morphological scaling and neuromechanics: computational ...aliceabr/ucs_2008_slides.pdf ·...

Morphological Scaling and

Neuromechanics: computational

and experimental approaches.

Bradly Alicea (http://www.msu.edu/~aliceabr, [email protected])

Michigan State University

UCS 2008, Champaign-Urbana, IL

IntroductionCentral Problem:

What are the main features of physiological and behavioral adaptation associated with

prior and current environmental selection, and how are these systems maintained (what is

their regulatory structure over time)?

The genotype-phenotype problem can be understood using virtual environment manipulations

and by focusing on a certain class of easily-to-manipulate adaptive behaviors.

Genotype-to-phenotype approach:

* largely theoretical, but can provide a framework for experimentation.

* interplay between functional anatomy and physiological adaptation.

* technological, experimental means to get at this relationship.

* role of biological variation

* current work focuses largely on short-term mechanisms of adaptation.

* computational, future work on variability/adaptability to get at this relationship.

Introduction (con’t)Genotype-to-Phenotype problem: what is the mapping of genetic, biochemical

Information to the phenotype or behavior?

* due to epistasis, GxE effects, massive

amounts of complexity – not isomorphic.

1) Wagner (2000): Fitness Landscapes

for RNA sequences

* RNA sequences must mutate n steps to

affect a change in the phenotype

2) Metabolic Flux Analysis

* changes in stochiometry effects changes

in gene expression pathways, effect on

phenotype and behavior (gene expression

in tissues).

3) QTL Analysis

* evaluate phenotype, map to a chromosomal position

(based on crossover, probabilities, actually P-to-G).

Introduction (con’t)

My approach to G-to-P mappings (so far) – better suited to investigations of behavioral

phenotypes and systems-level physiology:

* use virtual environments in conjunction with real-time in vivo assays (behavior, physiological

output can be digitized, integrated). A unique set of experimental approaches.

* use of fitness landscapes and physiological

control systems to better understand potential

variation

* statistical approaches to understanding

actual and potential variation.

1) performance (allometric) scaling

(optimizing nonlinear regressions).

2) sizing, shaping, and factoring the phenotype.

3) multivariate approaches (n-dimensional

fitness landscapes, machine learning)

Role of Virtual EnvironmentsWhy do we care about virtual environments and how are they scientific instrumentation?

1) Distortion of sensory cues in an “enriched”, naturalistic

context.

In VR, every object in this painting would be interactive and

computationally salient (i.e. every object and interaction in

environment has a number attached).

2) alternate immersion and

non-immersion (mixed-

reality).

3) selective application of

force fields (virtual-to-

physical “mapping”).

May uncover physiological “switching”

mechanisms (observed in motor

learning, gene regulation).

* switching mechanisms may either

inhibit, promote further adaptation.

Role of Virtual Environments (con’t)

Direct and indirect mapping of kinematic and kinetic

variables into manipulable environment (i.e. feedback).


Approach borrowed from aerospace medicine – perturb the

physical environment (i.e. gravitation), observe effect.


Using animal models or

clinical populations –

Observe known mutant or

knockdown, observe result.

Systems Approach to Adaptation,

Physiology, and BehaviorForce learning (adaptive sensorimotor

behavior based on proprioception).

* network centered on the cerebellum,

site of motor learning and VOR

conditioning (“internal model”

proposed by several groups).

Muscles, spinal cord also involved.

(neuromuscular system is regulatory,

has control system quality).

Homeostasis: system is able to

maintain current state through

a single regulatory mechanism

(brain region, gene regulation).

Allostasis: system moves to a new

state via multiple regulatory

mechanisms (cognition, molecular

memory).


Physiology, and Behavior (con’t)Mechanism both highly-conserved and

dervied in humans, other species:

* locomotory specializations, tool use, etc.

Has been successfully replicated in robots:

* interlimb coordination, force production

modeling of internal mechanisms (sensorimotor

integration).

Homeostasis vs. allostatic drive:

Homeostasis: a single regulatory mechanism

modulated by multiple feedback pathways.

Allostasis: multiple, distributed regulatory

mechanisms modulated by only a few

feedback pathways.


Physiology, and Behavior (con’t)Simple models of first-order feedback

in sensorimotor integration:

Pole balancing model:

* 1-D model, keep the pole balanced

using a series of corrections (positive

and negative feedbacks).

* approximates simple neural integrator.

* relevant to robotics, balance research.

PDW models:

* One way to quantify optimal energy

requirements for maintaining balance.


Physiology, and Behavior (con’t)

When considering this problem from a

systems-level perspective:

* using the concepts of homeostasis

and allostasis provide a unified

framework.

* various aspects of function exhibit

either robustness or brittleness, closely

tied to homeostasis and allostasis (or

allostatic drive).

* robustness and brittleness relate to a

control-system characteristics (“robust”

mechanisms are responsive to both

positive and negative feedbacks, while

this is less so for “brittle” systems).


Physiology, and Behavior (con’t)Considering the genotype-to-phenotype

mapping as a complex system involving

interaction with a technological

environment (behavior) and physiology:

* input device to virtual environment or

prosthetic device can introduce a

perturbation to the sensorimotor system.

* neuromuscular perturbation: effect of

decoupling of visual and force information,

creates a condition of non-isomorphy.

* nervous system, tissues fill gap with

autonomous regulation, adaptation.

* lack of isomorphy or coupling can be

described using a fitness landscape

(which are descriptive of forces imposed

by abnormal environment).

Experimental approach to physiology-

computation “coupling” Performance scaling test:

Subjects performed reaching activity, motion of

end-effector (hand or foot) mapped to a virtual

environment. Add (hard distortion), remove

(weak distortion) weights and force fields.

How does static allometry of body dimensions

contribute to range of behavioral outputs and

ability of physiological (internal) systems to

adapt to novel environmental conditions?

Variables:

1) force contributed to movement of a virtual object / force required for movement of virtual

object (referred to as mapped physiological output, related to muscle power).

2) muscle activity in arm segments (measured using electromyography, muscle biopsy).

3) spikiness of data series (also used to determine “fitness” of mapped physiological output):

z = mini-maxi / meani where i is a set of trials over time (set of trials, block of trials)

4) Morphological measurements (body segments): length, width, and circumference.

Theoretical approach to physiology-

computation “coupling” Simple (binary) representation of:

* genotype of physiology (Gt)

* phenotype of computational

device (Gp)

Gt + Gp = augmented phenotype

Frame #1: isometric mapping

(Gp dominant)

Frame #2: mixed mapping (some

effect from both Gt, Gp )

Frame #3: robust augmented

phenotype (protected from

effects of Gp on phenotype).Combinations of binary states Gt, Gp = logic

gates (i.e. AND, OR, NAN)

Coupling and Robustness: an exampleMeasurement of “fitness” for mapped physiological output for alternate methods of delivering

force perturbations:

Condition 1: hard distortion =

black, red functions, interleaved

with weak distortion.

Condition 2: weak distortion =

black, red functions, interleaved

with hard distortion.

Condition 3: weak distortion =

black, red functions, with hard

distortion delivered before

compared blocks.

Condition 4: hard distortion =

black, red functions, with weak

distortion delivered before

compared blocks.

Conditions 1 and 2: robustness with positive and negative

feedbacks.

Condition 3: weak correlation and regression coefficients.

Condition 4: big dropoff in fitness for secondary learning

(third) set of trials.

Coupling and Robustness: an

example (con’t)

As observed in the data, scenarios A through D can occur given different sequences of

stimulus delivery.

* In this case, the degree of coupling ranges from tight to ill-fitting, while the fitness

landscape topology (series of fitnesses attained by a certain phenotype under a range of

environmental manipulations) ranges from smooth to rugged.

Allometry: scaling characteristics of different anatomical segments are “linked” due to genomic and

developmental factors. Consequences for function:

Y = ax + b, Y = axb, Y = -Ax2 + Bx – c

Functional effects of allometry:

Herr et.al (J. Experimental Biology, 205, 2005):

* static allometry may affect movement

performance (differences seen within and

between species) in a systematic fashion.

* provides mechanism for determining

functional effects of scaling.

* Collins et.al (Science, 307, 1996) have

found that there is an optimal ratio of 1.06

between the length of the shank and thigh

in human bipedalism.

Performance Scaling: an introduction

(con’t)

For this presentation, focus

is on 2nd order polynomial

Performance Scaling: an introduction

(con’t)Geometric, mechanical properties + neural coordination = nonlinear effect on reaching movements

and muscle activity.

* biotensegrity = the dynamic opposition of forces maintains the integrity of a structure

(i.e. a system of muscles and body segments, opposing tension forces, reduces amount of work

required by muscles, brain – learn how to move arm “optimally”).

* equilibrium point theory = the mechanical advantage of the arm during movement

(i.e. the position of the humerus relative to the forearm) determines the “stiffness” of the

arm and ultimately its precision control capabilities.

* this further determines adaptive movement and the amount of force produced by

muscles in the arm. A role for robustness and fragility……

Genomic linkage: parts of the body that strongly predict patterns of phenotypic function (muscle,

metabolic activity) or movement behavior.

* individuals with the right allelic background will adapt to manipulated environmental conditions

more easily.

Performance Scaling sensitivity analysis

Performance scaling relationships

not immediately apparent:

* sensitivity algorithm used to uncover

datapoints that fit the predicted function

(nonlinear regression).

Sensitivity analysis = take key data

points out, changes regression coefficient

improves fit of theoretically-defined

curve.

* many different scalings, comparisons

of different body dimensions can be used.

* in some cases, removing a few individual

datapoints will improve these features

greatly.

Predicts an “optimum” point: morphology

predicts optimal performance, but falls

off as morphology gets too large, small.

Performance Scaling sensitivity

analysis (con’t)Parameters tell you how good scaling

fits the theoretical function:

* fewer steps = this particular scaling

predicts performance for a broader range

of individuals, perhaps this is critically

organized somehow.

* larger regression coefficient value

given smaller regression coefficient

Value = greater improvement of taking

out single individuals.

Algorithm converges when removing

another datapoint (i.e. taking another

step) will not improve the regression

coefficient value.


analysis (con’t)

Results of various performance scalings for muscle in humerus (left) and forearm (right).

Pseudocode for sensitivity analysis.


analysis (con’t)How does this relate to performance?

* when a perturbation is introduced in the first

(A-C) or second (B-D) block of trials, the

homeostatic (blue) vs. the allostatic (red)

response demonstrate differences .

* in Frame A, allostasis results in a higher

overall performance measurement value, but

trend mimics homeostatic function.

* in Frame B, allostasis results in a steady

decrease in performance.

* Frame C vs. Frame D for performance

scaling (hyper-allometry for C, neutral for D).

* regression coefficient for C much higher

(.746) than for D (.351).

Hyper- and hypo-allometry

experiments

α = range along x-axis (morphological scaling)

β = range along y-axis (performance measure)

artificial scaling factor (1.0, .75, .50, .25)

Dataset can be manipulated to examine

“theoretical” performance and morphological

parameters:

* body dimensions and performance indicators

can be reduced, enlarged to simulate evolution

and adaptation.

* extrapolate, interpolate changes in function

that reflect potential changes in phenotypic

growth and genomic linkage across within-

species variation, evolution, and development.

* artificial scaling factors meant to uncover

the effects of “hidden” variation or environmental

conditions not previously encountered.


experiments (con’t)In a linear context, changes in the size of

one trait relative to another are referred

to as hyper- and hypoallometry:

* when slope of a scaling/performance

relationship is > 1, = hyperallometry.

* when slope is <1, = hypoallometry.

* when slope is = 1, neutral.

In a nonlinear context, the polynomial

function also changes. Relationship still

exists, but more complex:

RBC = (α * x) / (β * y) – 1

* the range of each axis weighted by the

artificial scaling factor -1 (0 = “neutral”

linear relationship).


experiments (con’t)Observations regarding data

* b1 and b2 are variable in the nonlinear

regression equation:

* as polynomial function becomes more cane-

shape and vertical, b1 gets very large and b2

approaches zero).

* size and shape are variables derived from:

* size (internal volume) and shape (degree of

elongation vs. girth) of the humerus and

forearm

* scaling of humerus against forearm).

* size variable for both muscles and mapped

physiological output always yields large

degrees of hyperallometry.

* shape variable for mapped physiological

output consistently yields hypoallometry.

Part II: role of standing biological

variation in adaptationSpecial Case of Phenotypic Capacitance:

Capacitance: “hidden” polymorphism is selectively exposed in the phenotype (normally

developmental).

* “stored” in the genotype, and released during times of stress.

* Hsp90 (heat shock protein). Upregulated in times of stress, produces “extreme”

phenotypes.

This approach relies upon “standing variation”, or the set of allelic variants already in the

population (having gotten there by previous evolutionary processes) that do not normally

experience selection for their expression.

* once a trigger is presented (environmental mutation/selection), what new or extreme

phenotypes will be revealed?

* how do these relate to the genotype?


variation in adaptationPotential Effects of Environmental Mutation/Selection:

Mutation/Selection model (population genetics):

Freq(allelen) = 1/2N, where N = population size

* in general, many alleles with low frequencies in the overall population (recessive deleterious

alleles never entirely removed, new variants rare unless population undergoes extreme drift).

* relatively few “freaks”, with lots of variation, regardless of the population size (although more

in larger populations).

* medical resequencing (Nature Genetics, 39(4), 407) shows that rare phenotypes (5 th, 95th

percentile) show high degree of variation at less than 5% of loci involved in trait. Promising

approach……..

Differences in response to environmental training across individuals (expression of “freak”

variation). Presence of underutilized alleles might provide advantage to certain individuals in

context.

* comes down to a difference in how robust or brittle the physiological system will be to variation

in environmental stimuli.


variation in adaptation (con’t)Differential responses to same amount of training with same initial condition:

Robustness in training -- see Coyle, Journal of Applied Physiology, 98, 2191-2196 (2005):

Lance Armstrong’s muscle power:

Gross- production of muscle power.

Net(∆)- production of muscle power not related

to metabolic processes.

Rises over several years, regardless of detraining

(chemotherapy), intense training (before W.C., Tour

de France) intervals.

Differences in morphological size, shape,

internal mechanisms all provide a different

response to the same set of stimuli.

* previous performance levels, hereditary factors

can determine level of adaptation attained.


variation in adaptation (con’t)

Proprioception can drive the upregulation of genes involved in tissue adaptation, learning

and memory.

* Ischemic tolerance: limited exposure to cold temperatures (preconditioning) can inhibit

brain damage caused by acute insults.

* neuroprotection involves controlling /inhibiting cell death (apoptosis) pathway.

* presenting perturbations (preconditioning trials) to a normal physiology in particular

repetitive patterns ~ greater protection.

* Learning and Memory: exposure to alternating forces can affect consolidation and recall of

movement patterns.

* adaptation involves upregulation of early immediate genes, cAMP, CREB, and MAP

kinases at specific synapses, emergent effects.

* perturbation with one set of forces can interfere with the memory trace for another. If

“memory trace” is brittle enough (i.e. not robust), catastrophic forgetting may result.


variation in adaptation (con’t)Most (if not all) physiological traits related to behavior are:

* polygenic (multiple genes required to explain variance)

* pleiotropic (single gene = multiple effects; alternative splicings, multiple transcripts)

* GxG (epistasis; multiplicative gene-gene interactions)

* GxE (multiplicative gene-environmental interactions)

Experimental design allows for the teasing out of these complexities:

* virtual environment manipulations allow us to fix E, solve for G

* existing mutants (clinical populations and animal models, solve part of G by knowing

functional effect of one term in G)

* rTMS (knockdown, stimulate entire circuits in brain, constrain number of terms in G)

* Cre/loxP system (controlled knockdown of genes – animal models only, really reduce

number of terms in G)

Conclusions: Adaptability of

Physiological States (con’t)Wheel Plot of Physiological States:

* arcs = transitions between states

(allostasis).

* nodes = homeostasis (state

maintained, some flexibility in

measurements, but not a true

state transition).

* structure of network – allostasis

and robustness are not random.

* adjacent nodes = small changes

in metabolic, gene expression pathways.

* distant nodes = large-scale changes in

metabolic, gene expression pathways.

Wiring of network (exclusively local, random, scale-

free) may provide insights into gene expression

networks, complex effects of physiology on behavior.


Physiological States (con’t)

Perturbations that trigger an adaptation that

leads to a higher measure of fitness may

produce intermediate responses of lower

fitness before this optimum is reached.

Fitness Landscape: concept from

theoretical biology that characterizes

all possible physiological states as they

relate to some measure of fitness.

* smooth or rugged – how do each relate to

the states and their potential transitions as

depicted in the wheel plot?

* the fitness of a certain physiological

state (the “topographic features”)

* a function of how much adaptation

is required to get there (distance of the

path denoted by arrows).


Physiological States (con’t)Examples (A, B) of two theoretical

fitness landscapes as they might

relate to physiological states:

* A = homeostatic system

* one state, most of landscape flat,

less variation in performance

overall.

* overall, system is more robust

to perturbation (can adapt to global

optimum, narrow range of variation

achieved).

* B = allostatic system

* multitude of states, landscape is

rugged, greater variation in

performance.

* can get “stuck” at local optima,

system is less adaptable overall, but

more capable of achieving rare,

extreme states.

Conclusions

What else can this knowledge be used for?

* Human Factors/Ergonomics design

Impact of training, performance variation on prosthetic, computer controller

design (not one size fits all, issues with adaptation).

* Neurorehabilitation

Motion-controlled VR (Wii) currently used.

Design better interventions?

* Medical Applications

Uncovering variation underlying traits

(behavioral or otherwise) – combined with

use of rTMS and FES (functional electrical

stimulation).

* Greater theoretical understanding of biological

variation

Genomics, connectomics research can be connected

to experimental methods to yield interesting

results and overarching principles.

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