Krishna Manoj, Theodore W. Grunberg, Domitilla Del Vecchio
The discovery of CRISPR-mediated gene activation (CRISPRa) has transformed the way in which we perform genetic screening, bioproduction and therapeutics through its ability to scale and multiplex. However, the emergence of loads on the key molecular resources constituting CRISPRa by the orthogonal short RNA that guide such resources to gene targets, couple theoretically independent CRISPRa modules. This coupling negates the ability of CRISPRa systems to concurrently regulate multiple genes independent of one another. In this paper, we propose to reduce this coupling by mitigating the loads on the molecular resources that constitute CRISPRa. In particular, we design a multi-variable controller that makes the concentration of these molecular resources robust to variations in the level of the short RNA loads. This work serves as a foundation to design and implement CRISPRa controllers for practical applications.
{"title":"Multi-variable control to mitigate loads in CRISPRa networks","authors":"Krishna Manoj, Theodore W. Grunberg, Domitilla Del Vecchio","doi":"arxiv-2409.07384","DOIUrl":"https://doi.org/arxiv-2409.07384","url":null,"abstract":"The discovery of CRISPR-mediated gene activation (CRISPRa) has transformed\u0000the way in which we perform genetic screening, bioproduction and therapeutics\u0000through its ability to scale and multiplex. However, the emergence of loads on\u0000the key molecular resources constituting CRISPRa by the orthogonal short RNA\u0000that guide such resources to gene targets, couple theoretically independent\u0000CRISPRa modules. This coupling negates the ability of CRISPRa systems to\u0000concurrently regulate multiple genes independent of one another. In this paper,\u0000we propose to reduce this coupling by mitigating the loads on the molecular\u0000resources that constitute CRISPRa. In particular, we design a multi-variable\u0000controller that makes the concentration of these molecular resources robust to\u0000variations in the level of the short RNA loads. This work serves as a\u0000foundation to design and implement CRISPRa controllers for practical\u0000applications.","PeriodicalId":501325,"journal":{"name":"arXiv - QuanBio - Molecular Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206273","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present some results helpful for parameterising positive equilibria, and bounding the number of positive nondegenerate equilibria, in mass action networks. Any mass action network naturally gives rise to a set of polynomial equations whose positive solutions are precisely the positive equilibria of the network. Here we derive alternative systems of equations, often also polynomial, whose solutions are in smooth, one-to-one correspondence with positive equilibria of the network. Often these alternative systems are simpler than the original mass action equations, and allow us to infer useful bounds on the number of positive equilibria. The alternative equation systems can also be helpful for parameterising the equilibrium set explicitly, for deriving descriptions of the parameter regions for multistationarity, and for studying bifurcations. We present the main construction, some bounds which follow for particular classes of networks, numerous examples, and some open questions and conjectures.
{"title":"Some bounds on positive equilibria in mass action networks","authors":"Murad Banaji","doi":"arxiv-2409.06877","DOIUrl":"https://doi.org/arxiv-2409.06877","url":null,"abstract":"We present some results helpful for parameterising positive equilibria, and\u0000bounding the number of positive nondegenerate equilibria, in mass action\u0000networks. Any mass action network naturally gives rise to a set of polynomial\u0000equations whose positive solutions are precisely the positive equilibria of the\u0000network. Here we derive alternative systems of equations, often also\u0000polynomial, whose solutions are in smooth, one-to-one correspondence with\u0000positive equilibria of the network. Often these alternative systems are simpler\u0000than the original mass action equations, and allow us to infer useful bounds on\u0000the number of positive equilibria. The alternative equation systems can also be\u0000helpful for parameterising the equilibrium set explicitly, for deriving\u0000descriptions of the parameter regions for multistationarity, and for studying\u0000bifurcations. We present the main construction, some bounds which follow for\u0000particular classes of networks, numerous examples, and some open questions and\u0000conjectures.","PeriodicalId":501325,"journal":{"name":"arXiv - QuanBio - Molecular Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Carlos Floyd, Aaron R. Dinner, Arvind Murugan, Suriyanarayanan Vaikuntanathan
Many biological decision-making processes can be viewed as performing a classification task over a set of inputs, using various chemical and physical processes as "biological hardware." In this context, it is important to understand the inherent limitations on the computational expressivity of classification functions instantiated in biophysical media. Here, we model biochemical networks as Markov jump processes and train them to perform classification tasks, allowing us to investigate their computational expressivity. We reveal several unanticipated limitations on the input-output functions of these systems, which we further show can be lifted using biochemical mechanisms like promiscuous binding. We analyze the flexibility and sharpness of decision boundaries as well as the classification capacity of these networks. Additionally, we identify distinctive signatures of networks trained for classification, including the emergence of correlated subsets of spanning trees and a creased "energy landscape" with multiple basins. Our findings have implications for understanding and designing physical computing systems in both biological and synthetic chemical settings.
{"title":"Limits on the computational expressivity of non-equilibrium biophysical processes","authors":"Carlos Floyd, Aaron R. Dinner, Arvind Murugan, Suriyanarayanan Vaikuntanathan","doi":"arxiv-2409.05827","DOIUrl":"https://doi.org/arxiv-2409.05827","url":null,"abstract":"Many biological decision-making processes can be viewed as performing a\u0000classification task over a set of inputs, using various chemical and physical\u0000processes as \"biological hardware.\" In this context, it is important to\u0000understand the inherent limitations on the computational expressivity of\u0000classification functions instantiated in biophysical media. Here, we model\u0000biochemical networks as Markov jump processes and train them to perform\u0000classification tasks, allowing us to investigate their computational\u0000expressivity. We reveal several unanticipated limitations on the input-output\u0000functions of these systems, which we further show can be lifted using\u0000biochemical mechanisms like promiscuous binding. We analyze the flexibility and\u0000sharpness of decision boundaries as well as the classification capacity of\u0000these networks. Additionally, we identify distinctive signatures of networks\u0000trained for classification, including the emergence of correlated subsets of\u0000spanning trees and a creased \"energy landscape\" with multiple basins. Our\u0000findings have implications for understanding and designing physical computing\u0000systems in both biological and synthetic chemical settings.","PeriodicalId":501325,"journal":{"name":"arXiv - QuanBio - Molecular Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206275","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
I. Mihalcescu, H. Kaji, H. Maruyama, J. Giraud, M. Van-Melle Gateau, B. Houchmandzadeh, H. Ito
The in vivo circadian clock in single cyanobacteria is studied here by time-lapse fluorescence microscopy when the temperature is lowered below 25{deg}C . We first disentangle the circadian clock behavior from the bacterial cold shock response by identifying a sequence of "death steps" based on cellular indicators. By analyzing only "alive" tracks, we show that the dynamic response of individual oscillatory tracks to a step-down temperature signal is described by a simple Stuart-Landau oscillator model. The same dynamical analysis applied to in vitro data (KaiC phosphorylation level following a temperature step-down) allows for extracting and comparing both clock's responses to a temperature step down. It appears, therefore, that both oscillators go through a similar supercritical Hopf bifurcation. Finally, to quantitatively describe the temperature dependence of the resulting in vivo and in vitro Stuart-Landau parameters $mu(T)$ and $omega_c(T)$, we propose two simplified analytical models: temperature-dependent positive feedback or time-delayed negative feedback that is temperature compensated. Our results provide strong constraints for future models and emphasize the importance of studying transitory regimes along temperature effects in circadian systems.
{"title":"When lowering temperature, the in vivo circadian clock in cyanobacteria follows and surpasses the in vitro protein clock trough the Hopf bifurcation","authors":"I. Mihalcescu, H. Kaji, H. Maruyama, J. Giraud, M. Van-Melle Gateau, B. Houchmandzadeh, H. Ito","doi":"arxiv-2409.05537","DOIUrl":"https://doi.org/arxiv-2409.05537","url":null,"abstract":"The in vivo circadian clock in single cyanobacteria is studied here by\u0000time-lapse fluorescence microscopy when the temperature is lowered below\u000025{deg}C . We first disentangle the circadian clock behavior from the\u0000bacterial cold shock response by identifying a sequence of \"death steps\" based\u0000on cellular indicators. By analyzing only \"alive\" tracks, we show that the\u0000dynamic response of individual oscillatory tracks to a step-down temperature\u0000signal is described by a simple Stuart-Landau oscillator model. The same\u0000dynamical analysis applied to in vitro data (KaiC phosphorylation level\u0000following a temperature step-down) allows for extracting and comparing both\u0000clock's responses to a temperature step down. It appears, therefore, that both\u0000oscillators go through a similar supercritical Hopf bifurcation. Finally, to\u0000quantitatively describe the temperature dependence of the resulting in vivo and\u0000in vitro Stuart-Landau parameters $mu(T)$ and $omega_c(T)$, we propose two\u0000simplified analytical models: temperature-dependent positive feedback or\u0000time-delayed negative feedback that is temperature compensated. Our results\u0000provide strong constraints for future models and emphasize the importance of\u0000studying transitory regimes along temperature effects in circadian systems.","PeriodicalId":501325,"journal":{"name":"arXiv - QuanBio - Molecular Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206279","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Reaction networks have been widely used as generic models in diverse areas of applied science, such as biology, chemistry, ecology, epidemiology, and computer science. Reaction networks incorporating noisy effect are modelled as continuous time Markov chains (CTMC), and are called stochastic reaction systems. Non-explosivity is a concept that characterizes regularity of CTMCs. In this paper, we study non-explosivity of stochastic reaction systems, in the sense of their underlying CTMCs. By constructing a simple linear Lyapunov function, we obtain non-explosivity for a class of endotactic stochastic reaction systems containing second-order endotactic stochastic mass-action systems as a subset. As a consequence, we prove that every bimolecular weakly reversible stochastic mass-action system is non-explosive. We apply our results to diverse models in biochemistry, epidemiology, ecology, and synthetic biology in the literature.
{"title":"Non-explosivity of endotactic stochastic reaction systems","authors":"Chuang Xu","doi":"arxiv-2409.05340","DOIUrl":"https://doi.org/arxiv-2409.05340","url":null,"abstract":"Reaction networks have been widely used as generic models in diverse areas of\u0000applied science, such as biology, chemistry, ecology, epidemiology, and\u0000computer science. Reaction networks incorporating noisy effect are modelled as\u0000continuous time Markov chains (CTMC), and are called stochastic reaction\u0000systems. Non-explosivity is a concept that characterizes regularity of CTMCs.\u0000In this paper, we study non-explosivity of stochastic reaction systems, in the\u0000sense of their underlying CTMCs. By constructing a simple linear Lyapunov\u0000function, we obtain non-explosivity for a class of endotactic stochastic\u0000reaction systems containing second-order endotactic stochastic mass-action\u0000systems as a subset. As a consequence, we prove that every bimolecular weakly\u0000reversible stochastic mass-action system is non-explosive. We apply our results\u0000to diverse models in biochemistry, epidemiology, ecology, and synthetic biology\u0000in the literature.","PeriodicalId":501325,"journal":{"name":"arXiv - QuanBio - Molecular Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yi Zhao, Thomas P. Wytock, Kimberly A. Reynolds, Adilson E. Motter
Irreversibility, in which a transient perturbation leaves a system in a new state, is an emergent property in systems of interacting entities. This property has well-established implications in statistical physics but remains underexplored in biological networks, especially for bacteria and other prokaryotes whose regulation of gene expression occurs predominantly at the transcriptional level. Focusing on the reconstructed regulatory network of emph{Escherichia coli}, we examine network responses to transient single-gene perturbations. We predict irreversibility in numerous cases and find that the incidence of irreversibility increases with the proximity of the perturbed gene to positive circuits in the network. Comparison with experimental data suggests a connection between the predicted irreversibility to transient perturbations and the evolutionary response to permanent perturbations.
{"title":"Irreversibility in Bacterial Regulatory Networks","authors":"Yi Zhao, Thomas P. Wytock, Kimberly A. Reynolds, Adilson E. Motter","doi":"arxiv-2409.04513","DOIUrl":"https://doi.org/arxiv-2409.04513","url":null,"abstract":"Irreversibility, in which a transient perturbation leaves a system in a new\u0000state, is an emergent property in systems of interacting entities. This\u0000property has well-established implications in statistical physics but remains\u0000underexplored in biological networks, especially for bacteria and other\u0000prokaryotes whose regulation of gene expression occurs predominantly at the\u0000transcriptional level. Focusing on the reconstructed regulatory network of\u0000emph{Escherichia coli}, we examine network responses to transient single-gene\u0000perturbations. We predict irreversibility in numerous cases and find that the\u0000incidence of irreversibility increases with the proximity of the perturbed gene\u0000to positive circuits in the network. Comparison with experimental data suggests\u0000a connection between the predicted irreversibility to transient perturbations\u0000and the evolutionary response to permanent perturbations.","PeriodicalId":501325,"journal":{"name":"arXiv - QuanBio - Molecular Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Molecular communication (MC) within the synaptic cleft is vital for neurotransmitter diffusion, a process critical to cognitive functions. In Alzheimer's Disease (AD), beta-amyloid oligomers (A$beta$os) disrupt this communication, leading to synaptic dysfunction. This paper investigates the molecular interactions between glutamate, a key neurotransmitter, and A$beta$os within the synaptic cleft, aiming to elucidate the underlying mechanisms of this disruption. Through stochastic modeling, we simulate the dynamics of A$beta$os and their impact on glutamate diffusion. The findings, validated by comparing simulated results with existing experimental data, demonstrate that A$beta$os serve as physical obstacles, hindering glutamate movement and increasing collision frequency. This impairment of synaptic transmission and long-term potentiation (LTP) by binding to receptors on the postsynaptic membrane is further validated against known molecular interaction behaviors observed in similar neurodegenerative contexts. The study also explores potential therapeutic strategies to mitigate these disruptions. By enhancing our understanding of these molecular interactions, this research contributes to the development of more effective treatments for AD, with the ultimate goal of alleviating synaptic impairments associated with the disease.
{"title":"A Molecular Communication Perspective of Alzheimer's Disease: Impact of Amyloid Beta Oligomers on Glutamate Diffusion in the Synaptic Cleft","authors":"Nayereh FallahBagheri, Ozgur B. Akan","doi":"arxiv-2409.03396","DOIUrl":"https://doi.org/arxiv-2409.03396","url":null,"abstract":"Molecular communication (MC) within the synaptic cleft is vital for\u0000neurotransmitter diffusion, a process critical to cognitive functions. In\u0000Alzheimer's Disease (AD), beta-amyloid oligomers (A$beta$os) disrupt this\u0000communication, leading to synaptic dysfunction. This paper investigates the\u0000molecular interactions between glutamate, a key neurotransmitter, and\u0000A$beta$os within the synaptic cleft, aiming to elucidate the underlying\u0000mechanisms of this disruption. Through stochastic modeling, we simulate the\u0000dynamics of A$beta$os and their impact on glutamate diffusion. The findings,\u0000validated by comparing simulated results with existing experimental data,\u0000demonstrate that A$beta$os serve as physical obstacles, hindering glutamate\u0000movement and increasing collision frequency. This impairment of synaptic\u0000transmission and long-term potentiation (LTP) by binding to receptors on the\u0000postsynaptic membrane is further validated against known molecular interaction\u0000behaviors observed in similar neurodegenerative contexts. The study also\u0000explores potential therapeutic strategies to mitigate these disruptions. By\u0000enhancing our understanding of these molecular interactions, this research\u0000contributes to the development of more effective treatments for AD, with the\u0000ultimate goal of alleviating synaptic impairments associated with the disease.","PeriodicalId":501325,"journal":{"name":"arXiv - QuanBio - Molecular Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The first passage time (FPT) is a generic measure that quantifies when a random quantity reaches a specific state. We consider the FTP distribution in nonlinear stochastic biochemical networks, where obtaining exact solutions of the distribution is a challenging problem. Even simple two-particle collisions cause strong nonlinearities that hinder the theoretical determination of the full FPT distribution. Previous research has either focused on analyzing the mean FPT, which provides limited information about a system, or has considered time-consuming stochastic simulations that do not clearly expose causal relationships between parameters and the system's dynamics. This paper presents the first exact theoretical solution of the full FPT distribution in a broad class of chemical reaction networks involving $A + B rightarrow C$ type of second-order reactions. Our exact theoretical method outperforms stochastic simulations, in terms of computational efficiency, and deviates from approximate analytical solutions. Given the prevalence of bimolecular reactions in biochemical systems, our approach has the potential to enhance the understanding of real-world biochemical processes.
{"title":"Exact first passage time distribution for second-order reactions in chemical networks","authors":"Changqian Rao, David Waxman, Wei Lin, Zhuoyi Song","doi":"arxiv-2409.02698","DOIUrl":"https://doi.org/arxiv-2409.02698","url":null,"abstract":"The first passage time (FPT) is a generic measure that quantifies when a\u0000random quantity reaches a specific state. We consider the FTP distribution in\u0000nonlinear stochastic biochemical networks, where obtaining exact solutions of\u0000the distribution is a challenging problem. Even simple two-particle collisions\u0000cause strong nonlinearities that hinder the theoretical determination of the\u0000full FPT distribution. Previous research has either focused on analyzing the\u0000mean FPT, which provides limited information about a system, or has considered\u0000time-consuming stochastic simulations that do not clearly expose causal\u0000relationships between parameters and the system's dynamics. This paper presents\u0000the first exact theoretical solution of the full FPT distribution in a broad\u0000class of chemical reaction networks involving $A + B rightarrow C$ type of\u0000second-order reactions. Our exact theoretical method outperforms stochastic\u0000simulations, in terms of computational efficiency, and deviates from\u0000approximate analytical solutions. Given the prevalence of bimolecular reactions\u0000in biochemical systems, our approach has the potential to enhance the\u0000understanding of real-world biochemical processes.","PeriodicalId":501325,"journal":{"name":"arXiv - QuanBio - Molecular Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206277","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Shingo Gibo, Teiji Kunihiro, Tetsuo Hatsuda, Gen Kurosawa
Numerous biological processes accelerate as temperatures increase, but the period of circadian rhythms remains constant, known as temperature compensation, while synchronizing with the 24h light-dark cycle. We theoretically explores the possible relevance of waveform distortions in circadian gene-protein dynamics to the temperature compensation and synchronization. Our analysis of the Goodwin model provides a coherent explanation of most of temperature compensation hypotheses. Using the renormalization group method, we analytically demonstrate that the decreasing phase of circadian protein oscillations should lengthen with increasing temperature, leading to waveform distortions to maintain a stable period. This waveform-period correlation also occurs in other oscillators like Lotka-Volterra and van der Pol models. A reanalysis of known data nicely confirms our findings on waveform distortion and its impact on synchronization range. Thus we conclude that circadian rhythm waveforms are fundamental to both temperature compensation and synchronization.
许多生物过程随着温度的升高而加快，但昼夜节律的周期却保持不变，即温度补偿，同时与 24 小时光暗周期同步。我们从理论上探讨了昼夜节律基因-蛋白质动力学的波形失真与温度补偿和同步的可能关系。我们对古德温模型的分析为大多数温度补偿假说提供了连贯的解释。利用归一化群方法，我们分析证明了昼夜节律蛋白振荡的递减相应该随着温度的升高而延长，从而导致波形畸变以维持稳定的周期。这种波形与周期的相关性也出现在其他振荡器中，如 Lotka-Volterra 和 van der Pol 模型。对已知数据的重新分析很好地证实了我们关于波形失真及其对同步范围影响的发现。因此，我们得出结论，昼夜节律波形对于温度补偿和同步都是至关重要的。
{"title":"Waveform distortion for temperature compensation and synchronization in circadian rhythms: An approach based on the renormalization group method","authors":"Shingo Gibo, Teiji Kunihiro, Tetsuo Hatsuda, Gen Kurosawa","doi":"arxiv-2409.02526","DOIUrl":"https://doi.org/arxiv-2409.02526","url":null,"abstract":"Numerous biological processes accelerate as temperatures increase, but the\u0000period of circadian rhythms remains constant, known as temperature\u0000compensation, while synchronizing with the 24h light-dark cycle. We\u0000theoretically explores the possible relevance of waveform distortions in\u0000circadian gene-protein dynamics to the temperature compensation and\u0000synchronization. Our analysis of the Goodwin model provides a coherent\u0000explanation of most of temperature compensation hypotheses. Using the\u0000renormalization group method, we analytically demonstrate that the decreasing\u0000phase of circadian protein oscillations should lengthen with increasing\u0000temperature, leading to waveform distortions to maintain a stable period. This\u0000waveform-period correlation also occurs in other oscillators like\u0000Lotka-Volterra and van der Pol models. A reanalysis of known data nicely\u0000confirms our findings on waveform distortion and its impact on synchronization\u0000range. Thus we conclude that circadian rhythm waveforms are fundamental to both\u0000temperature compensation and synchronization.","PeriodicalId":501325,"journal":{"name":"arXiv - QuanBio - Molecular Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Information processing in networks entails a dynamical transfer of information between stochastic variables. Transfer entropy is widely used for quantification of the directional transfer of information between input and output trajectories. However, currently there is no exact technique to quantify transfer entropy given the dynamical model of a general network. Here we introduce an exact computational algorithm, Transfer Entropy-Path Weight Sampling (TE-PWS), to quantify transfer entropy and its variants in an arbitrary network in the presence of multiple hidden variables, nonlinearity, transient conditions, and feedback. TE-PWS extends a recently introduced algorithm Path Weight Sampling (PWS) and uses techniques from the statistical physics of polymers and trajectory sampling. We apply TE-PWS to linear and nonlinear systems to reveal how transfer entropy can overcome naive applications of data processing inequalities in presence of feedback.
{"title":"Exact computation of Transfer Entropy with Path Weight Sampling","authors":"Avishek Das, Pieter Rein ten Wolde","doi":"arxiv-2409.01650","DOIUrl":"https://doi.org/arxiv-2409.01650","url":null,"abstract":"Information processing in networks entails a dynamical transfer of\u0000information between stochastic variables. Transfer entropy is widely used for\u0000quantification of the directional transfer of information between input and\u0000output trajectories. However, currently there is no exact technique to quantify\u0000transfer entropy given the dynamical model of a general network. Here we\u0000introduce an exact computational algorithm, Transfer Entropy-Path Weight\u0000Sampling (TE-PWS), to quantify transfer entropy and its variants in an\u0000arbitrary network in the presence of multiple hidden variables, nonlinearity,\u0000transient conditions, and feedback. TE-PWS extends a recently introduced\u0000algorithm Path Weight Sampling (PWS) and uses techniques from the statistical\u0000physics of polymers and trajectory sampling. We apply TE-PWS to linear and\u0000nonlinear systems to reveal how transfer entropy can overcome naive\u0000applications of data processing inequalities in presence of feedback.","PeriodicalId":501325,"journal":{"name":"arXiv - QuanBio - Molecular Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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