Fall 2000
Abstracts
When a helical bacterial flagellum, clamped at one end, is placed in an external flow, it has been observed that regions within the flagellum periodically transform to the opposite handedness and these domains travel down the length of the filament. We propose a dynamical model for this phenomenon based on the existence of two competing locally stable states of opposite chirality whose interaction with the flow is through the torque it produces. An associated PDE for the shape and chirality dynamics is solved numerically and displays many of the key features seen in experiment.
The transport of oxygen from the capillaries to the muscle fibres is essential for muscle contraction. Oxygen is required by the cellular machinery within the cell to produce the energy that drives the contracting fibres. A problem arises when a muscle is told to contract by the brain - the fibres receive signals from the nerves and activate accordingly, but the blood vessels receive no such direct signal. This creates a functional problem in matching the supply of oxygen with the demand. A computer model of oxygen diffusion in the muscle was used to visualise the levels of oxygen in the muscle, and what happens as the demand for oxygen increases as more and more muscle fibres are activated.
Collection of a timed urine sample and analysis of excretion rate have been shown in preliminary studies to be a better indicator of drug exposure than urine concentration in an untimed sample. In addition, if two related compounds are collected in the same sample (the parent and metabolite or two metabolites), information such as the time of dosing and the dose administered can, in theory, be estimated. The purpose of this proposal is the development and validation of a model for smoked compounds, using nicotine as a prototype drug. In order to meet these objectives, the following specific goals must be met.
1. Adapt and validate analytical methods developed for the quantitation
of nicotine and its metabolites in urine: cotinine and
3^R-hydroxycotinine.
2. Perform simulations to test and validate the model equations,
including Monte Carlo simulations, sensitivity analyses, and testing of
simulated "unknown" samples.
3. Using an animal model (swine), develop a complete pharmacokinetic
model to characterize the urinary excretion rate-time profile of
nicotine and its metabolites as a function of nicotine dose and route of
administration. Obtain estimates of average parameter values needed in
the model in order to assess errors in prediction.
4. Develop an overall statistical model to predict time of exposure and
dose based on urine data (aim #3) and test the predictions in blind
experiments. Validate the technique in a set of animals that were not
used for preliminary data collection.
Once validated in the animal study, this model should be tested in humans. The ultimate goal for this project is to extend the validated model to smoked drugs of abuse, such as marijuana and crack cocaine, in order to estimate the time of dosing and the dose administered in humans during a drug screen. In addition, this model can be adapted to other routes of drug ingestion, such as oral dosing, and can then be tested on humans. The ultimate goal for this project is to extend the validated model to smoked drugs of abuse, such as marijuana and crack cocaine, in order to estimate the time of dosing and the dose administered in humans during a drug screen. In addition, this model can be adapted to other routes of drug ingestion, such as oral dosing, and can then be tested on other drugs of abuse, such as methamphetamine, opioids, and barbiturates.
The classical ecological principle of competitive exclusion states that two similar species competing for a common resource cannot coexist indefinitely. This theory assumes that, when left alone, each species will reach an equilibrium state. This can be studied in the context of small colonies of flour beetles, which can be easily made to undergo periodic and chaotic fluctuations. This may possibly lead to coexistence, even in the presence of strong inter-specific competition.
How can exisiting maximum likelihood framework for molecular sequence data analysis be extended to better reflect biological reality?
What types of statistical tests can be implemented? How to keep the analyses from becoming too computationally difficult to carry out? I will overview methods currently being used and present some new ideas.
In the study of life history evolution, one considers the merits of alternative life history "strategies", including total lifespan, age at first reproduction, number of reproductive bouts, the amount of the organism's total biomass allocated to each reproductive bout, the size vs. number of offspring, etc. Indeed, an enormous diversity of life history strategies are evident in the natural world, and even in any particular natural community in space and time. I am studying the selective forces driving evolutionary transitions between the annual and perennial habit, where annuals are plants that germinate, grow, flower, and set seed all in one year, whereas perennials survive and reproduce more than one year. I will introduce the classic theory suggesting that the following three factors are important in causing these transitions: population structure, trade-offs, and environmentally-driven demographic stochasticity. I will then describe additional, biologically realistic factors that have not yet been modeled, and my current plan to model these factors. I am particularly interested in feedback on this plan, and discussion of what testable predictions could be extracted from the models.
The motor protein kinesin exhibits a number of interesting properties such as tight coupling, processivity, and Michaelis-Menten kinetics. A possible approach at analyzing stochastic models of this protein will be presented coupling the chemical cycle with the mechanical cycle coupled with thermal noise. I will introduce the properties of the kinesin motor, the basic concepts involved in the model and questions that can hopefully be addressed.
Despite the recent burst of host-parasite studies in ecology and evolution, we still have little understanding of why parasite species are found on certain host species and not others. My research focuses on the evolutionary and ecological determinants of host range in nematode (worm) parasites of mushroom-feeding Drosophila flies. These nematodes can have profound effect on their hosts, and vary greatly both in their host range and virulence. One goal of macroevolutionary studies of hosts and parasites has been to determine the degree to which the evolutionary history of parasites depends on that of their hosts. These studies have been mostly restricted to situations where parasites have little opportunity for dispersal or horizontal transmission; congruence between host and parasite phylogenies is therefore very high. In contrast, the phylogenies of the nematodes and flies in my study are highly incongruent, which is not surprising due to the opportunity for horizontal transmission in this system. In addition, I have conducted a large experimental study of the ability of 5 nematode species to infect and reproduce in 24 species of Drosophila. This will be the first study of the importance both host and parasite phylogeny on a parasite's potential host range. I am proposing to use this dataset as a first test of recently developed models of host-switching and cospeciation. However, because these models do not allow for parasites with multiple hosts, and vice versa, I will develop less restrictive ones that can accommodate more biologically realistic descriptions of host-parasite associations. I am also proposing to develop a mathematical model that will explore the roles of differing virulence and host range in maintaining a diverse community of hosts and parasites. This model will complement my experimental work that explored interactions between a specialist and a generalist parasite, and the effect of single versus mixed infection on their host's fecundity and survival.
The discovery that waking neural patterns are reactivated in the hippocampus after behavior presents a possible neural correlate to the memory consolidation process (Wilson and McNaughton, 1994). Consolidation is often affected by level of reward (Kesner et al., 1989). Accordingly, this experiment sought to determine whether hippocampal neural activity associated with high reward locations is preferentially reactivated relative to low reward sites. Three rats were implanted with microdrives, and multiple single-unit activity was recorded from the CA1 layer of the hippocampus. Each rat traversed a T shaped maze during 8 experimental sessions (1 per day). Reward sites were located at the end of each arm and had differential probabilities of containing food (20%, 50%, and 80%). After the fourth session, the location of the 80% and 20% reward sites were exchanged. Maze running periods were preceded and followed by at least 30 minutes of rest. An average of 34 simultaneously recorded units were present during each session. Reactivation during post-exploration periods was assessed using three measures. These measures allowed us to determine whether patterns were reactivated more often and/or with greater intensity. All three measures failed to show a significant relationship between reactivation and reward probability. This result is consistent with the 'incidental' nature of spatial learning and suggests that any enhancement of spatial memory that may result from positive reinforcement is likely to involve encoding processes outside the hippocampus.
The protein nitrophorin binds NO extremely well. It is seen to undergo a conformational change upon NO binding, which is hypothesized to be linked to the high affinity it exhibits to this ligand. My goal is to explain this connection between protein structure and function.
I will present two projects that I am beginning. One focuses on investigating the diffusion of the ligand inside the protein. I am in the process of writing a simulation which would look for most probable escape paths and eventually attempt to replicate the kinetics of NO escape. The second approach will attempt to model the protein as a set of coupled nonlinear oscillators, and investigate localized vibrational modes called breathers.
The relationship of electromyographic (EMG) activity and limb kinematics is important for understanding the OAbiomechanics of limb movement, aiding rehabilitation, and developing Functional Electrical (FES) devices. I will present a new technique that uses Bayes' Theorem to predict finger position from EMG. The Bayesian approach characterizes a probabilistic relationship between finger position and EMG during a training period in which both variables are known. This probabilistic relationship is then applied to new EMG data to predict finger position. Finally, the predicted position is evaluated by comparing it to the actual finger position. Determining the combined muscle activity used to generate digit positions could provide a better framework for FES devices.
Motivated by experiments on flagella of bacteria, I will show the existence (or not) of travelling fronts of twist in straight, bistable elastic rods. This talk will include the resolution of the problems I talked about in August.
Working skeletal muscles consume oxygen delivered by capillaries. This concept seems simple, but is complicated by the difficulties in matching capillary blood flow with active muscle fibres. Using known parameters for the behaviour of oxygen in muscle, the diffusion equation can be used to visualize the distribution of oxygen across the muscle. This model can be used to look at the effectiveness of different regimens of capillary activation.
The NMDA receptor seems to underlie important properties in learning and memory, as is suggested by numerous behavioral, physiological, and neural network modeling studies. It's exact functional role in learning and memory is poorly understood.
Network models of hippocampal cells endowed with the NMDA receptor property of long-term potentiation suggest these groups of neurons can store memory for place over time but that this representation changes with experience. Specifically, network models suggest that representations of place expand and shift backward relative to direction of motion.
A test of this model is to block NMDA receptors and observe how place representations are altered over time. In line with the predictions of network models, we do not observe shifts of place representations when NMDA receptors are blocked. Furthermore, other interesting properties emerge under NMDA blockade that present new challenges to network models of the hippocampus. This may have implications for aging animals, which appear to have similar deficits in NMDA receptor properties.
The classical ecological principle of competitive exclusion states that two similar species competing for a common resource cannot coexist indefinitely. This theory assumes that, when left alone, each species will reach an equilibrium state. Nonlinearities within a structured model can lead to more exotic dynamics, such as periodic and chaotic fluctuations. This can result in coexistence, even in the presence of strong inter-specific competition. I will examine a stage structured competition model motivated by populations of flour beetles, and discuss approaches to actual experimentation based on the model.
Traditionally, maximum likelihood methods for genetic sequence analysis assumed that all sites in the sequence shared the same evolutionary rate(s). Recently (1994) a method was introduced to allow evolutionary rates to vary from site to site. I will talk about how this method can be extended even further to allow for more biologically interesting models.
Molecular motor proteins such as kinesin exhibit processive motion by coupling a chemical cycle to spatial motion. I will discuss how I am trying to extract long-time behavior of a model consisting of a two-state cycle which imposes two different potential energy landscapes, but in the presence of no thermal noise.
Mushroom-feeding Drosophila are infected by a diverse group of parasitic nematodes, which vary greatly in host range and virulence. My research explores the evolutionary and ecological determinants of parasite host range. Despite the fact that most of these nematodes infect only one host species in the wild, host and parasite phylogenies are highly incongruent. In laboratory infections, the nematodes are able to infect a wide range of hosts, and this is largely determined by host phylogeny. I am proposing to use this dataset as a first test of recently developed models of host-switching and cospeciation.
Memory consolidation is the process by which recent memories become durable and lasting. This process is influenced by many factors, an important factor being reward. In particular, events associated with high levels of reward tend to be recalled more accurately than events associated with low levels of reward (Kesner and Andrus 1982). One important step towards revealing the neural basis for this effect is to determine how reward influences the activity of individual neurons and neural systems that are likely involved in memory consolidation. Such an investigation may now be possible with the observation that patterns of neural activity present during waking behavior are reactivated during subsequent rest periods (Pavlides and Winson 1989; Wilson and McNaughton 1994; Kudrimoti, Barnes et al. 1999). The following experiment sets out to determine whether the reactivation of waking neural activity associated with spatial locations having a high probability of containing a reward is more robust than the reactivation of neural activity associated with locations having a low probability of containing a reward. The simultaneous activity of 20 to 60 neurons was recorded as rats ran on a T shaped maze and during two 30-minute episodes occurring before and after the maze-running period. Each arm of the maze had a different probability of containing a food reward. If reward probability influences memory consolidation within either the hippocampus or its afferents, it might be expected that neural activity patterns associated with arms having a high probability of containing a reward would be more robustly reactivated than patterns associated with arms having a lower probability of containing a reward. No modulation of reactivation by reward was observed. If the robustness of reactivation does reflect the strength of a memory, these results imply that reward does not affect the consolidation process within the hippocampal formation during the 30 minutes following behavior. These results also suggest that the increased persistence of memories for highly reinforcing events is not a consequence of their more robust reactivation.
Many important proteins bind small ligands. The active site to which these molecules bind is generally buried inside the protein, and thus the ligand must travel through the protein interior. It is usually this navigational step which determines the rate of the binding reaction, and thus the biochemical function of the protein.
I will present preliminary results from my simulations of a small ligand navigating the interior of nitrophorin, a protein which binds NO reversibly.
I will also show results of simulations on other proteins and some theoretical results which connect ligand diffusion to the reaction rates.
The relationship of electromyographic (EMG) activity and limb kinematics is important for understanding the biomechanics of limb movement, aiding rehabilitation, and developing Functional Electrical (FES) devices. I will present a new technique that uses Bayes' Theorem to predict finger position from EMG. The Bayesian approach characterizes a probabilistic relationship between finger position and EMG during a training period in which both variables are known. This probabilistic relationship is then applied to new EMG data to predict finger position. Finally, the predicted position is evaluated by comparing it to the actual finger position. Determining the combined muscle activity used to generate digit positions could provide a better framework for FES devices.