A physiologically-based pharmacokinetic model to describe antisense oligonucleotide distribution after intrathecal administration.

Antisense oligonucleotides (ASOs) are promising therapeutic agents for a variety of neurodegenerative and neuromuscular disorders, e.g., Alzheimer's, Parkinson's and Huntington's diseases, spinal muscular atrophy (SMA) and amyotrophic lateral sclerosis (ALS), caused by genetic abnormalities or increased protein accumulation. The blood-brain barrier (BBB) represents a challenge to the delivery of systemically administered ASOs to the relevant sites of action within the central nervous system (CNS). Intrathecal (IT) delivery, in which drugs are administered directly into the cerebrospinal fluid (CSF) space, enables to bypass the BBB. Several IT-administered ASO therapeutics have already demonstrated clinical effect, e.g., nusinersen (SMA) and tofersen (ALS). Due to novelty of IT dosing for ASOs, very limited pharmacokinetic (PK) data is available and only a few modeling reports have been generated. The objective of this work is to advance fundamental understanding of whole-body distribution of IT-administered ASOs. We propose a physiologically-based pharmacokinetic modeling approach to describe the distribution along the neuroaxis based on PK data from non-human primate (NHP) studies. We aim to understand the key processes that drive and limit ASO access to the CNS target tissues. To elucidate the trade-off between parameter identifiability and physiological plausibility of the model, several alternative model structures were chosen and fitted to the NHP data. The model analysis of the NHP data led to important qualitative conclusions that can inform projection to human. In particular, the model predicts that the maximum total exposure in the CNS tissues, including the spinal cord and brain, is achieved within two days after the IT injection, and the maximum amount absorbed by the CNS tissues is about 4% of the administered IT dose. This amount greatly exceeds the CNS exposures delivered by systemic administration of ASOs. Clearance from the CNS is controlled by the rate of transfer from the CNS tissues back to CSF, whereas ASO degradation in tissues is very slow and can be neglected. The model also describes local differences in ASO concentration emerging along the spinal CSF canal. These local concentrations need to be taken into account when scaling the NHP model to human: due to the lengthier human spinal column, inhomogeneity along the spinal CSF may cause even higher gradients and delays potentially limiting ASO access to target CNS tissues.

A Post-Marketing Surveillance Study of Nusinersen for Spinal Muscular Atrophy in Routine Medical Practice in China: Interim Results.

INTRODUCTION: Spinal muscular atrophy (SMA) is a rare, autosomal recessive, neuromuscular disease that leads to progressive muscular weakness and atrophy. Nusinersen, an antisense oligonucleotide, was approved for SMA in China in February 2019. We report interim results from a post-marketing surveillance phase 4 study, PANDA (NCT04419233), that collects data on the safety, efficacy, and pharmacokinetics of nusinersen in children with SMA in routine clinical practice in China. METHODS: Participants enrolled in PANDA will be observed for 2 years following nusinersen treatment initiation. The primary endpoint is the incidence of adverse events (AEs)/serious AEs (SAEs) during the treatment period. Efficacy assessments include World Health Organization (WHO) Motor Milestones assessment, the Hammersmith Infant Neurological Examination (HINE), and ventilation support. Plasma and cerebrospinal fluid (CSF) concentrations of nusinersen are measured at each dose visit. RESULTS: Fifty participants were enrolled as of the January 4, 2023, data cutoff: 10 with infantile-onset (≤ 6 months) and 40 with later-onset (> 6 months) SMA. All 50 participants have received at least one dose of nusinersen; 6 have completed the study. AEs were experienced by 45 (90%) participants and were mostly mild/moderate; no AEs led to nusinersen discontinuation or study withdrawal. Eleven participants experienced SAEs, most commonly pneumonia (n = 9); none were considered related to study treatment. Stability or gain of WHO motor milestone was observed and mean HINE-2 scores improved in both subgroups throughout the study. No serious respiratory events occurred, and no permanent ventilation support was initiated during the study. Pre-dose nusinersen CSF concentrations increased steadily through the loading-dose period, with no accumulation in plasma after multiple doses. CONCLUSION: Nusinersen was generally well tolerated with an acceptable overall safety profile, consistent with the known safety of nusinersen. Efficacy, safety, and nusinersen exposure are consistent with prior observations. These results support continuing PANDA and evaluation of nusinersen in Chinese participants with SMA. TRIAL REGISTRATION: ClinicalTrials.gov identifier, NCT04419233.

Safety, tolerability, and pharmacokinetics of antisense oligonucleotide BIIB078 in adults with C9orf72-associated amyotrophic lateral sclerosis: a phase 1, randomised, double blinded, placebo-controlled, multiple ascending dose study.

BACKGROUND: Hexanucleotide repeat expansion of C9orf72 is a common genetic cause of amyotrophic lateral sclerosis (ALS). No C9orf72-targeted treatments are available. BIIB078 is an investigational antisense oligonucleotide targeting C9orf72 sense RNA. We aimed to assess the safety, tolerability, and pharmacokinetics of BIIB078 in participants with C9orf72-associated ALS. METHODS: This phase 1, randomised controlled trial was done at 22 sites in six countries (Canada, Ireland, Netherlands, Switzerland, UK, and USA). Adults with ALS and a pathogenic repeat expansion in C9orf72 were randomly assigned within six cohorts, via Interactive Response Technology in a 3:1 ratio per cohort, to receive BIIB078 (5 mg, 10 mg, 20 mg, 35 mg, 60 mg, or 90 mg in cohorts 1-6, respectively) or placebo, via an intrathecal bolus injection. The treatment period consisted of three loading doses of study treatment, administered approximately once every 2 weeks, followed by monthly maintenance doses during a treatment period of about 3 months for cohorts 1-3 and about 6 months for cohorts 4-6. Patients and investigators were masked to treatment assignment. The primary endpoint was the incidence of adverse events and serious adverse events. This trial was registered with ClinicalTrials.gov (NCT03626012) and is completed. FINDINGS: Between Sept 10, 2018, and Nov 17, 2021, 124 patients were screened for inclusion in the study. 18 patients were excluded and 106 participants were enrolled and randomly assigned to receive 5 mg (n=6), 10 mg (n=9), 20 mg (n=9), 35 mg (n=19), 60 mg (n=18), or 90 mg (n=18) of BIIB078, or placebo (n=27). 58 (55%) of 106 patients were female. All patients received at least one dose of study treatment and were included in all analyses. All participants had at least one adverse event; most adverse events were mild or moderate in severity and did not lead to treatment discontinuation. The most common adverse events in BIIB078-treated participants were falls, procedural pain, headache, and post lumbar puncture syndrome. 14 (18%) of 79 patients who received any dose of BIIB078 reported serious adverse events, compared with nine (33%) of 27 patients who received placebo. Five participants who received BIIB078 and three participants who received placebo had fatal adverse events: respiratory failure in a participant who received 10 mg BIIB078, ALS worsening in two participants who received 35 mg BIIB078, traumatic intracerebral haemorrhage in one participant who received 35 mg BIIB078, pulmonary embolism in one participant who received 60 mg BIIB078, and respiratory failure in three participants who received placebo. All deaths were assessed as not related to the study treatment by the reporting investigator. INTERPRETATION: On the basis of these phase 1 study results, including secondary and exploratory findings showing no reduction in neurofilament levels and no benefit on clinical outcomes relative to the placebo cohort, BIIB078 clinical development has been discontinued. However, these results will be informative in furthering our understanding of the complex pathobiology of C9orf72-associated ALS. FUNDING: Biogen.

DEVOTE Study Exploring Higher Dose of Nusinersen in Spinal Muscular Atrophy: Study Design and Part A Results.

BACKGROUND: Pharmacokinetic/pharmacodynamic modeling indicates that the higher dose of nusinersen may be associated with a clinically meaningful increase in efficacy above that seen with the 12-mg approved dose. OBJECTIVE: Here we describe both the design of DEVOTE (NCT04089566), a 3-part clinical study evaluating safety, tolerability, and efficacy of higher dose of nusinersen, and results from the initial Part A. METHODS: DEVOTE Part A evaluates safety and tolerability of a higher nusinersen dose; Part B assesses efficacy in a randomized, double-blind design; and Part C assesses safety and tolerability of participants transitioning from the 12-mg dose to higher doses. RESULTS: In the completed Part A of DEVOTE, all 6 enrolled participants aged 6.1-12.6 years have completed the study. Four participants experienced treatment-emergent adverse events (TEAEs), the majority of which were mild. Common TEAEs of headache, pain, chills, vomiting, and paresthesia were considered related to the lumbar puncture procedure. There were no safety concerns regarding clinical or laboratory parameters. Nusinersen levels in the cerebrospinal fluid were within the range of modeled predictions for higher dose of nusinersen. While Part A was not designed for assessing efficacy, most participants showed stabilization or improvement in motor function. Parts B and C of DEVOTE are ongoing. CONCLUSIONS: The findings from Part A of the DEVOTE study support further development of higher dose of nusinersen.

A pediatric quantitative systems pharmacology model of neurofilament trafficking in spinal muscular atrophy treated with the antisense oligonucleotide nusinersen.

Phosphorylated neurofilament heavy subunit (pNfH) has been recently identified as a promising biomarker of disease onset and treatment efficacy in spinal muscular atrophy (SMA). This study introduces a quantitative systems pharmacology model representing the SMA pediatric scenario in the age range of 0-20 years with and without treatment with the antisense oligonucleotide nusinersen. Physiological changes typical of the pediatric age and the contribution of SMA and its treatment to the peripheral pNfH levels were included in the model by extending the equations of a previously developed mathematical model describing the neurofilament trafficking in healthy adults. All model parameters were estimated by fitting data from clinical trials that enrolled SMA patients treated with nusinersen. The data from the control group of the study was employed to build an in silico population of untreated subjects, and the parameters related to the treatment were estimated by fitting individual pNfH time series of SMA patients followed during the treatment. The final model reproduces well the pNfH levels in the presence of SMA in both the treated and untreated conditions. The results were validated by comparing model predictions with the data obtained from an additional cohort of SMA patients. The reported good predictive model performance makes it a valuable tool for investigating pNfH as a biomarker of disease progression and treatment response in SMA and for the in silico evaluation of novel treatment protocols.

A detailed mathematical model predicts that serial engagement of IgE-Fc epsilon RI complexes can enhance Syk activation in mast cells.

The term serial engagement was introduced to describe the ability of a single peptide, bound to a MHC molecule, to sequentially interact with TCRs within the contact region between a T cell and an APC. In addition to ligands on surfaces, soluble multivalent ligands can serially engage cell surface receptors with sites on the ligand, binding and dissociating from receptors many times before all ligand sites become free and the ligand leaves the surface. To evaluate the role of serial engagement in Syk activation, we use a detailed mathematical model of the initial signaling cascade that is triggered when FcepsilonRI is aggregated on mast cells by multivalent Ags. Although serial engagement is not required for mast cell signaling, it can influence the recruitment of Syk to the receptor and subsequent Syk phosphorylation. Simulating the response of mast cells to ligands that serially engage receptors at different rates shows that increasing the rate of serial engagement by increasing the rate of dissociation of the ligand-receptor bond decreases Syk phosphorylation. Increasing serial engagement by increasing the rate at which receptors are cross-linked (for example by increasing the forward rate constant for cross-linking or increasing the valence of the ligand) increases Syk phosphorylation. When serial engagement enhances Syk phosphorylation, it does so by partially reversing the effects of kinetic proofreading. Serial engagement rapidly returns receptors that have dissociated from aggregates to new aggregates before the receptors have fully returned to their basal state.

An age-dependent mathematical model of neurofilament trafficking in healthy conditions.

Neurofilaments (Nfs) are the major structural component of neurons. Their role as a potential biomarker of several neurodegenerative diseases has been investigated in past years with promising results. However, even under physiological conditions, little is known about the leaking of Nfs from the neuronal system and their detection in the cerebrospinal fluid (CSF) and blood. This study aimed at developing a mathematical model of Nf transport in healthy subjects in the 20-90 age range. The model was implemented as a set of ordinary differential equations describing the trafficking of Nfs from the nervous system to the periphery. Model parameters were calibrated on typical Nf levels obtained from the literature. An age-dependent function modeled on CSF data was also included and validated on data measured in serum. We computed a global sensitivity analysis of model rates and volumes to identify the most sensitive parameters affecting the model's steady state. Age, Nf synthesis, and degradation rates proved to be relevant for all model variables. Nf levels in the CSF and in blood were observed to be sensitive to the Nf leakage rates from neurons and to the blood clearance rate, and CSF levels were also sensitive to rates representing CSF turnover. An additional parameter perturbation analysis was also performed to investigate possible transient effects on the model variables not captured by the sensitivity analysis. The model provides useful insights into Nf transport and constitutes the basis for implementing quantitative system pharmacology extensions to investigate Nf trafficking in neurodegenerative diseases.

Modeling multivalent ligand-receptor interactions with steric constraints on configurations of cell-surface receptor aggregates.

We use flow cytometry to characterize equilibrium binding of a fluorophore-labeled trivalent model antigen to bivalent IgE-FcepsilonRI complexes on RBL cells. We find that flow cytometric measurements are consistent with an equilibrium model for ligand-receptor binding in which binding sites are assumed to be equivalent and ligand-induced receptor aggregates are assumed to be acyclic. However, this model predicts extensive receptor aggregation at antigen concentrations that yield strong cellular secretory responses, which is inconsistent with the expectation that large receptor aggregates should inhibit such responses. To investigate possible explanations for this discrepancy, we evaluate four rule-based models for interaction of a trivalent ligand with a bivalent cell-surface receptor that relax simplifying assumptions of the equilibrium model. These models are simulated using a rule-based kinetic Monte Carlo approach to investigate the kinetics of ligand-induced receptor aggregation and to study how the kinetics and equilibria of ligand-receptor interaction are affected by steric constraints on receptor aggregate configurations and by the formation of cyclic receptor aggregates. The results suggest that formation of linear chains of cyclic receptor dimers may be important for generating secretory signals. Steric effects that limit receptor aggregation and transient formation of small receptor aggregates may also be important.

RuleMonkey: software for stochastic simulation of rule-based models.

BACKGROUND: The system-level dynamics of many molecular interactions, particularly protein-protein interactions, can be conveniently represented using reaction rules, which can be specified using model-specification languages, such as the BioNetGen language (BNGL). A set of rules implicitly defines a (bio)chemical reaction network. The reaction network implied by a set of rules is often very large, and as a result, generation of the network implied by rules tends to be computationally expensive. Moreover, the cost of many commonly used methods for simulating network dynamics is a function of network size. Together these factors have limited application of the rule-based modeling approach. Recently, several methods for simulating rule-based models have been developed that avoid the expensive step of network generation. The cost of these "network-free" simulation methods is independent of the number of reactions implied by rules. Software implementing such methods is now needed for the simulation and analysis of rule-based models of biochemical systems. RESULTS: Here, we present a software tool called RuleMonkey, which implements a network-free method for simulation of rule-based models that is similar to Gillespie's method. The method is suitable for rule-based models that can be encoded in BNGL, including models with rules that have global application conditions, such as rules for intramolecular association reactions. In addition, the method is rejection free, unlike other network-free methods that introduce null events, i.e., steps in the simulation procedure that do not change the state of the reaction system being simulated. We verify that RuleMonkey produces correct simulation results, and we compare its performance against DYNSTOC, another BNGL-compliant tool for network-free simulation of rule-based models. We also compare RuleMonkey against problem-specific codes implementing network-free simulation methods. CONCLUSIONS: RuleMonkey enables the simulation of rule-based models for which the underlying reaction networks are large. It is typically faster than DYNSTOC for benchmark problems that we have examined. RuleMonkey is freely available as a stand-alone application http://public.tgen.org/rulemonkey. It is also available as a simulation engine within GetBonNie, a web-based environment for building, analyzing and sharing rule-based models.

Simulation of large-scale rule-based models.

MOTIVATION: Interactions of molecules, such as signaling proteins, with multiple binding sites and/or multiple sites of post-translational covalent modification can be modeled using reaction rules. Rules comprehensively, but implicitly, define the individual chemical species and reactions that molecular interactions can potentially generate. Although rules can be automatically processed to define a biochemical reaction network, the network implied by a set of rules is often too large to generate completely or to simulate using conventional procedures. To address this problem, we present DYNSTOC, a general-purpose tool for simulating rule-based models. RESULTS: DYNSTOC implements a null-event algorithm for simulating chemical reactions in a homogenous reaction compartment. The simulation method does not require that a reaction network be specified explicitly in advance, but rather takes advantage of the availability of the reaction rules in a rule-based specification of a network to determine if a randomly selected set of molecular components participates in a reaction during a time step. DYNSTOC reads reaction rules written in the BioNetGen language which is useful for modeling protein-protein interactions involved in signal transduction. The method of DYNSTOC is closely related to that of StochSim. DYNSTOC differs from StochSim by allowing for model specification in terms of BNGL, which extends the range of protein complexes that can be considered in a model. DYNSTOC enables the simulation of rule-based models that cannot be simulated by conventional methods. We demonstrate the ability of DYNSTOC to simulate models accounting for multisite phosphorylation and multivalent binding processes that are characterized by large numbers of reactions. AVAILABILITY: DYNSTOC is free for non-commercial use. The C source code, supporting documentation and example input files are available at http://public.tgen.org/dynstoc/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Phase II Dose Selection for Alpha Synuclein-Targeting Antibody Cinpanemab (BIIB054) Based on Target Protein Binding Levels in the Brain.

This modeling and simulation analysis was aimed at selecting doses of cinpanemab (BIIB054), a monoclonal antibody targeting aggregated α-synuclein, for a phase II study in Parkinson's disease (PD). Doses and regimens were proposed based on anticipated target concentration in brain interstitial fluid (ISF); in vitro/in vivo data on the affinity of monoclonal antibodies to the target protein; and safety, tolerability, and pharmacokinetic data (1-135 mg/kg intravenous administration) from a phase I single ascending dose (SAD) study. A population pharmacokinetic modeling approach was used to select intravenous doses of 250, 1,250, and 3,500 mg every 4 weeks, to maintain 50%, 90%, and > 90% of target binding in ISF of PD participants. A favorable safety profile from the SAD study-which showed that cinpanemab was generally well-tolerated at doses up to 90 mg/kg, supported by modeling and simulations of the anticipated safety margins-allowed implementation of a fixed-dose approach.

Aggregation of membrane proteins by cytosolic cross-linkers: theory and simulation of the LAT-Grb2-SOS1 system.

Ligand-induced receptor aggregation is a well-known mechanism for initiating intracellular signals but oligomerization of distal signaling molecules may also be required for signal propagation. Formation of complexes containing oligomers of the transmembrane adaptor protein, linker for the activation of T cells (LAT), has been identified as critical in mast cell and T cell activation mediated by immune response receptors. Cross-linking of LAT arises from the formation of a 2:1 complex between the adaptor Grb2 and the nucleotide exchange factor SOS1, which bridges two LAT molecules through the interaction of the Grb2 SH2 domain with a phosphotyrosine on LAT. We model this oligomerization and find that the valence of LAT for Grb2, which ranges from zero to three, is critical in determining the nature and extent of aggregation. A dramatic rise in oligomerization can occur when the valence switches from two to three. For valence three, an equilibrium theory predicts the possibility of forming a gel-like phase. This prediction is confirmed by stochastic simulations, which make additional predictions about the size of the gel and the kinetics of LAT oligomerization. We discuss the model predictions in light of recent experiments on RBL-2H3 and Jurkat E6.1 cells and suggest that the gel phase has been observed in activated mast cells.

Signal transduction at point-blank range: analysis of a spatial coupling mechanism for pathway crosstalk.

The plasma membrane provides a physical platform for the orchestration of molecular interactions and biochemical conversions involved in the early stages of receptor-mediated signal transduction in living cells. In that context, we introduce here the concept of spatial coupling, wherein simultaneous recruitment of different enzymes to the same receptor scaffold facilitates crosstalk between different signaling pathways through the local release and capture of activated signaling molecules. To study the spatiotemporal dynamics of this mechanism, we have developed a Brownian dynamics modeling approach and applied it to the receptor-mediated activation of Ras and the cooperative recruitment of phosphoinositide 3-kinase (PI3K) by activated receptors and Ras. Various analyses of the model simulations show that cooperative assembly of multimolecular complexes nucleated by activated receptors is facilitated by the local release and capture of membrane-anchored signaling molecules (such as active Ras) from/by receptor-bound signaling proteins. In the case of Ras/PI3K crosstalk, the model predicts that PI3K is more likely to be recruited by activated receptors bound or recently visited by the enzyme that activates Ras. By this mechanism, receptor-bound PI3K is stabilized through short-range, diffusion-controlled capture of active Ras and Ras/PI3K complexes released from the receptor complex. We contend that this mechanism is a means by which signaling pathways are propagated and spatially coordinated for efficient crosstalk between them.

Kinetic Monte Carlo method for rule-based modeling of biochemical networks.

We present a kinetic Monte Carlo method for simulating chemical transformations specified by reaction rules, which can be viewed as generators of chemical reactions, or equivalently, definitions of reaction classes. A rule identifies the molecular components involved in a transformation, how these components change, conditions that affect whether a transformation occurs, and a rate law. The computational cost of the method, unlike conventional simulation approaches, is independent of the number of possible reactions, which need not be specified in advance or explicitly generated in a simulation. To demonstrate the method, we apply it to study the kinetics of multivalent ligand-receptor interactions. We expect the method will be useful for studying cellular signaling systems and other physical systems involving aggregation phenomena.

Quantitation and pharmacokinetic modeling of therapeutic antibody quality attributes in human studies.

A thorough understanding of drug metabolism and disposition can aid in the assessment of efficacy and safety. However, analytical methods used in pharmacokinetics (PK) studies of protein therapeutics are usually based on ELISA, and therefore can provide a limited perspective on the quality of the drug in concentration measurements. Individual post-translational modifications (PTMs) of protein therapeutics are rarely considered for PK analysis, partly because it is technically difficult to recover and quantify individual protein variants from biological fluids. Meanwhile, PTMs may be directly linked to variations in drug efficacy and safety, and therefore understanding of clearance and metabolism of biopharmaceutical protein variants during clinical studies is an important consideration. To address such challenges, we developed an affinity-purification procedure followed by peptide mapping with mass spectrometric detection, which can profile multiple quality attributes of therapeutic antibodies recovered from patient sera. The obtained data enable quantitative modeling, which allows for simulation of the PK of different individual PTMs or attribute levels in vivo and thus facilitate the assessment of quality attributes impact in vivo. Such information can contribute to the product quality attribute risk assessment during manufacturing process development and inform appropriate process control strategy.

Reconstruction and roughening of a catalytic Pt(110) surface coupled to kinetic oscillations.

Three-dimensional reconstruction and roughening of a Pt(110) surface is studied with the help of a qualitative Monte Carlo model. A distinct CO adsorption uptake on different surface phases is taken into account. The computations show that a "missing row" structure with defects relaxes to a more stable (111)-faceted structure. The CO+O2 reaction kinetics is modeled by a phenomenological equation with a cubic nonlinearity reproducing a correct qualitative picture of oscillations. The surface roughening developing under the reaction conditions causes slow changes in catalytic activity of the surface. A nanoscale front between the 1x1 and 1x2 phases disintegrates due to repeated phase transitions caused by CO coverage oscillations. Defect formation and roughening dominate the dynamics of surface phase transitions. A one-dimensional extension of the model reproduces microscopic traveling waves on the CO diffusion scale.

Modeling and simulation of aggregation of membrane protein LAT with molecular variability in the number of binding sites for cytosolic Grb2-SOS1-Grb2.

The linker for activation of T cells (LAT), the linker for activation of B cells (LAB), and the linker for activation of X cells (LAX) form a family of transmembrane adaptor proteins widely expressed in lymphocytes. These scaffolding proteins have multiple binding motifs that, when phosphorylated, bind the SH2 domain of the cytosolic adaptor Grb2. Thus, the valence of LAT, LAB and LAX for Grb2 is variable, depending on the strength of receptor activation that initiates phosphorylation. During signaling, the LAT population will exhibit a time-varying distribution of Grb2 valences from zero to three. In the cytosol, Grb2 forms 1:1 and 2:1 complexes with the guanine nucleotide exchange factor SOS1. The 2:1 complex can bridge two LAT molecules when each Grb2, through their SH2 domains, binds to a phosphorylated site on a separate LAT. In T cells and mast cells, after receptor engagement, receptor phosphoyrlation is rapidly followed by LAT phosphorylation and aggregation. In mast cells, aggregates containing more than one hundred LAT molecules have been detected. Previously we considered a homogeneous population of trivalent LAT molecules and showed that for a range of Grb2, SOS1 and LAT concentrations, an equilibrium theory for LAT aggregation predicts the formation of a gel-like phase comprising a very large aggregate (superaggregate). We now extend this theory to investigate the effects of a distribution of Grb2 valence in the LAT population on the formation of LAT aggregates and superaggregate and use stochastic simulations to calculate the fraction of the total LAT population in the superaggregate.

Cell population-based model of dermal wound invasion with heterogeneous intracellular signaling properties.

A deterministic model of dermal wound invasion, which accounts for the platelet-derived growth factor (PDGF) gradient sensing mechanism in fibroblasts mediated by cell surface receptors and the phosphoinositide 3-kinase (PI3K) signal transduction pathway, was previously described (Biophys J 2006; 90:2297-308). Here, we extend that work and implement a hybrid modeling strategy that treats fibroblasts as discrete entities endowed with heterogeneous properties, namely receptor, PI3K and 3' phosphoinositide phosphatase expression levels. Analysis of the model suggests that the wound environment fosters the advancement of cells within the population that are better fit to migrate and/or proliferate in response to PDGF stimulation. Thus, cell-to-cell variability results in a significantly higher rate of wound invasion as compared with the deterministic model, in a manner that depends on the way in which individual cell properties are sampled or inherited upon cell division.

Reactions on cell membranes: comparison of continuum theory and Brownian dynamics simulations.

Biochemical transduction of signals received by living cells typically involves molecular interactions and enzyme-mediated reactions at the cell membrane, a problem that is analogous to reacting species on a catalyst surface or interface. We have developed an efficient Brownian dynamics algorithm that is especially suited for such systems and have compared the simulation results with various continuum theories through prediction of effective enzymatic rate constant values. We specifically consider reaction versus diffusion limitation, the effect of increasing enzyme density, and the spontaneous membrane association/dissociation of enzyme molecules. In all cases, we find the theory and simulations to be in quantitative agreement. This algorithm may be readily adapted for the stochastic simulation of more complex cell signaling systems.

Ligand accumulation in autocrine cell cultures.

Cell-culture assays are routinely used to analyze autocrine signaling systems, but quantitative experiments are rarely possible. To enable the quantitative design and analysis of experiments with autocrine cells, we develop a biophysical theory of ligand accumulation in cell-culture assays. Our theory predicts the ligand concentration as a function of time and measurable parameters of autocrine cells and cell-culture experiments. The key step of our analysis is the derivation of the survival probability of a single ligand released from the surface of an autocrine cell. An expression for this probability is derived using the boundary homogenization approach and tested by stochastic simulations. We use this expression in the integral balance equations, from which we find the Laplace transform of the ligand concentration. We demonstrate how the theory works by analyzing the autocrine epidermal growth factor receptor system and discuss the extension of our methods to other experiments with cultured autocrine cells.