Methodology for development of single cell dendritic spine (SCDS) synaptic tagging and capture model using Virtual Cell (VCell).

Single cell dendritic spine modelling methodology has been adopted to explain structural plasticity and respective change in the neuronal volume previously. However, the single cell dendrite methodology has not been employed previously to explain one of the important aspects of memory allocation i.e., Synaptic tagging and Capture (STC) hypothesis. It is difficult to relate the physical properties of STC pathways to structural changes and synaptic strength. We create a mathematical model based on earlier reported synaptic tagging networks. We built the model using Virtual Cell (VCell) software and used it to interpret experimental data and investigate the behavior and characteristics of known Synaptic tagging candidates.•We investigate processes associated with synaptic tagging candidates and compare them to the assumptions based on the STC hypothesis.•We assess the behavior of several reported synaptic tagging candidates against the requirements outlined in the synaptic tagging hypothesis.

A multifarious exploration of synaptic tagging and capture hypothesis in synaptic plasticity: Development of an integrated mathematical model and computational experiments.

The synaptic tagging and capture (STC) hypothesis not only explain the integration and association of synaptic activities, but also the formation of learning and memory. The synaptic pathways involved in the synaptic tagging and capture phenomenon are called STC pathways. The STC hypothesis provides a potential explanation of the neuronal and synaptic processes underlying the synaptic consolidation of memories. Several mechanisms and molecules have been proposed to explain the process of memory allocation and synaptic tags, respectively. However, a clear link between the STC hypothesis and memory allocation is still missing because the encoding of memories in neural circuits is mainly associated with strongly recurrently connected groups of neurons. To explore the mechanisms of potential synaptic tagging candidates and their involvement in the process of memory allocation, we develop a mathematical model for a single dendritic spine based on five essential criteria of a synaptic tag. By developing a mathematical model, we attempt to understand the roles of the potentially critical molecular networks underlying the STC and the essential attributes of a synaptic tag. We include essential memory molecules in the STC model that have been identified in earlier studies as crucial for STC pathways. CaMKII activation is critical for the setting of the initial tag; however, coordinated activities with other kinases and the biochemical pathways are necessary for the tag to be stable. PKA modulates NMDAR-mediated Ca2+ signalling. Similarly, PKA and ERK crosstalk is essential for Ca2+ - mediated protein synthesis during l-LTP. Our theoretical model explains the quantitative contribution of Tags and protein synthesis during l-LTP in synaptic strength.

Modelling the dynamics of CaMKII-NMDAR complex related to memory formation in synapses: the possible roles of threonine 286 autophosphorylation of CaMKII in long term potentiation.

A synaptic protein, Ca(2+)/Calmodulin dependent protein kinase II (CaMKII), has complex state transitions and facilitates the emergence of long term potentiation (LTP), which is highly correlated to memory formation. Two of the state transitions are critical for LTP: (1) threonine 286 autophosphorylation of CaMKII; and (2) binding to N-methyl-d-aspartate receptor (NMDAR) in the postsynaptic density (PSD) to form CaMKII-NMDAR complex. Both of these state transitions retain the activity of CaMKII when the induction signal disappears which is very important for the long-lasting characteristics of LTP. However, the possible relationships between the state transitions in the emergence of LTP are not well understood. We develop a mathematical model of the formation of CaMKII-NMDAR complex with the full state transitions of CaMKII, including the autophosphorylation, based on ordinary differential equations. In addition, we formulate a probabilistic framework for the binding between CaMKII and NMDAR. The model gives accurate predictions of the behaviours of CaMKII in comparisons to the experimental observations. Using the model, we show that: (1) the formation of CaMKII-NMDAR complex is dependent not only on the binding affinity between CaMKII and NMDAR, but also on the translocation of CaMKII into PSD; and (2) the autophosphorylation is not a requirement for the formation of CaMKII-NMDAR complex, but is important for the rapid formation of CaMKII-NMDAR complex during LTP.

The meiotic-mitotic initiation switch in budding yeast maintains its function robustly against sensitive parameter perturbations.

Experiments show that the meiotic-mitotic initiation switch in budding yeast functions robustly during the early hours of meiosis initiation. In this study, we explain these experimental observations first by understanding how this switching occurs during the early hours of meiosis by studying the temporal variation of this switch at the gene expression level. Then, we investigate the effects on this meiotic-mitotic switching from the perturbations of the most sensitive parameters in budding yeast meiosis initiation network. We use a mathematical model of meiosis initiation in budding yeast for this task and find the most sensitive group of parameters that influence the expressions of meiosis and mitosis initiators at all stages of the meiotic-mitotic switch. The results indicate that the transition region of the switch, where a double negative feedback loop between meiosis (Ime2) and mitosis (Cdk1/Cln3) initiators plays a major role, shows lower robustness. Feedback loops are frequently observed serving as a major robust adaption mechanism in many biological networks. Consequences of this less robust region appear in the transition region of the resulting switches. Most importantly, despite the differences observed in the transition region, we find that the meiotic-mitotic switch robustly maintains its main function of transition from meiosis to mitosis when the nutrients are re-supplied, against the perturbations in the sensitive parameters.

Systems biology of synaptic plasticity: a review on N-methyl-D-aspartate receptor mediated biochemical pathways and related mathematical models.

Synaptic plasticity, an emergent property of synaptic networks, has shown strong correlation to one of the essential functions of the brain, memory formation. Through understanding synaptic plasticity, we hope to discover the modulators and mechanisms that trigger memory formation. In this paper, we first review the well understood modulators and mechanisms underlying N-methyl-D-aspartate receptor dependent synaptic plasticity, a major form of synaptic plasticity in hippocampus, and then comment on the key mathematical modelling approaches available in the literature to understand synaptic plasticity as the integration of the established functionalities of synaptic components.

A nutrient dependant switch explains mutually exclusive existence of meiosis and mitosis initiation in budding yeast.

Nutrients from living environment are vital for the survival and growth of any organism. Budding yeast diploid cells decide to grow by mitosis type cell division or decide to create unique, stress resistant spores by meiosis type cell division depending on the available nutrient conditions. To gain a molecular systems level understanding of the nutrient dependant switching between meiosis and mitosis initiation in diploid cells of budding yeast, we develop a theoretical model based on ordinary differential equations (ODEs) including the mitosis initiator and its relations to budding yeast meiosis initiation network. Our model accurately and qualitatively predicts the experimentally revealed temporal variations of related proteins under different nutrient conditions as well as the diverse mutant studies related to meiosis and mitosis initiation. Using this model, we show how the meiosis and mitosis initiators form an all-or-none type bistable switch in response to available nutrient level (mainly nitrogen). The transitions to and from meiosis or mitosis initiation states occur via saddle node bifurcation. This bidirectional switch helps the optimal usage of available nutrients and explains the mutually exclusive existence of meiosis and mitosis pathways.

Robustness of circadian rhythms in the presence of molecular fluctuations: an investigation based on a mechanistic, statistical theory and a simulation algorithm.

After a very brief introduction to a mechanistic and statistical theory of molecular fluctuations in chemical reactions developed by Joel Keizer, we explore the robustness of a circadian rhythm model by using the theory and the exact stochastic simulation (ESS). The comparative study shows that the theory reflects the effects of the dynamics of the model on the robustness more than ESS does. Even though the theory is a macroscopic one, the robustness of the model compares well with that computed from the ESS when the system size is larger than 50. The robustness increases nonlinearly with the system size and it reaches an asymptotic value at higher system sizes. As we can expect from the dynamics of the system, the robustness is minimum near the bifurcation point and as the most sensitive parameter increases away from the bifurcation point the robustness according to the theory as well as the ESS increases and then reaches to a steady value.

Distinct noise-controlling roles of multiple negative feedback mechanisms in a prokaryotic operon system.

Molecular fluctuations are known to affect dynamics of cellular systems in important ways. Studies aimed at understanding how molecular systems of certain regulatory architectures control noise therefore become essential. The interplay between feedback regulation and noise has been previously explored for cellular networks governed by a single negative feedback loop. However, similar issues within networks consisting of more complex regulatory structures remain elusive. The authors investigate how negative feedback loops manage noise within a biochemical cascade concurrently governed by multiple negative feedback loops, using the prokaryotic tryptophan (trp) operon system in Escherechia coli as the model system. To the authors knowledge, this is the first study of noise in the trp operon system. They show that the loops in the trp operon system possess distinct, even opposing, noise-controlling effects despite their seemingly analogous feedback structures. The enzyme inhibition loop, although controlling the last reaction of the cascade, was found to suppress noise not only for the tryptophan output but also for other upstream components. In contrast, the Repression (Rep) loop enhances noise for all systems components. Attenuation (Att) poses intermediate effects by attenuating noise for the upstream components but promoting noise for components downstream of its target. Regarding noise at the output tryptophan, Rep and Att can be categorised as noise-enhancing loops whereas Enzyme Inhibition as a noise-reducing loop. These findings suggest novel implications in how cellular systems with multiple feedback mechanisms control noise. [Includes supplementary material].

Modelling of circadian rhythms in Drosophila incorporating the interlocked PER/TIM and VRI/PDP1 feedback loops.

Circadian rhythms of gene activity, metabolism, physiology and behaviour are observed in all the eukaryotes and some prokaryotes. In this study, we present a model to represent the transcriptional regulatory network essential for the circadian rhythmicity in Drosophila. The model incorporates the transcriptional feedback loops revealed so far in the network of the circadian clock (PER/TIM and VRI/PDP1 loops). Conventional Hill functions are not assumed to describe the regulation of genes, instead of the explicit reactions of binding and unbinding processes of transcription factors to promoters are modelled. The model simulates sustained circadian oscillations in mRNA and protein concentrations in constant darkness in agreement with experimental observations. It also simulates entrainment by light-dark cycles, disappearance of the rhythmicity in constant light and the shape of phase response curves resembling that of the experimental results. The model is robust over a wide range of parameter variations. In addition, the simulated E-box mutation, per(S) and per(L) mutants are similar to that observed in the experiments. The deficiency between the simulated mRNA levels and experimental observations in per(01), tim(01) and clk(Jrk) mutants suggests some difference on the part of the model from reality.