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Bradley Monk - Qualifying Paper Proposal
Qual Paper SI Material


For my Qualifying Paper, I will provide (1) a critical review of the postsynaptic surface regulation of AMPA-type glutamate receptors (AMPARs), and (2) propose a unified quantitative model of AMPAR lateral diffusion into synapses. This topic is of predominate interest to scientists who investigate synaptic potentiation, and is fundamentally important to the scientific investigation of memory-related conditions such as dementia and addiction. A unified model of AMPAR membrane diffusion would provide significant insight into the basic physiological underpinnings of synaptic plasticity and potentiation -- the neural correlates of learning and memory.
{{Box|font=150%|width=50%|float=left|text=14px|boarder=solid #aaa 1px|Qual Project Source Code|[[File:Github2.png|left|100px]] All source code used in my qualifying exam project can be found [https://github.com/subroutines/djhbrm here in my github repo for the project]. An online version of my qual with enhanced features like citation data popup graphics and animations can be found on [[:Category:Synaptic Plasticity|this page]]}}
The expression of AMPARs at excitatory synapses can be thought of, theoretically, as a final product. That is, if it were possible to take a snapshot of a brain in its current state and then quantify the synaptic densities of AMPARs, it would reveal which excitatory pathways were the most potentiated. From there, one could predict how the neural network would respond to input at a given source. Small changes in the quantity of AMPARs at synapses can directly impact the firing-activity of a neuron; because of this, AMPARs are under tight regulation involving hundreds of coordinating molecular pathways. It is not in purview of my qualifying paper to review the legion of antecedent molecular cascades involved in the final product, but rather outline what happens after AMPARs are expressed at the dendritic membrane surface.
Once a pool of AMPARs are embedded into the extrasynaptic membrane, they must diffuse laterally along the dendritic surface before entering synapses. This means that any given single particle is not predestined to serve one particular synapse. This idea gives rise to a myriad of questions related to how synapses capture AMPARs from the diffusing swarm, how long they are held,


{{Clear}}


There has been a major shift over the last 5-10 years in how AMPARs are expressed at synapses. The emerging consensus among leaders in the field, including Choquet, Nicol, Svoboda, Malinow, Triller, Sabatini, Svoboda, and others is that AMPARs are not trafficked from the spine cytosol directly to the postsynaptic density (PSD), but rather diffuse laterally along the dendritic membrane before they enter synapses.


a primary questions revolve around the fate of these AMPARs as they diffuse laterally throughout the dendritic surface.  
==SI Fig. 1 - Actin Filament Surface Hull==


A second important question is what is the quantitative landscape that surrounds the drawing from a common pool.  
<html><iframe width="560" height="315" src="//www.youtube.com/embed/JH-hGjzhEFQ" frameborder="0" allowfullscreen></iframe></html>






This project aims to identify how receptors accumulate at synapses to produce and sustain long term potentiation (LTP), a neural correlate of long term memory [1-8]. It has been established that AMPA receptor (AMPAR) expression at synapses is fundamental to this memory-related neural plasticity [9-12]. These glutamatergic cation channels are primary mediators of excitatory neurotransmission in the CNS [13-16]. As such, characterizing the regulation of these receptors was a focus of early studies examining LTP [9, 17], followed by interest in memory maintenance mechanisms [1, 18]. 
==SI Fig. 2 - Brownian Motion Matlab Code==
Research on the induction of LTP has identified numerous molecular cascades important for the initial consolidation of memory [19]. Early efforts to characterize LTP induction worked under the assumption that AMPARs are trafficked directly to the potentiated membrane shortly after learning [20, 21]. Recent evidence suggests atypical kinases, PKMζ in particular, could help maintain LTP through constitutive site-directed receptor trafficking [26-34].


{{ExpandBox|width=80%|float=left|opener=View|Brownian Motion Matlab Code|


Various kinases (i.e. PKA, CaMKII, PKC) have been confirmed to be functionally important for AMPAR-related LTP induction [22-25], which has been studied extensively; however there remains uncertainty about the molecular dynamics that underlie plasticity., but subsequent work indicates that PKMζ has a non-critical role in long-term memory [35, 36].
<syntaxhighlight lang="matlab" line start="1" highlight="1" enclose="div">
While atypical kinases may be involved in memory maintenance, it may not be through site-directed constitutive trafficking of AMPARs as proposed [28, 29]. Receptor expression changes at synapses were thought to be mainly a function of cycling between intracellular and membrane compartments, but recent evidence suggests that receptors accumulate at synapses largely via lateral diffusion and association with scaffold associated proteins (SAP) [37]. Even atypical kinases like PKMζ may be involved with trafficking of SAPs instead of AMPARs directly: in cultured hippocampal neurons PKMζ was shown to increase PSD-95 cluster size, which then in turn increased postsynaptic expression of AMPARs [38]. PSD-95 and other SAPs contribute to the aggregation receptors at the synapse, and may have a central role in LTP maintenance. The intracellular C-terminus of the various AMPAR subunits interact with a family of SAPs with PDZ domains, including PSD-95, MAGI-2, SAP97, PICK1, and GRIP1 [39-46]. This interaction with PDZ proteins can be both direct [47-50] and indirect [51-54], and when the interaction site is mutated, potentiation is blocked [25]. Indeed, the dendritic localization of many membrane-associated proteins are regulated by PDZ-containing SAPs [55-58], which help determine the size and strength of synapses by organizing glutamate receptors at the postsynaptic density [59].
function [boom] = BradsBrownianMotionScript()
Several studies imaged the synaptic capture of AMPARs from the pool of receptors diffusing rapidly in the extra-synaptic membrane [60]; while tracking the location of new AMPARs, receptors were first shown to be distributed along dendrites, followed by their lateral translocation into a postsynaptic density. Single-particle imaging reveals the synaptic capture of laterally diffusing AMPARs is dependent on interactions between PSD-95 and Stargazin, an AMPAR auxiliary subunit [51]. When this interaction was disrupted, it strongly increased AMPAR diffusion, and prevented synaptic accumulation. Together, this indicates that LTP maintenance is a likely function of SAP proteins that continually annex diffusing AMPARs into the synaptic density. Missing from a complete model of memory maintenance, however, is (1) how neural activity modulates the expression of SAP, (2) how changes in SAP expression effect AMPAR diffusion at synaptic sites, and (3) the identity of SAPs that are important for in vivo memory maintenance. In order to address these gaps, this project has the following aims:
format compact;
format short;
close all;


Specific aim 1: Use single-particle tracking to examine SAP regulation responses to neural activity
% Note: This matlab script requires 'msdanalyzer' toolbox
Hypothesis 1: Neural activity will cause rapid redistribution of SAPs through lateral translocation or cytosolic internalization.
%-------------############################------------------%
Specific aim 2. Use single-particle tracking to examine how SAP expression alters AMPAR distribution
%                STARTING PARAMETERS
Hypothesis 2: Synaptic loss of SAP will lead to a net loss of AMPARs, while synapses that retain and/or gain SAP will recapture the highest proportion of receptors after a burst of neural activity.
%-------------############################------------------%
Specific aim 3. The MAGUK protein PSD-95 is thought to be important for synaptic plasticity. Using a PSD-95 dominant negative antimorph, we’ll test for deficiencies in fear and addiction-related memory.
D = .3;                    % Diffusion Rate
Hypothesis 3: The group expressing a PSD-95 dominant negative protein will have deficits in learning and memory compared to control subjects.
Ds = .1;                    % Diffusion Scalar (Ds = Dn)
Dn = D/(D/Ds);              % new D after scaling L
d = 2;                      % dimensions
dT = 1;                    % time step
k = sqrt(d*D);             % stdev of D's step size distribution
MSD = 2*d*D;                % mean squared displacement
L = sqrt(2*d*D);            % average diagonal (2D) step size
Lx = L/sqrt(2);            % average linear (1D) step size
Ls = 1/sqrt(D/Ds);          % scales Lx values for Dn




REFERENCES
MSDtest = [1 0 0]; % test: D, Dn, or L
Scale = 1/10; % scale of model
Ndots = 100;
Nsteps = Ndots;


1. Kandel, E.R., The molecular biology of memory: cAMP, PKA, CRE, CREB-1, CREB-2, and CPEB. Mol Brain, 2012. 5: p. 14.
2. Smolen, P., A model of late long-term potentiation simulates aspects of memory maintenance. PLoS One, 2007. 2(5): p. e445.
3. Carasatorre, M. and V. Ramirez-Amaya, Network, cellular, and molecular mechanisms underlying long-term memory formation. Curr Top Behav Neurosci, 2013. 15: p. 73-115.
4. Sies, H., Highlight: molecular and cellular mechanisms of memory. Biol Chem, 2009. 390(11): p. 1085.
5. Lombroso, P. and M. Ogren, Learning and memory, part II: molecular mechanisms of synaptic plasticity. J Am Acad Child Adolesc Psychiatry, 2009. 48(1): p. 5-9.
6. Ramirez-Amaya, V., Molecular Mechanisms of Synaptic Plasticity Underlying Long-Term Memory Formation, in Neural Plasticity and Memory: From Genes to Brain Imaging, F. Bermudez-Rattoni, Editor 2007: Boca Raton (FL).
7. Eichenbaum, H., Learning from LTP: a comment on recent attempts to identify cellular and molecular mechanisms of memory. Learn Mem, 1996. 3(2-3): p. 61-73.
8. Costa, C., et al., Mechanisms underlying the impairment of hippocampal long-term potentiation and memory in experimental Parkinson's disease. Brain, 2012. 135(Pt 6): p. 1884-99.
9. Carroll, R.C., et al., Role of AMPA receptor endocytosis in synaptic plasticity. Nat Rev Neurosci, 2001. 2(5): p. 315-24.
10. Barry, M.F. and E.B. Ziff, Receptor trafficking and the plasticity of excitatory synapses. Curr Opin Neurobiol, 2002. 12(3): p. 279-86.
11. Bassani, S., et al., AMPAR trafficking in synapse maturation and plasticity. Cell Mol Life Sci, 2013.
12. Keifer, J. and Z. Zheng, AMPA receptor trafficking and learning. Eur J Neurosci, 2010. 32(2): p. 269-77.
13. Palmer, C.L., L. Cotton, and J.M. Henley, The molecular pharmacology and cell biology of alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptors. Pharmacol Rev, 2005. 57(2): p. 253-77.
14. Bazhenov, A.V. and A.M. Kleshchevnikov, Reciprocal inhibition of the AMPA and NMDA components of excitatory postsynaptic potentials in field CA1 of the rat hippocampus in vitro. Neurosci Behav Physiol, 1999. 29(6): p. 719-25.
15. Obokata, K., H. Kamiya, and S. Ozawa, Differential effects of phorbol ester on AMPA and NMDA components of excitatory postsynaptic currents in dentate neurons of rat hippocampal slices. Neurosci Res, 1997. 29(2): p. 171-9.
16. Clark, K.A., A.D. Randall, and G.L. Collingridge, A comparison of paired-pulsed facilitation of AMPA and NMDA receptor-mediated excitatory postsynaptic currents in the hippocampus. Exp Brain Res, 1994. 101(2): p. 272-8.
17. Malenka, R.C., Synaptic plasticity and AMPA receptor trafficking. Ann N Y Acad Sci, 2003. 1003: p. 1-11.
18. Sacktor, T.C., PKMzeta, LTP maintenance, and the dynamic molecular biology of memory storage. Prog Brain Res, 2008. 169: p. 27-40.
19. Sanes, J.R. and J.W. Lichtman, Can molecules explain long-term potentiation? Nat Neurosci, 1999. 2(7): p. 597-604.
20. Bliss, T.V. and G.L. Collingridge, A synaptic model of memory: long-term potentiation in the hippocampus. Nature, 1993. 361(6407): p. 31-9.
21. Isaac, J.T., M.C. Ashby, and C.J. McBain, The role of the GluR2 subunit in AMPA receptor function and synaptic plasticity. Neuron, 2007. 54(6): p. 859-71.
22. Sutton, M.A. and T.J. Carew, Parallel molecular pathways mediate expression of distinct forms of intermediate-term facilitation at tail sensory-motor synapses in Aplysia. Neuron, 2000. 26(1): p. 219-31.
23. Schwartz, J.H. and S.M. Greenberg, Molecular mechanisms for memory: second-messenger induced modifications of protein kinases in nerve cells. Annu Rev Neurosci, 1987. 10: p. 459-76.
24. Derkach, V., Zooming in on AMPA receptor regulation by CaMKII. Nat Neurosci, 2011. 14(6): p. 674-5.
25. Hayashi, Y., et al., Driving AMPA receptors into synapses by LTP and CaMKII: requirement for GluR1 and PDZ domain interaction. Science, 2000. 287(5461): p. 2262-7.
26. Sacktor, T.C., et al., Persistent activation of the zeta isoform of protein kinase C in the maintenance of long-term potentiation. Proc Natl Acad Sci U S A, 1993. 90(18): p. 8342-6.
27. Ling, D.S., L.S. Benardo, and T.C. Sacktor, Protein kinase Mzeta enhances excitatory synaptic transmission by increasing the number of active postsynaptic AMPA receptors. Hippocampus, 2006. 16(5): p. 443-52.
28. Yao, Y., et al., PKM zeta maintains late long-term potentiation by N-ethylmaleimide-sensitive factor/GluR2-dependent trafficking of postsynaptic AMPA receptors. J Neurosci, 2008. 28(31): p. 7820-7.
29. Migues, P.V., et al., PKMzeta maintains memories by regulating GluR2-dependent AMPA receptor trafficking. Nat Neurosci, 2010. 13(5): p. 630-4.
30. Sacktor, T.C., How does PKMzeta maintain long-term memory? Nat Rev Neurosci, 2011. 12(1): p. 9-15.
31. Pastalkova, E., et al., Storage of spatial information by the maintenance mechanism of LTP. Science, 2006. 313(5790): p. 1141-4.
32. Shema, R., T.C. Sacktor, and Y. Dudai, Rapid erasure of long-term memory associations in the cortex by an inhibitor of PKM zeta. Science, 2007. 317(5840): p. 951-3.
33. Serrano, P., et al., PKMzeta maintains spatial, instrumental, and classically conditioned long-term memories. PLoS Biol, 2008. 6(12): p. 2698-706.
34. von Kraus, L.M., T.C. Sacktor, and J.T. Francis, Erasing sensorimotor memories via PKMzeta inhibition. PLoS One, 2010. 5(6): p. e11125.
35. Lee, A.M., et al., Prkcz null mice show normal learning and memory. Nature, 2013. 493(7432): p. 416-9.
36. Volk, L.J., et al., PKM-zeta is not required for hippocampal synaptic plasticity, learning and memory. Nature, 2013. 493(7432): p. 420-3.
37. Triller, A. and D. Choquet, Surface trafficking of receptors between synaptic and extrasynaptic membranes: and yet they do move! Trends Neurosci, 2005. 28(3): p. 133-9.
38. Shao, C.Y., et al., PKMzeta is necessary and sufficient for synaptic clustering of PSD-95. Hippocampus, 2012. 22(7): p. 1501-7.
39. Cai, C., et al., Interaction between SAP97 and PSD-95, two Maguk proteins involved in synaptic trafficking of AMPA receptors. J Biol Chem, 2006. 281(7): p. 4267-73.
40. Waites, C.L., et al., Synaptic SAP97 isoforms regulate AMPA receptor dynamics and access to presynaptic glutamate. J Neurosci, 2009. 29(14): p. 4332-45.
41. Schluter, O.M., W. Xu, and R.C. Malenka, Alternative N-terminal domains of PSD-95 and SAP97 govern activity-dependent regulation of synaptic AMPA receptor function. Neuron, 2006. 51(1): p. 99-111.
42. Jourdi, H. and M. Kabbaj, Acute BDNF treatment upregulates GluR1-SAP97 and GluR2-GRIP1 interactions: implications for sustained AMPA receptor expression. PLoS One, 2013. 8(2): p. e57124.
43. Douyard, J., et al., Differential neuronal and glial expression of GluR1 AMPA receptor subunit and the scaffolding proteins SAP97 and 4.1N during rat cerebellar development. J Comp Neurol, 2007. 502(1): p. 141-56.
44. Danielson, E., et al., S-SCAM/MAGI-2 is an essential synaptic scaffolding molecule for the GluA2-containing maintenance pool of AMPA receptors. J Neurosci, 2012. 32(20): p. 6967-80.
45. Lu, W. and E.B. Ziff, PICK1 interacts with ABP/GRIP to regulate AMPA receptor trafficking. Neuron, 2005. 47(3): p. 407-21.
46. Shao, X., et al., Threonine 82 at the PDZ domain of PICK1 is critical for AMPA receptor interaction and localization. Neurochem Int, 2010. 56(8): p. 962-70.
47. Valtschanoff, J.G., et al., SAP97 concentrates at the postsynaptic density in cerebral cortex. Eur J Neurosci, 2000. 12(10): p. 3605-14.
48. Leonard, A.S., et al., SAP97 is associated with the alpha-amino-3-hydroxy-5-methylisoxazole-4-propionic acid receptor GluR1 subunit. J Biol Chem, 1998. 273(31): p. 19518-24.
49. Haglerod, C., et al., Protein interacting with C kinase 1 (PICK1) and GluR2 are associated with presynaptic plasma membrane and vesicles in hippocampal excitatory synapses. Neuroscience, 2009. 158(1): p. 242-52.
50. Dev, K.K., S. Nakanishi, and J.M. Henley, The PDZ domain of PICK1 differentially accepts protein kinase C-alpha and GluR2 as interacting ligands. J Biol Chem, 2004. 279(40): p. 41393-7.
51. Bats, C., L. Groc, and D. Choquet, The interaction between Stargazin and PSD-95 regulates AMPA receptor surface trafficking. Neuron, 2007. 53(5): p. 719-34.
52. Deng, F., et al., Stargazin and other transmembrane AMPA receptor regulating proteins interact with synaptic scaffolding protein MAGI-2 in brain. J Neurosci, 2006. 26(30): p. 7875-84.
53. Schnell, E., et al., Direct interactions between PSD-95 and stargazin control synaptic AMPA receptor number. Proc Natl Acad Sci U S A, 2002. 99(21): p. 13902-7.
54. Chen, L., et al., Stargazin regulates synaptic targeting of AMPA receptors by two distinct mechanisms. Nature, 2000. 408(6815): p. 936-43.
55. Songyang, Z., et al., Recognition of unique carboxyl-terminal motifs by distinct PDZ domains. Science, 1997. 275(5296): p. 73-7.
56. Saras, J., et al., Characterization of the interactions between PDZ domains of the protein-tyrosine phosphatase PTPL1 and the carboxyl-terminal tail of Fas. J Biol Chem, 1997. 272(34): p. 20979-81.
57. Rongo, C., et al., LIN-10 is a shared component of the polarized protein localization pathways in neurons and epithelia. Cell, 1998. 94(6): p. 751-9.
58. Kim, J.H. and R.L. Huganir, Organization and regulation of proteins at synapses. Curr Opin Cell Biol, 1999. 11(2): p. 248-54.
59. Kim, E. and M. Sheng, PDZ domain proteins of synapses. Nat Rev Neurosci, 2004. 5(10): p. 771-81.
60. Czondor, K., et al., Unified quantitative model of AMPA receptor trafficking at synapses. Proc Natl Acad Sci U S A, 2012. 109(9): p. 3522-7.


xyl = ones(2,Ndots);
xyds = ones(2,Ndots);
lims = ((D+1)^2)*10;


 


Basic research aimed at defining the physiological mechanisms that underlie memory could help identify new targets for dementia and addiction treatment [1-8]. This project aims to identify how receptors accumulate at synapses to produce and sustain long term potentiation (LTP), a neural correlate of long term memory [9-16]. It has been established that AMPA receptor (AMPAR) expression at synapses is fundamental to this memory-related neural plasticity [17-20]. These glutamatergic cation channels are primary mediators of excitatory neurotransmission in the CNS [21-24]. As such, characterizing the regulation of these receptors was a focus of early studies examining LTP [17, 25], followed by interest in memory maintenance mechanisms [9, 26].
%===========================================================%
Research on the induction of LTP has identified numerous molecular cascades important for the initial consolidation of memory [27]. In the traditional scheme of LTP induction, AMPARs are trafficked directly to the potentiated membrane shortly after learning [28, 29], with various kinases (i.e. PKA, CaMKII, PKC) being functionally important for AMPAR-related LTP induction [30-33]. However it’s questionable whether continuous delivery of receptors from cytosol-to-membrane is also the primary mechanism behind memory maintenance. In this model of LTP, in order for a memory-trace to persist there would need to be molecular agents that keep synapses potentiated by continuously trafficking AMPARs to the membrane. The search for such agents has so far provided a single candidate thought to be functionally capable of this role - an atypical form of protein kinase C known as PKMζ was hypothesized to maintain LTP through constitutive site-directed receptor trafficking [34-42]. However, subsequent work indicates this atypical kinase has, at best, a non-critical role in long-term memory [43, 44].
%              LIVE PARTICLE DIFFUSION
Certainly, changes in receptor numbers at synapses can be due to cycling between surface and intracellular compartments. However, recent studies using updated single-particle tracking methods show that receptors diffuse along the membrane between synaptic and extrasynaptic locations, and localization of receptors at synapses results from their interactions with submembranous scaffold-associated proteins (SAP) [68][45]. This has changed our view of the organization of the neuronal membrane to include lateral diffusion of receptors as a key parameter in synaptic plasticity. In fact, there is now evidence that atypical kinases are more involved with the regulation of SAPs than the receptors themselves, as in one study that suggests PKMζ is involved with trafficking of the SAP molecule PSD-95, increasing its cluster size, and in turn increasing postsynaptic expression of AMPARs [46].
%-----------------------------------------------------------%
PSD-95 and other SAPs contribute to the aggregation receptors at the synapse, and may have a central role in LTP maintenance. The intracellular C-terminus of the various AMPAR subunits interact with a family of SAPs with PDZ domains (MAGUK proteins), including PSD-95, MAGI-2, SAP97, PICK1, and GRIP1 [47-54]. Indeed, the dendritic localization of many membrane-associated proteins are regulated by PDZ-containing SAPs [63-66], which help determine the size and strength of synapses by organizing glutamate receptors at the postsynaptic density [67]. This PDZ interaction can be direct [55-58] or indirect [59-62], and when the PDZ site is mutated, potentiation is blocked [33]. Other single-particle imaging experiments reveal the synaptic capture of laterally diffusing AMPARs is dependent on interactions between PSD-95 and Stargazin, an AMPAR auxiliary subunit [59]; blocking this interaction prevented AMPAR synaptic accumulation. Together, this indicates that LTP maintenance is a likely function of SAP proteins that continually annex diffusing AMPARs into the synaptic density. Missing from a complete model of memory maintenance, however, is (1) how neural activity modulates the expression of SAP, (2) how changes in SAP expression effect AMPAR diffusion at synaptic sites, and (3) the identity of SAPs that are important for in vivo memory maintenance. In order to address these gaps, this project has the following aims:
for t = 1:Nsteps


Specific aim 1: Use single-particle tracking to examine SAP regulation responses to neural activity
    xyds = STEPxyds(Ndots, k);
Hypothesis 1: Neural activity will cause rapid redistribution of SAPs through lateral translocation or cytosolic internalization.
[xyl] = AMPARSTEP(Ndots, xyds, xyl);
Specific aim 2. Use single-particle tracking to examine how SAP expression alters AMPAR distribution
MAINPLOT(xyl, lims);
Hypothesis 2: Synaptic loss of SAP will lead to a net loss of AMPARs, while synapses that retain and/or gain SAP will recapture the highest proportion of receptors after a burst of neural activity.
Specific aim 3. The MAGUK protein PSD-95 is thought to be important for synaptic plasticity. Using a PSD-95 dominant negative antimorph, we’ll test for deficiencies in fear and addiction-related memory.
Hypothesis 3: The group expressing a PSD-95 dominant negative protein will have deficits in learning and memory compared to control subjects.


end
%===========================================================%




%===========================================================%
%              MSD RANDOM STEPS ANALYSIS
%-----------------------------------------------------------%
tracks = cell(Ndots, 1);


stepN = 1;
for t = 1:Nsteps


Specific Aims are limited to one page.  
xyds = STEPxyds(Ndots, k);
State concisely the goals of the proposed research and summarize the expected outcome(s), including the impact that the results of the proposed research will exert on the research field(s) involved.  
[xyl] = AMPARSTEP(Ndots, xyds, xyl);
List succinctly the specific objectives of the research proposed, e.g., to test a stated hypothesis, create a novel design, solve a specific problem, challenge an existing paradigm or clinical practice, address a critical barrier to progress in the field, or develop new technology.
    [tracks] = MSDfun(stepN, Nsteps, tracks, xyds);
 
stepN = stepN+1;
end
MSDfunction(tracks,Ndots,Nsteps,D,Dn,L,dT,k,Scale,MSDtest);
 
 
 
 
 
%===========================================================%
%              MSD UNIFORM STEPS ANALYSIS
%-----------------------------------------------------------%
stepN = 1;
for t = 1:Nsteps
 
xyds = stepsize(Ndots, Lx);
[xyl xyds] = MSDAMPARSTEP(Ndots, xyds, xyl, Ls);
    [tracks] = MSDfun(stepN, Nsteps, tracks, xyds);
 
stepN = stepN+1;
end
MSDfunction(tracks,Ndots,Nsteps,D,Dn,L,dT,k,Scale,MSDtest);
 
 
boom = 'done';
%-------------############################------------------%
end %        ##    END MAIN FUNCTION  ##
%-------------############################------------------%
%%
 
 
 
 
 
%%
%-------------############################------------------%
%            ##      SUBFUNCTIONS      ##
%-------------############################------------------%
 
 
%-------------------------------------------%
% STEP SIZE GENERATOR
%-------------------------------------------%
function xyds = STEPxyds(Ndots, k)
 
    xyds = (k * randn(2,Ndots));
 
end
 
 
%-------------------------------------------%
% MOVE PARTICLES MAIN FUNCTION
%-------------------------------------------%
function [xyl] = AMPARSTEP(Ndots, xyds, xyl)
for j = 1:Ndots
        xyl(:,j) = xyl(:,j)+xyds(:,j);
end
end
 
 
%-------------------------------------------%
% LIVE DIFFUSION PLOT
%-------------------------------------------%
function [] = MAINPLOT(xyl, lims)
%-------------------------------------------%
xlim = [-lims lims];
ylim = [-lims lims];
zlim = [-5 5];
 
%=================================%
%      MAIN 2D PLOT
%---------------------------------%
figure(1)
subplot(2,1,1),
AMPARPlot = gscatter(xyl(1,:),xyl(2,:));
axis([xlim, ylim]);
set(AMPARPlot,'marker','.','markersize',[6],'color',[1 0 0])
 
 
%=================================%
%          3D PLOT
%---------------------------------%
figure(1);
subplot(2,1,2),
gscatter(xyl(1,:),xyl(2,:)); view(20, 30);
axis normal;
grid off
axis([xlim, ylim, zlim]);
set(gca, 'Box', 'on');
 
end
 
 
%-------------------------------------------%
% MANUAL STEP SIZE FUNCTION
%-------------------------------------------%
function xyds = stepsize(Ndots, Lx)
%-------------------------------------------%
 
  Lx(1:2,1:Ndots) = Lx;
  xyd = randi([0 1],Ndots,2)';
  xyd(xyd == 0) = -1;
  xyds = (Lx.*xyd);
 
end
 
 
%-------------------------------------------%
% MSD SCALED STEPS FUNCTION
%-------------------------------------------%
function [xyl xyds] = MSDAMPARSTEP(Ndots, xyds, xyl, Ls)
for j = 1:Ndots
        xyds(:,j) = xyds(:,j)*Ls;
        xyl(:,j) = xyl(:,j)+xyds(:,j);
end
end
 
 
%-------------------------------------------%
% MSD TRACKS GENERATOR
%-------------------------------------------%
function [tracks] = MSDfun(stepN, Nsteps, tracks, xyds)
    time = (0:Nsteps-1)';
    xymsd = xyds';
    xymsd = cumsum(xymsd,1);
    tracks{stepN} = [time xymsd];
 
end
 
 
%-------------------------------------------%
% MSD TRACKS ANALYSIS
%-------------------------------------------%
function [] = MSDfunction(tracks,Ndots,Nsteps,D,Dn,L,dT,k,Scale,MSDtest)
 
SPACE_UNITS = 'µm';
TIME_UNITS = 's';
N_PARTICLES = Ndots;
N_TIME_STEPS = Nsteps;
N_DIM = 2;
 
oD = D; % raw µm^2/s
D  = D*Scale;      % to-scale µm^2/s
 
oDn = Dn; % raw µm^2/s
Dn = Dn*Scale; % to-scale µm^2/s
 
oL = L; % raw µm
L = L*Scale; % to-scale µm
 
dTbase = dT; % raw time-step
dT = dT*Scale; % to-scale time-step
k = k; % stdv of step distribution
 
ma = msdanalyzer(2, SPACE_UNITS, TIME_UNITS);
ma = ma.addAll(tracks);
disp(ma)
 
figure
ma.plotTracks;
ma.labelPlotTracks;
 
ma = ma.computeMSD;
ma.msd;
 
t = (0 : N_TIME_STEPS)' * dT;
[T1, T2] = meshgrid(t, t);
all_delays = unique( abs(T1 - T2) );
 
figure
ma.plotMSD;
 
 
cla
ma.plotMeanMSD(gca, true)
 
mmsd = ma.getMeanMSD;
t = mmsd(:,1);
x = mmsd(:,2);
dx = mmsd(:,3) ./ sqrt(mmsd(:,4));
errorbar(t, x, dx, 'k')
 
[fo, gof] = ma.fitMeanMSD;
plot(fo)
ma.labelPlotMSD;
legend off
 
 
ma = ma.fitMSD;
 
good_enough_fit = ma.lfit.r2fit > 0.8;
Dmean = mean( ma.lfit.a(good_enough_fit) ) / 2 / ma.n_dim;
Dstd  =  std( ma.lfit.a(good_enough_fit) ) / 2 / ma.n_dim;
 
Dheader1 = ['Raw Unscaled Values'];
Dhead1 = ['    D        Dn        L'];
Ddat1 = [oD oDn oL];
disp(' ')
disp(Dheader1)
disp(Dhead1)
disp(Ddat1)
 
 
yourtesthead = ['YOU ARE TESTING DIFFUSION FOR:'];
if MSDtest(1)
yourtest = ['  D:  original diffusion rate'];
elseif MSDtest(2)
yourtest = ['  Dn:  new diffusion rate'];
elseif MSDtest(3)
yourtest = ['  L:  step length'];
else
yourtest = ['  generic diffusion rate'];
end
disp(yourtesthead)
disp(yourtest)
 
disp(' ')
fprintf('Estimation of raw D coefficient from MSD:\n')
fprintf('D = %.3g ± %.3g (mean ± std, N = %d)\n', ...
    Dmean, Dstd, sum(good_enough_fit));
 
 
 
 
% Retrieve instantaneous velocities, per track
trackV = ma.getVelocities;
 
% Pool track data together
TV = vertcat( trackV{:} );
 
% Velocities are returned in a N x (nDim+1) array: [ T Vx Vy ...]. So the
% velocity vector in 2D is:
V = TV(:, 2:3);
 
% Compute diffusion coefficient
varV = var(V);
mVarV = mean(varV); % Take the mean of the two estimates
Dest = mVarV / 2 * dT;
 
 
 
Dheader2 = ['Scaling to model...'];
Dhead2 = ['    D        Dn        L'];
Ddat2 = [D Dn L];
 
disp(' ')
disp(Dheader2)
disp(Dhead2)
disp(Ddat2)
fprintf('Estimation from velocities histogram:\n')
fprintf('Tested D = %.3g %s, compare to scaled Des value of %.3g %s\n', ...
    Dest, [SPACE_UNITS '²/' TIME_UNITS], D, [SPACE_UNITS '²/' TIME_UNITS]);
 
% printf('D.psd target value was %.3g %s\n', ...
%    Dest, msdDpsd, [SPACE_UNITS '²/' TIME_UNITS]);
 
end
 
 
</syntaxhighlight>
 
}}
 
<br /><br />
{{Clear}}
 
==SI Fig. 3 - Title==
Text Text Text
 
 
==SI Fig. 4 - Title==
Text Text Text
 
 
==SI Fig. 5 - Title==
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[[Category:Synaptic Plasticity]]

Latest revision as of 13:08, 5 January 2015

Qual Paper SI Material

Qual Project Source Code

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All source code used in my qualifying exam project can be found here in my github repo for the project. An online version of my qual with enhanced features like citation data popup graphics and animations can be found on this page


SI Fig. 1 - Actin Filament Surface Hull

<html><iframe width="560" height="315" src="//www.youtube.com/embed/JH-hGjzhEFQ" frameborder="0" allowfullscreen></iframe></html>


SI Fig. 2 - Brownian Motion Matlab Code

Brownian Motion Matlab Code 


function [boom] = BradsBrownianMotionScript()
format compact;
format short;
close all;

% Note: This matlab script requires 'msdanalyzer' toolbox
%-------------############################------------------%
%                 STARTING PARAMETERS
%-------------############################------------------%
D = .3;                     % Diffusion Rate
Ds = .1;                    % Diffusion Scalar (Ds = Dn)
Dn = D/(D/Ds);              % new D after scaling L
d = 2;                      % dimensions
dT = 1;                     % time step
k = sqrt(d*D);	            % stdev of D's step size distribution
MSD = 2*d*D;                % mean squared displacement
L = sqrt(2*d*D);            % average diagonal (2D) step size
Lx = L/sqrt(2);             % average linear (1D) step size
Ls = 1/sqrt(D/Ds);          % scales Lx values for Dn


MSDtest = [1 0 0];			% test: D, Dn, or L
Scale = 1/10;				% scale of model
Ndots = 100;
Nsteps = Ndots;


xyl = ones(2,Ndots);
xyds = ones(2,Ndots);
lims = ((D+1)^2)*10;


%===========================================================%
%               LIVE PARTICLE DIFFUSION
%-----------------------------------------------------------%
for t = 1:Nsteps

    xyds = STEPxyds(Ndots, k);
	[xyl] = AMPARSTEP(Ndots, xyds, xyl);
	MAINPLOT(xyl, lims);

end
%===========================================================%


%===========================================================%
%               MSD RANDOM STEPS ANALYSIS
%-----------------------------------------------------------%
tracks = cell(Ndots, 1);

stepN = 1;
for t = 1:Nsteps 

	xyds = STEPxyds(Ndots, k);
	[xyl] = AMPARSTEP(Ndots, xyds, xyl);
    [tracks] = MSDfun(stepN, Nsteps, tracks, xyds);

stepN = stepN+1;
end
MSDfunction(tracks,Ndots,Nsteps,D,Dn,L,dT,k,Scale,MSDtest);





%===========================================================%
%               MSD UNIFORM STEPS ANALYSIS
%-----------------------------------------------------------%
stepN = 1;
for t = 1:Nsteps 

xyds = stepsize(Ndots, Lx);
		
	[xyl xyds] = MSDAMPARSTEP(Ndots, xyds, xyl, Ls);
    [tracks] = MSDfun(stepN, Nsteps, tracks, xyds);

stepN = stepN+1;
end
MSDfunction(tracks,Ndots,Nsteps,D,Dn,L,dT,k,Scale,MSDtest);


boom = 'done';
%-------------############################------------------%
end %         ##    END MAIN FUNCTION   ##
%-------------############################------------------% 
%%





%%
%-------------############################------------------%
%             ##      SUBFUNCTIONS      ##
%-------------############################------------------% 


%-------------------------------------------%
% STEP SIZE GENERATOR
%-------------------------------------------%
function xyds = STEPxyds(Ndots, k)

    xyds = (k * randn(2,Ndots));

end


%-------------------------------------------%
% MOVE PARTICLES MAIN FUNCTION
%-------------------------------------------%
function [xyl] = AMPARSTEP(Ndots, xyds, xyl)
	
	for j = 1:Ndots
        xyl(:,j) = xyl(:,j)+xyds(:,j);
	end
	
end


%-------------------------------------------%
% LIVE DIFFUSION PLOT
%-------------------------------------------%
function [] = MAINPLOT(xyl, lims)
%-------------------------------------------%
xlim = [-lims lims];
ylim = [-lims lims];
zlim = [-5 5];

%=================================%
%       MAIN 2D PLOT
%---------------------------------%
figure(1)
subplot(2,1,1), 
AMPARPlot = gscatter(xyl(1,:),xyl(2,:));
axis([xlim, ylim]);
set(AMPARPlot,'marker','.','markersize',[6],'color',[1 0 0])


%=================================%
%           3D PLOT
%---------------------------------%
figure(1);
subplot(2,1,2), 
gscatter(xyl(1,:),xyl(2,:)); view(20, 30);
axis normal;
grid off
axis([xlim, ylim, zlim]);
set(gca, 'Box', 'on');

end


%-------------------------------------------%
% MANUAL STEP SIZE FUNCTION
%-------------------------------------------%
function xyds = stepsize(Ndots, Lx)
%-------------------------------------------%

   Lx(1:2,1:Ndots) = Lx;
   xyd = randi([0 1],Ndots,2)';
   xyd(xyd == 0) = -1;
   xyds = (Lx.*xyd);
   
end


%-------------------------------------------%
% MSD SCALED STEPS FUNCTION
%-------------------------------------------%
function [xyl xyds] = MSDAMPARSTEP(Ndots, xyds, xyl, Ls)
	
	for j = 1:Ndots
        xyds(:,j) = xyds(:,j)*Ls;
        xyl(:,j) = xyl(:,j)+xyds(:,j);
	end	
	
end


%-------------------------------------------%
% MSD TRACKS GENERATOR
%-------------------------------------------%
function [tracks] = MSDfun(stepN, Nsteps, tracks, xyds)
    time = (0:Nsteps-1)';
    xymsd = xyds';
    xymsd = cumsum(xymsd,1);
    tracks{stepN} = [time xymsd];

end


%-------------------------------------------%
% MSD TRACKS ANALYSIS
%-------------------------------------------%
function [] = MSDfunction(tracks,Ndots,Nsteps,D,Dn,L,dT,k,Scale,MSDtest)

SPACE_UNITS = 'µm';
TIME_UNITS = 's';
N_PARTICLES = Ndots;
N_TIME_STEPS = Nsteps;
N_DIM = 2;

oD = D;				% raw		µm^2/s
D  = D*Scale;       % to-scale	µm^2/s

oDn = Dn;			% raw		µm^2/s
Dn = Dn*Scale;		% to-scale	µm^2/s

oL = L;				% raw		µm
L = L*Scale;		% to-scale	µm

dTbase = dT;		% raw time-step 
dT = dT*Scale;		% to-scale time-step
k = k;				% stdv of step distribution

ma = msdanalyzer(2, SPACE_UNITS, TIME_UNITS);
ma = ma.addAll(tracks);
disp(ma)

figure
ma.plotTracks;
ma.labelPlotTracks;

ma = ma.computeMSD;
ma.msd;

t = (0 : N_TIME_STEPS)' * dT;
[T1, T2] = meshgrid(t, t);
all_delays = unique( abs(T1 - T2) );

figure
ma.plotMSD;


cla
ma.plotMeanMSD(gca, true)

mmsd = ma.getMeanMSD;
t = mmsd(:,1);
x = mmsd(:,2);
dx = mmsd(:,3) ./ sqrt(mmsd(:,4));
errorbar(t, x, dx, 'k')

[fo, gof] = ma.fitMeanMSD;
plot(fo)
ma.labelPlotMSD;
legend off


ma = ma.fitMSD;

good_enough_fit = ma.lfit.r2fit > 0.8;
Dmean = mean( ma.lfit.a(good_enough_fit) ) / 2 / ma.n_dim;
Dstd  =  std( ma.lfit.a(good_enough_fit) ) / 2 / ma.n_dim;

Dheader1 = ['Raw Unscaled Values'];
Dhead1 = ['    D        Dn        L'];
Ddat1 = [oD oDn oL];
disp(' ')
disp(Dheader1)
disp(Dhead1)
disp(Ddat1)


yourtesthead = ['YOU ARE TESTING DIFFUSION FOR:'];
if MSDtest(1)
	yourtest = ['   D:   original diffusion rate'];
elseif MSDtest(2)
	yourtest = ['   Dn:  new diffusion rate'];
elseif MSDtest(3)
	yourtest = ['   L:  step length'];
else
	yourtest = ['   generic diffusion rate'];
end
disp(yourtesthead)
disp(yourtest)

disp(' ')
fprintf('Estimation of raw D coefficient from MSD:\n')
fprintf('D = %.3g ± %.3g (mean ± std, N = %d)\n', ...
    Dmean, Dstd, sum(good_enough_fit));




% Retrieve instantaneous velocities, per track
 trackV = ma.getVelocities;

 % Pool track data together
 TV = vertcat( trackV{:} );

 % Velocities are returned in a N x (nDim+1) array: [ T Vx Vy ...]. So the
 % velocity vector in 2D is:
 V = TV(:, 2:3);

 % Compute diffusion coefficient
varV = var(V);
mVarV = mean(varV); % Take the mean of the two estimates
Dest = mVarV / 2 * dT;



Dheader2 = ['Scaling to model...'];
Dhead2 = ['    D        Dn        L'];
Ddat2 = [D Dn L];

disp(' ')
disp(Dheader2)
disp(Dhead2)
disp(Ddat2)
fprintf('Estimation from velocities histogram:\n')
fprintf('Tested D = %.3g %s, compare to scaled Des value of %.3g %s\n', ...
    Dest, [SPACE_UNITS '²/' TIME_UNITS], D, [SPACE_UNITS '²/' TIME_UNITS]);

% printf('D.psd target value was %.3g %s\n', ...
%     Dest, msdDpsd, [SPACE_UNITS '²/' TIME_UNITS]);

end



SI Fig. 3 - Title

Text Text Text


SI Fig. 4 - Title

Text Text Text


SI Fig. 5 - Title

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