehensive computational and physical phantom experiments using low-noise ultra-low-field (ULF) MRI technology were performed using two different source models within spherical phantoms. The source models, consisting of a single dipole and an extended dipole grid, were calibrated enabling the quantitative emulation of a long-lasting neuronal activity by the application of known current waveforms. The dcNCI experiments were also simulated by solving the Bloch equations using the calculated internal magnetic field distributions of the phantoms and idealized MRI fields. The simulations were then validated by physical phantom experiments using a moderate polarization field of 17 mT. A focal activity with an equivalent current dipole of about 150 nAm and a physiologically relevant depth of 35 mm could be resolved with an isotropic voxel size of 25 mm. The simulation tool enabled the optimization of the imaging parameters for sustained neuronal activities in order to predict maximum sensitivity.
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Bruineberg, Jelle, Krzysztof Dolega, Joe Dewhurst, and Manuel Baltieri. "The Emperor's New Markov Blankets." Behavioral and Brain Sciences, October 22, 2021, 1–63. http://dx.doi.org/10.1017/s0140525x21002351.
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Abstract The free energy principle, an influential framework in computational neuroscience and theoretical neurobiology, starts from the assumption that living systems ensure adaptive exchanges with their environment by minimizing the objective function of variational free energy. Following this premise, it claims to deliver a promising integration of the life sciences. In recent work, Markov Blankets, one of the central constructs of the free energy principle, have been applied to resolve debates central to philosophy (such as demarcating the boundaries of the mind). The aim of this paper is twofold. First, we trace the development of Markov blankets starting from their standard application in Bayesian networks, via variational inference, to their use in the literature on active inference. We then identify a persistent confusion in the literature between the formal use of Markov blankets as an epistemic tool for Bayesian inference, and their novel metaphysical use in the free energy framework to demarcate the physical boundary between an agent and its environment. Consequently, we propose to distinguish between ‘Pearl blankets’ to refer to the original epistemic use of Markov blankets and ‘Friston blankets’ to refer to the new metaphysical construct. Second, we use this distinction to critically assess claims resting on the application of Markov blankets to philosophical problems. We suggest that this literature would do well in differentiating between two different research programs: ‘inference with a model’ and ‘inference within a model’. Only the latter is capable of doing metaphysical work with Markov blankets, but requires additional philosophical premises and cannot be justified by an appeal to the success of the mathematical framework alone.
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Spiliotis, Konstantinos, Konstantin Butenko, Ursula van Rienen, Jens Starke, and Rüdiger Köhling. "Complex network measures reveal optimal targets for deep brain stimulation and identify clusters of collective brain dynamics." Frontiers in Physics 10 (October 18, 2022). http://dx.doi.org/10.3389/fphy.2022.951724.
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An important question in computational neuroscience is how to improve the efficacy of deep brain stimulation by extracting information from the underlying connectivity structure. Recent studies also highlight the relation of structural and functional connectivity in disorders such as Parkinson’s disease. Exploiting the structural properties of the network, we identify nodes of strong influence, which are potential targets for Deep Brain Stimulation (DBS). Simulating the volume of the tissue activated, we confirm that the proposed targets are reported as optimal targets (sweet spots) to be beneficial for the improvement of motor symptoms. Furthermore, based on a modularity algorithm, network communities are detected as set of nodes with high-interconnectivity. This allows to localise the neural activity, directly from the underlying structural topology. For this purpose, we build a large scale computational model that consists of the following elements of the basal ganglia network: subthalamic nucleus (STN), globus pallidus (external and internal parts) (GPe-GPi), extended with the striatum, thalamus and motor cortex (MC) areas, integrating connectivity from multimodal imaging data. We analyse the network dynamics under Healthy, Parkinsonian and DBS conditions with the aim to improve DBS treatment. The dynamics of the communities define a new functional partition (or segregation) of the brain, characterising Healthy, Parkinsonian and DBS treatment conditions.
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Fiandaca, Giada, Marcello Delitala, and Tommaso Lorenzi. "A Mathematical Study of the Influence of Hypoxia and Acidity on the Evolutionary Dynamics of Cancer." Bulletin of Mathematical Biology 83, no. 7 (June 15, 2021). http://dx.doi.org/10.1007/s11538-021-00914-3.
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AbstractHypoxia and acidity act as environmental stressors promoting selection for cancer cells with a more aggressive phenotype. As a result, a deeper theoretical understanding of the spatio-temporal processes that drive the adaptation of tumour cells to hypoxic and acidic microenvironments may open up new avenues of research in oncology and cancer treatment. We present a mathematical model to study the influence of hypoxia and acidity on the evolutionary dynamics of cancer cells in vascularised tumours. The model is formulated as a system of partial integro-differential equations that describe the phenotypic evolution of cancer cells in response to dynamic variations in the spatial distribution of three abiotic factors that are key players in tumour metabolism: oxygen, glucose and lactate. The results of numerical simulations of a calibrated version of the model based on real data recapitulate the eco-evolutionary spatial dynamics of tumour cells and their adaptation to hypoxic and acidic microenvironments. Moreover, such results demonstrate how nonlinear interactions between tumour cells and abiotic factors can lead to the formation of environmental gradients which select for cells with phenotypic characteristics that vary with distance from intra-tumour blood vessels, thus promoting the emergence of intra-tumour phenotypic heterogeneity. Finally, our theoretical findings reconcile the conclusions of earlier studies by showing that the order in which resistance to hypoxia and resistance to acidity arise in tumours depend on the ways in which oxygen and lactate act as environmental stressors in the evolutionary dynamics of cancer cells.
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Caudera, Elisa, Simona Viale, Sandro Bertolino, Jacopo Cerri, and Ezio Venturino. "A Mathematical Model Supporting a Hyperpredation Effect in the Apparent Competition Between Invasive Eastern Cottontail and Native European Hare." Bulletin of Mathematical Biology 83, no. 5 (March 27, 2021). http://dx.doi.org/10.1007/s11538-021-00873-9.
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AbstractIn this work a mathematical model is built in order to validate on theoretical grounds field study results on a three-species system made of two prey, of which one is native and another one invasive, together with a native predator. Specifically, our results mathematically describe the negative effect on the native European hare after the introduction of the invasive Eastern cottontail, mediated by an increased predation rate by foxes. Two nonexclusive assumptions can be made: an increase in cottontail abundance would lead to a larger fox population, magnifying their predatory impact (“hyperpredation”) on hares; alternatively, cottontails attract foxes in patches where they live, which are also important resting sites for hares and consequently the increased presence of foxes results in a higher predation rates on hares. The model results support hyperpredation of increasing fox populations on native hares.
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El Wajeh, Mohammad, Falco Jung, Dominik Bongartz, Chrysoula Dimitra Kappatou, Narmin Ghaffari Laleh, Alexander Mitsos, and Jakob Nikolas Kather. "Can the Kuznetsov Model Replicate and Predict Cancer Growth in Humans?" Bulletin of Mathematical Biology 84, no. 11 (September 29, 2022). http://dx.doi.org/10.1007/s11538-022-01075-7.
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AbstractSeveral mathematical models to predict tumor growth over time have been developed in the last decades. A central aspect of such models is the interaction of tumor cells with immune effector cells. The Kuznetsov model (Kuznetsov et al. in Bull Math Biol 56(2):295–321, 1994) is the most prominent of these models and has been used as a basis for many other related models and theoretical studies. However, none of these models have been validated with large-scale real-world data of human patients treated with cancer immunotherapy. In addition, parameter estimation of these models remains a major bottleneck on the way to model-based and data-driven medical treatment. In this study, we quantitatively fit Kuznetsov’s model to a large dataset of 1472 patients, of which 210 patients have more than six data points, by estimating the model parameters of each patient individually. We also conduct a global practical identifiability analysis for the estimated parameters. We thus demonstrate that several combinations of parameter values could lead to accurate data fitting. This opens the potential for global parameter estimation of the model, in which the values of all or some parameters are fixed for all patients. Furthermore, by omitting the last two or three data points, we show that the model can be extrapolated and predict future tumor dynamics. This paves the way for a more clinically relevant application of mathematical tumor modeling, in which the treatment strategy could be adjusted in advance according to the model’s future predictions.
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Aniţa, Sebastian, Vincenzo Capasso, and Simone Scacchi. "Controlling the Spatial Spread of a Xylella Epidemic." Bulletin of Mathematical Biology 83, no. 4 (February 17, 2021). http://dx.doi.org/10.1007/s11538-021-00861-z.
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AbstractIn a recent paper by one of the authors and collaborators, motivated by the Olive Quick Decline Syndrome (OQDS) outbreak, which has been ongoing in Southern Italy since 2013, a simple epidemiological model describing this epidemic was presented. Beside the bacterium Xylella fastidiosa, the main players considered in the model are its insect vectors, Philaenus spumarius, and the host plants (olive trees and weeds) of the insects and of the bacterium. The model was based on a system of ordinary differential equations, the analysis of which provided interesting results about possible equilibria of the epidemic system and guidelines for its numerical simulations. Although the model presented there was mathematically rather simplified, its analysis has highlighted threshold parameters that could be the target of control strategies within an integrated pest management framework, not requiring the removal of the productive resource represented by the olive trees. Indeed, numerical simulations support the outcomes of the mathematical analysis, according to which the removal of a suitable amount of weed biomass (reservoir of Xylella fastidiosa) from olive orchards and surrounding areas resulted in the most efficient strategy to control the spread of the OQDS. In addition, as expected, the adoption of more resistant olive tree cultivars has been shown to be a good strategy, though less cost-effective, in controlling the pathogen. In this paper for a more realistic description and a clearer interpretation of the proposed control measures, a spatial structure of the epidemic system has been included, but, in order to keep mathematical technicalities to a minimum, only two players have been described in a dynamical way, trees and insects, while the weed biomass is taken to be a given quantity. The control measures have been introduced only on a subregion of the whole habitat, in order to contain costs of intervention. We show that such a practice can lead to the eradication of an epidemic outbreak. Numerical simulations confirm both the results of the previous paper and the theoretical results of the model with a spatial structure, though subject to regional control only.